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Physical Review A

Parametric instability of a coupled atom-cavity system driven by a strong resonant pulse

G. M. Genkin

Published Apr 13, 2000• 0 citations
Publisher

Abstract

We investigate the behavior of a coupled atom-cavity system (a collection of two-level atoms inside a high-Q cavity) driven by a strong external resonant pulse. A different effect is predicted: parametric instability of a coupled atom-cavity system appears if the atomic number density in a cavity exceeds the threshold value that is proportional to the strong driving field. The increment of this instability is proportional to the atom-cavity coupling constant.

DOI
10.1103/physreva.61.055801

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We investigate the behavior of a coupled atom-cavity system (a collection of two-level atoms inside a high-Q cavity) driven by a strong external resonant pulse. A different effect is predicted: parametric instability of a coupled atom-cavity system appears if the atomic number density in a cavity exceeds the threshold value that is proportional to the strong driving field. The increment of this instability is proportional to the atom-cavity coupling constant.
We investigate the behaviour of the intracavity field in a strongly coupled atom–cavity system (a collection of two-level atoms inside a high-Q cavity) driven by a short strong external resonant pulse. A new effect is predicted, the amplification of the intracavity field appears if the atomic number density in a cavity exceeds the instability threshold which is proportional to the square of the strong driving field. The amplification gain is proportional to the amplitude of the strong driving field. The amplitude of the intracavity field in the vicinity of a critical point above the threshold is time-dependent modulated with harmonics of half of the Rabi frequency of the driving field.
We investigate the behavior of a two-component Bose-Einstein condensate (BEC) driven by a strong time-dependent resonant magnetic field. The external resonant field couples two hyperfine states via a one-photon transition. It is shown that a first-order parametric instability of a BEC appears if the local atomic number density exceeds a threshold value that is proportional to the driving field. It is shown that the spatial-dependent increment of instability is proportional to the square of the local atomic density. This instability is determined by the nonlinearity of the BEC associated with the short-range interactions between the atoms.
We study the quantum dynamics of an array of coherently driven two-level atoms coupled to an optical resonator. In the strong coupling regime the cavity field generated by atomic scattering interferes destructively with the pump on the atoms. In this configuration atomic excitation is suppressed even for strong driving fields, while the stationary intracavity field amplitude is almost independent of the atom number. The magnitude of this interference effect depends on the detuning between laser and cavity field and on the relative atomic positions and is strongest when the atoms are ordered in a wavelength spaced lattice placed at the antinodes of the cavity mode. In this case three dimensional intensity minima are created in the vicinity of each atom. We analyze the mechanical forces in the regime where the interference condition is fulfilled, and show that the atomic pattern is mechanically stable whenever the driving frequency is red detuned with respect to the cavity frequency, irrespective of the atomic transition frequency
We consider a composite system consisting of a degenerate optical parametric oscillator (DOPO) and a set of N homogeneously broadened two-level atoms. When the atoms are on or near resonance with the subharmonic-frequency field generated through the frequency down-conversion process, bistability appears in the intracavity field near the DOPO threshold. The bistability region will decrease as the detuning between the atomic transition frequency and the frequency of the subharmonic field increases. When the detuning becomes large enough, the atoms decouple from the cavity field and the system behaves like a normal DOPO. There are several features distinguishing this bistable behavior from the usual atomic optical bistability occurring with atoms in an optical cavity driven by an external field.
We study the nonlinear dynamics of the interaction of two-level atoms and a selected mode of a high- Q cavity with frequency modulation analytically and numerically. In the absence of modulation, the corresponding semiclassical Heisenberg equations for the expectation values of the collective atomic observables and the field-mode amplitudes allow, in the rotating wave approximation and in the strong-coupling limit, an exact solution with arbitrary detuning. Using this solution, we detect the coherent effect of trapping of the population of atomic levels and of trapping of the number of photons in the cavity. The explanation for this effect lies in the destructive interference of the atomic dipoles and the field mode. The integrable version of the system of equations exhibits a separatrix near which a stochastic layer is formed when modulation is introduced. The width of the layer is found to gradually increase with degree of modulation, and finally it fills the entire energy-permissible volume of the phase space. We show that the rotating wave approximation does not hinder the formation of Hamiltonian chaos in cavity semiclassical electrodynamics. The calculation of the maximum Lyapunov indices of nonlinear (in this approximation) equations of motion as functions of the modulation frequency δ and the frequency of natural Rabi oscillations of the atom-field system, Ω, suggests that Hamiltonian chaos appears first in the area of the fundamental parametric resonance, δ /2Ω≃1. Parametric instability increases with increasing modulation and decreasing detuning from the atom-field resonance, generating at exact resonance new areas of chaos corresponding to multiple parametric resonances. The results of numerical experiments and estimates of the characteristic parameters show that Rydberg atoms placed in a high- Q microwave cavity are possible objects for observing parametric instability and dynamical chaos.
We study an atom-cavity system composed of an ensemble of three-level atoms interacting with a high-finesse single-mode optical resonator. Two examples of physical models, the laser-driven $\ensuremath{\Lambda}$-type atomic system and the three-level ladder-type atomic system, are investigated in detail. By altering the collective atom-cavity dynamics via an intracavity optical parametric amplification process, a spin-boson model is realized when the composite system operates in the far-detuning regime. When the number of atoms exceeds a critical value, the quantum system undergoes a superradiant phase transition whose dependence on different experimentally adjustable parameters is explored in detail. The effects of the spontaneous emission of atoms and the cavity loss on the phase transition are considered, and measuring the cavity output field itself gives an experimental probe of the superradiant phase transition.