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arXiv:quant-ph/9805060 · Physical Review A

Dynamics of decoherence in continuous atom-optical quantum nondemolition measurements

Roberto Onofrio, Lorenza Viola

Published Jul 1, 1998• 18 citations
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Abstract

The Lindblad approach to continuous quantum measurements is applied to a system composed of a two-level atom interacting with a stationary quantized electromagnetic field through a dispersive coupling, fulfilling quantum nondemolition criteria. Two schemes of measurements are examined. The first one consists of measuring the atomic electric dipole, which indirectly allows one to infer the photon distribution inside the cavity. The second one schematizes a measurement of photon momentum, which permits one to describe the atomic level distribution. Decoherence of the corresponding reduced density matrices is studied in detail for both cases, and its relationship to recent experiments is finally discussed.

DOI
10.1103/physreva.58.69

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The Lindblad approach to continuous quantum measurements is applied to a system composed of a two-level atom interacting with a stationary quantized electromagnetic field through a dispersive coupling, fulfilling quantum nondemolition criteria. Two schemes of measurements are examined. The first one consists of measuring the atomic electric dipole, which indirectly allows one to infer the photon distribution inside the cavity. The second one schematizes a measurement of photon momentum, which permits one to describe the atomic level distribution. Decoherence of the corresponding reduced density matrices is studied in detail for both cases, and its relationship to recent experiments is finally discussed.
We propose a quantum nondemolition measurement of the photon-number distribution for a two-mode cavity field. In the scheme two sequences of two-level atoms interact dispersively with the respective cavity modes and resonantly with two classical fields, and then are detected continually. The field finally reduces to a two-mode Fock state. The probability of collapsing to a given Fock state is determined by the initial photon-number distribution. The scheme can be easily generalized to a field with N modes.
We propose a technique for quantum nondemolition (QND) measurement and heralded preparation of Fock states by dynamics of electromagnetically induced transparency (EIT). An atomic ensemble trapped in an optical cavity is driven by two external continuous-wave classical fields to form EIT in steady state. As soon as a weak coherent field is injected into the cavity, the EIT system departs from steady state, falls into transient state dynamics by the dispersive coupling between cavity injected photons and atoms. Because the imaginary part of time-dependent linear susceptibility Im[X(t)] of the atomic medium explicitly depends on the number n of photons during the process of transient state dynamics, the measurement on the change of transmission of the probe field can be used for QND measurement of small photon number, and thus create the photon Fock states in particular single-photon state in a heralded way.
We consider two modes of the electromagnetic field interacting via a three-level atom in a ladder configuration. We calculate the squeezing spectra of the sum and difference of the two output beams. The usefulness of this system as a quantum-nondemolition-measurement scheme is analyzed and a prediction is made using the parameters of a recent experiment by Grangier et al. [Phys. Rev. Lett. 66, 1418 (1991)]. We use a full three-level model in the most general case and in particular the influence of both the one-photon and the two-photon detunings are investigated.
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.
A common experimental setup in cavity quantum electrodynamics consists of a single two-level atom interacting with a single mode of the electromagnetic field inside an optical cavity. The cavity is externally driven and the output is continuously monitored via homodyne measurements. We derive formulas for the optimal rates at which these measurements provide information about (i) the quantum state of the system composed of atom and electromagnetic field, and (ii) the coupling strength between atom and field. We find that the two information rates are anticorrelated.