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Journal of Optics B Quantum and Semiclassical Optics

Quantum nondemolition measurement of the photon number usingΛ-type atoms

Andrey B. Matsko, Yuri V. Rostovtsev

Published Apr 5, 2002• 2 citations
Publisher

Abstract

We study a force acting on a three-level Λ -type atom in an inhomogeneous coherent electromagnetic field. We show that the magnitude of the force as well as incoherent scattering of the field is comparable with that of a two-level atom. Using Λ -type three-level atoms, one is able to realize a new kind of quantum nondemolition measurement of a photon number of modes of an open optical cavity.

DOI
10.1088/1464-4266/4/3/303

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We study a force acting on a three-level Λ -type atom in an inhomogeneous coherent electromagnetic field. We show that the magnitude of the force as well as incoherent scattering of the field is comparable with that of a two-level atom. Using Λ -type three-level atoms, one is able to realize a new kind of quantum nondemolition measurement of a photon number of modes of an open optical cavity.
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.
We describe the optimum detection procedure to follow in order to measure by atomic interferometry the number of photons present in a cavity by using a Quantum nondemolition scheme. The method we discuss is the one recently introduced by Brune et al. [1, 2], in which the field intensity is detected by recording atomic interferences in a Ramsey type set up. A succession of two-level atoms interacts with the cavity field which is the analog of a birefringent retarding plate for the atomic wave function. The information is acquired in the form of binary digits (atoms detected in one level or the other). We discuss an optimal strategy which yields the value of the photon number with a number of atoms of the order of the base 2 logarithm of the field photon number dispersion. The procedure described here is the one we intend to use in an experiment in preparation.
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.
Semi-quantum or full-quantum electromagnetically induced transparency has been fully studied for three-level atoms in a weak field approximation method, where probe field is very wea ker than the coupling field. The weak field approximation is no t valid in full-quantum model where the number of coupling photons is not so large. In the present article, the master equations for the interaction of two-mode photons with a three-level Λ -type atom are exactly solved and the exact dispersion and absorption spectra for the probe beam photons are also obtained analytically. The results of the exact scheme are compared with the corresponding results in the weak field approximation method in full-quantum and semi-classi cal models.