## Polarization-dependent photon switch in a one-dimensional coupled-resonator waveguide |

Optics Express, Vol. 21, Issue 18, pp. 20786-20799 (2013)

http://dx.doi.org/10.1364/OE.21.020786

Acrobat PDF (3094 KB)

### Abstract

Polarization-dependent photon switch is one of the most important ingredients in building future large-scale all-optical quantum network. We present a scheme for a single-photon switch in a one-dimensional coupled-resonator waveguide, where *N _{a}* Λ-type three-level atoms are individually embedded in each of the resonator. By tuning the interaction between atom and field, we show that an initial incident photon with a certain polarization can be transformed into its orthogonal polarization state. Finally, we use the fidelity as a figure of merit and numerically evaluate the performance of our photon switch scheme in varieties of system parameters, such as number of atoms, energy detuning and dipole couplings.

© 2013 OSA

## 1. Introduction

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6. S. Buckley, K. Rivoire, and J. Vučković, “Engineered quantum dot single-photon sources,” Rep. Prog. Phys. **75**, 126503 (2012). [CrossRef] [PubMed]

7. M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. **75**, 457–472 (2003). [CrossRef]

8. L. Chirolli, G. Burkard, S. Kumar, and D. P. DiVincenzo, “Superconducting resonators as beam splitters for linear-optics quantum computation,” Phys. Rev. Lett. **104**, 230502 (2010). [CrossRef] [PubMed]

9. J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguides,” Opt. Lett. **30**, 2001–2003 (2005). [CrossRef] [PubMed]

10. D. Roy, “Few-photon optical diode,” Phys. Rev. B **81**, 155117 (2010). [CrossRef]

11. Y. Shen, M. Bradford, and J. T. Shen, “Single-Photon Diode by Exploiting the Photon Polarization in a Waveguide,” Phys. Rev. Lett. **107**, 173902 (2011). [CrossRef] [PubMed]

12. M. Orrit, “Quantum light switch,” Nat. Phys. **3**, 755–756 (2007). [CrossRef]

13. D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. **3**, 807–812 (2007). [CrossRef]

9. J. T. Shen and S. Fan, “Coherent photon transport from spontaneous emission in one-dimensional waveguides,” Opt. Lett. **30**, 2001–2003 (2005). [CrossRef] [PubMed]

11. Y. Shen, M. Bradford, and J. T. Shen, “Single-Photon Diode by Exploiting the Photon Polarization in a Waveguide,” Phys. Rev. Lett. **107**, 173902 (2011). [CrossRef] [PubMed]

14. J. T. Shen and S. Fan, “Coherent single photon Transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett. **95**, 213001 (2005). [CrossRef] [PubMed]

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24. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. **2**, 849–855 (2006). [CrossRef]

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27. L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A **78**, 063827 (2008). [CrossRef]

29. J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A **81**, 042304 (2010). [CrossRef]

30. P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett. **104**, 023602 (2010). [CrossRef]

31. P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A **83**, 063828 (2011). [CrossRef]

32. L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. **101**, 100501 (2008). [CrossRef] [PubMed]

33. Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A **83**, 013825 (2011). [CrossRef]

34. Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A **86**, 023824 (2012). [CrossRef]

35. M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A **85**, 053840 (2012). [CrossRef]

8. L. Chirolli, G. Burkard, S. Kumar, and D. P. DiVincenzo, “Superconducting resonators as beam splitters for linear-optics quantum computation,” Phys. Rev. Lett. **104**, 230502 (2010). [CrossRef] [PubMed]

36. A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A **64**, 050301(R)(2001). [CrossRef]

37. 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]

17. T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A **80**, 033823 (2009). [CrossRef]

*N*Λ-type three-level atoms. The analytic expressions of the eigenvectors of the Hamiltonian are derived by using discrete-coordinate scattering approach. Precisely, our discussions are divided into two scenarios:

_{a}*N*= 1 and

_{a}*N*> 1. We then give an analysis of the effect of system dissipation on the transfer spectra. Next, we provide numerical evaluations of our photon switching scheme, with the fidelity as the figure of merit for polarization transformation. Other influence of atomic decay and loss in resonators are also included. This numerical study further elucidates the physics mechanism under which the three-level atom could enable the control of the scattering and polarization of a single photon.

_{a}## 2. Model Hamiltonian and eigenvectors

*ξ*[24

24. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. **2**, 849–855 (2006). [CrossRef]

*N*atoms individually embedded in one of the resonators in CRW. Here, the Λ-type atom in the

_{a}*j*th resonator consists of two degenerate ground states, which are represented as |

*H*〉

*and |*

_{j}*V*〉

*, and an excited state |*

_{j}*e*〉

*. These two ground states are coupled to the excited state with two orthogonal polarizations of the field,*

_{j}*H*and

*V*, with coupling strengths

*g*and

_{H}*g*respectively. The whole system Hamiltonian

_{V}25. L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A **77**, 013831 (2008). [CrossRef]

32. L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. **101**, 100501 (2008). [CrossRef] [PubMed]

*a*and

_{j,s}*s*(

*s*=

*V*,

*H*) of the

*j*th two-mode resonator with frequency

*ω*, Ω is the difference in the energy level between excited state and ground state. |

*m*〉

*〈*

_{j,j}*n*| (

*m*,

*n*=

*e*,

*s*) is the dipole transition operator between |

*m*〉

*and |*

_{j}*n*〉

*. In a single resonator, the scattering of a single photon packet from a Λ-type three-level atom have been investigated by Chen*

_{j}*et al*[38

38. T. W. Chen, C. K. Law, and P. T. Leung, “Single-photon scattering and quantum-state transformations in cavity QED,” Phys. Rev. A **69**, 063810 (2004). [CrossRef]

27. L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A **78**, 063827 (2008). [CrossRef]

32. L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. **101**, 100501 (2008). [CrossRef] [PubMed]

33. Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A **83**, 013825 (2011). [CrossRef]

*N*to

*N*, while the resonators with atoms are marked from 1 to

*N*. Notice that the total excitation number operator

_{a}*e*| is a conserved observable, i.e., [

*N̂*,

*H*] = 0. So we restrict our analysis of photon scattering on the single-excitation subspace. We assume that a

*H*-polarized photon with eigenenergy

*E*incidents from the left, and all atoms are initially in the ground states |

*H*〉. To study the 1D single-photon elastic scattering problem governed by the total Hamiltonian

*H*, it needs to find the eigenstate of

*H*with eigenenergy

*E*for the incident photon through eigenvalue equation

*H*|

*E*〉 =

*E*|

*E*〉.

### 2.1. *N*_{a} = 1 case

_{a}

**101**, 100501 (2008). [CrossRef] [PubMed]

*V*-polarized photon may be released after the incident

*H*-polarized photon is absorbed by the atom. We assume the stationary state of the system is where |

*j*〉 ⊗ |

_{s}*s*〉

_{1}denotes the state that the atom is at the ground state |

*s*〉 associated with a

*s*-polarized photon emitted into a mode of the

*j*th resonator, |0〉 ⊗ |

*e*〉

_{1}represents the state without any photon in the CRW and the atom is promoted to the excited state,

*j*≠ 1 are with transmission and reflection amplitudes

*t*and

_{s}*r*for

_{s}*s*-polarized photon, respectively. Substituting these solutions into Eq. (4) in the region of resonators without atom, we can easily get the cosine-type dispersion for the incident photon with momentum

*k*. Next, considering the continuous conditions

*j*= 1, we have Combining Eqs. (10)–(13), we obtain the transmission and reflection amplitudes of the

*s*-polarized photon where Δ =

*E*− Ω is the energy detuning between atom and incident photon. Because the momentum of incident photon is real, the range of the detuning is

*ω*− Ω −2|

*ξ*| ⩽ Δ ⩽

*ω*−Ω + 2|

*ξ*|. It is easy to check that |

*t*|

_{H}^{2}+|

*r*|

_{H}^{2}+ |

*t*|

_{V}^{2}+ |

*r*|

_{V}^{2}= 1, which satisfies the conservation of probability in the scattering problem.

*g*and

_{H}*g*. When

_{V}*g*= 0, the |

_{V}*V*〉

_{1}is decoupled with the field of resonator. In this case, we can recover the result of control-lable scattering of a single

*H*-polarized photon in [32

**101**, 100501 (2008). [CrossRef] [PubMed]

*H*-polarized photon is completely reflected. When

*g*≠ 0, after the atom is excited by absorbing incident photon, it can emit a

_{V}*V*-polarized photon with certain probability. From Eq. (16), we can conclude that the transmission coefficient |

*t*|

_{V}^{2}and reflection coefficient |

*r*|

_{V}^{2}of

*V*-polarized photon are the same. This phenomenon results from the fact that the released

*V*-polarized photon will be no preference of propagation direction. Especially, for the case of

*g*=

_{H}*g*=

_{V}*g*, the probabilities of emitting a polarized photon with forward and backward transmission are equal. However, due to the interfere with the incident

*H*-polarized photon, the transmission coefficient |

*t*|

_{H}^{2}is quite different from others. In Figs. 2(a)–2(d), we plot the transmission and reflection spectra for both of the polarization versus the detuning for only one atom. The parameters in these figures are chosen as

*g*=

_{H}*g*= 1,

_{V}*ω*= 5, Ω = 6, and

*ξ*= −1. These figures clearly show that |

*r*|

_{H}^{2}, |

*t*|

_{V}^{2}, and |

*r*|

_{V}^{2}are identical as we have pointed out. At the resonance, the transmission coefficient of

*H*-polarized photon |

*t*|

_{H}^{2}reaches its minimum and equals to the maximum of the other three transmission and reflection coefficients.

### 2.2. *N*_{a} > 1 case

_{a}

*H*〉, for a

*H*-polarized photon traveled from left, the eigenstate of the total Hamiltonian

*H*with eigenenergy

*E*can be written in the following form where Here we have assumed

*j*to be ranging from −

*N*to

*N*, and

*l*is used to number the resonator with an atom, |

*j*〉 ⊗ |

_{H}*H′*〉 represents that

*H*-polarized photon locates in the

*j*th resonator and each of the three-level atoms is in the state |

*H*〉, |

*j*〉 ⊗ |

_{V}*V′*〉 denotes that the atom in the

_{l}*l*th resonator is transferred to state |

*V*〉 and releases a

*V*-polarized photon, which has transmitted to the

*j*th resonator, |0〉 ⊗ |

*e′*〉 represents that the single photon is absorbed and the atom in the

*l*th resonator is excited to state |

*e*〉.

*H*〉 states,

*V*-polarized photon, is quite different from that of the single-atom case. In fact, once an atom is transferred to |

*V*〉 state, the scattered photon will propagate along the CRW without further interaction with other atoms. From the Schrödinger equation

*H*|

*E*〉 =

*E*|

*E*〉, the scattering equations for a single photon with discrete coordinate representation are given as These three equations show that

*V*-polarized photon may transfer into other resonators, the atom inside which is definitely in its |

*H*〉 state as we assumed. In this situation, the circumstance around the

*V*-polarized photon has no difference from the empty resonators. Substituting Eq. (21) into Eqs. (19) and (20), we get If only the scattering problem in one dimension is considered, and the eigenfunction only possesses the reflection and transmission waves, the solutions of Eqs. (22) and (23) are with transmission and reflection amplitudes

*t*,

_{H}*r*,

_{H}*r*, and

_{V,l}*t*, respectively. Where

_{V,l}*k′*is the momentum of

*H*-polarized photon, which transmits in the resonators with an atom. Next we apply the boundary conditions for

*V*-polarized photon of the solutions, which give

*r*

_{V,l}e^{−}

*=*

^{ikl}*t*. Combining the cosine-type dispersion of the CRW and conservation of energy, we can obtain momentum

_{V,l}e^{ikl}*k′*, which is the solution of the transcendental equation To obtain the analytical solution of eigenvectors, we consider the scattering Eqs. (22) and (23) at the boundary points. It is straightforward that the transmission and reflection amplitudes for

*s*-polarized photon are obtained as where The conservation of probability is satisfied.

*N*→ 1, we can get exactly the same results as shown in Fig. 2. While for

_{a}*g*= 0, the result in [33

_{V}33. Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A **83**, 013825 (2011). [CrossRef]

*H*-polarized photon in a wide band of frequency.

*t*|

_{H}^{2}, |

*r*|

_{H}^{2},

*T*,

_{H}*R*,

_{H}*T*, and

_{V}*R*, respectively. In Fig. 3(a), we see that there is an obvious drop for

_{V}*T*near the resonance when

_{H}*N*= 2. When more atoms are embedded into the system, the transmission coefficient of

_{a}*H*-polarized photon decrease quickly. When

*N*= 8, a band of forbidden transmission for incident photon, i.e.,

_{a}*T*≃ 0, emerges around the resonance. Such a band-gap-like structure for incident photon is also observed in a 1D waveguide [17

_{H}17. T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A **80**, 033823 (2009). [CrossRef]

*R*, which does not have distinct change except for the two boundaries of Δ as

_{H}*N*increases [Fig. 3(c)]. Meanwhile, due to the interference from multiple atoms,

_{a}*R*is much different from

_{H}*T*and

_{V}*R*even under the condition

_{V}*g*=

_{H}*g*. Because the released

_{V}*V*-polarized photon cannot transfer back to the

*H*-polarized photon, the transmission coefficient

*T*, which equals to the reflection coefficient

_{V}*R*, gradually accumulates as the number of atoms increases [Figs. 3(b) and 3(d)].

_{V}## 3. Influence of dissipation

*g*=

_{H}*g*= 1,

_{V}*ω*= 5, Ω = 6, and

*ξ*= −1. For

*γ*= 0.1 and

_{c}*γ*= 0.2. The Figs. 4(a)–4(d) show that the transmission and reflection spectra has a little change compared with that in ideal case when the dissipation is not very large. While

_{a}*γ*increases to 0.4, obvious changes emerge near the resonance, especially for the transmission and reflection spectra of

_{a}*V*-polarized photon. This phenomenon implies that the effect of dissipation on polarization-dependent photon switch is not very large. Even under strong dissipation, the influence is limited in a certain range of frequency of incident photon. In Fig. 4(e), it displays that the photon current is conserved in the ideal case, while it is not conserved any more when the dissipation is included in the system. Meanwhile, the loss of photon current raises as the decay rate increases.

## 4. Polarization dependent transmission and reflection

27. L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A **78**, 063827 (2008). [CrossRef]

29. J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A **81**, 042304 (2010). [CrossRef]

**101**, 100501 (2008). [CrossRef] [PubMed]

35. M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A **85**, 053840 (2012). [CrossRef]

17. T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A **80**, 033823 (2009). [CrossRef]

*ℱ*= 0, the transmission photon is only

*H*-polarized, while

*ℱ*= 1 means that the transmission photon is completely transformed into a

*V*-polarized one.

*T*and smaller

_{V}*T*are obtained [Figs. 3(a) and 3(b)]. According to the definition of

_{H}*ℱ*, it results in the increase of the fidelity. In Fig. 5, we present results of the fidelity (the red lines) as a function of detuning with multiple atoms. The other parameters are the same as that in Figure 2. It is shown that |

*t*|

_{H}^{2}= |

*t*|

_{V}^{2}at Δ = 0 in Fig. 2. For one atom in the CRW, a fidelity of

*ℱ*= 0.5 is thus obtained at resonance [Fig. 5(a)]. After embedding another atom into the CRW, we get a fidelity up to 0.8919 near the resonance point Δ = −0.0694 [Fig. 5(b)]. The highest fidelity at the resonance point raises as the number of atoms increases. When we embed further more atoms into the CRW, the perfect transformation of polarization appears in a wide band [Figs. 5(c)–5(f)]. It displays that for a given Ω the incident photon with higher energy are more likely to transmit through the CRW with converting its polarization. For a more realistic situation which includes the atomic decay and the resonator loss, we plot the fidelity spectrum

*ℱ*in Fig. 5 (the blue dashed line) with

*γ*= 0.3 and

_{a}*γ*= 0.15. It is shown in Fig. 5 that the frequency profiles of

_{c}*ℱ*are not sensitive to the system dissipation. In Figs. 5(d)–5(f), fidelity with decay even can be slightly higher than that in non-dissipative case (red line) in some range. This phenomenon results from the facts that input photon with

*H*polarization is almost completely blocked and loss when

*N*is very large [Fig. 6(a)], and on the other hand, the transmission

*T*of

_{V}*V*-polarized photon asymptotically closes to be a certain value even in the dissipation case when

*N*> 15 [Fig. 6(b)]. Figs. 6(a) and 6(b) show that the dissipation reduces the transmissions for both of the polarized photon. However, when differences

*δ*between the transmissions

_{s}*T*and

_{s}*T*satisfy the relation

_{s}L*T*>

_{V}δ_{H}*T*, the fidelity with dissipation will be larger than that without dissipation [Fig. 6(c)]. A similar phenomenon is also revealed in 1D waveguide [17

_{H}δ_{V}**80**, 033823 (2009). [CrossRef]

*g*,

_{V}*g*with two orthogonal polarizations. We plot the contour map of the fidelity in Fig. 7. The contour map can be regarded as a kind of phase diagram. In Fig. 7, the white areas denote that the

_{H}*ℱ*is near one, while the dark areas indicate that the

*ℱ*is close to zero. In Fig. 7(a), we choose the same parameters as that in Fig. 5 and

*g*= 1. It shows that the bigger

_{H}*g*, the wider range of white areas. However, the white areas appear due to different mechanism. In the strong coupling regime, the bigger

_{V}*g*means that the excited state of atom is easier to release a

_{V}*V*-polarized photon, which leads to

*ℱ*= 1. On the other hand, when

*g*is in the weak coupling regime, the

_{V}*ℱ*= 1 results from the band of forbidden transmission for incident photon, i.e.,

*T*≃ 0 [Fig. 3(a)]. In Fig. 7(b), we set

_{H}*g*= 1. It shows that associated with the increasing of

_{V}*g*the white areas are enlarged. Together with Figs. 7(a) and 7(b), it seems that fidelity becomes bigger accompany with the growing of both dipole couplings. This is further demonstrated in Fig. 8 when the contour map of the fidelity

_{H}*ℱ*is plotted as a function of the diploe couplings

*g*and

_{V}*g*for

_{H}*N*= 8 and Δ = −1.

_{a}## 5. Conclusion

*N*Λ-type atoms have been investigated. Based on the discrete-coordinate scattering method, we have derived analytic expressions of transmission and reflection coefficients for the case of a single atom. Then we generalize it to the case of multiple atoms. For the incident

_{a}*H*-polarized photon, we have shown that a band of forbidden transmission for incident photon emerges near the resonance as the number of atoms increases. Meanwhile, the probability of converting the

*H*-polarized photon to the

*V*-polarized photon raises. Such

*V*-polarized photon propagates forward and backward equally. We then prove the transmission and reflection spectra are not sensitive to the atomic decay and the resonator loss, although such dissipations of system can reduce the photon current in the CRW. Furthermore, we introduce fidelity to qualify the ability of polarization transformation, and study the fidelity in varieties of system parameters, such as number of atoms, energy detuning, dipole couplings with orthogonal polarizations. To get a better fidelity, we should embed more atoms into the CRW, and keep higher dipole couplings. The results of these analyses may be helpful for designing a polarization-dependent photon switch, which can blockade and convert the incident photon with certain polarization.

## Acknowledgments

## References and links

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12. | M. Orrit, “Quantum light switch,” Nat. Phys. |

13. | D. E. Chang, A. S. Sørensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. |

14. | J. T. Shen and S. Fan, “Coherent single photon Transport in a one-dimensional waveguide coupled with superconducting quantum bits,” Phys. Rev. Lett. |

15. | T. S. Tsoi and C. K. Law, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A |

16. | D. Witthaut and A. S. Sørensen, “Photon scattering by a three-level emitter in a one-dimensional waveguide,” New J. Phys. |

17. | T. S. Tsoi and C. K. Law, “Single-photon scattering on Λ-type three-level atoms in a one-dimensional waveguide,” Phys. Rev. A |

18. | J.-T. Shen and S. Fan, “Strongly correlated two-photon transport in a one-dimensional waveguide coupled to a two-level system,” Phys. Rev. Lett. |

19. | J.-T. Shen and S. Fan, “Strongly correlated multiparticle transport in one dimension through a quantum impurity,” Phys. Rev. A |

20. | D. Roy, “Two-photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparency,” Phys. Rev. Lett. |

21. | E. Rephaeli, Ş. E. Kocabaş, and S. Fan, “Quantum interference effects of a single photon interacting with an atomic chain inside a one-dimensional waveguide,” Phys. Rev. A |

22. | K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, S. Savel’ev, and F. Nori, “Unusual resonators: Plasmonics, metamaterials, and random media,” Rev. Mod. Phys. |

23. | D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, “Quantum optics with surface plasmons,” Phys. Rev. Lett. |

24. | M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Strongly interacting polaritons in coupled arrays of cavities,” Nat. Phys. |

25. | L. Zhou, Y. B. Gao, Z. Song, and C. P. Sun, “Coherent output of photons from coupled superconducting transmission line resonators controlled by charge qubits,” Phys. Rev. A |

26. | A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, “Quantum phase transitions of light,” Nat. Phys. |

27. | L. Zhou, H. Dong, Y. X. Liu, C. P. Sun, and F. Nori, “Quantum supercavity with atomic mirrors,” Phys. Rev. A |

28. | Z. R. Gong, H. Ian, L. Zhou, and C. P. Sun, “Controlling quasibound states in a one-dimensional continuum through an electromagnetically-induced-transparency mechanism,” Phys. Rev. A |

29. | J. Q. Liao, Z. R. Gong, L. Zhou, Y. X. Liu, C. P. Sun, and F. Nori, “Controlling the transport of single photons by tuning the frequency of either one or two cavities in an array of coupled cavities,” Phys. Rev. A |

30. | P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems interaction-induced radiation trapping,” Phys. Rev. Lett. |

31. | P. Longo, P. Schmitteckert, and K. Busch, “Few-photon transport in low-dimensional systems,” Phys. Rev. A |

32. | L. Zhou, Z. R. Gong, Y. X. Liu, C. P. Sun, and F. Nori, “Controllable scattering of a single photon inside a one-dimensional resonator waveguide,” Phys. Rev. Lett. |

33. | Y. Chang, Z. R. Gong, and C. P. Sun, “Multiatomic mirror for perfect reflection of single photons in a wide band of frequency,” Phys. Rev. A |

34. | Z. H. Wang, Y. Li, D. L. Zhou, C. P. Sun, and P. Zhang, “Single-photon scattering on a strongly dressed atom,” Phys. Rev. A |

35. | M. T. Cheng, X. S. Ma, M. T. Ding, Y. Q. Luo, and G. X. Zhao, “Single-photon transport in one-dimensional coupled-resonator waveguide with local and nonlocal,” Phys. Rev. A |

36. | A. Rauschenbeutel, P. Bertet, S. Osnaghi, G. Nogues, M. Brune, J. M. Raimond, and S. Haroche, “Controlled entanglement of two field modes in a cavity quantum electrodynamics experiment,” Phys. Rev. A |

37. | 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. |

38. | T. W. Chen, C. K. Law, and P. T. Leung, “Single-photon scattering and quantum-state transformations in cavity QED,” Phys. Rev. A |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(230.4555) Optical devices : Coupled resonators

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: July 16, 2013

Revised Manuscript: August 12, 2013

Manuscript Accepted: August 13, 2013

Published: August 28, 2013

**Citation**

Zhe-Yong Zhang, Yu-Li Dong, Sheng-Li Zhang, and Shi-Qun Zhu, "Polarization-dependent photon switch in a one-dimensional coupled-resonator waveguide," Opt. Express **21**, 20786-20799 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20786

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