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arXiv:1305.6460 · Journal of Physics B Atomic Molecular and Optical Physics

Optical bistability in strong-coupling cavity QED with a few atoms

A Dombi, A Vukics, P. Domokos

Published Nov 7, 2013• 29 citations
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Abstract

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)

DOI
10.1088/0953-4075/46/22/224010

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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)
In the strong coupling regime of cavity QED where the characteristic damping rates are orders of magnitude below the coherent coupling, resolved multi-photon resonances can be observed for strong enough driving strength. In a certain frequency range, the external coherent drive field hits multi-photon resonances which correspond to very high order transitions that cannot be excited at the given power of the driving field. We found that in this range the cavity field evolves into a robust semiclassical solution which is the mixture of the vacuum and an excited quasi-classical state. The system is reminiscent of optical bistability, however, here a single atom produces a telegraph signal for the outgoing intensity by switching between two states with large photon number difference. We calculate this behavior also for the Tavis-Cummings model representing three qubits in an existing circuit QED experimental setting.
The radiative properties of atoms inside an optical cavity can be dramatically changed with respect to those in free space. In the strong-coupling limit, the reversible dipole interaction between an atom and the cavity field dominates the irreversible decay resulting from spontaneous emission and cavity damping. In this limit the atom and field can no longer be regarded as separate quantities but instead form a composite dynamic system. To enhance the dipole coupling constant and increase the photon storage time, our experiments are performed with a small cavity 1 mm long, with a finesse of 8 × 104. On average, 0.4 photons are sufficient to saturate the resonance transition at 852 nm for the cesium atoms used, while the cooperativity parameter for a single atom is 2. Optical bistability is studied in this system over the range 3 < N < 65 atoms inside the cavity, with the semiclassical theory predicting bistability for N > 5. We report observations of manifestly quantum effects in this regime, including photon antibunching and sub-Poissonian photon statistics, with the magnitude of these nonclassical effects observed to be largely independent of the number of intracavity atoms.
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 analyze the Jaynes-Cummings model of quantum optics, in the strong-dispersive regime. In the bad-cavity limit and on time scales short compared to the atomic coherence time, the dynamics are those of a nonlinear oscillator. A steady-state nonperturbative semiclassical analysis exhibits a finite region of bistability delimited by a pair of critical points, unlike the usual dispersive bistability from a Kerr nonlinearity. This analysis explains our quantum trajectory simulations that show qualitative agreement with recent experiments from the field of circuit quantum electrodynamics.
We adapt the Jaynes-Cummings model to study the interface of cavity quantum electrodynamics with strong field and attosecond physics. We show how multi-photon resonances in the Jaynes- Cummings system driven by a strong low-frequency classical light field lead to the generation of highly non-classical, quantum-correlated harmonics of the classical driver. Our treatment assumes no approximations, apart from the typical Jaynes-Cummings model assumption of only a few discrete quantum modes of light. The paper is dedicated to Joseph Henry Eberly, whose remarkable research has left indelible mark on both strong field physics and quantum optics.