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Annual Meeting Optical Society of America

Squeezed slate generation for two-level atoms in a spatially varying field mode

Min Xiao, H. Jeffrey Kimble, H. J. Carmichael

Published Jan 1, 1987• 0 citations
Publisher

Abstract

Squeezed state generation for a system of two-level atoms interacting with the field of a high-finesse cavity has been extensively discussed both experimentally and theoretically in recent years. Most theories describing these systems take the cavity field as a plane traveling wave for simplicity. With this assumption it is quite difficult to make quantitative comparisons between theory and recent experiments. However, by employing the formalism developed in Ref. 1, we are able to treat rather general spatial variations of the intracavity field subject to the constraint of the good-cavity limit of optical bistability. Squeezed state generation for the three particular examples of a plane-wave ring interferometer, a Gaussian-mode ring cavity, and a plane-wave field in a standing-wave interferometer are considered to illustrate the formalism. Somewhat surprisingly, in regimes for which the plane-wave theory predicts 50-70% squeezing (cooperatively C ~102–103), the standing-wave structure produces only modest reductions in the squeezing (a few percent), while the radial variations of the field reduce the squeezing by ~10%.

DOI
10.1364/oam.1987.mq7

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Squeezed state generation for a system of two-level atoms interacting with the field of a high-finesse cavity has been extensively discussed both experimentally and theoretically in recent years. Most theories describing these systems take the cavity field as a plane traveling wave for simplicity. With this assumption it is quite difficult to make quantitative comparisons between theory and recent experiments. However, by employing the formalism developed in Ref. 1, we are able to treat rather general spatial variations of the intracavity field subject to the constraint of the good-cavity limit of optical bistability. Squeezed state generation for the three particular examples of a plane-wave ring interferometer, a Gaussian-mode ring cavity, and a plane-wave field in a standing-wave interferometer are considered to illustrate the formalism. Somewhat surprisingly, in regimes for which the plane-wave theory predicts 50-70% squeezing (cooperatively C ~102–103), the standing-wave structure produces only modest reductions in the squeezing (a few percent), while the radial variations of the field reduce the squeezing by ~10%.
A spatially varying field mode is included in calculating the squeezing effect for a system of two-level atoms in the good-cavity limit. Two examples of a Gaussian mode field in a ring cavity and a plane-wave field in a standing-wave interferometer are used to demonstrate the quite general method. In qualitative terms, the squeezing predicted for plane waves is preserved. However, for a given value of atomic cooperativity parameter C, there is a degradation in squeezing because of the spatially varying field structure.
We investigate the effect of a spatially varying field mode on the squeezing generated by two-level atoms interacting with a single mode of an optical cavity. The mode structure is incorporated into a quantum theory that does not employ adiabatic elimination of field or atomic variables. Thus we are able to consider the regime in which cavity and atomic decay rates are approximately equal as well as the good- and bad-cavity limits. Calculations show that squeezing is reduced by the inclusion of a Gaussian transverse mode profile and a standing-wave structure for a particular value of atomic cooperativity C. The model is consistent with recent measurements of squeezing. The degree of squeezing reduction depends on the ratio of cavity and atomic damping rates, in the regime where they are similar in size.
A theoretical and experimental investigation of the generation of squeezed states of light has been carried out for a system of two-level atoms inside a high-finesse cavity. The regime that we consider is such that the coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom-field system (the so-called vacuum-field Rabi splitting). We have employed this splitting to generate squeezing with observed reductions in photocurrent noise of 30 % below the shot-noise level. A degree of squeezing of ~50% is inferred for the field state in the absence of propagation and detection losses. Squeezing has been observed in two different cavity geometries with quite different coupling coefficients. In each case, the frequency of best squeezing corresponds to that of the normal mode splitting g N (g= single atom coupling coefficent and N = number of atoms) in good agreement with our theoretical predictions. Regions of parameter space with very large degrees of squeezing (>20×) are identified. Preliminary extensions of the theory into a transient regime with (cavity lifetime) ≪ (interaction time) ≪ (atomic lifetime) are described.
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.
A new regime for the generation of squeezed states of the electromagnetic field is described for a collection of atoms within a high-finesse cavity. The process responsible for squeezing is a coupling-induced splitting in the normal-mode structure of the atom-field system. A theoretical analysis is presented that predicts large degrees of squeezing for modest operating conditions. An experimental investigation of this regime has produced noise reductions of 30% relative to the vacuum noise level.
An extension of the quantum theory of the atom-field interaction within a high-finesse resonator is made to include spatial variations of the field mode in the limit of small cavity decay rate. The two particular examples of a Gaussian mode field in a ring cavity and a plane-wave field in a standing-wave interferometer are presented to illustrate the method. Analytic expressions are obtained for the incoherent intensity and photon correlations of the transmitted field. In qualitative terms, effects such as sub-Poissonian photon statistics predicted by the plane-wave theory in a ring cavity are preserved. In either the weak-field or dispersive limit the results of the plane-wave theory in a ring cavity are recovered independent of the form of the spatial dependence of the cavity mode.