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Physical Review A

Cooperative effects in a system of strongly driven three-level atoms

S. V. Lawande, B. N. Jagatap

Published Jan 1, 1989• 10 citations
Publisher

Abstract

Cooperative effects in a system of three-level atoms in cascade configuration interacting with intense resonant fields are investigated. Analytical expressions for atomic populations in the excited levels, fluorescence intensities, and normalized intensity correlations are presented. The intensity correlations are used to test the violation of the Cauchy-Schwarz inequalities. The analytical results predict in the cooperative limit N\ensuremath{\rightarrow}\ensuremath{\infty}, a discontinuous behavior of all atomic observables with respect to a parameter related to the field amplitudes and the atomic decay coefficients. This discontinuous behavior is analogous to a typical nonequilibrium first-order phase transition.

DOI
10.1103/physreva.39.683

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Cooperative effects in a system of three-level atoms in cascade configuration interacting with intense resonant fields are investigated. Analytical expressions for atomic populations in the excited levels, fluorescence intensities, and normalized intensity correlations are presented. The intensity correlations are used to test the violation of the Cauchy-Schwarz inequalities. The analytical results predict in the cooperative limit N\ensuremath{\rightarrow}\ensuremath{\infty}, a discontinuous behavior of all atomic observables with respect to a parameter related to the field amplitudes and the atomic decay coefficients. This discontinuous behavior is analogous to a typical nonequilibrium first-order phase transition.
Atomic ensembles strongly interacting with light constitute rich quantum-optical many-body systems, with the potential for observing cooperative effects and dissipative nonequilibrium phase transitions. We theoretically analyze the conditions under which a driven atomic ensemble in free space, characterized by strong dipole-dipole interactions and large spatial extent, can undergo a superradiant phase transition, also known as cooperative resonance fluorescence. In an atomic array, stationary states that conserve the collective pseudospin exhibit completely cooperative decay and undergo a second-order phase transition in the large atom number limit. In contrast, decay mechanisms on longer timescales that fail to conserve pseudospin can lead to discontinuous first-order phase transition at a critical finite atom number, disrupting cooperation despite sharing many similar observable characteristics. A hallmark of the superradiant phase transition is an abrupt shift from total light reflection off the atoms to rapidly increasing transmission, accompanied by significant quantum fluctuations, as a function of light intensity.
We examine the various two-time fluorescence intensity correlations emitted by a driven three-level atom in a cascade configuration. For a strongly driven atom, the two intensity autocorrelation functions, one from the upper transition, the other from the lower transition, exhibit different behaviors. In addition to the an oscillation similar to the two-level intensity correlation we find an additional oscillation for the upper transition only. This is shown to be due to the spontaneous decay between the lower transition levels. \textcopyright{} 1996 The American Physical Society.
Atoms strongly interacting with light constitute rich quantum-optical systems with the potential for observing cooperative effects and dissipative nonequilibrium phase transitions. We analyze the conditions under which a driven atomic array, characterized by strong dipole–dipole interactions and a large spatial extent, can undergo a superradiant phase transition, also known as cooperative resonance fluorescence. We find that the array can exhibit completely cooperative decay that conserves the collective pseudospin, resulting in a second-order quantum phase transition, with a key hallmark being an abrupt shift from total light reflection by the atoms to rapidly increasing transmission and significant quantum fluctuations. We compare the results with decay mechanisms that fail to conserve pseudospin, leading to a discontinuous first-order phase transition at a critical finite atom number.
We have performed a numerical calculation for the excitation spectra arising from the interaction of a three-level atom in the lambda configuration with a strong electromagnetic field whose frequency mode is initially populated. The excitation spectra are considered for equal detunings, which refer to the cooperative two-photon resonance process, as well as for different detunings. The computed cooperative two-photon resonance spectra are compared with those derived by analytical methods. In the presence of different detunings, conditions are established under which the laser field induces sidebands at the frequency equal to that for the forbidden transition. Numerical calculations for a wide range of Rabi frequencies and detunings are presented graphically. Detailed discussion of the computed spectral intensities is given and a comparison is made between the spectra of three-level atoms in the lambda and cascade configurations.