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Nonlinearities in the strong coupling regime of the Tavis-Cummings model: from multi-photon resonances to bistability

András Dombi, András Vukics, P. Domokos

Published Apr 30, 2014• 0 citations
OpenAlex

Abstract

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.

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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.
Current research in single-atom cavity quantum electrodynamics largely emphasizes the input-output properties of strongly coupled systems, from normal mode splitting to photon blockade. But over the last decade, experiments have, with few exceptions, focused on relatively weak driving conditions. This thesis concentrates on a range of quantum nonlinear phenomena in the strong driving regime. In particular, I discuss the observation of random-telegraph phase switching in the light transmitted through a Fabry-Perot resonator containing one strongly coupled atom and 10-100 photons, confirming long-standing predictions of a phenomenon known as single-atom phase bistability. These results highlight the relevance of cavity quantum electrodynamics in the development of attojoule nanophotonic logic and signal processing. In addition, I consider a general class of bifurcation phenomena that are manifest within this physical setting. Here, focus is placed on the investigation of quantum-classical correspondence near semiclassical bifurcation points.
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 interaction of an ensemble of NNN two-level quantum emitters with a single-mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by gN=Ng‾1{g}_{N}=\sqrt{N}{\overline{g}}_{1}gN​=N​g​1​, where g‾1{\overline{g}}_{1}g​1​ is the ensemble-averaged single-emitter coupling strength. This model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into noncavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive emitters. We show that the predictions of our cascaded model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.
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 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.