Abstract

Recent studies of two-photon excitation of exciton-polaritons in microcavities have considered the possibility of an allowed absorption process into the 2p-state of the excitons that participate in the polariton effect. Here we report time-resolved measurements of two-photon excitation directly into the lower polariton states, invoking the 1s state of the excitons. Although this process is forbidden by symmetry for light at normal incidence, it is allowed at a nonzero angle of incidence due to state mixing. We examine the polarization dependence of two-photon absorption at finite k both theoretically and experimentally. Previous results should be reevaluated in light of the mechanism observed here.

© 2017 Optical Society of America

1. INTRODUCTION

The exciton-polariton is a quantum superposition of light and matter that has been studied extensively for its bosonic properties. The canonical system consists of quantum well (QW) excitons embedded in a two-dimensional microcavity (for reviews see, e.g., Refs. [14]). At low temperatures, this system exhibits Bose–Einstein condensation [57], superfluidity [810], and quantized vortices [1115] and may have applications as low-threshold coherent light source and highly nonlinear optical system. Polaritons are metastable particles, as they can leak through the mirrors into external photons.

Recently, two-photon excitation of exciton-polaritons has gained attention [1618] for its possible application in polariton lasers [16,19,20]. In general, two-photon excitation of polaritons provides another way of using the super-nonlinearities of the polaritons for optical modulation schemes. References [16,18] proposed a mechanism via absorption into the 2p state, while Ref. [17] investigated this claim using a narrowband source and cast doubt on that mechanism because they saw no strong two-photon absorption at the energy of the 2p state. Since there exist other mechanisms that could permit the conversion of dark excitons into the lower polaritons, in this paper we perform time-resolved measurements to investigate this possibility and show successful direct excitation of exciton-polaritons by two-photon absorption [21]. We show that this is possible with an incident beam with a finite in-plane momentum due to “bright” state/“dark” state mixing and study the polarization dependence of this absorption both theoretically and experimentally.

In the GaAs-based structures we use, the lowest QW exciton states consist of the two J=1 “bright” states and two J=2 “dark” states. These states are made of the conduction electrons with spin=±1/2 and the heavy holes with angular momentum ±3/2. In our samples with narrow (7 nm) QWs, the light hole exciton states are about 30 meV higher than the heavy hole states, which is greater than the upper polariton/lower polariton splitting and greater than the spectral width of the lasers we use, so the light hole states are unlikely to be excited in resonant excitation of the heavy hole states. The polaritons are formed by coupling the cavity photon to the J=1 “bright” heavy hole exciton state. The coupling of the photon and exciton states leads to two new sets of states, the upper polariton and lower polariton states, split by about 12 meV. The J=2 “dark” exciton states do not couple to photons to make polaritons.

2. METHODS

Our exciton-polariton samples are made up of GaAs QWs with AlAs barriers, in three sets of four, placed at the antinodes of the microcavity made of two Bragg mirrors, which are made of AlAs and AlxGa1x repeating layers. The details of these long lifetime samples are given in Ref. [22], and the measurement of the lifetime (180±10ps) is discussed in Ref. [23]. This lifetime corresponds to a quality factor of over 300,000, compared to a quality factor of less than 10,000 for the samples used in Refs. [17,18]. The long lifetime of the samples allowed us to study ballistic propagation of the population injected by two-photon excitation. The ballistic propagation was good evidence that the injection was directly into polariton states, rather than higher-energy states that would have to thermalize/scatter into the lower polariton states.

These samples were mounted in a cryostat and held at a fixed temperature in the range of 4 K–8 K. Two-photon excitation of the samples was done using a Coherent optical parametric amplifier (OPA) system consisting of a femtosecond pulsed Ti-sapphire laser, a regenerative amplifier with a repetition rate of 250 kHz, and an OPA pumped with tunable output wavelength. Since the energy of the lower polariton in our samples was about 1.593 eV, we tuned the OPA to give a beam with half that energy (0.7965 eV). This output beam had a spectral full width at half-maximum (FWHM) of 15 meV. A pictorial representation of our experimental setup is provided in Appendix A.

We used a dichroic mirror and a 1000 nm longpass filter in the path of our pump beam in order to remove leaked signal coming from the regenerative amplifier. Also, since the photon energy of the regenerative amplifier beam is much lower than the energy of the polariton emission, it was not detected by our spectrally resolved detection system. The emission signal from the polaritons was spectrally resolved using a 0.25 m spectrometer and time resolved using a Hamamatsu streak camera. The time-averaged signal was simultaneously viewed on a Princeton CCD camera. Figure 1(a) shows a typical spatially resolved, time-averaged spectrum. The energy of the emission from the polaritons varies across the sample because there is a wedge in the cavity thickness, giving a spatial gradient to the photon energy. Figure 1(b) shows a typical time-resolved spectrum. As seen in this figure [as well as in Fig. 3(b)], there is a fast rise time of the emission, comparable to our time resolution. The fast fall time of the emission is actually an artifact due to the motion of the polaritons in the cavity gradient. Instead of remaining at the spot where they were generated, the polaritons accelerate in the direction of lower cavity photon energy. This leads to two effects that suppress their collection by our detection system. First, as they move, they can move out of the spatial field of view of the lens collecting the emission. Second, as they accelerate to higher momentum in the plane (corresponding to higher in-plane wavenumber k), their photon emission occurs at a higher angle, and therefore will not be collected by a low-NA system.

 figure: Fig. 1.

Fig. 1. (a) Time-averaged spectrum while exciting with half the energy of the lower polariton with a laser focused at x=0μm. There is a spatial gradient to the polariton energy, because there is a wedge in the cavity thickness across the sample. (b) Time-resolved spectrum at the generation spot while exciting with half the energy of the lower polariton. There is a fast rise time of the emission comparable to our time resolution, which indicates there is direct excitation of the lower polariton.

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3. RESULTS

In order to ensure that we were observing two-photon excitation and not a higher-order excitation or single-photon excitation due to leaked photons in the pump beam, we did a power series measurement by varying the pump power and measured the time-averaged intensity. As seen in Fig. 2, the good fit to the IP2 power law confirms that we have observed two-photon excitation.

 figure: Fig. 2.

Fig. 2. Power dependence of the polariton emission intensity at the creation spot. Solid line: fit to the square of the pump power, indicating two-photon absorption.

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Figure 3 shows the results of the time-resolved measurements for various pump wavelengths. The wavelength of 1555 nm corresponds to the resonant condition of the pump photon energy, exactly half the lower polariton energy. When exciting with exactly half the resonant energy [Fig. 3(b)], we see a short (16 ps) peak. However, as we increase the pump photon energy, we see the initial peak disappear and a signal with a long rise time take its place.

 figure: Fig. 3.

Fig. 3. Intensity versus time for different pump wavelengths of (a) 1565 nm, (b) 1555 nm, (c) 1540 nm, (d) 1530 nm, (e) 1525 nm, and (f) 1515 nm. A fast initial peak appears when the median pump photon energy is at half the lower polariton energy (λ=1555nm). A later population dominates for higher pump energies.

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Figure 4 shows the polariton intensity at constant pump power as the pump wavelength is varied. When we plot only the intensity of the initial peak, as shown in Fig. 4(a), we see that the intensity is the maximum when the pump photon energy is half the lower polariton energy and disappears at a higher pump photon energy. The FWHM of this peak is 15 meV, which is the same as the pump laser spectral FWHM. If we plot the total intensity, as shown in Fig. 4(b), we see that the intensity increases with increasing pump photon energy. We also observe a small peak while pumping at an energy corresponding to half the energy of the upper polariton energy (0.807 eV) in both cases. The apparent dip is within the uncertainty of our measurements.

 figure: Fig. 4.

Fig. 4. Polariton emission intensity versus pump photon energy from the time-resolved data. (a) Initial peak intensity, showing maximum absorption at the lower polariton energy with a slight peak at the UP energy, (b) total integrated intensity, showing an increase in intensity as the energy is increased. The circles and diamonds represent two data sets viewed on two different days.

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For each wavelength, we measured the power dependence for the initial fast-risetime peak and the slow-risetime signal separately. Both signals had an intensity that was proportional to the square of the pump power, indicating that both cases corresponded to two-photon absorption.

In order to understand the slow-risetime signal, we measured the signal as a function of temperature. As seen in Fig. 5, when the temperature is lower, the slow-risetime signal has a greater relative weight. This is consistent with higher-energy states cooling down into the ground state of the lower polariton. At a higher temperature, these states will be scattered to higher k-states, while at a lower temperature, they can cool down to states near k=0. Since k=0 corresponds to emission normal to the cavity, and our detection system has a low NA, we observe only states with k0 in our experiment. The short initial peak shows no change in intensity in the temperature range we studied (2.5 K to 10 K).

 figure: Fig. 5.

Fig. 5. Time versus intensity at (a) 8.3 K and (b) 2.5 K. As the temperature is increased, the intensity of the latter peak decreases. (c) Summary of the late-time intensity data as a function of T.

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4. DISCUSSION

The picture thus arises that polaritons are created by two different mechanisms. One mechanism is direct two-photon creation of polaritons, which occurs most efficiently when the pump laser photon energy is at exactly half the lower polariton energy. The second process is two-photon absorption into excitons in higher-energy states, which then relax down into the lower polariton states with a time constant of several hundred picoseconds. These higher-energy states may be either “dark” (J=2) exciton states or 2p states of the J=1 excitons. The short peak (due to direct creation of the lower polariton by resonant excitation) remains unaffected by temperature, since two-photon absorption cross sections do not change with temperature. However, nonresonant excitation (which causes the long peak) results in thermalization into all states and is affected by changes in temperature.

In order to explain the luminescence from two-photon absorption, other works [16,18] considered a mechanism based on absorption into the 2p state of the exciton, which then relaxes into the lower polariton by emitting a terahertz photon, while Ref. [17] has found no evidence of direct two-photon pumping into the 2p state. Time resolving the luminescence (Figs. 3 and 4) leads us to believe that we are directly exciting the polariton states. Although two-photon excitation of the J=1 states is forbidden by symmetry at k=0 (normal incidence), away from k=0, mixing of the J=1 and J=2 states occurs.

The coupling between the “dark” and “bright” exciton states can be derived from the Luttinger–Kohn (L–K) Hamiltonian [24,25]:

HLK|uk=(P+QSR0S/22RS*PQ0R2Q3/2SR0PQS3/2S2Q0R*S*P+Q2RS*/2S*/22Q*3/2S2RP+δ02R*3/2S*2Q*S/20P+δ)(|32,32|32,12|32,12|32,32|12,12|12,12)J,mj,
where
P=γ12m0(kx2+ky2+kz2),Q=γ22m0(kx2+ky22kz2),R=2m0(3γ2(kx2ky2)+i23γ3kxky),S=γ32m03(kxiky)kz.
Because δ is about 100 meV, we can ignore the split-off holes. We therefore restrict our attention to the 4×4 submatrix of the light-hole/heavy-hole states. The “bright” (J=1) excitons for the heavy holes have conduction-band electrons with spin in the direction opposite to the hole angular momentum, i.e., |32,±32;12, where the first label gives the value of J for the hole, the second label gives the value of mj for the hole, and the third, the spin of the electron. “Dark” heavy-hole (J=2) excitons correspond to electron spin in the same direction as the hole angular momentum, i.e., |32,±32;±12.

Our pump photons are linearly polarized (along the x axis). Since linear polarization can be viewed as the superposition of two opposite circular polarizations, two photons from the pump beam will couple to a net J=0 state of the excitons. Such a state exists for the light holes, corresponding to the two states |32,12;12 and |32,12;12. The “bright” state polaritons are nominally defined as α|32,12+β|1 and α|32,12+β|1, where |±1 are the cavity photon states with J=1. The J=0 light-hole states couple to the J=1 heavy-hole states through the L–K Hamiltonian when S0. The S term increases linearly with kx and ky and is zero for kx=ky=0. The value of kz is determined by the QW confinement. While the light-hole states are 30 meV higher in energy, due to coupling between the heavy-hole and light-hole states in the L–K Hamiltonian, we are able to a access the J=0 states by exciting at nonzero k.

We thus see that the lower polaritons are not purely made from heavy-hole excitons for finite in-plane k; the excitonic part of the polariton includes a “dark” exciton fraction. The “dark” exciton fraction will slightly reduce the polaritonic coupling to the cavity photons but will not lead to drastic changes of the polariton behavior. Diagonalizing the L–K Hamiltonian, setting R=0, P+Q=Ehh, PQ=Elh, Δ=ElhEhh, which, as mentioned above, is about 30 meV, and SΔ, the hole eigenstates are

|32,32+SΔ|32,12SΔ|32,32+|32,12,|32,32+SΔ|32,12SΔ|32,32+|32,12.
Although in these experiments we excited the sample at normal incidence, we used a focusing lens that introduced a finite range of angles of incidence, and therefore finite kx and ky, which caused direct excitation of the lower polariton through coupling with the “dark” state excitons. The above interpretation implies that an increase in kx and ky should increase the absorption of the two-photon absorption.

We further note that the eigenstates of the light holes are given by [24]

|32,12=16|(cosθcosφisinφ)x^+(cosθsinφ+icosφ)y^sinθz^|+23|sinθcosφx^+sinθsinφy^+cosθz^|,
|32,12=16|(cosθcosφ+isinφ)x^+(cosθsinφicosφ)y^sinθz^|+23|sinθcosφx^+sinθsinφy^+cosθz^|,
where θ is the angle between the normal to the sample and the polarization vector of the incoming light, and φ is the angle of rotation about the normal.

Calculating the optical momentum matrix element between these states and the conduction band states for the “dark” exciton, we obtain

iS|p|32,12=23(sinθcosφx^+sinθsinφy^+cosθz^)P,
iS|p|32,12=23(sinθcosφx^+sinθsinφy^+cosθz^)P,
where p is the dipole operator, |S and |S are the conduction band eigenstates, and P is the dipole element.

If the plane of incidence is the xz plane, then φ=0 and the TE polarization is along the y axis. We obtain the relevant matrix elements by looking at the y^ component, which gives us sinθsinφ=0, since φ=0. To obtain the matrix element corresponding to the TM polarization, we look at the z^ component, which gives us cosθ. In our experiment, we measure the angle θ, where θ is the angle between the normal to the sample and the incident beam and θ=π2θ, giving us a matrix element sinθkx.

The dependence of the S term on kx and the dependence of the polarization selection rule on kx give us a factor of kx2 for the matrix element. The rate of two-photon absorption is proportional to the square of the matrix element, which means that we should see the intensity increase as k||4 for TM-polarized light, and we should not see any luminescence from purely TE-polarized light. To check this, we varied k for incident TM- and TE-polarized light and observed that the intensity was consistent with a k||4 dependence in the TM-polarized case (Fig. 6) and no luminescence in the TE-polarized case. The spread of angles in the incoming beam gives a nonzero contribution, even at k||=0, i.e., normal incidence. When the signal was sent through a polarizer, the polaritons formed were seen to be TM polarized as well. A change in the polarization of the pump beam from linear to circular polarization caused a decrease in absorption.

 figure: Fig. 6.

Fig. 6. Intensity of the light from two-photon absorption versus the central in-plane momentum of the incoming light beam. The dots represent our data, and the solid line is a convolution fit A(f*g)+B, where f=k4 and g=ek2σ2 with σ2=0.07, which takes into account the finite width of our laser spot. A=0.95 and B=0.14 are scaling parameters that take into account background light. This indicates that the absorption is k4.

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Further support for this conclusion comes from experiments in which we placed the sample in a magnetic field. No change in the intensity of the polariton emission generated by two-photon excitation was seen. Since the “dark” state/“bright” state mixing is already allowed at finite in-plane k||, a change in the magnetic field up to 1T did not produce a substantial increase in the mixing.

5. CONCLUSION

In conclusion, direct two-photon excitation of the lower polariton branch of exciton-polaritons in a microcavity is possible at a nonzero angle of incidence, without involving higher-lying J=2 or 2p exciton states. When the pump photon energy is tuned to be resonant with those higher-lying states, we do see evidence for those states being excited, which then leads to polaritons appearing at lower energy with a long rise time. If the two-photon beam has TM polarization and is incident at an angle, we have a direct excitation of the lower polariton, while we see no excitation if the incident beam is TE polarized. Direct two-photon excitation of polaritons leads us to expect novel nonlinear effects with interaction of macroscopically occupied polariton states and light waves at half their frequency. Future work will address this.

APPENDIX A

Figure 7 shows a pictorial representation of our experimental setup. The beam from our laser is sent through longpass filters. Telescope and microscope objectives help focus the beam onto the sample. Quarter-wave plates are used to control the polarization of the beam. The beam from the sample is analyzed using a spectrometer and a streak camera.

 figure: Fig. 7.

Fig. 7. Schematic of the experimental setup.

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Funding

National Science Foundation (NSF) (DMR-0819860, PHY-1205762); Gordon and Betty Moore Foundation.

Acknowledgment

The work at the University of Pittsburgh was supported by the NSF under grant PHY-1205762. The work at Princeton University was partially funded by the Gordon and Betty Moore Foundation as well as the NSF MRSEC Program through the Princeton Center for Complex Materials (DMR-0819860).

REFERENCES

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

2. I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013). [CrossRef]  

3. A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007).

4. D. Sanvitto and V. Timofeev, Exciton Polaritons in Microcavities: New Frontiers (Springer, 2012).

5. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006). [CrossRef]  

6. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007). [CrossRef]  

7. T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10, 803–813 (2014). [CrossRef]  

8. A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009). [CrossRef]  

9. P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013). [CrossRef]  

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

11. G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015). [CrossRef]  

12. K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009). [CrossRef]  

13. D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010). [CrossRef]  

14. R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014). [CrossRef]  

15. 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, 201303 (2013). [CrossRef]  

16. A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108, 197401 (2012). [CrossRef]  

17. J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014). [CrossRef]  

18. G. Lemenager, F. Pisanello, J. Bloch, A. V. Kavokin, A. Amo, A. Lemaître, E. Galopin, I. Sagnes, M. De Vittorio, E. Giacobino, and A. Bramati, “Two-photon injection of polaritons in semiconductor microstructures,” Opt. Lett. 39, 307–310 (2014). [CrossRef]  

19. P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013). [CrossRef]  

20. C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013). [CrossRef]  

21. Preliminary results from this work were reported in August 2013; see C. Gautham and D. Snoke, “Modulation of two-photon excitation by a polariton condensate,” in Fundamental Optical Processes and Semiconductors 2013, Kodiak Island, Alaska, 12 –16 August 2013.

22. B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013). [CrossRef]  

23. M. Steger, C. Gautham, D. Snoke, L. Pfeiffer, and K. West, “Slow reflection and two-photon generation of microcavity exciton-polaritons,” Optica 2, 1–5 (2015). [CrossRef]  

24. S. Chaung, Physics of Photonic Devices, Wiley Series in Pure and Applied Optics (Wiley, 2009), p. 399.

25. J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015). [CrossRef]  

References

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  1. H. Deng, H. Haug, and Y. Yamamoto, “Exciton-polariton Bose–Einstein condensation,” Rev. Mod. Phys. 82, 1489–1537 (2010).
    [Crossref]
  2. I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
    [Crossref]
  3. A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007).
  4. D. Sanvitto and V. Timofeev, Exciton Polaritons in Microcavities: New Frontiers (Springer, 2012).
  5. J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
    [Crossref]
  6. R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
    [Crossref]
  7. T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10, 803–813 (2014).
    [Crossref]
  8. A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
    [Crossref]
  9. P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
    [Crossref]
  10. A. Amo, D. Sanvitto, F. P. Laussy, D. Ballarini, E. del Valle, M. Martin, A. Lemaitre, J. Bloch, D. Krizhanovskii, M. Skolnick, C. Tejedor, and L. Vina, “Collective fluid dynamics of a polariton condensate in a semiconductor microcavity,” Nature 457, 291–295 (2009).
    [Crossref]
  11. G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015).
    [Crossref]
  12. K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
    [Crossref]
  13. D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
    [Crossref]
  14. R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
    [Crossref]
  15. 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, 201303 (2013).
    [Crossref]
  16. A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108, 197401 (2012).
    [Crossref]
  17. J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
    [Crossref]
  18. G. Lemenager, F. Pisanello, J. Bloch, A. V. Kavokin, A. Amo, A. Lemaître, E. Galopin, I. Sagnes, M. De Vittorio, E. Giacobino, and A. Bramati, “Two-photon injection of polaritons in semiconductor microstructures,” Opt. Lett. 39, 307–310 (2014).
    [Crossref]
  19. P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
    [Crossref]
  20. C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
    [Crossref]
  21. Preliminary results from this work were reported in August 2013; see C. Gautham and D. Snoke, “Modulation of two-photon excitation by a polariton condensate,” in Fundamental Optical Processes and Semiconductors 2013, Kodiak Island, Alaska, 12–16 August2013.
  22. B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
    [Crossref]
  23. M. Steger, C. Gautham, D. Snoke, L. Pfeiffer, and K. West, “Slow reflection and two-photon generation of microcavity exciton-polaritons,” Optica 2, 1–5 (2015).
    [Crossref]
  24. S. Chaung, Physics of Photonic Devices, Wiley Series in Pure and Applied Optics (Wiley, 2009), p. 399.
  25. J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
    [Crossref]

2015 (3)

G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015).
[Crossref]

M. Steger, C. Gautham, D. Snoke, L. Pfeiffer, and K. West, “Slow reflection and two-photon generation of microcavity exciton-polaritons,” Optica 2, 1–5 (2015).
[Crossref]

J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
[Crossref]

2014 (4)

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

G. Lemenager, F. Pisanello, J. Bloch, A. V. Kavokin, A. Amo, A. Lemaître, E. Galopin, I. Sagnes, M. De Vittorio, E. Giacobino, and A. Bramati, “Two-photon injection of polaritons in semiconductor microstructures,” Opt. Lett. 39, 307–310 (2014).
[Crossref]

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10, 803–813 (2014).
[Crossref]

2013 (6)

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
[Crossref]

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
[Crossref]

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[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, 201303 (2013).
[Crossref]

2012 (1)

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108, 197401 (2012).
[Crossref]

2010 (2)

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

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

2009 (3)

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

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[Crossref]

2007 (1)

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref]

2006 (1)

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Adrados, C.

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

Amo, A.

G. Lemenager, F. Pisanello, J. Bloch, A. V. Kavokin, A. Amo, A. Lemaître, E. Galopin, I. Sagnes, M. De Vittorio, E. Giacobino, and A. Bramati, “Two-photon injection of polaritons in semiconductor microstructures,” Opt. Lett. 39, 307–310 (2014).
[Crossref]

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

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

Amthor, M.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

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, 201303 (2013).
[Crossref]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[Crossref]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Aßmann, M.

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

Baas, A.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Balili, R.

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[Crossref]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref]

Ballarini, D.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

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

Baudisch, M.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

Baumberg, J. J.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007).

Bayer, M.

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

Berloff, N. G.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Bhattacharya, P.

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
[Crossref]

Bhowmick, S.

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
[Crossref]

Bloch, J.

G. Lemenager, F. Pisanello, J. Bloch, A. V. Kavokin, A. Amo, A. Lemaître, E. Galopin, I. Sagnes, M. De Vittorio, E. Giacobino, and A. Bramati, “Two-photon injection of polaritons in semiconductor microstructures,” Opt. Lett. 39, 307–310 (2014).
[Crossref]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

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

Boulier, T.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

Bramati, A.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

G. Lemenager, F. Pisanello, J. Bloch, A. V. Kavokin, A. Amo, A. Lemaître, E. Galopin, I. Sagnes, M. De Vittorio, E. Giacobino, and A. Bramati, “Two-photon injection of polaritons in semiconductor microstructures,” Opt. Lett. 39, 307–310 (2014).
[Crossref]

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

Byrnes, T.

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10, 803–813 (2014).
[Crossref]

Cancellieri, E.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

Carusotto, I.

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
[Crossref]

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

Chaung, S.

S. Chaung, Physics of Photonic Devices, Wiley Series in Pure and Applied Optics (Wiley, 2009), p. 399.

Christmann, G.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Ciuti, C.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
[Crossref]

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

Cristofolini, P.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Czerniuk, T.

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

Daley, A.

G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015).
[Crossref]

Dang, L.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Das, A.

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
[Crossref]

De Vittorio, M.

del Valle, E.

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

Deng, H.

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

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, 201303 (2013).
[Crossref]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Deveaud-Plédran, B.

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[Crossref]

Dreismann, A.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Fischer, J.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Forchel, A.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Franchetti, G.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Galopin, E.

Gautham, C.

M. Steger, C. Gautham, D. Snoke, L. Pfeiffer, and K. West, “Slow reflection and two-photon generation of microcavity exciton-polaritons,” Optica 2, 1–5 (2015).
[Crossref]

Preliminary results from this work were reported in August 2013; see C. Gautham and D. Snoke, “Modulation of two-photon excitation by a polariton condensate,” in Fundamental Optical Processes and Semiconductors 2013, Kodiak Island, Alaska, 12–16 August2013.

Giacobino, E.

G. Lemenager, F. Pisanello, J. Bloch, A. V. Kavokin, A. Amo, A. Lemaître, E. Galopin, I. Sagnes, M. De Vittorio, E. Giacobino, and A. Bramati, “Two-photon injection of polaritons in semiconductor microstructures,” Opt. Lett. 39, 307–310 (2014).
[Crossref]

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

Glazov, M. M.

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108, 197401 (2012).
[Crossref]

Hartwell, V.

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref]

Hatzopoulos, Z.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Haug, H.

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

Heo, J.

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
[Crossref]

Hivet, R.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

Hofling, S.

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

Höfling, S.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Houdré, R.

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

Jeambrun, P.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Kamp, M.

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Kasprzak, J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Kavokin, A. V.

G. Lemenager, F. Pisanello, J. Bloch, A. V. Kavokin, A. Amo, A. Lemaître, E. Galopin, I. Sagnes, M. De Vittorio, E. Giacobino, and A. Bramati, “Two-photon injection of polaritons in semiconductor microstructures,” Opt. Lett. 39, 307–310 (2014).
[Crossref]

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108, 197401 (2012).
[Crossref]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[Crossref]

A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007).

Keeling, J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Kim, N. Y.

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10, 803–813 (2014).
[Crossref]

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Krizhanovskii, D.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

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

Kulakovskii, V.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Kundermann, S.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Lagoudakis, K. G.

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, 201303 (2013).
[Crossref]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[Crossref]

Laussy, F.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

Laussy, F. P.

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

A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007).

Lefrere, J.

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

Lemaitre, A.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

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

Lemaître, A.

Lemenager, G.

Lermer, M.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Liew, T. C. H.

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, 201303 (2013).
[Crossref]

Littlewood, P.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Liu, G.

G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015).
[Crossref]

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[Crossref]

Malpuech, G.

A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007).

Manni, F.

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, 201303 (2013).
[Crossref]

Marchetti, F.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Marchetti, F. M.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

Marrucci, L.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

Martin, M.

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

Nelsen, B.

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[Crossref]

Ostatnický, T.

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[Crossref]

Ouellet-Plamondon, C.

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, 201303 (2013).
[Crossref]

Pfeiffer, L.

G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015).
[Crossref]

M. Steger, C. Gautham, D. Snoke, L. Pfeiffer, and K. West, “Slow reflection and two-photon generation of microcavity exciton-polaritons,” Optica 2, 1–5 (2015).
[Crossref]

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[Crossref]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref]

Pfeiffer, L. N.

J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
[Crossref]

Pigeon, S.

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

Pisanello, F.

Rahimi-Iman, A.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Reitzenstein, S.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Richard, M.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Rubo, Y. G.

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[Crossref]

Sagnes, I.

Sanvitto, D.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

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

D. Sanvitto and V. Timofeev, Exciton Polaritons in Microcavities: New Frontiers (Springer, 2012).

Savenko, I. G.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Savona, V.

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, 201303 (2013).
[Crossref]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Savvidis, P. G.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Schmutzler, J.

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

Schneider, C.

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Shelykh, I.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Shelykh, I. A.

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108, 197401 (2012).
[Crossref]

Sinclair, N. W.

J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
[Crossref]

Skolnick, M.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

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

Snoke, D.

G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015).
[Crossref]

M. Steger, C. Gautham, D. Snoke, L. Pfeiffer, and K. West, “Slow reflection and two-photon generation of microcavity exciton-polaritons,” Optica 2, 1–5 (2015).
[Crossref]

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[Crossref]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref]

Preliminary results from this work were reported in August 2013; see C. Gautham and D. Snoke, “Modulation of two-photon excitation by a polariton condensate,” in Fundamental Optical Processes and Semiconductors 2013, Kodiak Island, Alaska, 12–16 August2013.

Snoke, D. W.

J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
[Crossref]

Staehli, J.

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Steger, M.

M. Steger, C. Gautham, D. Snoke, L. Pfeiffer, and K. West, “Slow reflection and two-photon generation of microcavity exciton-polaritons,” Optica 2, 1–5 (2015).
[Crossref]

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[Crossref]

Szymanska, M.

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
[Crossref]

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

Szymanska, M. H.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

Taylor, T.

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108, 197401 (2012).
[Crossref]

Tejedor, C.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

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

Timofeev, V.

D. Sanvitto and V. Timofeev, Exciton Polaritons in Microcavities: New Frontiers (Springer, 2012).

Tosi, G.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

Tsotsis, P.

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Vina, L.

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

Viña, L.

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

Voros, Z.

J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
[Crossref]

West, K.

M. Steger, C. Gautham, D. Snoke, L. Pfeiffer, and K. West, “Slow reflection and two-photon generation of microcavity exciton-polaritons,” Optica 2, 1–5 (2015).
[Crossref]

G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015).
[Crossref]

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[Crossref]

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref]

West, K. W.

J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
[Crossref]

Wolf, A.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Worschech, L.

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Wuenschell, J. K.

J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
[Crossref]

Xiao, B.

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
[Crossref]

Yamamoto, Y.

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10, 803–813 (2014).
[Crossref]

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

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

Nat. Phys. (3)

T. Byrnes, N. Y. Kim, and Y. Yamamoto, “Exciton-polariton condensates,” Nat. Phys. 10, 803–813 (2014).
[Crossref]

A. Amo, J. Lefrere, S. Pigeon, C. Adrados, C. Ciuti, I. Carusotto, R. Houdré, E. Giacobino, and A. Bramati, “Superfluidity of polaritons in semiconductor microcavities,” Nat. Phys. 5, 805–810 (2009).
[Crossref]

D. Sanvitto, F. M. Marchetti, M. H. Szymańska, G. Tosi, M. Baudisch, F. Laussy, D. Krizhanovskii, M. Skolnick, L. Marrucci, A. Lemaitre, J. Bloch, C. Tejedor, and L. Viña, “Persistent currents and quantized vortices in a polariton superfluid,” Nat. Phys. 6, 527–533 (2010).
[Crossref]

Nature (3)

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

J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. André, J. Staehli, V. Savona, P. Littlewood, B. Deveaud, and L. Dang, “Bose–Einstein condensation of exciton polaritons,” Nature 443, 409–414 (2006).
[Crossref]

C. Schneider, A. Rahimi-Iman, N. Y. Kim, J. Fischer, I. G. Savenko, M. Amthor, M. Lermer, A. Wolf, L. Worschech, V. Kulakovskii, I. Shelykh, M. Kamp, S. Reitzenstein, A. Forchel, Y. Yamamoto, and S. Höfling, “An electrically pumped polariton laser,” Nature 497, 348–352 (2013).
[Crossref]

Opt. Lett. (1)

Optica (1)

Phys. Rev. B (4)

J. K. Wuenschell, N. W. Sinclair, Z. Voros, D. W. Snoke, L. N. Pfeiffer, and K. W. West, “Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transistion,” Phys. Rev. B 92, 235415 (2015).
[Crossref]

J. Schmutzler, M. Aßmann, T. Czerniuk, M. Kamp, C. Schneider, S. Hofling, and M. Bayer, “Nonlinear spectroscopy of exciton-polaritons in a GaAs-based microcavity,” Phys. Rev. B 90, 075103 (2014).
[Crossref]

R. Hivet, E. Cancellieri, T. Boulier, D. Ballarini, D. Sanvitto, F. Marchetti, M. Szymanska, C. Ciuti, E. Giacobino, and A. Bramati, “Interaction-shaped vortex-antivortex lattices in polariton fluids,” Phys. Rev. B 89, 134501 (2014).
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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, 201303 (2013).
[Crossref]

Phys. Rev. Lett. (3)

A. V. Kavokin, I. A. Shelykh, T. Taylor, and M. M. Glazov, “Vertical cavity surface emitting terahertz laser,” Phys. Rev. Lett. 108, 197401 (2012).
[Crossref]

P. Bhattacharya, B. Xiao, A. Das, S. Bhowmick, and J. Heo, “Solid state electrically injected exciton-polariton laser,” Phys. Rev. Lett. 110, 206403 (2013).
[Crossref]

P. Cristofolini, A. Dreismann, G. Christmann, G. Franchetti, N. G. Berloff, P. Tsotsis, Z. Hatzopoulos, P. G. Savvidis, and J. J. Baumberg, “Optical superfluid phase transitions and trapping of polariton condensates,” Phys. Rev. Lett. 110, 186403 (2013).
[Crossref]

Phys. Rev. X (1)

B. Nelsen, G. Liu, M. Steger, D. Snoke, R. Balili, K. West, and L. Pfeiffer, “Dissipationless flow and sharp threshold of a polariton condensate with long lifetime,” Phys. Rev. X 3, 041015 (2013).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

G. Liu, D. Snoke, A. Daley, L. Pfeiffer, and K. West, “A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate,” Proc. Natl. Acad. Sci. USA 112, 2676–2681 (2015).
[Crossref]

Rev. Mod. Phys. (2)

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

I. Carusotto and C. Ciuti, “Quantum fluids of light,” Rev. Mod. Phys. 85, 299–366 (2013).
[Crossref]

Science (2)

R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, “Bose–Einstein condensation of microcavity polaritons in a trap,” Science 316, 1007–1010 (2007).
[Crossref]

K. G. Lagoudakis, T. Ostatnický, A. V. Kavokin, Y. G. Rubo, R. André, and B. Deveaud-Plédran, “Observation of half-quantum vortices in an exciton-polariton condensate,” Science 326, 974–976 (2009).
[Crossref]

Other (4)

A. V. Kavokin, J. J. Baumberg, G. Malpuech, and F. P. Laussy, Microcavities (Oxford University, 2007).

D. Sanvitto and V. Timofeev, Exciton Polaritons in Microcavities: New Frontiers (Springer, 2012).

Preliminary results from this work were reported in August 2013; see C. Gautham and D. Snoke, “Modulation of two-photon excitation by a polariton condensate,” in Fundamental Optical Processes and Semiconductors 2013, Kodiak Island, Alaska, 12–16 August2013.

S. Chaung, Physics of Photonic Devices, Wiley Series in Pure and Applied Optics (Wiley, 2009), p. 399.

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Figures (7)

Fig. 1.
Fig. 1. (a) Time-averaged spectrum while exciting with half the energy of the lower polariton with a laser focused at x = 0 μm . There is a spatial gradient to the polariton energy, because there is a wedge in the cavity thickness across the sample. (b) Time-resolved spectrum at the generation spot while exciting with half the energy of the lower polariton. There is a fast rise time of the emission comparable to our time resolution, which indicates there is direct excitation of the lower polariton.
Fig. 2.
Fig. 2. Power dependence of the polariton emission intensity at the creation spot. Solid line: fit to the square of the pump power, indicating two-photon absorption.
Fig. 3.
Fig. 3. Intensity versus time for different pump wavelengths of (a) 1565 nm, (b) 1555 nm, (c) 1540 nm, (d) 1530 nm, (e) 1525 nm, and (f) 1515 nm. A fast initial peak appears when the median pump photon energy is at half the lower polariton energy ( λ = 1555 nm ). A later population dominates for higher pump energies.
Fig. 4.
Fig. 4. Polariton emission intensity versus pump photon energy from the time-resolved data. (a) Initial peak intensity, showing maximum absorption at the lower polariton energy with a slight peak at the UP energy, (b) total integrated intensity, showing an increase in intensity as the energy is increased. The circles and diamonds represent two data sets viewed on two different days.
Fig. 5.
Fig. 5. Time versus intensity at (a) 8.3 K and (b) 2.5 K. As the temperature is increased, the intensity of the latter peak decreases. (c) Summary of the late-time intensity data as a function of T .
Fig. 6.
Fig. 6. Intensity of the light from two-photon absorption versus the central in-plane momentum of the incoming light beam. The dots represent our data, and the solid line is a convolution fit A ( f * g ) + B , where f = k 4 and g = e k 2 σ 2 with σ 2 = 0.07 , which takes into account the finite width of our laser spot. A = 0.95 and B = 0.14 are scaling parameters that take into account background light. This indicates that the absorption is k 4 .
Fig. 7.
Fig. 7. Schematic of the experimental setup.

Equations (7)

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H L K | u k = ( P + Q S R 0 S / 2 2 R S * P Q 0 R 2 Q 3 / 2 S R 0 P Q S 3 / 2 S 2 Q 0 R * S * P + Q 2 R S * / 2 S * / 2 2 Q * 3 / 2 S 2 R P + δ 0 2 R * 3 / 2 S * 2 Q * S / 2 0 P + δ ) ( | 3 2 , 3 2 | 3 2 , 1 2 | 3 2 , 1 2 | 3 2 , 3 2 | 1 2 , 1 2 | 1 2 , 1 2 ) J , m j ,
P = γ 1 2 m 0 ( k x 2 + k y 2 + k z 2 ) , Q = γ 2 2 m 0 ( k x 2 + k y 2 2 k z 2 ) , R = 2 m 0 ( 3 γ 2 ( k x 2 k y 2 ) + i 2 3 γ 3 k x k y ) , S = γ 3 2 m 0 3 ( k x i k y ) k z .
| 3 2 , 3 2 + S Δ | 3 2 , 1 2 S Δ | 3 2 , 3 2 + | 3 2 , 1 2 , | 3 2 , 3 2 + S Δ | 3 2 , 1 2 S Δ | 3 2 , 3 2 + | 3 2 , 1 2 .
| 3 2 , 1 2 = 1 6 | ( cos θ cos φ i sin φ ) x ^ + ( cos θ sin φ + i cos φ ) y ^ sin θ z ^ | + 2 3 | sin θ cos φ x ^ + sin θ sin φ y ^ + cos θ z ^ | ,
| 3 2 , 1 2 = 1 6 | ( cos θ cos φ + i sin φ ) x ^ + ( cos θ sin φ i cos φ ) y ^ sin θ z ^ | + 2 3 | sin θ cos φ x ^ + sin θ sin φ y ^ + cos θ z ^ | ,
i S | p | 3 2 , 1 2 = 2 3 ( sin θ cos φ x ^ + sin θ sin φ y ^ + cos θ z ^ ) P ,
i S | p | 3 2 , 1 2 = 2 3 ( sin θ cos φ x ^ + sin θ sin φ y ^ + cos θ z ^ ) P ,

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