Abstract

An alternative scheme is proposed for the generation of an N-qubit Greenberger-Horne-Zeilinger (GHZ) state with distant nitrogen-vacancy (N-V) centers confined in spatially separated photonic crystal (PC) nanocavities via input-output process of photon. The GHZ state is produced by the phase shift brought by the input-output photon. The certain polarized photon transmitted from a PC nanocavity side-coupled a waveguide can obtain different phase shifts due to the different spin states in diamond N-V centers and the optical spin selection rule. Our calculations show that the proposed scheme can work well with a large cavity damping rate which ensures the efficient output of photon.

© 2012 OSA

1. Introduction

As a striking feature of quantum mechanics, entanglement is well-known today. Over past decades, the generation and engineering of quantum entanglement has attracted much attention because of its extensive applications for fundamental tests of local hidden variable theories [1,2], for high-precision measurements [3], and, in particular, for implementation of quantum communication and computation [4]. Compared with two-partite entangled states, many inequivalent classes of multipartite entangled states, such as W states [5], GHZ states [6] and cluster states [7], cannot be transformed into each other under local operations and classical communication (LOCC) protocols, and their potential applications in quantum information processes have been reported [810]. So far, a lots of works have been done for the generation of multiple-partite entangled states with different quantum systems [1123]. Among the multiple-partite entangled states, GHZ state is usually referred to as “maximally entangled in several senses, e.g., it violates Bell inequalities maximally. In addition, entanglement with spatially separated subsystems is very useful for distributed quantum computation [24]. Recently, many theoretical and experimental works have been proposed for the implementation of GHZ states [1623]. For example, based on the process of selectively reading qubits, three-qubit GHZ state was observed in an experiment by Roos et al. [16]. Xia et al. [21] provided a linear optical protocol to generate GHZ state with N distant photons based on multiphoton interference, ancillary entangled photon states, and conventional photon detectors. More recently, through photon emission and absorption processes, Lü et al. [17] proposed another scheme for the generation of three-qubit GHZ states with three distant atoms trapped individually in three cavities.

In recent years, on the one hand, studies of cavity quantum electrodynamics (CQED) for light-matter interactions inside nanoscale cavities provide an ideal platform for quantum optics. Tremendous progress has been made by coupling single emitters to different nanocavities (for a review, see Ref. [25]). Among them, photonic crystal (PC) nanocavity [26] is most promising due to its extremely high Q factor, ultrasmall mode volume, excellent scalability and ease for low-loss transport of nonclassical states using a tapered waveguide. On the other hand, nitrogen-vacancy (NV) centers in diamond nanocrystal have recently emerged as an excellent test bed for solid-state quantum physics experiments and quantum information processing because they possess long-lived spin triplets at room temperature [2735]. Combining high-Q PC nanocavities and NV centers represents a promising solid-state CQED system, and attracts much attention both theoretically and experimentally [3641]. Barth et al. [40] have addressed controlled coupling of a single-diamond nanocrystal to a planar PC double-heterostructure cavity. Recent experimental investigations by Wolters et al. [41] have developed and demonstrated a scheme to enhance the zero phonon line emission from a single N-V center in a nanodiamond via coupling to a PC cavity.

Based on these achievements, in the present work we proposed an alternative scheme to generate an N-qubit GHZ state with remote spin qubits through the input-output process of photon. In Ref. [23], a single-side cavity absorbed a vertically (V)-polarized photon and then emitted a horizontally (H)-polarized photon, by this way, the atoms in the cavities were entangled in GHZ state. Our proposed scheme, however, works on the weak excited limit. The polarized state of the photon is maintained unchanged after passing through the cavities and only phase shift is brought to the corresponding spin state by the input photon. The major advantages of applying our considered composite PC nanocavity-N-V system over other approaches are as follows:

  • Firstly, GHZ state with separate N-V centers is encoded in the electronic spin ground states. The optical control of spin states, long decoherence and the robustness of the spin coherence have enabled the demonstration of basic building blocks for quantum computing even at room temperature [42, 43].
  • Secondly, our scheme can work well with the large cavity damping rate, i.e., the low-quality cavity or the so-called bad cavity.
  • Thirdly, the composite PC nanocavity-N-V scheme is deterministic and GHZ state can be realized with only one step.

2. Physical principles and analytical estimates

The optical coupled system under consideration in this paper is illustrated schematically in Fig. 1. This device is made up of a diamond N-V center, a point-defect PC nanocavity and a line-defect PC waveguide. The negatively charged N-V center is confined in a PC nanocavity with two modes, i.e., left(L)-polarization (σ) and right(R)-polarization (σ+). As shown in Refs. [44, 45], the PC nanocavity, which supports both σ+- and σ-polarized modes, can be fabricated experimentally. The N-V center considered is composed of a substitutional nitrogen atom and a adjacent vacancy in diamond lattice. According to the C3v symmetry group, an optically transition is allowed between orbital 3A2 ground state and an orbital 3E excited state [46]. The ground states 3A2 consist of spin triplets (S = 1), which are split by 2.88 GHz into the lower level |3A2, ms = 0〉 and the upper levels |3A2, ms = ±1〉 [47]. There is a likewise split in the excited states 3E [48]. In this paper, by combining with the two cavity modes, the N-V center are modelled as a Λ-type three-level structure shown in the bubble of Fig. 1, (i.e., |−〉 = |3A2, ms = −1〉, |+〉 = |3A2, ms = +1〉 and |1〉 = |3E, ms = 0〉). The |−〉 ⇔ |1〉 and |+〉 ⇔ |1〉 transitions (with the identical transition frequency ω0) in the N-V center are resonantly coupled to the right (R) σ+ and left (L) σ polarized photons with the coupling strengths gL and gR, respectively. For simplicity, the energy of the states |−〉 and |+〉 have been set as zero. Under the rotating-wave approximation (RWA), the total Hamiltonian of the hybrid system can be given by (setting h̄ = 1) [4952]

H^=k=R,L{ωcCkCk+ωak(ω)ak(ω)dω+κ2π[iak(ω)Ckiak(ω)Ck]dω}+(ω0iγ2)|11|+(igR|1|CR+igL|1+|CL+H.C.),
where H.C. means Hermitian conjugation. Ck(Ck) is the annihilation (creation) operator of the nanocavity with the frequency ωc. γ and κ are the decay rates of the excited state |1〉 and the cavity damping, respectively. ak(ω) and ak(ω) are the annihilation and creation operators for the two modes of frequency ω in the waveguide channel, with the commutation relation [ak(ω),ak(ω)]=δ(ωω).

 

Fig. 1 Schematic of the coupled PC nanocavity and waveguide system. A two-mode PC nanocavity containing an N-V center is side-coupled to a waveguide with the coupling strength κ, i.e., the cavity damping. a+in, ain and a+out, aout denote the input and output optical field operators in the waveguide. σ+ (σ) shows the corresponding photon with right(left)-polarized state. In the bubble, the detailed energy configuration is described for N-V center in diamond nanocrystal. The transitions |−〉 ⇔ |1〉 and |+〉 ⇔ |1〉 are driven by the R(σ+)- and L(σ)-polarized photon, respectively.

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Before proceeding further, it is instructive to briefly illuminate the physical picture of the above Hamiltonian operator (1). The first term is the energy of the two PC nanocavity modes σ+ and σ with frequency ωc. The second term stands for the energy of the optical modes with frequency ω in the waveguide channel. The third term describes the coupling of the nanocavity modes to the waveguide continuum. The nanocavity-waveguide coupling strength can be taken as a constant: κ(ω)=κ2π within the first Markov approximation [5357]. The fourth term is the unperturbed parts of the three-level Λ-type N-V center, which represent the energy of the excited state |1〉. For simplicity, the energy of the ground states |+〉 and |−〉 are set as zero. In the fifth term, the transition |−〉 ⇔ |1〉 of the N-V center is coupled to the nanocavity mode CR with a coupling strength gR. At the same time, the transition |+〉 ⇔ |1〉 of the N-V center is coupled to the nanocavity mode CL with a coupling strength gL.

The coupled system, described by the Hamiltonian (1), has an interesting invariant Hilbert subspace, with the bases |−, 1R〉|vac〉, |+, 1L〉|vac〉, |1, 0〉|vac〉, |−, 0〉|ωR〉 and |+, 0〉|ωL〉, where in |m,n〉 (m = −,+,1) denotes the state of the Λ-type three-level N-V center and n denotes the number of photons in the cavity, |ωk〉 (k = R,L) denotes the one-photon Fock state of the waveguide channel mode of frequency ω in the k-polarized modes, and |vac〉 denotes the vacuum state of the waveguide mode. If the initial state of the system is in the state |±, 0〉|ωk〉, the evolution the the whole system can be generally described by the wave function

|ψ(t)=k=R,L[d1(t)|1,0|vac+dkc(t)|,1k|vac+dka(t)ak(ω)|,0|vacdω].

By making use of the Hamiltonian (1) and the well-known Schrödinger equation ih¯t|ψ(t)=H^|ψ(t), we can obtain the time evolution of the amplitudes for the PC nanocavity modes, PC waveguide modes and N-V center in diamond lattice as follows

id˙kc(t)=ωcdkc(t)id1(t)gkiκ2πdka(t)dω,
id˙ka(t)=ωdka(t)+iκ2πdkc(t),
id˙1(t)=(ω0iγ2)d1(t)+i[dRc(t)gR+dLc(t)gL].
Integrating Eq. (4) formally yields
dka(t)=eiωtdka(t0)+κ2πt0teiω(tt)dkc(t)dtfort>t0
where dka(t0) denotes the value of dka(t) at t = t0.

Now, by substituting dka(t) from Eq. (6) into Eq. (3) as well as taking the decay rate κ into account (which can be obtained by following the established procedures of the Weisskopf-Wigner approximation [5355]), we can obtain

d˙kc(t)=iωcdkc(t)κ2dkc(t)d1(t)gkκakin,
where
akin=12πeiωtdka(t0)dω
is the input field operator in the waveguide channel.

Finally, we perform the Fourier transformations F(ω)=12π+F(t)eiωtdt on the amplitudes dkc and d1 in the linear Eq. (5) and Eq. (7), respectively. Combing with the standard input-output relation akout=akin+κdkc [54, 55], we carry out some algebraic calculations and can get the amplitude of the output pulse akout with the resonant condition ω = ω0 = ωc as

akout=(4gk24gk¯2κγ)akin+8gkgk¯ak¯in4gk2+4gk¯2+κγ,
where {k, k̄} ∈ {R, L} and kk̄. If the N-V center is in the initial state |−〉(|+ 〉) and the input pulse is a L(R)-polarized photon, the cavity is in resonance with the input photon and uncoupled to the N-V center. Therefor we can obtain the transmission coefficient from Eq. (9) as
T(ω)=akoutakin=1,
when gk = 0 and g = 0.

However, if the initial state of N-V center is |−〉(|+ 〉), the input photon with R(L)-polarized will resonantly drive the transition |−〉 ⇔ |1〉 (|+〉 ⇔ |1〉). When 4gk2κγ, we can get the transmission coefficient

T(ω)=1.
The transmission coefficient |T(ω)| = 1 reveals the fact that the input photon leaks out of the nanocavity without being absorbed by the cavity mode. The above cases can be summarized as follows
{|R|+|R|+|R||R||L|+|L|+|L||L|,
where |R〉(|L〉) denotes the input photon in R(L)-polarized state.

3. Generation of GHZ entangled state

In this section, we begin to describe how to realize N-qubit GHZ state with distant N-V centers via the input-output process. First of all, we address the realization of three-qubit GHZ state in this hybrid PC nanocavity-N-V system. Then such an approach is extend to implement N-qubit GHZ state on our scheme. The concrete process is shown in Fig. 2. Three N-V centers are located at three PC nanocavity individually and the nanocavities are identically coupled to the waveguide. All N-V centers are initialized to be in the superposition state 12(|+|+), and we input a single-photon pulse in an equal superposition of horizontal (H) and vertical (V) polarizations, i.e., 12(|H+|V). The |H〉 component is reflected by the polarization beam splitter (PBS) and then goes through the half-wave plate (HWP), which interchanges the polarized photons (|H〉 ⇔ |V〉). On the other hand, the |V〉 component passes through the PBS and changes to R-polarized state after going through the first quarter-wave plate (QWP), then enters the first nanocavity. In the first nanocavity, the |R〉-polarized photon interacts with the N-V center and leads to the transition |R〉 (|−〉 + |+〉) → |R〉 (|−〉 − |+〉). Then the same component |R〉 is transmitted and goes into the second nanocavity. The similar case will occur in other nanocavities. The second QWP changes R-polarized photon into V-polarized state. At last, these two V-polarized components from two different paths are mixed by a beam splitter (BS) at the output and which-path information is also erased. We set |0+=12(|+|+) and |0=12(||+). Summing up the above evolution process is as follows

12(|H+|V)|0+0+0+12(|H+|R)|0+0+0+12(|H|0+0+0++|R|000)12(|H|0+0+0++|V|000)12|V(|0+0+0++|000).
As a result, the three-qubit GHZ state is formed. In our scheme, there is no direct interaction between the N-V centers, and the GHZ state of diamond N-V centers is realized by mediation of quantum information by a photon which is just like a bus. Thus, the proposed scheme is readily extended to implement N-qubit GHZ state with distant N-V centers.

 

Fig. 2 Schematic of the setup for the generation of three-qubit GHZ state of three N-V centers which are confined individually in three PC nanocavities. All the nanocavities are coupled identically to a common waveguide. Polarization beam splitters (PBS) transmit V–polarized photons and transmit H–polarized photons; Half-wave plates (HWP) interchange the polarization of photons HV; Quarter-wave plates (QWP) achieve the porlarization changes of the single-photon pulse as |V〉 ⇔ |R〉; Beam splitters (BS) mix the two polarized components.

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4. Analysis and discussion

In this paper, the transmission amplitude and phase shift of the output photon play important roles during the process of generating a deterministic GHZ state. To consider the effect of light transmission on our scheme, we have plotted the amplitude [i.e., the absolute value of complex transmission coefficient |T(ω)|] and phase shift [i.e., the phase of complex transmission coefficient ϕ = arg(T(ω))] of the transmission coefficient T(ω) in Fig. 3. With ω0 = ωc and κ = 1000γ, Fig. 3(a) shows the amplitude of the transmission coefficient |T(ω)| as a function of (ωcω)/γ for gk = 0 and gk = 500γ. In the case of no interaction between the nanocavity mode and N-V center (i.e., gk = 0 and g = 0), the input photon leaks out the nanocavity without absorbtion and experiences a perfect transmission in the whole frequency regime. In contrast, due to the strong resonant coupling between the nanocavity mode and N-V center, the transmission coefficient is nearly unity under the condition of gk225κγ. In addition, there is an interesting phenomena that the transmission coefficient has two valleys. The two valleys are caused by the large vacuum splitting which leads to the shifting of the energy levels of the PC nanocavity [49]. And there is a large detuning between the input photon and the dressed nanocavity modes. As shown in Fig. 3(b), for the no interaction case, i.e., gk = 0, the phase shift ϕ of the transmitted photon is ±π at the cavity resonance ω = ωc. Once the frequency of the input photon ω deviates the resonant point, the phase shift will reduce to zero rapidly. As to the case of gk225κγ, the phase shift has a similar splitting, as shown in Fig. 3(b). However, the phase shift is zero at ω = ωc and varies quickly from zero to ±π when we increase or decrease the frequency of the input pulse from the resonant point.

 

Fig. 3 (a) The absolute value of the transmission coefficient |T(ω)| as a function of frequency detuning (ωcω)/γ between the input pulse and PC nanocavity mode with gk = 500γ (red solid curve) and gk = 0 (blue dashed curve); (b) The phase shift ϕ/π as a function of frequency detuning (ωcω)/γ with gk = 500γ (red solid curve) and gk = 0 (blue dashed curve). The other system parameters are chosen as κ = 1000γ and ω0 = ωc.

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We have also examined the effect of the coupling strength gk on the transmission amplitude |T(ω)| in Fig. 4(a). The transmission amplitude |T(ω)| increases as the coupling strength gk increases. The transmission amplitude is nearly unity and the requirement on gk is loosen. The present scheme only needs 4gk2κγ but does not need gkκ, γ. In fact, we have chosen gk = 500γ < κ = 1000γ in the above analysis, therefore our proposed scheme can work well even if the PC nanocavity is bad. As shown in Fig. 4(b), the influence of the cavity damping κ on the amplitude of the photon transmission is negligible. When the frequency of the input photon satisfies the resonant condition ω = ωc = ω0, the smaller the value of the cavity damping κ is, the higher the transmission amplitude |T(ω)| is.

 

Fig. 4 (a) The absolute value of the transmission coefficient |T(ω)| versus the coupling strength gk/γ with κ = 1000γ; (b) |T(ω)| versus the cavity damping κ/γ with gk = 500γ. The other system parameters are chosen as ω = ω0 = ωc.

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In the present work, three identical N-V centers are individually confined in three identical PC nanocavities and the input pulse passes through the nanocavities one after the other. The ideal GHZ state will be realized only if the shape of the pulse is maintained unchanged. We set a Gaussian shape for the input pulse with fin(t) ∝ exp[−(tT/2)2/(T/5)2], where t varies from 0 to T and T is the period of the pulse [56]. With T = 10/γ, in Fig. 5 we plot the input and output pulse profiles |fin(t)| and |fout (t)| as a function of time t/γ for the given system parameters in Fig. 2. All the pulse shapes of the output optical field are basically indistinguishable from the input pulse. Different from other works [50,56], we have set 4gk2γκ and κγ, which ensure that the shapes of the output and input pulses closely match.

 

Fig. 5 The shape functions for the input pulse (blue solid curve) and the transmitted pulses with the N-V centers in spin states |−〉 (red dashed curve) and in spin states |+〉 (red dotted curve). The transmitted pulses and the input pulse closed match and are hardly distinguishable in the figure.

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It should be pointed out that the implementation of GHZ state dependents on the effective transmission of the input photon from the PC nanocavity. The above analysis in Fig. 3 and Fig. 4 shows that the frequency detuning, the coupling strength and the cavity damping rate have little effect on the transmission amplitude |T(ω)|. However, the change of frequency detuning will effect strictly the phase shift ϕ of the transmitted photon. GHZ state can be generated successfully only if the phase shift is maintained as zero or π for different ground states. Therefore, the frequency resonant condition ωc = ω is required for the realization of GHZ state. On the other hand, the shape mismatching of input and output pulses will result in the reduction of fidelity. We have taken the Gaussian pulse as example and plotted the shapes of the output pulse for the cases of N-V ground states |−〉 and |+〉 in Fig. 5, respectively. In our proposed scheme, the two conditions 4gk2γκ and κγ ensure very good overlap between the shapes of the input and output pulses, i.e.,based on our scheme, GHZ state can be generated with high fidelity.

Before ending this section, we would like to consider the experimental feasibility of our scheme. Firstly, the identical energy level configuration is required by the generation of the GHZ state with high fidelity in our scheme. Each PC nanocavity contains only one N-V center, thus, we can adjust the energy interval by an external laser [57] or by applying different magnetic fields to induce fine structure splitting of the N-V centers [58]. Note that the N-V center transition frequency increases with increasing temperature [33]. Secondly, in our scheme, we choose γ = 2π × 10 MHz, κ = 2π × 10 GHz and gk = 2π × 5 GHz, which are available in current experiments [35, 59, 60]. Thirdly, the present scheme is essentially based on the efficient output of photons which implies the large cavity decay rate, i.e., the bad cavity [49, 61]. In the above analysis, our scheme can work well with the large cavity damping. Fourthly, in our scheme, we have ignored the effect of the intrinsic cavity loss (κi) into non-waveguide channels on the generation of GHZ state. According to Refs. [6163], the condition of κκi can be satisfied by the parameter optimization and the intrinsic cavity loss κi can be discarded in the present scheme. We also have reconsidered the intrinsic decay rates κi of the PC nanocavity. However, under the condition that an external loss rate κ is about ten times higher than an intrinsic loss rate κi, we find that the shape, number and location of peaks in the transmission spectra have no change, except for some quantitative differences in peak heights (not shown here). Another reason for ignoring intrinsic cavity loss into non-waveguide channels is due to its simplicity in mathematical treatment, which permits us to obtain simple analytical expressions, and its transparency in the physical explanation of the results obtained. Finally, it should be point out that in the present study we only focus on scattering light in the forward direction. As a matter of fact, the PC nanocavities side-coupled to the waveguide typically exhibit standing waves that can scatter both in the forward and backward directions. This model is of course oversimplified. A realistic quantitative description would need to include the scatter light in the backward direction. Nevertheless, it has already been possible to minimize light reflections (i.e., scattering light in the backward direction) by using inverse tapers at the end of the strip waveguides nowadays. Details on the fabrication process are given in Refs. [6468]. Therefore, we believe that the present model can provide a quantitative illustration for the generation of the GHZ states.

5. Conclusion

To summarize, we have put forward a new scheme for the generation of the GHZ states with distant N-V centers in spatially separate PC nanocavities via the input-output process of photon. The scheme proposed here is deterministic and is promising for generating an N-qubit GHZ state with the current techniques.

Acknowledgment

We would like to thank Professor X. X. Yang for her encouragement and helpful discussion. This research was supported in part by the National Natural Science Foundation of China under Grants No. 11004069, No. 10975054 and No. 91021011, by the Doctoral Foundation of the Ministry of Education of China under Grant No. 20100142120081, by the National Basic Research Program of China under Contract No. 2012CB922103.

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34. M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009). [CrossRef]   [PubMed]  

35. E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London) 466, 730–734 (2010). [CrossRef]  

36. T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, “Deterministic nanoassembly of a coupled quantum emitter-photonic crystal cavity system,” Appl. Phys. Lett. 98, 193103 (2011). [CrossRef]  

37. D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010). [CrossRef]   [PubMed]  

38. S. Tomljenovic-Hanic, M. J. Steel, and C. Martijn de Sterke, “Diamond based photonic crystal microcavities,” Opt. Express 14, 3556–3562 (2006). [CrossRef]   [PubMed]  

39. M. W. McCutcheon and M. Lončar, “Design of a silicon nitride photonic crystal nanocavity with a quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19136–19145 (2008). [CrossRef]  

40. M. Barth, N. Nüsse, B. Löchel, and O. Benson, “Controlled coupling of a single-diamond nanocrystal to a photonic crystal cavity,” Opt. Lett. 34, 1108–1110 (2009). [CrossRef]   [PubMed]  

41. J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010). [CrossRef]  

42. F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004). [CrossRef]   [PubMed]  

43. F. Z. Fan, X. Rong, N. Y. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. Schoenfeld, W. Harneit, M. Feng, and J. F. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010). [CrossRef]  

44. S. H. Kim and Y. H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE J. Quantum Electron. 39, 1081–1085 (2003). [CrossRef]  

45. Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett. 106, 160501 (2011). [CrossRef]   [PubMed]  

46. A. Lenef and S. C. Rand, “Electronic structure of the N-V center in diamond: theory,” Phys. Rev. B 53, 13441–13455 (1995). [CrossRef]  

47. E. van Oort, N. B. Manson, and M. Glasbeek, “Optically detected spin coherence of the diamond NV centre in its triplet ground state,” J. Phys. C 21, 4385–4391 (1988). [CrossRef]  

48. C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, S. Rubanov, D. N. Jamieson, and S. Prawer, “Coherent population trapping in diamond N-V centers at zero magnetic field,” Opt. Express 14, 7986–7994 (2006). [CrossRef]   [PubMed]  

49. J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low- Q cavities,” Phys. Rev. A 79, 032303 (2009). [CrossRef]  

50. L. M. Duan, B. Wang, and H. J. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005). [CrossRef]  

51. Y. Wu and X. Yang, “Exact eigenstates for a class of models describing two-mode multiphoton processes,” Opt. Lett. 28, 1793–1795 (2003). [CrossRef]   [PubMed]  

52. J. H. Li and R. Yu, “Single-plasmon scattering grating using nanowire surface plasmon coupled to nanodiamond nitrogen-vacancy center,” Opt. Express 19, 20991–21002 (2011). [CrossRef]   [PubMed]  

53. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, 1997).

54. D. Walls and G. Milburm, Quantum Optics (Springer, 1994).

55. C. W. Gardiner and P. Zoller, Quantum Noise, 3rd ed. (Springer, 2004).

56. L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004). [CrossRef]   [PubMed]  

57. T. Pellizzari, “Quantum networking with optical fibres,” Phys. Rev. Lett. 79, 5242–5245 (1997). [CrossRef]  

58. P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009). [CrossRef]  

59. Q. Chen, W. L. Yang, M. Feng, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011). [CrossRef]  

60. P. E. Barclay, K. M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers,” Opt. Express 17, 9588–9601 (2009). [CrossRef]   [PubMed]  

61. B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008). [CrossRef]   [PubMed]  

62. C. Manolatou, M. J. Khan, S. Fan, Pierre R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1330 (1999). [CrossRef]  

63. E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96,153601 (2006). [CrossRef]   [PubMed]  

64. J. Pan, S. Sandhu, Y. Huo, M. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Experimental demonstration of an all-optical analogue to the superradiance effect in an on-chip photonic crystal resonator system,” Phys. Rev. B 81, 041101 (2010). [CrossRef]  

65. J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett. 97, 101102 (2010). [CrossRef]  

66. Y. Huo, S. Sandhu, J. Pan, N. Stuhrmann, M. L. Povinelli, J. M. Kahn, J. S. Harris, M. M. Fejer, and S. Fan, “Experimental demonstration of two methods for controlling the group delay in a system with photonic-crystal resonators coupled to a waveguide,” Opt. Lett. 36, 1482–1484 (2011). [CrossRef]   [PubMed]  

67. D. Sridharan, R. Bose, H. Kim, G. S. Solomon, and E. Waks, “Attojoule all-optical switching with a single quantum dot,” arXiv: 1107.3751.

68. R. Bose, D. Sridharan, G. Solomon, and E. Waks, “Observation of strong coupling through transmission modification of a cavity-coupled photonic crystal waveguide,” Opt. Express 19, 5398–5409 (2011). [CrossRef]   [PubMed]  

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    [CrossRef]
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    [CrossRef] [PubMed]

2011 (7)

A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, “Controlled coupling of a single nitrogen-vacancy center to a silver nanowire,” Phys. Rev. Lett. 106, 096801 (2011).
[CrossRef] [PubMed]

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, “Deterministic nanoassembly of a coupled quantum emitter-photonic crystal cavity system,” Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett. 106, 160501 (2011).
[CrossRef] [PubMed]

Q. Chen, W. L. Yang, M. Feng, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[CrossRef]

R. Bose, D. Sridharan, G. Solomon, and E. Waks, “Observation of strong coupling through transmission modification of a cavity-coupled photonic crystal waveguide,” Opt. Express 19, 5398–5409 (2011).
[CrossRef] [PubMed]

Y. Huo, S. Sandhu, J. Pan, N. Stuhrmann, M. L. Povinelli, J. M. Kahn, J. S. Harris, M. M. Fejer, and S. Fan, “Experimental demonstration of two methods for controlling the group delay in a system with photonic-crystal resonators coupled to a waveguide,” Opt. Lett. 36, 1482–1484 (2011).
[CrossRef] [PubMed]

J. H. Li and R. Yu, “Single-plasmon scattering grating using nanowire surface plasmon coupled to nanodiamond nitrogen-vacancy center,” Opt. Express 19, 20991–21002 (2011).
[CrossRef] [PubMed]

2010 (8)

J. Pan, S. Sandhu, Y. Huo, M. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Experimental demonstration of an all-optical analogue to the superradiance effect in an on-chip photonic crystal resonator system,” Phys. Rev. B 81, 041101 (2010).
[CrossRef]

J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett. 97, 101102 (2010).
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F. Z. Fan, X. Rong, N. Y. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. Schoenfeld, W. Harneit, M. Feng, and J. F. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
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D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
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E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London) 466, 730–734 (2010).
[CrossRef]

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
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K. Koshino, S. Ishizaka, and Y. Nakamura, “Deterministic photon-photon SWAP gate using a Λ system,” Phys. Rev. A 82, 010301(R) (2010).
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X. Wang, A. Bayat, S. Bose, and S. G. Schirmer, “Global control methods for Greenberger-Horne-Zeilinger-state generation on a one-dimensional Ising chain,” Phys. Rev. A 82, 012330 (2010).
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2009 (8)

S. B. Zheng, “Generation of Greenberger-Horne-Zeilinger states for multiple atoms trapped in separated cavities,” Eur. Phys. J. D 54, 719–722 (2009).
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X. Y. Lü, L. G. Si, X. Y. Hao, and X. X. Yang, “Achieving multipartite entanglement of distant atoms through selective photon emission and absorption processes,” Phys. Rev. A 79, 052330 (2009).
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M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009).
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J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low- Q cavities,” Phys. Rev. A 79, 032303 (2009).
[CrossRef]

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[CrossRef]

M. Barth, N. Nüsse, B. Löchel, and O. Benson, “Controlled coupling of a single-diamond nanocrystal to a photonic crystal cavity,” Opt. Lett. 34, 1108–1110 (2009).
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P. E. Barclay, K. M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers,” Opt. Express 17, 9588–9601 (2009).
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X. Y. Lü, P. J. Song, J. B. Liu, and X. X. Yang, “N-qubit W state of spatially separated single molecule magnets,” Opt. Express 17, 14298–14311 (2009).
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2008 (4)

M. W. McCutcheon and M. Lončar, “Design of a silicon nitride photonic crystal nanocavity with a quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19136–19145 (2008).
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B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
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R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, “Coherent dynamics of a single spin interacting with an adjustable spin bath,” Science 320, 352–355 (2008).
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Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger-Horne-Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127 (2008).
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2007 (1)

M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316, 1312–1316 (2007).
[CrossRef]

2006 (6)

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
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G. Khitrova, H. M. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum Rabi splitting in semiconductors,” Nat. Phys. 2, 81–90 (2006).
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T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006).
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E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96,153601 (2006).
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S. Tomljenovic-Hanic, M. J. Steel, and C. Martijn de Sterke, “Diamond based photonic crystal microcavities,” Opt. Express 14, 3556–3562 (2006).
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C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, S. Rubanov, D. N. Jamieson, and S. Prawer, “Coherent population trapping in diamond N-V centers at zero magnetic field,” Opt. Express 14, 7986–7994 (2006).
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2005 (3)

L. M. Duan, B. Wang, and H. J. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005).
[CrossRef]

R. J. Epstein, F. M. Mendoza, Y. K. Kato, and D. D. Awschalom, “Anisotropic interactions of a single spin and dark-spin spectroscopy in diamond,” Nat. Phys. 1, 94–98 (2005).
[CrossRef]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
[CrossRef]

2004 (8)

S. Mancini and S. Bose, “Engineering an interaction and entanglement between distant atoms,” Phys. Rev. A 70, 022307 (2004).
[CrossRef]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[CrossRef] [PubMed]

C. F. Roos, M. Riebe, H. Haffner, W. Hansel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
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F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
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L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef] [PubMed]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
[CrossRef]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

Y. Wu and L. Deng, “Achieving multifrequency mode entanglement with ultraslow multiwave mixing,” Opt. Lett. 29, 1144–1146 (2004).
[CrossRef] [PubMed]

2003 (3)

Y. Wu and X. Yang, “Exact eigenstates for a class of models describing two-mode multiphoton processes,” Opt. Lett. 28, 1793–1795 (2003).
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S. H. Kim and Y. H. Lee, “Symmetry relations of two-dimensional photonic crystal cavity modes,” IEEE J. Quantum Electron. 39, 1081–1085 (2003).
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X. B. Zou, K. Pahlke, and W. Mathis, “Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay,” Phys. Rev. A 68, 024302 (2003).
[CrossRef]

2001 (2)

S. B. Zheng, “One-step synthesis of multiatom Greenberger-Horne-Zeilinger states,” Phys. Rev. Lett. 87, 230404 (2001).
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H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef] [PubMed]

2000 (2)

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515–519 (2000).
[CrossRef]

1999 (2)

R. Cleve, D. Gottesman, and H. K. Lo, “How to share a quantum secret,” Phys. Rev. Lett. 83, 648–651 (1999).
[CrossRef]

C. Manolatou, M. J. Khan, S. Fan, Pierre R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1330 (1999).
[CrossRef]

1998 (1)

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
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1997 (2)

N. Gisin and S. Massar, “Optimal quantum cloning machines,” Phys. Rev. Lett. 79, 2153–2156 (1997).
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T. Pellizzari, “Quantum networking with optical fibres,” Phys. Rev. Lett. 79, 5242–5245 (1997).
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1996 (1)

J. J. Bollinger, W. M. Itano, D. Wineland, and D. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, 4649–4652(R) (1996).
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1995 (1)

A. Lenef and S. C. Rand, “Electronic structure of the N-V center in diamond: theory,” Phys. Rev. B 53, 13441–13455 (1995).
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1990 (2)

D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1143 (1990).
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N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states,” Phys. Rev. Lett. 65, 1838–1840 (1990).
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1988 (1)

E. van Oort, N. B. Manson, and M. Glasbeek, “Optically detected spin coherence of the diamond NV centre in its triplet ground state,” J. Phys. C 21, 4385–4391 (1988).
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1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935).
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Akahane, Y.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
[CrossRef]

An, J. H.

J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low- Q cavities,” Phys. Rev. A 79, 032303 (2009).
[CrossRef]

Andersen, U. L.

A. Huck, S. Kumar, A. Shakoor, and U. L. Andersen, “Controlled coupling of a single nitrogen-vacancy center to a silver nanowire,” Phys. Rev. Lett. 106, 096801 (2011).
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Aoki, T.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
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Asano, T.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
[CrossRef]

Awschalom, D. D.

R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, “Coherent dynamics of a single spin interacting with an adjustable spin bath,” Science 320, 352–355 (2008).
[CrossRef] [PubMed]

R. J. Epstein, F. M. Mendoza, Y. K. Kato, and D. D. Awschalom, “Anisotropic interactions of a single spin and dark-spin spectroscopy in diamond,” Nat. Phys. 1, 94–98 (2005).
[CrossRef]

Balasubramanian, G.

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[CrossRef]

Barclay, P. E.

Barth, M.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[CrossRef]

M. Barth, N. Nüsse, B. Löchel, and O. Benson, “Controlled coupling of a single-diamond nanocrystal to a photonic crystal cavity,” Opt. Lett. 34, 1108–1110 (2009).
[CrossRef] [PubMed]

Batalov, A.

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[CrossRef]

Bayat, A.

X. Wang, A. Bayat, S. Bose, and S. G. Schirmer, “Global control methods for Greenberger-Horne-Zeilinger-state generation on a one-dimensional Ising chain,” Phys. Rev. A 82, 012330 (2010).
[CrossRef]

Beausoleil, R. G.

Becher, C.

C. F. Roos, M. Riebe, H. Haffner, W. Hansel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef] [PubMed]

Beck, J.

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
[CrossRef]

Benhelm, J.

C. F. Roos, M. Riebe, H. Haffner, W. Hansel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef] [PubMed]

Benson, O.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[CrossRef]

M. Barth, N. Nüsse, B. Löchel, and O. Benson, “Controlled coupling of a single-diamond nanocrystal to a photonic crystal cavity,” Opt. Lett. 34, 1108–1110 (2009).
[CrossRef] [PubMed]

Blatt, R.

C. F. Roos, M. Riebe, H. Haffner, W. Hansel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef] [PubMed]

Bollinger, J. J.

J. J. Bollinger, W. M. Itano, D. Wineland, and D. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, 4649–4652(R) (1996).
[CrossRef]

Bose, R.

Bose, S.

X. Wang, A. Bayat, S. Bose, and S. G. Schirmer, “Global control methods for Greenberger-Horne-Zeilinger-state generation on a one-dimensional Ising chain,” Phys. Rev. A 82, 012330 (2010).
[CrossRef]

S. Mancini and S. Bose, “Engineering an interaction and entanglement between distant atoms,” Phys. Rev. A 70, 022307 (2004).
[CrossRef]

Bourennane, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef] [PubMed]

A. Karlsson and M. Bourennane, “Quantum teleportation using three-particle entanglement,” Phys. Rev. A 58, 4394–4400 (1998).
[CrossRef]

Bouwmeester, D.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, “Deterministic nanoassembly of a coupled quantum emitter-photonic crystal cavity system,” Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515–519 (2000).
[CrossRef]

Briegel, H. J.

H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001).
[CrossRef] [PubMed]

Chen, Q.

Q. Chen, W. L. Yang, M. Feng, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[CrossRef]

Childress, L.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London) 466, 730–734 (2010).
[CrossRef]

M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316, 1312–1316 (2007).
[CrossRef]

Chong, B.

F. Z. Fan, X. Rong, N. Y. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. Schoenfeld, W. Harneit, M. Feng, and J. F. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[CrossRef]

Chu, Y.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London) 466, 730–734 (2010).
[CrossRef]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

Cirac, J. I.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Cleve, R.

R. Cleve, D. Gottesman, and H. K. Lo, “How to share a quantum secret,” Phys. Rev. Lett. 83, 648–651 (1999).
[CrossRef]

Cook, A. K.

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[CrossRef] [PubMed]

Daniell, M.

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515–519 (2000).
[CrossRef]

Dayan, B.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef] [PubMed]

Deng, L.

Y. Wu and L. Deng, “Achieving multifrequency mode entanglement with ultraslow multiwave mixing,” Opt. Lett. 29, 1144–1146 (2004).
[CrossRef] [PubMed]

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69, 063803 (2004).
[CrossRef]

Dinyari, K. N.

M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009).
[CrossRef] [PubMed]

Dobrovitski, V. V.

R. Hanson, V. V. Dobrovitski, A. E. Feiguin, O. Gywat, and D. D. Awschalom, “Coherent dynamics of a single spin interacting with an adjustable spin bath,” Science 320, 352–355 (2008).
[CrossRef] [PubMed]

Domhan, M.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006).
[CrossRef]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
[CrossRef] [PubMed]

Döscher, H.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
[CrossRef]

Draganski, M.

Du, J. F.

Q. Chen, W. L. Yang, M. Feng, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
[CrossRef]

F. Z. Fan, X. Rong, N. Y. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. Schoenfeld, W. Harneit, M. Feng, and J. F. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[CrossRef]

Duan, L. M.

L. M. Duan, B. Wang, and H. J. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005).
[CrossRef]

L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef] [PubMed]

Dür, W.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Dutt, M. V. G.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London) 466, 730–734 (2010).
[CrossRef]

Eibl, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
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Ueda, M.

Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett. 106, 160501 (2011).
[CrossRef] [PubMed]

Vahala, K. I.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science 319, 1062–1065 (2008).
[CrossRef] [PubMed]

van der Sar, T.

T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, “Deterministic nanoassembly of a coupled quantum emitter-photonic crystal cavity system,” Appl. Phys. Lett. 98, 193103 (2011).
[CrossRef]

van Oort, E.

E. van Oort, N. B. Manson, and M. Glasbeek, “Optically detected spin coherence of the diamond NV centre in its triplet ground state,” J. Phys. C 21, 4385–4391 (1988).
[CrossRef]

Vidal, G.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

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C. Manolatou, M. J. Khan, S. Fan, Pierre R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35, 1322–1330 (1999).
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Vuckovic, J.

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
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E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96,153601 (2006).
[CrossRef] [PubMed]

Waks, E.

R. Bose, D. Sridharan, G. Solomon, and E. Waks, “Observation of strong coupling through transmission modification of a cavity-coupled photonic crystal waveguide,” Opt. Express 19, 5398–5409 (2011).
[CrossRef] [PubMed]

E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96,153601 (2006).
[CrossRef] [PubMed]

D. Sridharan, R. Bose, H. Kim, G. S. Solomon, and E. Waks, “Attojoule all-optical switching with a single quantum dot,” arXiv: 1107.3751.

Walls, D.

D. Walls and G. Milburm, Quantum Optics (Springer, 1994).

Wang, B.

L. M. Duan, B. Wang, and H. J. Kimble, “Robust quantum gates on neutral atoms with cavity-assisted photon scattering,” Phys. Rev. A 72, 032333 (2005).
[CrossRef]

Wang, H.

M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett. 9, 1447–1450 (2009).
[CrossRef] [PubMed]

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett. 6, 2075–2079 (2006).
[CrossRef] [PubMed]

Wang, X.

X. Wang, A. Bayat, S. Bose, and S. G. Schirmer, “Global control methods for Greenberger-Horne-Zeilinger-state generation on a one-dimensional Ising chain,” Phys. Rev. A 82, 012330 (2010).
[CrossRef]

Wang, Y.

F. Z. Fan, X. Rong, N. Y. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. Schoenfeld, W. Harneit, M. Feng, and J. F. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
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M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
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J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515–519 (2000).
[CrossRef]

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J. J. Bollinger, W. M. Itano, D. Wineland, and D. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, 4649–4652(R) (1996).
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Wittmann, C.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys. 2, 408–413 (2006).
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J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
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P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
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F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett. 93, 130501 (2004).
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F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillations in a single electron spin,” Phys. Rev. Lett. 92, 076401 (2004).
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F. Z. Fan, X. Rong, N. Y. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. Schoenfeld, W. Harneit, M. Feng, and J. F. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
[CrossRef]

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Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger-Horne-Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127 (2008).
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F. Z. Fan, X. Rong, N. Y. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. Schoenfeld, W. Harneit, M. Feng, and J. F. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105, 040504 (2010).
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Q. Chen, W. L. Yang, M. Feng, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
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Yang, X. X.

X. Y. Lü, L. G. Si, X. Y. Hao, and X. X. Yang, “Achieving multipartite entanglement of distant atoms through selective photon emission and absorption processes,” Phys. Rev. A 79, 052330 (2009).
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X. Y. Lü, P. J. Song, J. B. Liu, and X. X. Yang, “N-qubit W state of spatially separated single molecule magnets,” Opt. Express 17, 14298–14311 (2009).
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Yu, R.

Zeilinger, A.

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515–519 (2000).
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Y. Eto, A. Noguchi, P. Zhang, M. Ueda, and M. Kozuma, “Projective measurement of a single nuclear spin qubit by using two-mode cavity QED,” Phys. Rev. Lett. 106, 160501 (2011).
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S. B. Zheng, “Generation of Greenberger-Horne-Zeilinger states for multiple atoms trapped in separated cavities,” Eur. Phys. J. D 54, 719–722 (2009).
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M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science 316, 1312–1316 (2007).
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C. W. Gardiner and P. Zoller, Quantum Noise, 3rd ed. (Springer, 2004).

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X. B. Zou, K. Pahlke, and W. Mathis, “Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay,” Phys. Rev. A 68, 024302 (2003).
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Am. J. Phys. (1)

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Appl. Phys. Lett. (4)

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett. 97, 141108 (2010).
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T. van der Sar, J. Hagemeier, W. Pfaff, E. C. Heeres, S. M. Thon, H. Kim, P. M. Petroff, T. H. Oosterkamp, D. Bouwmeester, and R. Hanson, “Deterministic nanoassembly of a coupled quantum emitter-photonic crystal cavity system,” Appl. Phys. Lett. 98, 193103 (2011).
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J. Pan, Y. Huo, S. Sandhu, N. Stuhrmann, M. L. Povinelli, J. S. Harris, M. M. Fejer, and S. Fan, “Tuning the coherent interaction in an on-chip photonic-crystal waveguide-resonator system,” Appl. Phys. Lett. 97, 101102 (2010).
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Eur. Phys. J. D (1)

S. B. Zheng, “Generation of Greenberger-Horne-Zeilinger states for multiple atoms trapped in separated cavities,” Eur. Phys. J. D 54, 719–722 (2009).
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Nano Lett. (3)

D. Englund, B. Shields, K. Rivoire, F. Hatami, J. Vučković, H. Park, and M. D. Lukin, “Deterministic coupling of a single nitrogen vacancy center to a photonic crystal cavity,” Nano Lett. 10, 3922–3926 (2010).
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Nature (London) (2)

J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement,” Nature (London) 403, 515–519 (2000).
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E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London) 466, 730–734 (2010).
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New J. Phys. (1)

P. Neumann, R. Kolesov, V. Jacques, J. Beck, J. Tisler, A. Batalov, L. Rogers, N. B. Manson, G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Excited-state spectroscopy of single NV defects in diamond using optically detected magnetic resonance,” New J. Phys. 11, 013017 (2009).
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Phys. Rev. A (12)

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X. B. Zou, K. Pahlke, and W. Mathis, “Conditional generation of the Greenberger-Horne-Zeilinger state of four distant atoms via cavity decay,” Phys. Rev. A 68, 024302 (2003).
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X. Y. Lü, L. G. Si, X. Y. Hao, and X. X. Yang, “Achieving multipartite entanglement of distant atoms through selective photon emission and absorption processes,” Phys. Rev. A 79, 052330 (2009).
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Q. Chen, W. L. Yang, M. Feng, and J. F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A 83, 054305 (2011).
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J. H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low- Q cavities,” Phys. Rev. A 79, 032303 (2009).
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E. Waks and J. Vuckovic, “Dipole induced transparency in drop-filter cavity-waveguide systems,” Phys. Rev. Lett. 96,153601 (2006).
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Other (5)

D. Sridharan, R. Bose, H. Kim, G. S. Solomon, and E. Waks, “Attojoule all-optical switching with a single quantum dot,” arXiv: 1107.3751.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, 1997).

D. Walls and G. Milburm, Quantum Optics (Springer, 1994).

C. W. Gardiner and P. Zoller, Quantum Noise, 3rd ed. (Springer, 2004).

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

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Figures (5)

Fig. 1
Fig. 1

Schematic of the coupled PC nanocavity and waveguide system. A two-mode PC nanocavity containing an N-V center is side-coupled to a waveguide with the coupling strength κ, i.e., the cavity damping. a + in, a in and a + out, a out denote the input and output optical field operators in the waveguide. σ+ (σ) shows the corresponding photon with right(left)-polarized state. In the bubble, the detailed energy configuration is described for N-V center in diamond nanocrystal. The transitions |−〉 ⇔ |1〉 and |+〉 ⇔ |1〉 are driven by the R(σ+)- and L(σ)-polarized photon, respectively.

Fig. 2
Fig. 2

Schematic of the setup for the generation of three-qubit GHZ state of three N-V centers which are confined individually in three PC nanocavities. All the nanocavities are coupled identically to a common waveguide. Polarization beam splitters (PBS) transmit V–polarized photons and transmit H–polarized photons; Half-wave plates (HWP) interchange the polarization of photons HV; Quarter-wave plates (QWP) achieve the porlarization changes of the single-photon pulse as |V〉 ⇔ |R〉; Beam splitters (BS) mix the two polarized components.

Fig. 3
Fig. 3

(a) The absolute value of the transmission coefficient |T(ω)| as a function of frequency detuning (ωcω)/γ between the input pulse and PC nanocavity mode with gk = 500γ (red solid curve) and gk = 0 (blue dashed curve); (b) The phase shift ϕ/π as a function of frequency detuning (ωcω)/γ with gk = 500γ (red solid curve) and gk = 0 (blue dashed curve). The other system parameters are chosen as κ = 1000γ and ω0 = ωc.

Fig. 4
Fig. 4

(a) The absolute value of the transmission coefficient |T(ω)| versus the coupling strength gk/γ with κ = 1000γ; (b) |T(ω)| versus the cavity damping κ/γ with gk = 500γ. The other system parameters are chosen as ω = ω0 = ωc.

Fig. 5
Fig. 5

The shape functions for the input pulse (blue solid curve) and the transmitted pulses with the N-V centers in spin states |−〉 (red dashed curve) and in spin states |+〉 (red dotted curve). The transmitted pulses and the input pulse closed match and are hardly distinguishable in the figure.

Equations (13)

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H ^ = k = R , L { ω c C k C k + ω a k ( ω ) a k ( ω ) d ω + κ 2 π [ i a k ( ω ) C k i a k ( ω ) C k ] d ω } + ( ω 0 i γ 2 ) | 1 1 | + ( i g R | 1 | C R + i g L | 1 + | C L + H . C . ) ,
| ψ ( t ) = k = R , L [ d 1 ( t ) | 1 , 0 | vac + d k c ( t ) | , 1 k | vac + d k a ( t ) a k ( ω ) | , 0 | vac d ω ] .
i d ˙ k c ( t ) = ω c d k c ( t ) i d 1 ( t ) g k i κ 2 π d k a ( t ) d ω ,
i d ˙ k a ( t ) = ω d k a ( t ) + i κ 2 π d k c ( t ) ,
i d ˙ 1 ( t ) = ( ω 0 i γ 2 ) d 1 ( t ) + i [ d R c ( t ) g R + d L c ( t ) g L ] .
d k a ( t ) = e i ω t d k a ( t 0 ) + κ 2 π t 0 t e i ω ( t t ) d k c ( t ) d t for t > t 0
d ˙ k c ( t ) = i ω c d k c ( t ) κ 2 d k c ( t ) d 1 ( t ) g k κ a k in ,
a k in = 1 2 π e i ω t d k a ( t 0 ) d ω
a k out = ( 4 g k 2 4 g k ¯ 2 κ γ ) a k in + 8 g k g k ¯ a k ¯ in 4 g k 2 + 4 g k ¯ 2 + κ γ ,
T ( ω ) = a k out a k in = 1 ,
T ( ω ) = 1 .
{ | R | + | R | + | R | | R | | L | + | L | + | L | | L | ,
1 2 ( | H + | V ) | 0 + 0 + 0 + 1 2 ( | H + | R ) | 0 + 0 + 0 + 1 2 ( | H | 0 + 0 + 0 + + | R | 0 0 0 ) 1 2 ( | H | 0 + 0 + 0 + + | V | 0 0 0 ) 1 2 | V ( | 0 + 0 + 0 + + | 0 0 0 ) .

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