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Physical Review A

Generation of atomic-squeezed states in an optical cavity with an injected squeezed vacuum

Arup Banerjee

Published Dec 1, 1996• 13 citations
Publisher

Abstract

We study the generation of atomic-squeezed states in an optical cavity. The cavity encloses a pair of two-level atoms and is coupled to a broadband squeezed vacuum. Using the bad-cavity limit, cavity field is adiabatically eliminated to obtain the equations of motion for collective atomic operators. These equations are then employed to obtain the atomic density-matrix elements and to study the generation of atomic-squeezed states in the steady state. To characterize atomic-squeezed states we use the squeezing parameter defined recently by Wineland et al. [Phys. Rev. A 46, 6797 (1992)] for spectroscopic purposes. The aforementioned parameter is also compared with the squeezing parameter obtained from the uncertainty principle satisfied by the collective atomic operators. We show that in a cavity arrangement, unlike free space, atomic-squeezed states can be generated only for a restricted range of values of the parameters \ensuremath{\lambda} and N which characterize the cavity and the squeezed field driving the cavity, respectively. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.5327

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We study the generation of atomic-squeezed states in an optical cavity. The cavity encloses a pair of two-level atoms and is coupled to a broadband squeezed vacuum. Using the bad-cavity limit, cavity field is adiabatically eliminated to obtain the equations of motion for collective atomic operators. These equations are then employed to obtain the atomic density-matrix elements and to study the generation of atomic-squeezed states in the steady state. To characterize atomic-squeezed states we use the squeezing parameter defined recently by Wineland et al. [Phys. Rev. A 46, 6797 (1992)] for spectroscopic purposes. The aforementioned parameter is also compared with the squeezing parameter obtained from the uncertainty principle satisfied by the collective atomic operators. We show that in a cavity arrangement, unlike free space, atomic-squeezed states can be generated only for a restricted range of values of the parameters \ensuremath{\lambda} and N which characterize the cavity and the squeezed field driving the cavity, respectively. \textcopyright{} 1996 The American Physical Society.
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.
We study the two-photon excitation rate and the spectrum of a three-level atom in the \ensuremath{\Xi} configuration interacting with a resonant cavity mode which is coupled to a broadband squeezed vacuum through its input-output mirror. We show that the optical Bloch equations in the cavity environment are formally identical to these in free space but, in the bad-cavity limit, with cavity-modified parameters describing the injected squeezed vacuum. It is shown that the two-photon excitation rate (which is proportional to the upper-level population) has two components, one depending linearly and the other quadratically on the squeezed photon number N, in excellent agreement with experiment [Georgiades et al., Phys. Rev. Lett. 75, 3426 (1995)]. The presence of the term quadratic in N is entirely due to the effectively imperfect correlation of the squeezed photon pairs in the bad cavity. We also find that the two-photon excitation spectrum (as measured by the fluorescent emission from the upper level to the intermediate level) exhibits an extremely narrow peak at line center, under appropriate choices of the bad-cavity parameters. All these results are independent of the squeezed phase. \textcopyright{} 1996 The American Physical Society.
Abstract We analyze the generation of spin-squeezed states via coupling of three-level atoms to an optical cavity and continuous quantum measurement of the transmitted cavity field in order to monitor the evolution of the atomic ensemble. Using analytical treatment and microscopic simulations of the dynamics, we show that one can achieve significant spin squeezing, favorably scaling with the number of atoms N. However, contrary to some previous literature, we clarify that it is not possible to obtain Heisenberg scaling without the continuous feedback that is proposed in optimal approaches. In fact, in the adiabatic cavity removal approximation and large N limit, we find the scaling behavior N − 2 / 3 for spin squeezing and N − 1 / 3 for the corresponding protocol duration. These results can be obtained only by considering the curvature of the Bloch sphere, since linearizing the collective spin operators tangentially to its equator yields inaccurate predictions. With full simulations, we characterize how spin-squeezing generation depends on the system parameters and departs from the bad cavity regime, by gradually mixing with cavity-filling dynamics until metrological advantage is lost. Finally, we discuss the relevance of this spin-squeezing protocol to state-of-the-art optical clocks.
As a realistic system for observing the distinctive features of the interaction of squeezed light with atoms, we consider a single, coherently driven, two-level atom in a resonant optical cavity coupled to a broadband squeezed vacuum field. In the bad cavity limit we derive equations of motion for the atomic operators that are identical to those for the free-space situation, except for having modified parameters. We focus our attention on the resonance fluorescence from this system and show that, in the above limit, many of the unusual spectral features previously reported for the free atom situation persist. We also confirm the link between these anomalous spectra and the collapse of an atom into a pure state. The cavity parameter values needed to verify some of these interesting effects appear to be within the range of present day technology. \textcopyright{} 1996 The American Physical Society.
We consider a two-level atom in an optical cavity driven by a coherent field and coupled to broadband squeezed vacuum. In the bad-cavity limit, the cavity field can be adiabatically eliminated, leaving equations of motion for atomic operators similar to those of free-space resonance fluorescence. We calculate the incoherent spectrum of the fluorescent light field and find that the cavity-enhanced spontaneous emission can be suppressed, and a subnatural linewidth obtained, for the correct choice of the phase of the squeezed input relative to the coherent driving field.
Experiments to generate squeezed states of light are described for a collection of two-level atoms within a high-finesse cavity. The investigation is conducted in a regime for which the weak-field coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom–field system that is large compared with the atomic linewidth. Reductions in photocurrent noise of 30% (−1.55 dB) below the noise level set by the vacuum state of the field are observed in a balanced homodyne detector. A degree of squeezing of approximately 50% is inferred for the field state in the absence of propagation and detection losses. The observed spectrum of squeezing extends over a very broad range of frequencies (~±75 MHz), with the frequency of best squeezing corresponding to an offset from the optical carrier given by the normal mode splitting.