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Physical Review A

Squeezed states in multiple atomic fluorescence

M. Artoni, Roberta Marani

Published Sep 1, 1996• 1 citation
Publisher

Abstract

We study the propagation of squeezing in the resonance fluorescence from a two-atom system within the weak-field approximation. We show that squeezing occurs in the fluorescence from both atoms, although with different falloff in time. \textcopyright{} 1996 The American Physical Society.
DOI
10.1103/physreva.54.2280

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We examine squeezing properties of resonance fluorescence from two interacting atoms. Previous theoretical analyses of this model have predicted squeezing on one-photon resonance. Here we show that it is possible to obtain squeezing in two-atom resonance fluorescence through two-photon transitions induced by a cooperative atomic interaction. The squeezing occurs near a two-photon resonance and is not sensitive to the duration of the detection time in comparison with the decay time of the subradiant state. Moreover, squeezing near a two-photon resonance is completely independent of the direction of observation in respect to the atomic axis and can be significantly larger than that previously found on one-photon resonance.
It is shown that a squeezing pattern is produced in resonance fluorescence from NNN atoms distributed at regular positions. The squeezing pattern has twice the periodicity of the ordinary diffraction pattern. Directions in which squeezed coherent states are observed alternate with directions in which squeezed vacuum states occur. The squeezing effect is NNN times stronger than in resonance fluorescence from a single atom.
Phase-sensitive squeezing in the resonance fluorescence of two-level atoms, that are coherently driven by a near-resonant laser field in free space, was observed recently (Lu et al 1998 Phys. Rev .L ett. 81 3635). This was accomplished via homodyne detection at a phase near ±45 ◦ relative to the driving field for strong off-resonant excitation of ‘long-lived’ atoms (where th ea tomic lifetime far exceeded the laser–atom interaction time, meaning that relaxation effects could be ignored). On the other hand, traditional theoretical predictions of phase-sensitive squeezing in the resonance fluorescence from two-level atoms have emphasized in- and out-of-phase (i.e., 0 ◦ and 90 ◦ ) quadratures, and weak, on-resonant excitation of ‘short-lived’ atoms (where the observation time for laser–atom interaction fa re xceeded the natural atomic lifetime, meaning that relaxation effects dominate). Here, we calculate the probability of a delayed-coincidence detection in the interference field of a fluorescing dipole with a local oscillator (LO). We show that, despite the strikingly different conditions in which squeezing occurs in short- and long-lived atoms, squeezing in both cases can be shown to arise from a joint detection of two photons which are related by a quantum jump in the following way: the first photodetection precipitates a quantum jump of the atom to the ground state, and the second measures the mean amplitude of the fluorescent field subsequent to the quantum jump.
We study how the spectral properties of resonance fluorescence propagate through a two-atom system. Within the weak-driving-field approximation we find that, as we go from one atom to the next, the power spectrum exhibits both subnatural linewidth narrowing and large asymmetries while the noise spectrum of the squeezed quadrature narrows but remains otherwise unchanged. Analytical results for the observed spectral features of the fluorescence are provided and their origin is thoroughly discussed.