## A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices: reply to comment |

Optics Express, Vol. 22, Issue 2, pp. 1784-1786 (2014)

http://dx.doi.org/10.1364/OE.22.001784

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### Abstract

We regret that such a misleading comment [Opt. Express (2013)] has been made to our paper. First Lo states in his abstract that “However, the nonlinear Rabi model has already been rigorously proven to be undefined” to later recoil and use the contradictory statement ”(. . . ) regarding the BS model with the counter-rotating terms (. . . ) Lo and his co-authors have proven that the model is well defined only if the coupling stregth *g* is smaller than a critical value *g _{c}* =

*ω*/4”. While Lo focuses on the validity of the quantum optics Hamiltonians and gives a misleading assesment of our manuscript, the focus of our paper is the method to map such a set of Hamiltonians from quantum optics to photonic lattices. Our method is valid for the given class of Hamiltonians and, indeed, precaution must be exerted on the paramater ranges where those Hamiltonians are valid and where their classical simulation is feasible. These parameter ranges have to be specified in for each particular case studied. Furthermore, we gave as example the Buck-Sukumar model including counter-rotating terms which is a valid Hamiltonian for some coupling parameters.

© 2014 Optical Society of America

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

*g*<

*ω*/4 [4

4. 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]

1. B. M. Rodríguez-Lara, F. Soto-Eguibar, A. Z. Cárdenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices,” Opt. Express **21**, 12888–128981 (2013). [CrossRef]

*g*in which the Buck-Sukumar Hamiltonian including counter-rotating terms is valid; for example

*g*= 0.249

*ω*in Fig. 1 here. However, it is true also that for large

_{f}*g*’s the first neighbor interaction is not valid any more for large

*n*’s, and at least second neighbor interactions should be considered. As in every classical simulation, any particular instance of

*f*(

*n̂*) in our model should be studied with care in order to choose a parameter range where both the quantum model is valid and the photonic lattice is experimentally feasible.

## References and links

1. | B. M. Rodríguez-Lara, F. Soto-Eguibar, A. Z. Cárdenas, and H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices,” Opt. Express |

2. | C. F. Lo, “A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices: comment,” Opt. Express (2013). |

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

4. | 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 |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5580) Quantum optics : Quantum electrodynamics

(350.5500) Other areas of optics : Propagation

(310.2785) Thin films : Guided wave applications

(230.4555) Optical devices : Coupled resonators

(230.5298) Optical devices : Photonic crystals

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: December 19, 2013

Manuscript Accepted: December 23, 2013

Published: January 17, 2014

**Citation**

B. M. Rodríguez-Lara, Francisco Soto-Eguibar, Alejandro Zárate Cárdenas, and H. M. Moya-Cessa, "A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices: reply to comment," Opt. Express **22**, 1784-1786 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1784

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### References

- B. M. Rodríguez-Lara, F. Soto-Eguibar, A. Z. Cárdenas, H. M. Moya-Cessa, “A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices,” Opt. Express 21, 12888–128981 (2013). [CrossRef]
- C. F. Lo, “A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices: comment,” Opt. Express (2013).
- C. F. Lo, K. L. Liu, K. M. Ng, “The multiquantum Jaynes–Cummings model with the counter-rotating terms,” Europhys. Lett. 42, 1–6 (1998). [CrossRef]
- 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]

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