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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 2 — Jan. 27, 2014
  • pp: 1787–1788
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A classical simulation of nonlinear Jaynes-Cummings and Rabi models in photonic lattices: comment

C. F. Lo  »View Author Affiliations


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

In recent years much attention has been attracted to the classical simulation of quantum and relativistic systems due to the technological advancement in manufacturing arrays of optical waveguides. For instance, Crespi 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]

] reported a successful realization of a classical simulator of the quantum Rabi model, which is also known as the Jaynes-Cummings (JC) model with the counter-rotating term, via light transport in femtosecond-laser-written waveguide supperlattices. The classical simulator is able to provide an experimentally accessible test bed to explore the physics of light-matter interaction in the deep strong coupling regime. Similarly, Rodriguez-Lara 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]

] proposed to simulate the dynamics of the nonlinear Rabi model (or equivalently, the nonlinear JC model with the counter-rotating term) by propagating classical light fields in a set of two photonic lattices. For illustration, they performed the classical simulation to the Buck-Sukumar (BS) model, 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.

The aim of this comment is to point out that the nonlinear Rabi model considered in Ref. [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]

] has already been rigorously proven to be undefined by Lo [3

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

]. In other words, the system does not have eigenstates in the Hilbert space spanned by the eigenstates of the corresponding nonlinear JC model. The nonlinear Rabi model is thus qualitatively different from the nonlinear JC model for the counter-rotating term does drastically alter the nature of the nonlinear JC model. The same conclusion has also been drawn for some other generalised JC models with the counter-rotating terms, namely the 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]

], the 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 265557–564 (1999). [CrossRef]

], the nonlinear k-photon JC model with the counter-rotating term for k ≥ 1 [3

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

], and the k-photon q-deformed JC model with the counter-rotating term for 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]

]. Accordingly, the classical simulation analysis discussed in Ref. [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]

] is actually not applicable to the nonlinear Rabi model at all.

In conclusion, the classical simulation analysis proposed by Rodriguez-Lara 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. 108, 163601 (2012). [CrossRef] [PubMed]

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. 10L57–L61 (1998). [CrossRef]

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]

5.

C. F. Lo, K. L. Liu, and K. M. Ng, “The multiquantum intensity-dependent Jaynes-Cummings model with the counterrotating terms,” Physica A 265557–564 (1999). [CrossRef]

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]

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 6, 119–126 (1999).

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 275, 463–474 (2000). [CrossRef]

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,” Proceedings of the International Conference on Frontiers in Quantum Physics (July 9–11, 1997), S.C. Lim, R. Abd-Shukor, and K.H. Kwek, eds. (Springer-Verlag, Singapore, 1998) 285–290.

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

  1. A. Crespi, S. Longhi, R. Osellame, “Photonic Realization of the Quantum Rabi Model,” Phys. Rev. Lett. 108, 163601 (2012). [CrossRef] [PubMed]
  2. 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]
  3. C. F. Lo, “Nonlinear multiquantum Jaynes-Cummings model with counter-rotating terms,” Quantum Semiclass. Opt. 10L57–L61 (1998). [CrossRef]
  4. 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]
  5. 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]
  6. 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]
  7. 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).
  8. 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]
  9. 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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