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Physical Review A

Squeezed vacuum as an accelerator of revivals in the Dicke model

M. Kozierowski, S. M. Chumakov

Published Nov 1, 1995• 5 citations
Publisher

Abstract

A two-level atom interacting with a single-mode squeezed vacuum cavity field does not manifest collapses and revivals of the oscillations [Milburn, Opt. Acta 31, 671 (1984)]. Here we show that the dynamic response of the inversion of an assemblage of A two-level atoms to such a field (Dicke model) may be qualitatively different. The dynamic properties of the model with an initial squeezed vacuum field differ from those for coherent or thermal fields, which have been stressed in the title.

DOI
10.1103/physreva.52.4293

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When the displacement and squeeze parameters for a squeezed coherent state are chosen appropriately, the squeezed state has an oscillatory photon number distribution P(n). Schleich and Wheeler1 have shown that the oscillations arise from the interference between contributions to P(n) from two regions in phase space where an elongated error ellipse, characterizing the squeezed coherent state, overlaps the annuli characterizing the number states. We study the Jaynes-Cummings model for the interaction of a two-level atom with a single mode of the radiation field when the radiation field is initially in such a squeezed coherent state. Revivals of the atomic inversion occur which have a quite different appearance from those produced when the radiation field is initially In a coherent state.2 Each revival is followed by a series of echoes—a phenomenon we call ringing revivals. We discuss the relationship between these echoes and the oscillations in P(n). There is a one-to-one correspondence between echoes and the peaks in P(n); however, interference between the contributions to the inversion from different peaks in P(n) plays an important role in forming the ringing structure of the revivals.

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A two-level atom interacting with a single-mode squeezed vacuum cavity field does not manifest collapses and revivals of the oscillations [Milburn, Opt. Acta 31, 671 (1984)]. Here we show that the dynamic response of the inversion of an assemblage of A two-level atoms to such a field (Dicke model) may be qualitatively different. The dynamic properties of the model with an initial squeezed vacuum field differ from those for coherent or thermal fields, which have been stressed in the title.
The resonant interaction of A initially unexcited two-level atoms with different quantum fields in a high-Q single-mode cavity (Dicke model) is studied analytically in one of the limits in which the eigenvalues spectrum of the model may be assumed as equidistant. The time evolution of atomic inversion of a single two-level atom coupled to squeezed vacuum or thermal cavity fields (Jaynes-Cummings model) is irregular. Here we show that the dynamical response of the inversion of an assemblage of A two-level atoms to such fields may be regular, i.e., may reveal collapses and revivals and that the properties of the model with an initial squeezed vacuum field differ from those for coherent or thermal fields.
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.
We study the resonant interaction of A initially unexcited two-level atoms with single-mode Fock, coherent and thermal cavity fields of arbitrary intensity. Two mechanisms lead to a spread of the eigenfrequencies: one is due to the photon-number distribution in the initial state and the other reflects the cooperativity of the system. Both affect the evolution of the photon number and photon statistics. We present approximate expressions for the eigenvalues and eigenvectors of the system. Its regular dynamical regions are found and the difference in shape of the collapses and revivals connected with the above mechanisms is discussed.
When the displacement and squeeze parameters for a squeezed coherent state are chosen appropriately, the squeezed state has an oscillatory photon number distribution P(n). Schleich and Wheeler1 have shown that the oscillations arise from the interference between contributions to P(n) from two regions in phase space where an elongated error ellipse, characterizing the squeezed coherent state, overlaps the annuli characterizing the number states. We study the Jaynes-Cummings model for the interaction of a two-level atom with a single mode of the radiation field when the radiation field is initially in such a squeezed coherent state. Revivals of the atomic inversion occur which have a quite different appearance from those produced when the radiation field is initially In a coherent state.2 Each revival is followed by a series of echoes—a phenomenon we call ringing revivals. We discuss the relationship between these echoes and the oscillations in P(n). There is a one-to-one correspondence between echoes and the peaks in P(n); however, interference between the contributions to the inversion from different peaks in P(n) plays an important role in forming the ringing structure of the revivals.