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Journal of Modern Optics

Quantum non-demolition measurements using cold atoms in an optical cavity

Alice Sinatra, Jean-François Roch, K. Vigneron, Philippe Grelu, J.-Ph. Poizat, Philippe Grangier

Published Oct 1, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1080/09500349708231859

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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.
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We have investigated possible implementations of optical quantum nondemolition measurements, using rubidium atoms in a magneto-optical trap as a nonlinear medium. Using a $\ensuremath{\Lambda}$-type three-level system in the D1 line of 87Rb{}^{87}\mathrm{Rb}87Rb, the observed performances are quantitatively the best obtained so far for a single back action evading measurement. Moreover, the magneto-optical trap and the quantum nondemolition effect are both running continuously at the same time and mutual perturbations have been avoided by using a ``dark spot'' technique. This experiment demonstrates clearly the interest of using cold atoms for controlling the quantum fluctuations of light.
We discuss some theoretical and experimental aspects of quantum non-demolition (QND) measurements in the optical domain. The efficiency of a QND measurement can be characterized using three criteria, which describe respectively the quality of the quantum measurement, the non-destruction of the signal, and the conditional variance of the output signal beam, given the output meter beam (quantum-state-preparation criterion). Quantitative limits can be defined with respect to these criteria, delimiting "classical" and "quantum" domains of operation. We describe the implementation of two experiments which fulfill these criteria, using either three-level atoms inside a doubly-resonant optical cavity, or semiconductors emitters and receivers.
This thesis investigates the generation of atomic spin-squeezed states by quantum non-demolition (QND) measurements in a high-finesse optical cavity. Cold atom interferometry has demonstrated state of the art performance for the measurement of tiny rotations, accelerations and time. The sensitivity of atom interferometers has already reached the atomic shot noise level, a limit that could be overcome by the use of non-classical atomic states. In this context, we developed a crossed high-finesse cavity resonating both at 1560 nm and 780 nm. Laser light at 1560 nm injected in the cavity generates a far off resonance optical dipole trap where Rb 87 cold atoms are loaded from a magneto-optical trap. The lifetime of the atoms in this dipole trap is limited by the residual background collisions, indicating that further evaporation process should be effective. The concepts of QND measurement are introduced and a wavefunction formalism that describes the spin-squeezing dynamics of the atomic state is discussed. This formalism is applied to practical measurement apparatus that are the Mach-Zehnder interferometer and the heterodyne detection. Experimentally, this non-destructive measurement was implemented at 780 nm in a frequency modulation scheme strongly immune to noise. The influence of this non-demolition probe on the atomic sample has been characterized in single pass and this tool has been applied to follow in real time the state of atomic interferometers. In addition to this work, a narrow linewidth Raman laser suitable for high precision spectroscopy was implemented with cold atoms as the gain medium.
We present a theoretical study of the quantum non-demolition (QND) measurement of an optical intensity in an atomic three-level system, using a quantum linear response theory recently developed. The principle of this scheme is to use the two-photon crossed-phase- modulation effect, in order to couple the quantum intensity fluctuations of the `signal' beam to the quantum phase fluctuations of the `meter' beam. The predictions of the complete theory are compared with recent experimental results using a sodium atomic beam, which include the observation of both squeezing and QND effects.