Abstract

We propose a scheme to generate optical vortices through exciting exciton polariton vortices by a Gaussian beam in a pillar microcavity. With coupled Gross-Piteavskii equations we find that the structure of the exciton polariton vortices and antivortices shows a strong dependence on the microcavity radius, pump geometry, and nonlinear exciton-exciton interaction. Due to the nonlinear exciton-exciton interaction the strong Gaussian beam cannot excite more exciton polariton vortices or antivortices with respect to the weak one. The calculation demonstrates that the weak Gaussian beam can excite vortex-antivortex pairs, vortices with high total orbital angular momentum, and superposition states of vortex and antivortex with high total opposite orbital angular momentum. The pump geometry for the Gaussian beam to excite these vortex structures is analyzed in detail, which shows a potential application for generating optical vortex beams.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Since optical vortices were demonstrated a few decades ago [1], researchers have paid much attention to their generation and application [2–4]. Optical vortices are topological excitations characterized by the vanishing of the field density at a given point (the vortex core) and by the quantized winding of the field phase from 0 to 2πl (l is an integer) [1]. They have been extensively studied and observed in cold atoms [5–7], optical systems [8–10], and matter waves [11–14]. Exciton polariton condensates [15–17] as a type of matter waves in semiconductor microcavities provide a platform for generating optical vortex beams. The semiconductor microcavities, consisting of two distributed Bragg reflectors, can exhibit spontaneous coherence for exciton polaritons that are bosonic quasiparticles — a superposition state of excitons in quantum wells and photons in cavities [15]. The polaritons, due to the photonic part, can be coherently excited by an incident laser and detected by their emitted light. The optical beams emitted from the exciton polariton vortices inherit the exciton polariton orbital angular momentum.

Various vortex states in exciton polariton condensates continue gaining much attention on disorder effects [18, 19], vortex-antivortex pairs [11, 20], and vortex-vortex control [21]. These vortices show a strong dependence on the potential landscape designed by fabrication techniques [22] or using optical potentials induced by exciton-exciton interactions [23,24]. The vortex properties of the non-equilibrium exciton polariton condensates have been diagnosed from experiments [25] and theories [13,26] in last decades, such as lattices of vortices [27] and superposition of vortex-antivortex states [28]. To create exciton polariton vortices one can use Laguerre-Gauss optical beams that carry a well-defined external orbital angular momentum [29–31]. The vortex-antivortex superposition states are of potential interest to Sagnac interferometry [28], being a gyroscope which has been archived in atomic systems [32], and to quantum information [33]. The exciton polariton vortices also show a potential application for generating optical vortex beams.

The application of the exciton polariton vortices for generating optical vortex beams strongly depends on their excitation in a semiconductor microcavity, so that we will study how to effectively excite them in the present work. As a rational expectation researchers hope that the exciton polariton vortices could be directly generated by Gaussian beams rather than Laguerre-Gauss beams. This can be achieved by using the splitting between transverse-electric and transverse-magnetic polariton modes [34–36] and polariton optical-parametric oscillators [37,38]. In the present work, we will show that Gaussian beams can also excite the exciton polariton vortices in a finite microcavity without these conditions. In the finite microcavity the geometry of the Gaussian beam and microcavity boundaries play major roles. In addition, the polariton-polariton interaction needs to be considered in the strong pump regime, though it can be neglected in the weak pump regime. Therefore, we will focus on their effects on the excitation of the polariton vortices and antivortices in the present work. Fig. 1 shows two possible excitation processes by Gaussian beams. When the polaritons arrive at the microcavity boundary they will change their motion direction and thus can form the vortices. We will find that this boundary-based scheme is a very efficient method for generating optical vortex beams.

 figure: Fig. 1

Fig. 1 Schematic drafts for creating polariton vortices in pillar semiconductor microcavities by one Gaussian beam whose center locates on the x axis and wave vector is (a) along and (b) normal to the x axis. The blue curves show the possible motion path of the polaritons, resulting in polariton vortices or antivortices.

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The present work is organized as follows. In Sec. II, we first introduce the coupled dynamic equations for the quantum well excitons and cavity photons from quantum field theory and then give the system parameters adopted in numerical calculation. Numerical results and discussion are shown in Sec. III which is separated into two subsections according to the pump strength. Finally, a brief conclusion is summarized in Sec. IV.

2. Gross-Pitaevskii equations

The polariton field in a planar microcavity can be described as the coupling of the quantum well exciton field, Ψ̂X(r, t), and the cavity photon field, Ψ̂C(r, t). They are Bose fields and meet the Bose commutation rules. The mean-field approximation, namely, ψX/C(r) = 〈Ψ̂X/C(r)〉, has proven to be an efficient way to describe the fluid properties of the polariton condensate. The motion equation of ψX/C(r), known as the Gross-Pitaevskii equations [39,40], can be written as

iddt(ψX(r)ψC(r))=[h0+(VX(r)i2γX+gX|ψX(r)|200VC(r)i2γC)](ψX(r)ψC(r))+(0Fp(r)),
where r = (x, y) is the in-plane spatial coordinate. The single-particle Hamiltonian, h0, reads
h0=(ωX(i)ΩRΩRωC(i))
where the Rabi frequency ΩR describes the exciton-photon coupling. The photon dispersion, ωC(k)=ωC01+k2/kz2, is a function of the in-plane wavevector, k, and the quantized photon wavevector in the growth direction, kz. For simplicity, we approximate it to be ωC(k)=ωC0+2k22mC with the cavity photon effective mass mC. Because the effective mass is far larger for the excitons than for the cavity photons, we take a flat exciton dispersion, namely, ωX(k)=ωX0. In this framework, the polaritons simply arise as the eigenmodes of the linear Hamiltonian in Eq. (2) and the eigenvalues for the two-branch (upper and lower) polaritons are ωUP/LP(k)=12{[ωX0+ωC(k)]±[ωX0ωC(k)]2+4ΩR2}. VX(r) and VC(r) in Eq. (1) are the single particle potentials acting on the exciton and photon fields, respectively. They can break the translational symmetry of the microcavity along the two in-plane directions. The exciton potential generally dates from natural interface or alloy disorder in the quantum wells, while the photon potential is mainly determined by the cavity height or transversal size. Therefore, it is much easier to design the photon potential than to design the exciton potential [22, 41]. The quantities γX and γC are the exciton and photon decay rates, respectively. At last, gX and Fp(r) measure the exciton-exciton interaction and the external pump field, respectively. For convenience, ħ is set to 1 in the following part if there is no ambiguity.

The Gaussian pump beam considered in the present work is defined as

Fp(r)=fpe(rrp)2/w2eikpreiωpt
where fp, w, and ωp denote the amplitude, spot size, and frequency of the pump field, respectively. rp = (xp, yp) is the center coordinate of the pump spot. The pump wave vector, kp = (kpx, kpy), can be adjusted by the incident angle of the pump field with respect to the growth direction. The incident strength of the Gaussian beam is proportional to |fp|2. When kp ≠ 0 the excited polaritons have a non-zero flow velocity along the cavity plane and therefore, it is possible for them to form the polariton vortices. Without loss of generality, we consider a pillar microcavity as shown in Fig. 1. For a pillar microcavity VC(r) is infinite outside the cavity region due to the total internal reflection on the boundaries [39]. In calculation VC(r) = 100 meV for r > R and 0 for others, which cuts out the required pillar microcavity with radius R. Note that we mainly focus on the effects of the pump geometry in the present work and therefore, VX(r) is set to zero to avoid the disorder influence.

In the following numerical calculation the parameters of a typical GaAs-based microcavity are adopted. The energy of the excitons is taken as the zero point, i.e., ωX0=0, and other parameters are mC = 1 × 10−5me where me is the free electron mass, γX = γC = 0.01 meV, gX = 0.015 meV · μm2 [42], ΩR = 2.5 meV. In addition, two pump cases, namely, weak pump regime with fp = 0.1 meV · μm−1 and another strong with fp = 10 meV · μm−1, are considered to show the influence of the nonlinear interaction on the polariton vortices. As is well known the exciton part concerns the nonlinear interaction, while the photon part in the polaritons relates to the pump efficiency. Consequently, the polaritons with k = kp had better have a suitable ratio between them, for example, half over half. This requires ωC(kp)=ωX0, always maintained in the following calculation. Besides, we take the pump detuning to be δp = ωpωLP(kp) = −0.2 meV and the Gaussian beam size to be w = 4 μm.

3. Numerical results and discussion

The polariton fluid has been generated by several types of pump fields [24,43]. In the present work we use the “resonant injection” scheme that the pump frequency ωp is set to be near the lower-branch polariton energy at the pump wave vector, ωLP(kp). The Gaussian beam creates the polariton condensate and determines its properties (such as momentum, energy, density, phase). This controllable scheme allows to study the excitation of vortices and antivortices [20,44]. For clear we divide the present section into two subsections according to the pump field strength: (A) weak pump regime and (B) strong pump regime. For the former the exciton density is low and thus the nonlinear exciton-exciton interaction can be neglected, while for the later the exciton density is so high that the nonlinear interaction must be considered.

The main results are obtained by numerically solving Eq. (1) on a two-dimensional grid 320×320 for a square 32 μm×32 μm microcavity region. The discretization area is 0.1 μm×0.1 μm, smaller than the requirement of the maximum pump wave vector 4.0 μm−1 adopted in calculation. The fourth-order Runge-Kutta algorithm is used to evaluate the photon and exciton fields ψC/X(r, t).

3.1. Weak pump regime

In the weak pump regime the energy due to the exciton-exciton interaction, gX |ψX(r)|2, is far less than the polariton kinetic energy and therefore, its effect can be neglected and the polariton evolution can reach a steady state. Figure 2 shows the steady density distributions of the photon field, |ψC(r)|2, in the first column and corresponding field phases in the second column for four microcavities with radii R = 2 μm, 4 μm, 8 μm, and 16 μm. The exciton field has a similar distribution and so is not shown. The typical velocity of the polariton is dωLP(k)dk and therefore, the characteristic length ξ~dωLP(k)dkγc. When kp = 2 μm−1, ξ ∼ 150 μm and subsequently the polaritons in the four microcavities shown in Fig. 2 can reach the boundary. Due to R less than half of 150 μm the boundary exerts manifest influence on the polariton condensate in four cases. The width of the Gaussian pump beam with center at the original point is w = 4 μm, thus with increasing R the microcavity boundary is increasingly away from the pump beam. The pump beam covers all the microcavity when Rw [see Figs. 2(a–b)], while only a central part when R > w [see Fig. 2(d)]. Accounting for the loss of the polaritons in traveling, the boundary plays a major role on the forming of the polariton states for the small microcavities, that is, the boundary effect decreases with increasing R. This can be seen from the variation of the photon density distribution from Figs. 2(a) to 2(d).

 figure: Fig. 2

Fig. 2 Steady density distribution of photon fields, |ψC(r)|2 (left panel in each subfigure) and corresponding phase (with unit of π) distribution (right panel). The numbers in the bottom left corner denote the maximum value of the photon density and the green circles represent the pillar boundaries with radii (a) R = 2 μm, (b) R = 4 μm, (c) R = 8 μm, and (d) R = 16 μm. As an example, the vortices and antivortices are denoted by dots and stars in (b). Other parameters: fp = 0.1 meV · μm−1, kp = (2, 0) μm−1, rp = (0, 0), and w = 4 μm.

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As is known the Gaussian beam has no orbital angular momentum and so cannot excite the vortex by itself. For the present circular and no disorder microcavities to excite the vortices requires two conditions: (i) the microcavity boundary can influence the movement of the polaritons and (ii) the Gaussian pump beam has a nonzero in-plane wave vector. As illustrated in Fig. 1, the polaritons change their moving direction once they arrive at the boundary, accompanied by a complex polariton interference. The polariton interference leads to different spatial structures for the vortices and antivortices, see Figs. 2 and 3. In Fig. 2 the Gaussian beam has a wave vector kp = (2, 0) μm−1 and therefore, can induce the vortices and antivortices, referred to the vortices and antivortices in Fig. 2(b) denoted by dots and stars, respectively. The numbers of the dots and stars are same due to the mirror symmetry of the pump beam along direction x. From Fig. 2(b) the distance between two adjacent vortices can be estimated to be ∼ 1.8 μm (about half of the polariton wavelength) for kp = 2 μm−1. Therefore, it is impossible to generate the vortex excitation for small enough microcavities, also called as photonic dots [42]. Since R = 2 μm ∼ 1.8 μm in Fig. 2(a), no vortex or antivortex is generated in the microcavity. With increasing R more complex polariton vortices can be excited [see Fig. 2(b)], even the vortices with high orbital angular momentum [see Figs. 2(c–d)]. The photon density distributions in Figs. 2(c–d) represent the superposition state of the vortex and antivortex with l = ±3, which is important for application of polaritons to the Sagnac interferometry [28]. The Sagnac interferometry requires large l whose value is mainly determined by kp in the present pump geometry.

 figure: Fig. 3

Fig. 3 Steady density distributions of photon fields, |ψC(x, y, t)|2 (left panel in each subfigure) and corresponding phase distributions (right panel). Color scale bars are the same to Fig. 2. The number in the bottom left corner represents the maximum value of the photon density and all green circles denoting the microcavity boundaries have the same radii R = 8 μm. The wave vector of the pump beam, kp, is along the x axis and its value given in the above of each figure. As an example, the vortices and antivortices are shown by dots and stars in (c). Other parameters: fp = 0.1 meV · μm−1, rp = (0, 0), and w = 4 μm.

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The variation of the vortex excitation with kp is shown in Fig. 3 where the pillar radii are set to R = 8 μm. When kp is small [Fig. 3(a)] no vortex or antivortex is excited, while with increasing kp the pattern of the photon density shows more and more complexity and subsequently the vortex and antivortex structures are generated [Figs. 3(b–h)]. In other words, the argument that the distance between two adjacent vortices decreases with increasing kp is responsible for the complicated density patterns of the high total orbital angular momentum states in the large-kp cases. Due to the boundary reflection the high total orbital angular momentum states are composed of several vortex-antivortex pairs with l = ±1, as shown in Figs. 3(b–d). The superposition states of the vortex and antivortex with high orbital angular momentums can also be excited. For examples, the superposition states in Figs. 2(c–d) with l = ±3 and in Fig. 3(e) with l = ±6. Since kp is along the x axis in Fig. 3, there is a mirror symmetry for the vortices and antivortices along the x axis, referred to Fig. 3(c). This mirror symmetry can be broken up by changing the pump geometry from Fig. 1(a) to Fig. 1(b).

We take the pump geometry of Fig. 1(b) in Fig. 4 where the pump position is set to rp = (4, 0) μm and the wave vector kp is along the y axis. Since this pump beam has a non-zero angular momentum with respect to the center of the pillar microcavity, the number of the vortices is different from that of the antivortices. The angular momentum of the pump field is

Lpump=iF(r)|ϕ|F(r)F(r)|F(r)=rp×kp
where ϕ is the azimuth angle of r. When rp = (0, 0) there is no net angular momentum for polaritons, i.e., the cases shown in Fig. 3. On the contrary, for a nonzero rp the net angular momentum of the polariton condensates should be proportional to kp, see Fig. 4 where the total angular momentum is 0, 1ħ, 4ħ, 6ħ, 3ħ, 6ħ, 11ħ, 15ħ, and 20ħ from Figs. 4(a) to 4(i), respectively. Because the angular momentum is not conserved, these values are not exactly equal to Lpump, but maintain the approximate proportional relation with kp.

 figure: Fig. 4

Fig. 4 Steady density distributions of photon fields, |ψC(x, y, t)|2 (left panel in each subfigure) and corresponding phase distributions (right panel). Color scale bars are the same to Fig. 2. The number in the bottom left corner represents the maximum value of the photon density and all green circles denoting the microcavity boundaries have the same radii R = 8 μm. The wave vector of the pump beam, kp, is along the y axis and its value is given in the above of each figure. As an example, the vortices and antivortices are shown by dots and stars in (c). Other parameters: fp = 0.1 meV · μm−1, rp = (4, 0) μm, and w = 4 μm.

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For convenient analysis we expand the exciton and photon fields, i.e., ψX(r) and ψC(r), as follow

(ψX(r)ψC(r))=n,l(Xn,lCn,l)ϕn,l(r)
where ϕn,l(r) is a basis function with the angular momentum of , namely,
ϕn,l(r)=Jn,|l|(r)×12πeilφ.
n and l represent the radial and angular quantum numbers, respectively. Jn,|l|(r) = J|l|(knr) is a normalized Bessel function with boundary condition J|l|(knR) = 0 and corresponding energy ωn,l=2kn22mC. In the weak pump regime the coefficients Cn,l and Xn,l for the steady states can be found with the approximation of neglecting the nonlinear exciton-exciton interaction, i.e.,
Cn,l=[ωp(ωX0i2γX)]×fn,leiωpt[ωp(ωC0+ωn,li2γC)][ωp(ωX0i2γX)]ΩR2,
Xn,l=Ω×fn,leiωpt[ωp(ωC0+ωn,li2γC)][ωp(ωX0i2γX)]ΩR2,
where fn,l is the expanding coefficient of the state ϕn,l(r) for the pump field Fp(r). The total orbital angular momentum for the photon field, LC, is given by
LC=n,ll|Cn,l|2n,l|Cn,l|2.
According to Eq. (7), the angular momentum of the photon field is mainly determined by the pump coefficient fn,l and the corresponding energy ωn,l. In other words, the excitation of the high angular momentum states requires that the pump beam should have a large angular momentum about the pillar center, see Fig. 4. For example, the states of ϕ1,0, ϕ1,1, ϕ1,4, and ϕ4,3 dominate in Figs. 4(a), 4(b), 4(c), and 4(e), respectively. Even if the photon fields have the same total orbital angular momentum, their density distribution could be much different from each other, as shown in Figs. 4(d) and 4(f). Both of their total orbital angular momentums are 6. When kp is large the photon density distribution appears more complex, see Figs. 4(g–i) where more than one states of ϕn,l are excited. If one wants to excite only one angular momentum state ϕn,l [see Figs. 2(c), 3(e), and 4(e)], equation (7) provides a guidance: (i) increase fn,l by controlling the pump geometry and (ii) achieve a resonant excitation for ϕn,l by tuning ωp. To summarize, by designing the pump geometry the Gaussian beam can efficiently excite the polariton vortices and antivortices in the pillar microcavity, which holds potential applications for Sagnac interferometry and generating optical vortex beams.

3.2. Strong pump regime

When the pump field is strong enough the nonlinear exciton-exciton interaction plays an important role in exciting the polariton vortices and antivortices and can further, make the steady state of the polaritons unreachable. Figure 5 shows the density and phase distributions for the photon and exciton fields under a strong pump field fp = 10 meV · μm−1, where the exciton density is always smaller than its saturation density (∼ 500 μm−2 for GaAs-based quantum wells [15]). In the strong pump regime the exciton energy is blueshifted due to the nonlinear exciton-exciton interaction. The maximum values of gX |ψX(r)|2 are about 0.49 meV, 1.1 meV, 3.7 meV, and 4.0 meV from Figs. 5(e) to 5(h), which approximate to the Rabi splitting 2ΩR = 5.0 meV gradually. Considered that ωp = ωLP(kp) − 0.2 meV is set, the photon density is larger than the exciton density, comparing Figs. 5(a–d) with Figs. 5(e–h), respectively.

 figure: Fig. 5

Fig. 5 Density and phase distributions for (a–d) photon fields and (e–h) exciton fields. The left and right panels in each subfigure show the density and phase distributions, respectively. The distributions in (a–c) and (e–f) are steady, while those in (d) and (h) at the evolution time of 1600 ħ · meV−1 are not. Color scale bars are the same to Fig. 2. The number in the bottom left corner represents the maximum value of the field densities and all green circles denoting that the microcavity boundaries have the same radii R = 8 μm. The wave vector of the pump beam, kp, is along the y axis and its value is given in the above of each subfigure. As an example, the vortices are shown by dots in (c) and (g). Other parameters: fp = 10 meV · μm−1, rp = (4, 0) μm, and w = 4 μm.

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This can also be seen from Eqs. (7) and (8): Cn,lXn,l if the exciton energy ωX0 is much larger than ωp. Note that in the weak pump regime the densities for the photon and exciton fields are in the same order of magnitude. For small kp [see Figs. 5(a–c) and 5(e–g)] the polariton system can reach a steady state, while for large kp the polariton system is unstable [see Figs. 5(d) and 5(h)]. This is owed to that the case with kp = 1.5 μm−1 displayed by Figs. 5(d) and 5(h) has the largest exciton density, as well as the strongest nonlinear effect. Since gX |ψX(r)|2 depends on the coordinate, the exciton field has different oscillation frequencies at different positions, which is not negligible in the strong pump regime. Subsequently, the oscillation of the exciton field at different positions is out of step and appears a random density/phase distribution, referred to Fig. 5(h). This kind of randomness cannot be seen from the photon field, because it is stronger than the exciton field.

For the steady cases in Figs. 5(a–c) the total orbital angular momentums, respectively, are 0, 0, and 3ħ. Compared with Figs. 4(b–c) the Figs. 5(b–c) hold less total orbital angular momentum, indicating that the strong pump cannot excite more steady vortices. This can be argued as follow: the nonlinear exciton-exciton interaction prefers to spread the polariton density equally, while the vortices and antivortices have zero-density points. Consequently, the nonlinear exciton-exciton interaction is harmful to the excitation of the polariton vortices. In addition, since it is not easy to observe the vortices or antivortices in an unstable state, a not-too-strong pump beam is the better choice for generating the polariton vortices.

4. Conclusion

We have studied the excitation of exciton polariton vortices and antivortices in the pillar microcavities by Gaussian pump beams. The structure of vortices and antivortices strongly depends on the microcavity radius, pump geometry, and nonlinear exciton-exciton interactions. We found that it is hard to observe the excited polariton vortices in the strong pump regime for a pillar microcavity, because the nonlinear exciton-exciton interaction prefers to spread the polariton density equally and can cause the system to be unstable. On the contrary, the polariton system can reach a steady state in the weak pump regime. Though the Gaussian pump beams do not carry angular momentums, they can also excite many kinds of the vortex and antivortex structures in the pillar microcavities, such as vortices with high total orbital angular momentum, and superposition states of vortex and antivortex with high total opposite orbital angular momentums. Our results demonstrated that exciting vortices and antivortices by Gaussian beams are possible for experimental observation, which holds potential applications for Sagnac interferometry and generating optical vortex beams with high angular momentum.

Funding

National Natural Science Foundation of China (NSFC) (11304015); Beijing Higher Education Young Elite Teacher Project (YETP1228).

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22. O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006). [CrossRef]  

23. A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010). [CrossRef]  

24. E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010). [CrossRef]  

25. J. Jimenez-Garcia, P. Rodriguez, T. Guillet, and T. Ackemann, “Spontaneous formation of vector vortex beams in vertical-cavity surface-emitting lasers with feedback,” Phys. Rev. Lett. 119(11), 113902 (2017). [CrossRef]   [PubMed]  

26. E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014). [CrossRef]  

27. G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012). [CrossRef]   [PubMed]  

28. F. I. Moxley, J. P. Dowling, W. Dai, and T. Byrnes, “Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates,” Phys. Rev. A 93(5), 053603 (2016). [CrossRef]  

29. K. T. Kapale and J. P. Dowling, “Vortex phase qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005). [CrossRef]   [PubMed]  

30. R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012). [CrossRef]   [PubMed]  

31. V. L. Y. Loke, T. Asavei, A. B. Stilgoe, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Driving corrugated donut rotors with laguerre-gauss beams,” Opt. Express 22(16), 19692–19706 (2014). [CrossRef]   [PubMed]  

32. A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80(6), 063604 (2009). [CrossRef]  

33. T. Byrnes, Y. Yamamoto, and P. van Loock, “Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates,” Phys. Rev. B 87(20), 201301 (2013). [CrossRef]  

34. T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Excitation of vortices in semiconductor microcavities,” Phys. Rev. B 75(24), 241301 (2007). [CrossRef]  

35. F. Manni, K. G. Lagoudakis, T. K. Paraïso, R. Cerna, Y. Léger, T. C. H. Liew, I. A. Shelykh, A. V. Kavokin, F. Morier-Genoud, and B. Deveaud-Plédran, “Spin-to-orbital angular momentum conversion in semiconductor microcavities,” Phys. Rev. B 83(24), 241307 (2011). [CrossRef]  

36. S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015). [CrossRef]   [PubMed]  

37. D. M. Whittaker, “Vortices in the microcavity optical parametric oscillator,” Superlatt. Microstruct. 41(5), 297–300 (2007). [CrossRef]  

38. F. M. Marchetti, M. H. Szymańska, C. Tejedor, and D. M. Whittaker, “Spontaneous and triggered vortices in polariton optical-parametric-oscillator superfluids,” Phys. Rev. Lett. 105(6), 063902 (2010). [CrossRef]   [PubMed]  

39. Y. Zhang, G. Jin, and Y.-Q. Ma, “Boundary effects on the dynamics of exciton polaritons in semiconductor microcavities,” J. Appl. Phys. 105(3), 033105 (2009). [CrossRef]  

40. K. Lagoudakis, The Physics of Exciton-Polariton Condensates (EPFL Press, 2013). [CrossRef]  

41. T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(12), 803 (2014). [CrossRef]  

42. A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006). [CrossRef]  

43. A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009). [CrossRef]   [PubMed]  

44. F. Manni, T. C. H. Liew, K. G. Lagoudakis, C. Ouellet-Plamondon, R. André, V. Savona, and B. Deveaud, “Spontaneous self-ordered states of vortex-antivortex pairs in a polariton condensate,” Phys. Rev. B 88(20), 201303 (2013). [CrossRef]  

References

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    [Crossref] [PubMed]
  26. E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
    [Crossref]
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    [Crossref] [PubMed]
  28. F. I. Moxley, J. P. Dowling, W. Dai, and T. Byrnes, “Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates,” Phys. Rev. A 93(5), 053603 (2016).
    [Crossref]
  29. K. T. Kapale and J. P. Dowling, “Vortex phase qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
    [Crossref] [PubMed]
  30. R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  32. A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80(6), 063604 (2009).
    [Crossref]
  33. T. Byrnes, Y. Yamamoto, and P. van Loock, “Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates,” Phys. Rev. B 87(20), 201301 (2013).
    [Crossref]
  34. T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Excitation of vortices in semiconductor microcavities,” Phys. Rev. B 75(24), 241301 (2007).
    [Crossref]
  35. F. Manni, K. G. Lagoudakis, T. K. Paraïso, R. Cerna, Y. Léger, T. C. H. Liew, I. A. Shelykh, A. V. Kavokin, F. Morier-Genoud, and B. Deveaud-Plédran, “Spin-to-orbital angular momentum conversion in semiconductor microcavities,” Phys. Rev. B 83(24), 241307 (2011).
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    [Crossref] [PubMed]
  37. D. M. Whittaker, “Vortices in the microcavity optical parametric oscillator,” Superlatt. Microstruct. 41(5), 297–300 (2007).
    [Crossref]
  38. F. M. Marchetti, M. H. Szymańska, C. Tejedor, and D. M. Whittaker, “Spontaneous and triggered vortices in polariton optical-parametric-oscillator superfluids,” Phys. Rev. Lett. 105(6), 063902 (2010).
    [Crossref] [PubMed]
  39. Y. Zhang, G. Jin, and Y.-Q. Ma, “Boundary effects on the dynamics of exciton polaritons in semiconductor microcavities,” J. Appl. Phys. 105(3), 033105 (2009).
    [Crossref]
  40. K. Lagoudakis, The Physics of Exciton-Polariton Condensates (EPFL Press, 2013).
    [Crossref]
  41. T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(12), 803 (2014).
    [Crossref]
  42. A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
    [Crossref]
  43. A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
    [Crossref] [PubMed]
  44. F. Manni, T. C. H. Liew, K. G. Lagoudakis, C. Ouellet-Plamondon, R. André, V. Savona, and B. Deveaud, “Spontaneous self-ordered states of vortex-antivortex pairs in a polariton condensate,” Phys. Rev. B 88(20), 201303 (2013).
    [Crossref]

2017 (5)

Z. Liu, Y. Liu, Y. Ke, Y. Liu, W. Shu, H. Luo, and S. Wen, “Generation of arbitrary vector vortex beams on hybrid-order poincaré sphere,” Photon. Res. 5(1), 15–21 (2017).
[Crossref]

S. Fu, T. Wang, S. Zhang, Z. Zhang, Y. Zhai, and C. Gao, “Non-probe compensation of optical vortices carrying orbital angular momentum,” Photon. Res. 5(3), 251–255 (2017).
[Crossref]

T. Horikiri, T. Byrnes, K. Kusudo, N. Ishida, Y. Matsuo, Y. Shikano, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Highly excited exciton-polariton condensates,” Phys. Rev. B 95(24), 245122 (2017).
[Crossref]

X. Ma and S. Schumacher, “Vortex-vortex control in exciton-polariton condensates,” Phys. Rev. B 95(23), 235301 (2017).
[Crossref]

J. Jimenez-Garcia, P. Rodriguez, T. Guillet, and T. Ackemann, “Spontaneous formation of vector vortex beams in vertical-cavity surface-emitting lasers with feedback,” Phys. Rev. Lett. 119(11), 113902 (2017).
[Crossref] [PubMed]

2016 (6)

2015 (4)

S. Greschner, D. Huerga, G. Sun, D. Poletti, and L. Santos, “Density-dependent synthetic magnetism for ultracold atoms in optical lattices,” Phys. Rev. B 92(11), 115120 (2015).
[Crossref]

K. S. Daskalakis, S. A. Maier, and S. Kéna-Cohen, “Spatial coherence and stability in a disordered organic polariton condensate,” Phys. Rev. Lett. 115(3), 035301 (2015).
[Crossref] [PubMed]

G. Dagvadorj, J. M. Fellows, S. Matyjaśkiewicz, F. M. Marchetti, I. Carusotto, and M. H. Szymańska, “Nonequilibrium phase transition in a two-dimensional driven open quantum system,” Phys. Rev. X 5(4), 041028 (2015).

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

2014 (4)

V. L. Y. Loke, T. Asavei, A. B. Stilgoe, T. A. Nieminen, and H. Rubinsztein-Dunlop, “Driving corrugated donut rotors with laguerre-gauss beams,” Opt. Express 22(16), 19692–19706 (2014).
[Crossref] [PubMed]

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
[Crossref]

Y. Zhang, G. J. Sreejith, N. D. Gemelke, and J. K. Jain, “Fractional angular momentum in cold-atom systems,” Phys. Rev. Lett. 113(16), 160404 (2014).
[Crossref] [PubMed]

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(12), 803 (2014).
[Crossref]

2013 (4)

F. Manni, T. C. H. Liew, K. G. Lagoudakis, C. Ouellet-Plamondon, R. André, V. Savona, and B. Deveaud, “Spontaneous self-ordered states of vortex-antivortex pairs in a polariton condensate,” Phys. Rev. B 88(20), 201303 (2013).
[Crossref]

O. Romero-Isart, C. Navau, A. Sanchez, P. Zoller, and J. I. Cirac, “Superconducting vortex lattices for ultracold atoms,” Phys. Rev. Lett. 111(14), 145304 (2013).
[Crossref] [PubMed]

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
[Crossref]

T. Byrnes, Y. Yamamoto, and P. van Loock, “Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates,” Phys. Rev. B 87(20), 201301 (2013).
[Crossref]

2012 (2)

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
[Crossref] [PubMed]

2011 (2)

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7(2), 129–133 (2011).
[Crossref]

F. Manni, K. G. Lagoudakis, T. K. Paraïso, R. Cerna, Y. Léger, T. C. H. Liew, I. A. Shelykh, A. V. Kavokin, F. Morier-Genoud, and B. Deveaud-Plédran, “Spin-to-orbital angular momentum conversion in semiconductor microcavities,” Phys. Rev. B 83(24), 241307 (2011).
[Crossref]

2010 (4)

F. M. Marchetti, M. H. Szymańska, C. Tejedor, and D. M. Whittaker, “Spontaneous and triggered vortices in polariton optical-parametric-oscillator superfluids,” Phys. Rev. Lett. 105(6), 063902 (2010).
[Crossref] [PubMed]

H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys. 82(2), 1489–1537 (2010).
[Crossref]

A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010).
[Crossref]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

2009 (4)

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80(6), 063604 (2009).
[Crossref]

M. D. Fraser, G. Roumpos, and Y. Yamamoto, “Vortex-antivortex pair dynamics in an exciton-polariton condensate,” New J. Phys. 11(11), 113048 (2009).
[Crossref]

Y. Zhang, G. Jin, and Y.-Q. Ma, “Boundary effects on the dynamics of exciton polaritons in semiconductor microcavities,” J. Appl. Phys. 105(3), 033105 (2009).
[Crossref]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
[Crossref] [PubMed]

2008 (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
[Crossref]

2007 (2)

T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Excitation of vortices in semiconductor microcavities,” Phys. Rev. B 75(24), 241301 (2007).
[Crossref]

D. M. Whittaker, “Vortices in the microcavity optical parametric oscillator,” Superlatt. Microstruct. 41(5), 297–300 (2007).
[Crossref]

2006 (2)

O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006).
[Crossref]

A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
[Crossref]

2005 (1)

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
[Crossref] [PubMed]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Ackemann, T.

J. Jimenez-Garcia, P. Rodriguez, T. Guillet, and T. Ackemann, “Spontaneous formation of vector vortex beams in vertical-cavity surface-emitting lasers with feedback,” Phys. Rev. Lett. 119(11), 113902 (2017).
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Adrados, C.

A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010).
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Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
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L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Amo, A.

A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010).
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A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
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André, R.

F. Manni, T. C. H. Liew, K. G. Lagoudakis, C. Ouellet-Plamondon, R. André, V. Savona, and B. Deveaud, “Spontaneous self-ordered states of vortex-antivortex pairs in a polariton condensate,” Phys. Rev. B 88(20), 201303 (2013).
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Asavei, T.

Baas, A.

O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006).
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Ballarini, D.

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
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A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
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Baumberg, J. J.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
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Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
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Berloff, N. G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
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Biermann, K.

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
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Bloch, J.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
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Boulier, T.

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
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Bradley, R. A.

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
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Bramati, A.

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
[Crossref]

A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010).
[Crossref]

Brantut, J.-P.

O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006).
[Crossref]

Byrnes, T.

T. Horikiri, T. Byrnes, K. Kusudo, N. Ishida, Y. Matsuo, Y. Shikano, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Highly excited exciton-polariton condensates,” Phys. Rev. B 95(24), 245122 (2017).
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F. I. Moxley, J. P. Dowling, W. Dai, and T. Byrnes, “Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates,” Phys. Rev. A 93(5), 053603 (2016).
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T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(12), 803 (2014).
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T. Byrnes, Y. Yamamoto, and P. van Loock, “Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates,” Phys. Rev. B 87(20), 201301 (2013).
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Cancellieri, E.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
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Canuel, B.

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80(6), 063604 (2009).
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Carusotto, I.

G. Dagvadorj, J. M. Fellows, S. Matyjaśkiewicz, F. M. Marchetti, I. Carusotto, and M. H. Szymańska, “Nonequilibrium phase transition in a two-dimensional driven open quantum system,” Phys. Rev. X 5(4), 041028 (2015).

A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
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Cerda-Méndez, E. A.

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
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Cerna, R.

F. Manni, K. G. Lagoudakis, T. K. Paraïso, R. Cerna, Y. Léger, T. C. H. Liew, I. A. Shelykh, A. V. Kavokin, F. Morier-Genoud, and B. Deveaud-Plédran, “Spin-to-orbital angular momentum conversion in semiconductor microcavities,” Phys. Rev. B 83(24), 241307 (2011).
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Chaibi, W.

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80(6), 063604 (2009).
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Chaitanya, N. A.

Chi, H.

Christmann, G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
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Cirac, J. I.

O. Romero-Isart, C. Navau, A. Sanchez, P. Zoller, and J. I. Cirac, “Superconducting vortex lattices for ultracold atoms,” Phys. Rev. Lett. 111(14), 145304 (2013).
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Ciuti, C.

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
[Crossref]

A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010).
[Crossref]

A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
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Clarke, E.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
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Dagvadorj, G.

G. Dagvadorj, J. M. Fellows, S. Matyjaśkiewicz, F. M. Marchetti, I. Carusotto, and M. H. Szymańska, “Nonequilibrium phase transition in a two-dimensional driven open quantum system,” Phys. Rev. X 5(4), 041028 (2015).

Dai, W.

F. I. Moxley, J. P. Dowling, W. Dai, and T. Byrnes, “Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates,” Phys. Rev. A 93(5), 053603 (2016).
[Crossref]

Daïf, O. E.

O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006).
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Daskalakis, K. S.

K. S. Daskalakis, S. A. Maier, and S. Kéna-Cohen, “Spatial coherence and stability in a disordered organic polariton condensate,” Phys. Rev. Lett. 115(3), 035301 (2015).
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del Valle, E.

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
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Deng, H.

H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys. 82(2), 1489–1537 (2010).
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Deveaud, B.

F. Manni, T. C. H. Liew, K. G. Lagoudakis, C. Ouellet-Plamondon, R. André, V. Savona, and B. Deveaud, “Spontaneous self-ordered states of vortex-antivortex pairs in a polariton condensate,” Phys. Rev. B 88(20), 201303 (2013).
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O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006).
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Deveaud-Plédran, B.

F. Manni, K. G. Lagoudakis, T. K. Paraïso, R. Cerna, Y. Léger, T. C. H. Liew, I. A. Shelykh, A. V. Kavokin, F. Morier-Genoud, and B. Deveaud-Plédran, “Spin-to-orbital angular momentum conversion in semiconductor microcavities,” Phys. Rev. B 83(24), 241307 (2011).
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Devi, K.

Dowling, J. P.

F. I. Moxley, J. P. Dowling, W. Dai, and T. Byrnes, “Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates,” Phys. Rev. A 93(5), 053603 (2016).
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K. T. Kapale and J. P. Dowling, “Vortex phase qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
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Dufferwiel, S.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
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Durska, M.

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
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Ebrahim-Zadeh, M.

Fellows, J. M.

G. Dagvadorj, J. M. Fellows, S. Matyjaśkiewicz, F. M. Marchetti, I. Carusotto, and M. H. Szymańska, “Nonequilibrium phase transition in a two-dimensional driven open quantum system,” Phys. Rev. X 5(4), 041028 (2015).

Ferrier, L.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
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Fickler, R.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
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Forchel, A.

T. Horikiri, T. Byrnes, K. Kusudo, N. Ishida, Y. Matsuo, Y. Shikano, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Highly excited exciton-polariton condensates,” Phys. Rev. B 95(24), 245122 (2017).
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G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7(2), 129–133 (2011).
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Franke, H.

M. Thunert, A. Janot, H. Franke, C. Sturm, T. Michalsky, M. D. Martín, L. Viña, B. Rosenow, M. Grundmann, and R. Schmidt-Grund, “Cavity polariton condensate in a disordered environment,” Phys. Rev. B 93(6), 064203 (2016).
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Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
[Crossref]

Fras, F.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

Fraser, M. D.

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7(2), 129–133 (2011).
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M. D. Fraser, G. Roumpos, and Y. Yamamoto, “Vortex-antivortex pair dynamics in an exciton-polariton condensate,” New J. Phys. 11(11), 113048 (2009).
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Fu, S.

Gao, C.

Gao, T.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
[Crossref] [PubMed]

Gauguet, A.

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80(6), 063604 (2009).
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Y. Zhang, G. J. Sreejith, N. D. Gemelke, and J. K. Jain, “Fractional angular momentum in cold-atom systems,” Phys. Rev. Lett. 113(16), 160404 (2014).
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E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
[Crossref]

A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010).
[Crossref]

Giriunas, L.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
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S. Greschner, D. Huerga, G. Sun, D. Poletti, and L. Santos, “Density-dependent synthetic magnetism for ultracold atoms in optical lattices,” Phys. Rev. B 92(11), 115120 (2015).
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Grousson, R.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Grundmann, M.

M. Thunert, A. Janot, H. Franke, C. Sturm, T. Michalsky, M. D. Martín, L. Viña, B. Rosenow, M. Grundmann, and R. Schmidt-Grund, “Cavity polariton condensate in a disordered environment,” Phys. Rev. B 93(6), 064203 (2016).
[Crossref]

Guda, K.

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
[Crossref]

Guillet, T.

J. Jimenez-Garcia, P. Rodriguez, T. Guillet, and T. Ackemann, “Spontaneous formation of vector vortex beams in vertical-cavity surface-emitting lasers with feedback,” Phys. Rev. Lett. 119(11), 113902 (2017).
[Crossref] [PubMed]

O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006).
[Crossref]

Hatzopoulos, Z.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
[Crossref] [PubMed]

Haug, H.

H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys. 82(2), 1489–1537 (2010).
[Crossref]

Hey, R.

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
[Crossref]

Hivet, R.

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
[Crossref]

Höfling, S.

T. Horikiri, T. Byrnes, K. Kusudo, N. Ishida, Y. Matsuo, Y. Shikano, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Highly excited exciton-polariton condensates,” Phys. Rev. B 95(24), 245122 (2017).
[Crossref]

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7(2), 129–133 (2011).
[Crossref]

Horikiri, T.

T. Horikiri, T. Byrnes, K. Kusudo, N. Ishida, Y. Matsuo, Y. Shikano, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Highly excited exciton-polariton condensates,” Phys. Rev. B 95(24), 245122 (2017).
[Crossref]

Houdré, R.

A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010).
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M. Thunert, A. Janot, H. Franke, C. Sturm, T. Michalsky, M. D. Martín, L. Viña, B. Rosenow, M. Grundmann, and R. Schmidt-Grund, “Cavity polariton condensate in a disordered environment,” Phys. Rev. B 93(6), 064203 (2016).
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[Crossref]

Skolnick, M. S.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
[Crossref]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
[Crossref] [PubMed]

Skryabin, D. V.

Smith, J. M.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

Solnyshkov, D. D.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Sreejith, G. J.

Y. Zhang, G. J. Sreejith, N. D. Gemelke, and J. K. Jain, “Fractional angular momentum in cold-atom systems,” Phys. Rev. Lett. 113(16), 160404 (2014).
[Crossref] [PubMed]

Staehli, J. L.

O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006).
[Crossref]

Stilgoe, A. B.

Sturm, C.

M. Thunert, A. Janot, H. Franke, C. Sturm, T. Michalsky, M. D. Martín, L. Viña, B. Rosenow, M. Grundmann, and R. Schmidt-Grund, “Cavity polariton condensate in a disordered environment,” Phys. Rev. B 93(6), 064203 (2016).
[Crossref]

Sun, G.

S. Greschner, D. Huerga, G. Sun, D. Poletti, and L. Santos, “Density-dependent synthetic magnetism for ultracold atoms in optical lattices,” Phys. Rev. B 92(11), 115120 (2015).
[Crossref]

Szymanska, M. H.

G. Dagvadorj, J. M. Fellows, S. Matyjaśkiewicz, F. M. Marchetti, I. Carusotto, and M. H. Szymańska, “Nonequilibrium phase transition in a two-dimensional driven open quantum system,” Phys. Rev. X 5(4), 041028 (2015).

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
[Crossref]

F. M. Marchetti, M. H. Szymańska, C. Tejedor, and D. M. Whittaker, “Spontaneous and triggered vortices in polariton optical-parametric-oscillator superfluids,” Phys. Rev. Lett. 105(6), 063902 (2010).
[Crossref] [PubMed]

Tejedor, C.

F. M. Marchetti, M. H. Szymańska, C. Tejedor, and D. M. Whittaker, “Spontaneous and triggered vortices in polariton optical-parametric-oscillator superfluids,” Phys. Rev. Lett. 105(6), 063902 (2010).
[Crossref] [PubMed]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
[Crossref] [PubMed]

Thunert, M.

M. Thunert, A. Janot, H. Franke, C. Sturm, T. Michalsky, M. D. Martín, L. Viña, B. Rosenow, M. Grundmann, and R. Schmidt-Grund, “Cavity polariton condensate in a disordered environment,” Phys. Rev. B 93(6), 064203 (2016).
[Crossref]

Tosi, G.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
[Crossref] [PubMed]

Trichet, A. A. P.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

Tsotsis, P.

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
[Crossref] [PubMed]

van Loock, P.

T. Byrnes, Y. Yamamoto, and P. van Loock, “Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates,” Phys. Rev. B 87(20), 201301 (2013).
[Crossref]

Verger, A.

A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
[Crossref]

Viña, L.

M. Thunert, A. Janot, H. Franke, C. Sturm, T. Michalsky, M. D. Martín, L. Viña, B. Rosenow, M. Grundmann, and R. Schmidt-Grund, “Cavity polariton condensate in a disordered environment,” Phys. Rev. B 93(6), 064203 (2016).
[Crossref]

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
[Crossref] [PubMed]

Walker, P. M.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
[Crossref]

Wang, J.

Wang, T.

Wen, S.

Wertz, E.

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

Whittaker, D. M.

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
[Crossref]

F. M. Marchetti, M. H. Szymańska, C. Tejedor, and D. M. Whittaker, “Spontaneous and triggered vortices in polariton optical-parametric-oscillator superfluids,” Phys. Rev. Lett. 105(6), 063902 (2010).
[Crossref] [PubMed]

D. M. Whittaker, “Vortices in the microcavity optical parametric oscillator,” Superlatt. Microstruct. 41(5), 297–300 (2007).
[Crossref]

Woerdman, J. P.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

Yamamoto, Y.

T. Horikiri, T. Byrnes, K. Kusudo, N. Ishida, Y. Matsuo, Y. Shikano, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Highly excited exciton-polariton condensates,” Phys. Rev. B 95(24), 245122 (2017).
[Crossref]

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(12), 803 (2014).
[Crossref]

T. Byrnes, Y. Yamamoto, and P. van Loock, “Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates,” Phys. Rev. B 87(20), 201301 (2013).
[Crossref]

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7(2), 129–133 (2011).
[Crossref]

H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys. 82(2), 1489–1537 (2010).
[Crossref]

M. D. Fraser, G. Roumpos, and Y. Yamamoto, “Vortex-antivortex pair dynamics in an exciton-polariton condensate,” New J. Phys. 11(11), 113048 (2009).
[Crossref]

Zeilinger, A.

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

Zhai, Y.

Zhang, S.

Zhang, W.

Zhang, X.

Zhang, Y.

Y. Zhang, G. J. Sreejith, N. D. Gemelke, and J. K. Jain, “Fractional angular momentum in cold-atom systems,” Phys. Rev. Lett. 113(16), 160404 (2014).
[Crossref] [PubMed]

Y. Zhang, G. Jin, and Y.-Q. Ma, “Boundary effects on the dynamics of exciton polaritons in semiconductor microcavities,” J. Appl. Phys. 105(3), 033105 (2009).
[Crossref]

Zhang, Z.

Zheng, S.

Zoller, P.

O. Romero-Isart, C. Navau, A. Sanchez, P. Zoller, and J. I. Cirac, “Superconducting vortex lattices for ultracold atoms,” Phys. Rev. Lett. 111(14), 145304 (2013).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

O. E. Daïf, A. Baas, T. Guillet, J.-P. Brantut, R. I. Kaitouni, J. L. Staehli, F. Morier-Genoud, and B. Deveaud, “Polariton quantum boxes in semiconductor microcavities,” Appl. Phys. Lett. 88(6), 061105 (2006).
[Crossref]

J. Appl. Phys. (1)

Y. Zhang, G. Jin, and Y.-Q. Ma, “Boundary effects on the dynamics of exciton polaritons in semiconductor microcavities,” J. Appl. Phys. 105(3), 033105 (2009).
[Crossref]

Laser Photon. Rev. (1)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2(4), 299–313 (2008).
[Crossref]

Nat. Commun. (1)

G. Tosi, G. Christmann, N. G. Berloff, P. Tsotsis, T. Gao, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Geometrically locked vortex lattices in semiconductor quantum fluids,” Nat. Commun. 3, 1243 (2012).
[Crossref] [PubMed]

Nat. Phys. (3)

G. Roumpos, M. D. Fraser, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Single vortex-antivortex pair in an exciton-polariton condensate,” Nat. Phys. 7(2), 129–133 (2011).
[Crossref]

E. Wertz, L. Ferrier, D. D. Solnyshkov, R. Johne, D. Sanvitto, A. Lemaître, I. Sagnes, R. Grousson, A. V. Kavokin, P. Senellart, G. Malpuech, and J. Bloch, “Spontaneous formation and optical manipulation of extended polariton condensates,” Nat. Phys. 6(11), 860–864 (2010).
[Crossref]

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10(12), 803 (2014).
[Crossref]

Nature (1)

A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. D. Martin, A. Lemaître, J. Bloch, D. N. Krizhanovskii, M. S. Skolnick, C. Tejedor, and L. Viña, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457(7227), 291–295 (2009).
[Crossref] [PubMed]

New J. Phys. (1)

M. D. Fraser, G. Roumpos, and Y. Yamamoto, “Vortex-antivortex pair dynamics in an exciton-polariton condensate,” New J. Phys. 11(11), 113048 (2009).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Optica (1)

Photon. Res. (4)

Phys. Rev. A (3)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992).
[Crossref] [PubMed]

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80(6), 063604 (2009).
[Crossref]

F. I. Moxley, J. P. Dowling, W. Dai, and T. Byrnes, “Sagnac interferometry with coherent vortex superposition states in exciton-polariton condensates,” Phys. Rev. A 93(5), 053603 (2016).
[Crossref]

Phys. Rev. B (12)

X. Ma and S. Schumacher, “Vortex-vortex control in exciton-polariton condensates,” Phys. Rev. B 95(23), 235301 (2017).
[Crossref]

A. Amo, S. Pigeon, C. Adrados, R. Houdré, E. Giacobino, C. Ciuti, and A. Bramati, “Light engineering of the polariton landscape in semiconductor microcavities,” Phys. Rev. B 82(8), 081301 (2010).
[Crossref]

T. Byrnes, Y. Yamamoto, and P. van Loock, “Unconditional generation of bright coherent non-Gaussian light from exciton-polariton condensates,” Phys. Rev. B 87(20), 201301 (2013).
[Crossref]

T. C. H. Liew, A. V. Kavokin, and I. A. Shelykh, “Excitation of vortices in semiconductor microcavities,” Phys. Rev. B 75(24), 241301 (2007).
[Crossref]

F. Manni, K. G. Lagoudakis, T. K. Paraïso, R. Cerna, Y. Léger, T. C. H. Liew, I. A. Shelykh, A. V. Kavokin, F. Morier-Genoud, and B. Deveaud-Plédran, “Spin-to-orbital angular momentum conversion in semiconductor microcavities,” Phys. Rev. B 83(24), 241307 (2011).
[Crossref]

E. Cancellieri, T. Boulier, R. Hivet, D. Ballarini, D. Sanvitto, M. H. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Merging of vortices and antivortices in polariton superfluids,” Phys. Rev. B 90(21), 214518 (2014).
[Crossref]

S. Greschner, D. Huerga, G. Sun, D. Poletti, and L. Santos, “Density-dependent synthetic magnetism for ultracold atoms in optical lattices,” Phys. Rev. B 92(11), 115120 (2015).
[Crossref]

K. Guda, M. Sich, D. Sarkar, P. M. Walker, M. Durska, R. A. Bradley, D. M. Whittaker, M. S. Skolnick, E. A. Cerda-Méndez, P. V. Santos, K. Biermann, R. Hey, and D. N. Krizhanovskii, “Spontaneous vortices in optically shaped potential profiles in semiconductor microcavities,” Phys. Rev. B 87(8), 081309 (2013).
[Crossref]

T. Horikiri, T. Byrnes, K. Kusudo, N. Ishida, Y. Matsuo, Y. Shikano, A. Löffler, S. Höfling, A. Forchel, and Y. Yamamoto, “Highly excited exciton-polariton condensates,” Phys. Rev. B 95(24), 245122 (2017).
[Crossref]

M. Thunert, A. Janot, H. Franke, C. Sturm, T. Michalsky, M. D. Martín, L. Viña, B. Rosenow, M. Grundmann, and R. Schmidt-Grund, “Cavity polariton condensate in a disordered environment,” Phys. Rev. B 93(6), 064203 (2016).
[Crossref]

F. Manni, T. C. H. Liew, K. G. Lagoudakis, C. Ouellet-Plamondon, R. André, V. Savona, and B. Deveaud, “Spontaneous self-ordered states of vortex-antivortex pairs in a polariton condensate,” Phys. Rev. B 88(20), 201303 (2013).
[Crossref]

A. Verger, C. Ciuti, and I. Carusotto, “Polariton quantum blockade in a photonic dot,” Phys. Rev. B 73(19), 193306 (2006).
[Crossref]

Phys. Rev. Lett. (7)

K. S. Daskalakis, S. A. Maier, and S. Kéna-Cohen, “Spatial coherence and stability in a disordered organic polariton condensate,” Phys. Rev. Lett. 115(3), 035301 (2015).
[Crossref] [PubMed]

O. Romero-Isart, C. Navau, A. Sanchez, P. Zoller, and J. I. Cirac, “Superconducting vortex lattices for ultracold atoms,” Phys. Rev. Lett. 111(14), 145304 (2013).
[Crossref] [PubMed]

Y. Zhang, G. J. Sreejith, N. D. Gemelke, and J. K. Jain, “Fractional angular momentum in cold-atom systems,” Phys. Rev. Lett. 113(16), 160404 (2014).
[Crossref] [PubMed]

F. M. Marchetti, M. H. Szymańska, C. Tejedor, and D. M. Whittaker, “Spontaneous and triggered vortices in polariton optical-parametric-oscillator superfluids,” Phys. Rev. Lett. 105(6), 063902 (2010).
[Crossref] [PubMed]

J. Jimenez-Garcia, P. Rodriguez, T. Guillet, and T. Ackemann, “Spontaneous formation of vector vortex beams in vertical-cavity surface-emitting lasers with feedback,” Phys. Rev. Lett. 119(11), 113902 (2017).
[Crossref] [PubMed]

S. Dufferwiel, F. Li, E. Cancellieri, L. Giriunas, A. A. P. Trichet, D. M. Whittaker, P. M. Walker, F. Fras, E. Clarke, J. M. Smith, M. S. Skolnick, and D. N. Krizhanovskii, “Spin textures of exciton-polaritons in a tunable microcavity with large TE-TM splitting,” Phys. Rev. Lett. 115(24), 246401 (2015).
[Crossref] [PubMed]

K. T. Kapale and J. P. Dowling, “Vortex phase qubit: Generating arbitrary, counterrotating, coherent superpositions in Bose-Einstein condensates via optical angular momentum beams,” Phys. Rev. Lett. 95(17), 173601 (2005).
[Crossref] [PubMed]

Phys. Rev. X (1)

G. Dagvadorj, J. M. Fellows, S. Matyjaśkiewicz, F. M. Marchetti, I. Carusotto, and M. H. Szymańska, “Nonequilibrium phase transition in a two-dimensional driven open quantum system,” Phys. Rev. X 5(4), 041028 (2015).

Rev. Mod. Phys. (1)

H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose-Einstein condensation,” Rev. Mod. Phys. 82(2), 1489–1537 (2010).
[Crossref]

Science (1)

R. Fickler, R. Lapkiewicz, W. N. Plick, M. Krenn, C. Schaeff, S. Ramelow, and A. Zeilinger, “Quantum entanglement of high angular momenta,” Science 338(6107), 640–643 (2012).
[Crossref] [PubMed]

Superlatt. Microstruct. (1)

D. M. Whittaker, “Vortices in the microcavity optical parametric oscillator,” Superlatt. Microstruct. 41(5), 297–300 (2007).
[Crossref]

Other (2)

A. Kavokin and G. Malpuech, Cavity Polaritons (Academic Press, 2003).

K. Lagoudakis, The Physics of Exciton-Polariton Condensates (EPFL Press, 2013).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Schematic drafts for creating polariton vortices in pillar semiconductor microcavities by one Gaussian beam whose center locates on the x axis and wave vector is (a) along and (b) normal to the x axis. The blue curves show the possible motion path of the polaritons, resulting in polariton vortices or antivortices.
Fig. 2
Fig. 2 Steady density distribution of photon fields, |ψC(r)|2 (left panel in each subfigure) and corresponding phase (with unit of π) distribution (right panel). The numbers in the bottom left corner denote the maximum value of the photon density and the green circles represent the pillar boundaries with radii (a) R = 2 μm, (b) R = 4 μm, (c) R = 8 μm, and (d) R = 16 μm. As an example, the vortices and antivortices are denoted by dots and stars in (b). Other parameters: fp = 0.1 meV · μm−1, kp = (2, 0) μm−1, rp = (0, 0), and w = 4 μm.
Fig. 3
Fig. 3 Steady density distributions of photon fields, |ψC(x, y, t)|2 (left panel in each subfigure) and corresponding phase distributions (right panel). Color scale bars are the same to Fig. 2. The number in the bottom left corner represents the maximum value of the photon density and all green circles denoting the microcavity boundaries have the same radii R = 8 μm. The wave vector of the pump beam, kp, is along the x axis and its value given in the above of each figure. As an example, the vortices and antivortices are shown by dots and stars in (c). Other parameters: fp = 0.1 meV · μm−1, rp = (0, 0), and w = 4 μm.
Fig. 4
Fig. 4 Steady density distributions of photon fields, |ψC(x, y, t)|2 (left panel in each subfigure) and corresponding phase distributions (right panel). Color scale bars are the same to Fig. 2. The number in the bottom left corner represents the maximum value of the photon density and all green circles denoting the microcavity boundaries have the same radii R = 8 μm. The wave vector of the pump beam, kp, is along the y axis and its value is given in the above of each figure. As an example, the vortices and antivortices are shown by dots and stars in (c). Other parameters: fp = 0.1 meV · μm−1, rp = (4, 0) μm, and w = 4 μm.
Fig. 5
Fig. 5 Density and phase distributions for (a–d) photon fields and (e–h) exciton fields. The left and right panels in each subfigure show the density and phase distributions, respectively. The distributions in (a–c) and (e–f) are steady, while those in (d) and (h) at the evolution time of 1600 ħ · meV−1 are not. Color scale bars are the same to Fig. 2. The number in the bottom left corner represents the maximum value of the field densities and all green circles denoting that the microcavity boundaries have the same radii R = 8 μm. The wave vector of the pump beam, kp, is along the y axis and its value is given in the above of each subfigure. As an example, the vortices are shown by dots in (c) and (g). Other parameters: fp = 10 meV · μm−1, rp = (4, 0) μm, and w = 4 μm.

Equations (9)

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i d d t ( ψ X ( r ) ψ C ( r ) ) = [ h 0 + ( V X ( r ) i 2 γ X + g X | ψ X ( r ) | 2 0 0 V C ( r ) i 2 γ C ) ] ( ψ X ( r ) ψ C ( r ) ) + ( 0 F p ( r ) ) ,
h 0 = ( ω X ( i ) Ω R Ω R ω C ( i ) )
F p ( r ) = f p e ( r r p ) 2 / w 2 e i k p r e i ω p t
L pump = i F ( r ) | ϕ | F ( r ) F ( r ) | F ( r ) = r p × k p
( ψ X ( r ) ψ C ( r ) ) = n , l ( X n , l C n , l ) ϕ n , l ( r )
ϕ n , l ( r ) = J n , | l | ( r ) × 1 2 π e i l φ .
C n , l = [ ω p ( ω X 0 i 2 γ X ) ] × f n , l e i ω p t [ ω p ( ω C 0 + ω n , l i 2 γ C ) ] [ ω p ( ω X 0 i 2 γ X ) ] Ω R2 ,
X n , l = Ω × f n , l e i ω p t [ ω p ( ω C 0 + ω n , l i 2 γ C ) ] [ ω p ( ω X 0 i 2 γ X ) ] Ω R2 ,
L C = n , l l | C n , l | 2 n , l | C n , l | 2 .

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