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arXiv:1904.02270 · Journal of Modern Optics

Comparison of semiclassical and quantum models of a two-level atom-cavity QED system in the strong coupling regime

M. O. Musa, Helmi Temimi

Published Jun 3, 2019• 4 citations
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Abstract

We present a numerical study comparing semiclassical and quantum models of a damped, strongly interacting cavity QED system composed of a single two-level atom interacting with a single quantized cavity mode driven externally by a tunable monochromatic field. We compute the steady state transmission spectrum of the coupled system under each model and show that in the strong coupling regime, the two models yield starkly different results. The fully quantum mechanical model of the system correctly yields the expected multiphoton transmission spectra while the semiclassical approach results in a bistable spectrum.

DOI
10.1080/09500340.2019.1614237

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We present a numerical study comparing semiclassical and quantum models of a damped, strongly interacting cavity QED system composed of a single two-level atom interacting with a single quantized cavity mode driven externally by a tunable monochromatic field. We compute the steady state transmission spectrum of the coupled system under each model and show that in the strong coupling regime, the two models yield starkly different results. The fully quantum mechanical model of the system correctly yields the expected multiphoton transmission spectra while the semiclassical approach results in a bistable spectrum.
We present detailed numerical simulations of semiclassical and quantum spectra of a cavity QED system consisting of a single three-level atom in Λ-configuration interacting with a quantized cavity mode through one of its transitions while its other transition is driven by a coherent classical field. We compute the semiclassical and quantum spectra of the system under various levels of external driving field strengths. In the semiclassical approach, we neglect the correlations between the cavity and atomic operators, whereas in the quantum case no such assumption is made. Our results show that the two approaches yield identical results under sufficiently weak driving field conditions. However, the two approaches yield starkly different results at stronger driving field intensities: the fully quantum approach yields a well-defined multiphoton spectrum whereas the semiclassical approach results in a bistable spectrum. Furthermore, our calculations reveal a complex Raman structure at the position of the dark-state transition.
In this dissertation we study the interaction of a single atom with a single mode of the electromagnetic field in an optical cavity. We emphasize strong coupling conditions, where the dipole coupling strength is larger than the dissipation rates of the cavity and the atom. By exciting the coupled atom and cavity mode with an external field, the excited-state spectroscopy of the coupled system is explored. Both quantum mechanical and semiclassical calculations are performed and their results are compared. In the limit of a weak driving field, both results show a two-peak ("vacuum" Rabi) spectrum. With increased strength of the driving field, differences are observed. The quantum calculation shows a multi-peak ( two "vacuum" Rabi peaks plus additional peaks) spectrum, while the semiclassical calculation does not. These additional peaks are produced by transitions between the excited states of the Jaynes-Cummings IV Hamiltonian indicative of the quantum nature of the coupled atom-cavity-mode system.
We present exact numerical solutions of the damped-driven Jaynes-Cummings model adapted to describe absorptive optical bistability in the limit of a few atoms strongly coupled to a high-finesse resonator.We show that the simplifying semiclassical result for many physical quantities of interest is well reproduced by the quantum model including even with only a few atoms in the strongly coupled system.Non-trivial atom-field quantum cross-correlations show up in the strong-driving limit.(Some figures may appear in colour only in the online journal)
The prototypical system constituted by a two-level atom interacting with a quantized single-mode electromagnetic field is described by the quantum Rabi model (QRM). The QRM is potentially valid at any light-matter interaction regime, ranging from the weak (where the decay rates exceeds the coupling rate) to the deep strong coupling (where the interaction rate exceeds the bare transition frequencies of the subsystems). However, when reaching the ultrastrong coupling regime, several theoretical issues may prevent the correct description of the observable dynamics of such a system: (i) the standard quantum optics master equation fails to correctly describe the interaction of this system with the reservoirs; (ii) the correct output photon rate is no longer proportional to the intracavity photon number; and (iii) they appear to violate gauge invariance. Here, we study the photon flux emission rate of this system under the incoherent excitation of the two-level atom for any light-matter interaction strength and consider different effective temperatures. The dependence of the emission spectra on the coupling strength is the result of the interplay between energy levels, matrix elements of the observables, and the density of states of the reservoirs. Within this approach, we also study the occurrence of light-matter decoupling in the deep strong-coupling regime and show how all of the obtained results are gauge invariant.
With the aid of supercomputer models we numerically investigate the exact solutions for a small number of atoms (typically 1–10) interacting with a single quantized mode of an electromagnetic cavity that is driven by an external coherent field. Effects of spontaneous emission and a nonzero cavity decay rate are included. We investigate the strong coupling regime where the atom-field coupling constant is much greater than the dissipation rates to the external environment. In this regime, the usual system size expansions of quantum statistical physics are not applicable and a full numerical solution is required. We model the recently reported experimental observations of Rabi oscillations in the second order coherence function1 g(2)(τ) and compare and contrast the results with an effective single atom-cavity model with an appropriately scaled coupling constant. In addition, the steady state field distribution for the few-atom-cavity system is explored. A multipeaked phase distribution is found that generalizes the bimodal phase distribution found in the single-atom-cavity case.2 Spectra for the few-atom-cavity system are investigated in the weak and strong driving field limits.