## A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices: comment

Optics Express, Vol. 22, Issue 2, pp. 1787-1788 (2014)

http://dx.doi.org/10.1364/OE.22.001787

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### Abstract

Recently Rodriguez-Lara *et al*. [Opt. Express **21**(10), 12888 (2013)] proposed a classical simulation of the dynamics of the nonlinear Rabi model by propagating classical light fields in a set of two photonic lattices. However, the nonlinear Rabi model has already been rigorously proven to be undefined by Lo [Quantum Semiclass. Opt. **10**, L57 (1998)]. Hence, the proposed classical simulation is actually not applicable to the nonlinear Rabi model and the simulation results are completely invalid.

© 2013 Optical Society of America

*et al*. [1

1. A. Crespi, S. Longhi, and R. Osellame, “Photonic Realization of the Quantum Rabi Model,” Phys. Rev. Lett. **108**, 163601 (2012). [CrossRef] [PubMed]

*et al*. [2

2. R. M. Rodriguez-Lara, F. Soto-Eguibar, A. Z. Cardenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices,” Opt. Express **21**(10), 12888–12898 (2013). [CrossRef] [PubMed]

*i.e.*the intensity-dependent JC model, with the counter-rotating term, which is a special case of the nonlinear Rabi model, and presented the simulation results of the model.

2. R. M. Rodriguez-Lara, F. Soto-Eguibar, A. Z. Cardenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices,” Opt. Express **21**(10), 12888–12898 (2013). [CrossRef] [PubMed]

3. C. F. Lo, “Nonlinear multiquantum Jaynes-Cummings model with counter-rotating terms,” Quantum Semiclass. Opt. **10**L57–L61 (1998). [CrossRef]

*k*-photon JC model with the counter-rotating term for

*k*> 2 [4

4. C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum Jaynes-Cummings model with the counter-rotating terms,” Europhys. Lett. **42**(1), 1–6 (1998). [CrossRef]

*k*-photon intensity-dependent JC model with the counter-rotating term for

*k*> 1 [5

5. C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes-Cummings model with the counterrotating terms,” Physica A **265**557–564 (1999). [CrossRef]

*k*≥ 1 [3

3. C. F. Lo, “Nonlinear multiquantum Jaynes-Cummings model with counter-rotating terms,” Quantum Semiclass. Opt. **10**L57–L61 (1998). [CrossRef]

*k*≥ 1 [6

6. C. F. Lo and K. L. Liu, “The multiquantum q-deformed Jaynes-Cummings model with the counter-rotating terms,” Physica A **271**, 405–410 (1999). [CrossRef]

2. R. M. Rodriguez-Lara, F. Soto-Eguibar, A. Z. Cardenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices,” Opt. Express **21**(10), 12888–12898 (2013). [CrossRef] [PubMed]

*et al*. is applicable to the nonlinear JC model only because the nonlinear Rabi model is undefined.

## References and links

1. | A. Crespi, S. Longhi, and R. Osellame, “Photonic Realization of the Quantum Rabi Model,” Phys. Rev. Lett. |

2. | R. M. Rodriguez-Lara, F. Soto-Eguibar, A. Z. Cardenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices,” Opt. Express |

3. | C. F. Lo, “Nonlinear multiquantum Jaynes-Cummings model with counter-rotating terms,” Quantum Semiclass. Opt. |

4. | C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum Jaynes-Cummings model with the counter-rotating terms,” Europhys. Lett. |

5. | C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes-Cummings model with the counterrotating terms,” Physica A |

6. | C. F. Lo and K. L. Liu, “The multiquantum q-deformed Jaynes-Cummings model with the counter-rotating terms,” Physica A |

7. | K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term,” Eur. Phys. J. D |

8. | K. M. Ng, C. F. Lo, and K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes-Cummings model with the counter-rotating term,” Physica A |

9. | K.M. Ng, C.F. Lo, and K.L. Liu, “Exact dynamics of the two-mode two-photon Jaynes-Cummings
model without the rotating-wave approximation,” |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5580) Quantum optics : Quantum electrodynamics

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 4, 2013

Manuscript Accepted: November 11, 2013

Published: January 17, 2014

**Citation**

C. F. Lo, "A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices: comment," Opt. Express **22**, 1787-1788 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1787

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### References

- A. Crespi, S. Longhi, R. Osellame, “Photonic Realization of the Quantum Rabi Model,” Phys. Rev. Lett. 108, 163601 (2012). [CrossRef] [PubMed]
- R. M. Rodriguez-Lara, F. Soto-Eguibar, A. Z. Cardenas, H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices,” Opt. Express 21(10), 12888–12898 (2013). [CrossRef] [PubMed]
- C. F. Lo, “Nonlinear multiquantum Jaynes-Cummings model with counter-rotating terms,” Quantum Semiclass. Opt. 10L57–L61 (1998). [CrossRef]
- C. F. Lo, K. L. Liu, K. M. Ng, “The multiquantum Jaynes-Cummings model with the counter-rotating terms,” Europhys. Lett. 42(1), 1–6 (1998). [CrossRef]
- C. F. Lo, K. L. Liu, K. M. Ng, “The multiquantum intensity-dependent Jaynes-Cummings model with the counterrotating terms,” Physica A 265557–564 (1999). [CrossRef]
- C. F. Lo, K. L. Liu, “The multiquantum q-deformed Jaynes-Cummings model with the counter-rotating terms,” Physica A 271, 405–410 (1999). [CrossRef]
- K. M. Ng, C. F. Lo, K. L. Liu, “Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term,” Eur. Phys. J. D 6, 119–126 (1999).
- K. M. Ng, C. F. Lo, K. L. Liu, “Exact eigenstates of the intensity-dependent Jaynes-Cummings model with the counter-rotating term,” Physica A 275, 463–474 (2000). [CrossRef]
- K.M. Ng, C.F. Lo, K.L. Liu, “Exact dynamics of the two-mode two-photon Jaynes-Cummings model without the rotating-wave approximation,” Proceedings of the International Conference on Frontiers in Quantum Physics (July 9–11, 1997), S.C. Lim, R. Abd-Shukor, K.H. Kwek, eds. (Springer-Verlag, Singapore, 1998) 285–290.

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