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Physical Review A

Three-level approach to squeezing with cold atoms

Antonio Zelaquett Khoury, T. Coudreau, Claude Fabre, E. Giacobino

Published Jun 1, 1998• 4 citations
Publisher

Abstract

We report on recent theoretical and experimental developments on the problem of quantum noise reduction in a laser beam interacting with a cloud of cold atoms. We have used a three-level model for the trapped atoms which allows a more realistic treatment of the problem including the effects of the trapping and repumping beams. Moreover, we have observed squeezing under stable conditions and our experimental results are in good agreement with the theoretical model developed.

DOI
10.1103/physreva.57.4770

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We report on recent theoretical and experimental developments on the problem of quantum noise reduction in a laser beam interacting with a cloud of cold atoms. We have used a three-level model for the trapped atoms which allows a more realistic treatment of the problem including the effects of the trapping and repumping beams. Moreover, we have observed squeezing under stable conditions and our experimental results are in good agreement with the theoretical model developed.
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Light and atoms couple together via the electromagnetic interaction. The simplest form of this interaction is the electric dipole interaction, and in its quantised form it provides a useful starting point for the investigation of quantum effects in optics. Two examples of quantum noise manipulation of the light field due to interaction with atoms will be presented, as well as an analysis of a simple model for laser cooling of trapped atoms. The first example of quantum noise manipulation is the investigation of a quantum non-demolition measurement scheme based on a three-level atomic system in the ladder configuration. An effective two-level model of the atomic system is used, which enables the inclusion of spontaneous emission noise from the upper atomic level. The system is found to perform well, when detuned far from resonance. The second example is the treatment of squeezing in the intensity difference between two modes coupled by a three-level atomic system in the ladder configuration. The noise correlations are similar to those occurring in the optical parametric oscillator, and give rise to good squeezing when the system is well detuned from the intermediate level. The simple model of laser cooling consists of a single two-level atom with quantised centre-of-mass motion constrained to move in a one-dimensional harmonic potential while interacting with a single-mode classical travelling light field. It is shown that there is an analogy between this model and the Jaynes-Cummings model. This gives rise to interesting coherent effects including quantum collapses and revivals in the atomic inversion. Sideband cooling occurs for this model when the light field is tuned to the atom's first lower vibrational sideband. The strong sideband and Lamb-Dicke perturbation regimes are defined. Analytic results have previously been obtained for the latter regime, but we carry out a numerical investigation of the steady state and time evolution behaviour in the former regime. Differences in the behaviour in the two regimes are discussed. Finally the possibility of observing quantum jumps between trap levels is discussed.
The theory of an atom dipole trap composed of a focused, far red-detuned, trapping laser beam, and a pair of red-detuned, counterpropagating, cooling beams is developed for the simplest realistic multilevel dipole interaction scheme based on a model of a (3+5)-level atom. The description of atomic motion in the trap is based on the quantum kinetic equations for the atomic density matrix and the reduced quasiclassical kinetic equation for atomic distribution function. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with low saturation, the one-photon absorption (emission) processes responsible for the trapping potential can be well separated from the two-photon processes responsible for sub-Doppler cooling atoms in the trap. Two conditions are derived that are necessary and sufficient for stable atomic trapping. The conditions show that stable atomic trapping in the optical dipole trap can be achieved when the trapping field has no effect on the two-photon cooling process and when the cooling field does not change the structure of the trapping potential but changes only the numerical value of the trapping potential well. It is concluded that the separation of the trapping and cooling processes in a pure optical dipole trap allows one to cool trapped atoms down to a minimum temperature close to the recoil temperature, keeping simultaneously a deep potential well.
In this paper we present a theoretical analysis of a recent quantum non-demolition experiment in optics using cold atoms in a magneto-optical trap as a nonlinear medium. A signal beam and a meter beam from two independent lasers are coupled within a A-type three-level scheme in the D1 line of 87Rb atoms. The experimental results for the relevant quantum correlations of the fields represent up to now the best achievement for a single back-action evading measurement. Moreover, they are found to be in remarkably good agreement with the theoretical predictions from a fully quantum model for three-level atoms in a doubly resonant cavity.