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Physical Review A

Squeezing in cooperative resonance fluorescence

Q. V. Lawande, S. V. Lawande

Published Jul 1, 1988• 8 citations
Publisher

Abstract

Cooperative effects on squeezing in resonance fluorescence from a finite number N of atoms are examined. Analytical expressions for the spectrum of squeezing and a quantity Q(T) related to the photon-counting statistics of the squeezed states are presented for N=1 and 2. These expressions are obtained by invoking the high-field approximation of the relevant master equation. The analytical results are supplemented by the numerical solutions of the exact master equation for N\ensuremath{\le}10. It is shown that for intense fields or large detunings, squeezing in resonance fluorescence is predominantly due to the quantum nature of the sidebands of the Mollow triplet. As a manifestation of cooperative effects, squeezing present in the total as well as the sideband radiation increases with the number of atoms. This is further confirmed from the behavior of the photon-statistics function Q(T).

DOI
10.1103/physreva.38.800

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Cooperative effects on squeezing in resonance fluorescence from a finite number N of atoms are examined. Analytical expressions for the spectrum of squeezing and a quantity Q(T) related to the photon-counting statistics of the squeezed states are presented for N=1 and 2. These expressions are obtained by invoking the high-field approximation of the relevant master equation. The analytical results are supplemented by the numerical solutions of the exact master equation for N\ensuremath{\le}10. It is shown that for intense fields or large detunings, squeezing in resonance fluorescence is predominantly due to the quantum nature of the sidebands of the Mollow triplet. As a manifestation of cooperative effects, squeezing present in the total as well as the sideband radiation increases with the number of atoms. This is further confirmed from the behavior of the photon-statistics function Q(T).
The photon-counting statistics of squeezed states in collective time-dependent resonance fluorescence is calculated for the homodyne detection technique. The secular approximation is applied to obtain analytical expressions for the photon-counting distribution produced by homodyning the fluorescent field and coherent radiation. Squeezing is shown to appear only in the transient regime of resonance fluorescence. The time location of squeezing is independent of the number of atoms, N, but squeezing increases with increasing N. Moreover, squeezing occurs only for a judicious choice of the phase of the local oscillator and occurs over long counting times T. The time interval T is strongly dependent on the initial atomic population. If initially all atoms are in their excited states, squeezing appears with a delay twice as long as that for initially nonexcited atoms.
Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak-field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. Heisenberg equations of motion are solved in the steady-state and analytic expressions for the fluorescent-light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed, and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation, the second-order intensity correlation function does not factorize. This and other differences are discussed, and curves are presented to illustrate the behavior of various quantities. We also present results for thermal excitation of the atom.
We report on the semiclassical solution of the Bloch equations for cooperative resonance fluorescence with collective damping. These equations are shown to be equivalent to the relevant master equation, in the limit of large cooperation number and time scales faster than the one-atom lifetime (reciprocal Einstein AAA coefficient). The resulting spectrum is derived for a coherent driving field of arbitrary intensity. Additional spectral peaks, as well as the central triplet, are predicted above threshold. A physical explanation of the extra peaks is proposed.
Resonance fluorescence from a single two-level atom driven by a beam of squeezed light is studied in the weak field limit. We consider the situation where the atom is coupled to the ordinary vacuum and only a few field modes corresponding to the driving field are squeezed. The field produced by the degenerate optical parametric oscillator is used as the driving field. This driving field can be described in terms of two real independent Gaussian processes. Heisenberg equations of motion are solved in the steady-state, and analytic expressions for the fluorescent light intensity and the spectrum of fluorescent light are derived. We also consider photon statistics of fluorescent light. In particular, squeezing, antibunching, and sub-Poissonian statistics of fluorescent photons are discussed and analytic expressions for the quadrature variance and the two-time intensity correlation function are presented. Contrary to the case of coherent excitation the second-order intensity correlation function does not factorize.
We study the statistical properties of fluorescence from a coherently driven two-level atom placed in a broadband squeezed vacuum. The photon statistics are studied in terms of waiting time distribution or the delay function that describes the probability of emission of the very next photon following an emission of a photon initially. In an intense field limit, we analytically obtain the delay function for total emission and examine its phase-dependent behavior in a squeezed vacuum. We further analytically calculate the delay functions for the Mollow sidebands and use them to discuss the time correlation and successive emission of photons belonging to the left and right sidebands.