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Physical Review A

Quantum nondemolition measurements using a crossed Kerr effect between atomic and light fields

J.-Y. Courtois, Jean-Michel Courty, Serge Reynaud

Published Aug 1, 1995• 12 citations
Publisher

Abstract

We analyze the coupling between the fluctuations of an atomic beam incident on an evanescent wave mirror and the fluctuations of the laser beam producing the evanescent potential barrier. We show that this coupling is equivalent to a crossed Kerr effect between an atomic field and a light field, and that the consistency of the theory requires that both fields be subject to symmetrical commutation relations and quantum fluctuations. We show in particular that the phase shift undergone by the light field during the atomic reflection process permits a quantum nondemolition measurement of the incident atomic intensity.

DOI
10.1103/physreva.52.1507

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We analyze the coupling between the fluctuations of an atomic beam incident on an evanescent wave mirror and the fluctuations of the laser beam producing the evanescent potential barrier. We show that this coupling is equivalent to a crossed Kerr effect between an atomic field and a light field, and that the consistency of the theory requires that both fields be subject to symmetrical commutation relations and quantum fluctuations. We show in particular that the phase shift undergone by the light field during the atomic reflection process permits a quantum nondemolition measurement of the incident atomic intensity.
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.
We calculate the reflection probability for ultracold atoms incident on an evanescent-wave atomic mirror, and analyze the optimum conditions to observe quantum reflection. We find that averaging over the Gaussian profile of the laser beam dramatically reduces the quantum signature, and consider the effects of an appropriate aperture that limits the variation of beam intensity. We show that quantum reflection is particularly sensitive to details of the atom-surface potential, and could be used to resolve retardation effects.
The parity of photonic number states is known to be an important observable for quantized electromagnetic fields with applications to quantum information processing and to Heisenberg-limited measurement of phase shifts in quantum interferometry performed with maximally entangled states and with twin number states. In this paper we describe an approach to the quantum nondemolition measurement of parity for quantized optical fields. The method proposed involves the use of a cross-Kerr interaction where we assume a large Kerr nonlinearity is available through the techniques of electromagnetically induced transparency. Our proposed method does not require the measurement of photon number but rather measures parity directly. The method not only allows for the quantum nondemolition measurement of parity but also allows for the von Neumann projection of parity eigenstates from an arbitrary field state. The generation and detection of higher-order parity eigenstates is also discussed. Losses from dissipation and the effects of detector efficiency are considered.
According to quantum mechanics, there exists a class of observables for which is possible to confine the perturbation produced by a continuous measurement to the conjugate variable. Therefore, it is possible to devise experimental schemes that allow estimating the observed variable with arbitrary accuracy, or preparing it in a well-known state. Such schemes are referred to as quantum non-demolition measurements (QND). Among these observables there is the amplitude of the light field. Indeed, it is possible to exploit a movable mirror to implement a QND scheme [1]. Intensity fluctuations of an optical field impinging on it are not affected by the interaction. However, the movable mirror is excited by the associated radiation pressure. This, in turn, affects the phase of the field.
We present a detailed analysis of the quantum-nondemolition (QND) properties of a measurement scheme employing coherently driven three-level atoms in the \ensuremath{\Lambda} or cascade configuration inside an optical cavity. We propose to use a strong signal field to empty one of the transitions and dress the signal-transition levels. The atoms become transparent for the signal beam, which sees a ``ghost transition.'' When a probe is applied and tuned to the vicinity of one of the light-shifted levels, the probe phase is extremely sensitive to fluctuations of the signal intensity. This enhances the QND coupling and enables the system to operate at lower cooperativities.
Conventional devices for measuring the amplitude of a light wave absorb the light, thus destroying it. Recently, quantum nondemolition (QND) methods based on the optical Kerr effect have been shown capable of measuring optical amplitude fluctuations with near quantum-limited sensitivity.1 In these experiments, amplitude fluctuations of a signal beam are transferred to the phase fluctuation quadrature of a probe beam which co-propagates with the signal beam, by the intensity-dependent refractive index, without absorption of the signal beam. A pure Kerr nonlinearity can cause only phase modulation of the light wave, and the amplitude of the signal wave is preserved. Such methods should more properly be called back-action evading measurement schemes since the quantity being measured is not perturbed by the back-action that quantum mechanics requires for any measurement. The signal-to-noise ratio achieved in these experiments was limited by the small magnitude of the Kerr nonlinearity relative to the excess phase noise imposed on the probe beam by thermal light scattering processes in the glass fibers that were employed.