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Physical Review A

Amplitude-phase multistability in multiatomic optical systems

S. Ya. Kilin, T. B. Krinitskaya

Published Nov 1, 1993• 13 citations
Publisher

Abstract

The effect of amplitude-phase multistability in the Dicke model inside a coherently driven cavity is discussed for the case of large Rabi frequencies and a small rate of atomic decay, compared with the decay of the cavity mode. The quantum and semiclassical interpretations of the predicted effect are given on the basis of the Tavis-Cummings model and a proposed model of weakly coupled harmonic oscillators. The analytical solution is obtained for a two-atom system. The possibility of observing amplitude-phase multistability is also considered.

DOI
10.1103/physreva.48.3870

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The effect of amplitude-phase multistability in the Dicke model inside a coherently driven cavity is discussed for the case of large Rabi frequencies and a small rate of atomic decay, compared with the decay of the cavity mode. The quantum and semiclassical interpretations of the predicted effect are given on the basis of the Tavis-Cummings model and a proposed model of weakly coupled harmonic oscillators. The analytical solution is obtained for a two-atom system. The possibility of observing amplitude-phase multistability is also considered.
The Tavis-Cummings model (the Dicke model treated in the rotating-wave approximation), describing many two-level systems coupled to a single bosonic mode, has been long known to show collective semiclassical oscillations when prepared in an inverted state, with all two-level systems excited and the bosonic mode is empty. This paper discusses how the quantum dynamics approaches this semiclassical result for large numbers of two-level systems, focusing on how the eigenvalues approach their semiclassical limit. The approach to the semiclassical result is found to be slow, scaling like a power of the logarithm of the system size. Considering also the effect of weak detuning between the two-level system and the bosonic field, quantum corrections are again found to decay slowly with system size, such that for a fixed detuning, the quantum effects of detuning are greater than the classical effect.
Resonant interaction of a collection of two-level atoms with a single-mode coherent cavity field is considered in the framework of the Dicke model. We focus on the role of collective atomic effects in the phenomenon of collapses and revivals of the Rabi oscillations. It is shown that the behavior of the system strongly depends on the initial atomic state. In the case of the initial half-excited Dicke state we account for a number of interesting phenomena. The correlations between the atoms result in a suppression of the revival amplitude, and the revival time is halved, compared to the uncorrelated fully excited and ground states. The phenomenon of squeezing of the radiation field in the atom-field interaction is also discussed. For the initial fully excited and ground atomic states, the field is squeezed on the short-time scale, and squeezing can be enhanced by increasing the number of atoms. Some empirical formulas are found which describe the behavior of the system in excellent agreement with numerical results. For the half-excited Dicke state, the field can be strongly squeezed on the long-time scale in the case of two atoms. This kind of squeezing is enhanced by increasing the intensity of the initial coherent field and is of the same nature as revival-time squeezing in the Jaynes-Cummings model. The appearance of this long-time squeezing can be explained using the factorization approximation for semiclassical atomic states.
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.
Motivated by experiments observing self-organization of cold atoms in optical cavities, we investigate the collective dynamics of the associated nonequilibrium Dicke model. The model displays a rich semiclassical phase diagram of long-time attractors including distinct superradiant fixed points, bistable and multistable coexistence phases, and regimes of persistent oscillations. We explore the intrinsic time scales for reaching these asymptotic states and discuss the implications for finite-duration experiments. On the basis of a semiclassical analysis of the effective Dicke model, we find that sweep measurements over 200 ms may be required in order to access the asymptotic regime. We briefly comment on the corrections that may arise due to quantum fluctuations and states outside of the effective two-level Dicke model description.
By modelling the coupling of multiple superconducting qubits to a single cavity in the circuit-quantum electrodynamics (QED) framework we find that it should be possible to observe superradiance and phase multistability using currently available technology. Owing to the exceptionally large couplings present in circuit QED, we predict that superradiant microwave pulses should be observable with only a very small number of qubits (just three or four), in the presence of energy relaxation and non-uniform qubit–field coupling strengths. This paves the way for circuit-QED implementations of superradiant state readout and decoherence free subspace state encoding in subradiant states. The system considered here also exhibits phase multistability when driven with large field amplitudes, and this effect may have applications for collective qubit readout and for quantum feedback protocols.
The hybrid quantum system of cold atomic gas and optical cavity can host many exotic phenomena including phase transitions and multistabilities. In this Letter, we investigate the effect of photon hopping between two Dicke cavities and show rich quantum phases for steady states and dynamic processes. Starting from a generic dimer system where the two cavities are not necessarily identical, we analytically obtain all possible steady-state phases and confirm their existence by numerical calculations. We then focus on the special case where the two cavities are identical, where exact solutions of all phases are obtained. Our results suggest that photon hopping is a convenient and powerful tool to manipulate the quantum phases and induce multistable behavior in this system.