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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 2 — Jan. 27, 2014
  • pp: 1784–1786
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A classical simulation of nonlinear Jaynes–Cummings and Rabi models in photonic lattices: reply to comment

B. M. Rodríguez-Lara, Francisco Soto-Eguibar, Alejandro Zárate Cárdenas, and H. M. Moya-Cessa  »View Author Affiliations


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 gc = 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

In conclusion, the statement “Hence, the proposed classical simulation is actually not applicable to the nonlinear Rabi model and the simulation results are completely invalid” is misleading as it should not refer to the classical simulation. The mapping from the quantum models to the classical analog is correct. The quantum Rabi model with any given parameter set [3

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]

] and the Buck-Sukumar model with counter-rotating terms for 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]

] are valid as stated by Lo [2

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

].

We only agree with Lo that the numerical simulation presented in Fig. 3 of our paper [1

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]

] should have been done for an adequate value of g in which the Buck-Sukumar Hamiltonian including counter-rotating terms is valid; for example g = 0.249ωf in Fig. 1 here. However, it is true also that for large 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() 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.

Fig. 1 The classical simulation of the time evolution for the separable initial state |ψ(0)〉 = |2, e〉 under the Buck-Sukumar model plus counter-rotating terms on resonance, ω0 = ωf, and coupling parameters g = g+ = 0.249ωf. (a) Propagation of the initial field in the corresponding negative parity photonic lattice of the classical simulator. The time evolution of the (b) mean photon number, (c) mean atomic excitation energy, (d) mean von Neumann entropy, and (e) fidelity reconstructed from the classical simulation. The lattice is composed by two hundred coupled photonic waveguides.

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 21, 12888–128981 (2013). [CrossRef]

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. 42, 1–6 (1998). [CrossRef]

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]

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

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