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International Journal of Modern Physics B

SCATTERING OF ATOMS BY LIGHT: MEASURING THE QUANTUM STATE OF THE FIELD IN A CAVITY

Guilherme Colherinhas, Agnaldo Rosa de Almeida, Marta João Francisco Silva Souza, Arthur M. Moraes, CELIA M. A. DANTAS

Published Jan 30, 2006• 0 citations
Publisher

Abstract

This work consists in a generalization of the developed method to measure the quantum state of the field in a cavity with all non null coefficients, in the number representation, through one photon interaction. We present a strategy to measure the quantum state of the field when it has all non-null coefficients or only even or odd coefficients through a two-photons atom-field interaction.

DOI
10.1142/s0217979206033231

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This work consists in a generalization of the developed method to measure the quantum state of the field in a cavity with all non null coefficients, in the number representation, through one photon interaction. We present a strategy to measure the quantum state of the field when it has all non-null coefficients or only even or odd coefficients through a two-photons atom-field interaction.
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 present various schemes for measuring the quantum state of a single mode of the electromagnetic field. These involve measuring the photon statistics for the mode before and after an interaction with either one or two two-level atoms. The photon statistics conditioned on the final state of the atoms, for two choices of the initial set of atomic states, along with the initial photon statistics, may be used to calculate the complete quantum state in a simple manner. Alternatively, when one atom is used, two unconditioned sets of photon statistics, each after interaction with a single atom in different initial states, along with the initial photon statistics may be used to calculate the initial state in a simple manner. When the cavity is allowed to interact with just one atom, only pure cavity states which do not contain zeros in the photon distribution may be reconstructed. When two atoms are used we may reconstruct pure states which do not contain adjacent zeros in the photon distribution. Coherent states and number states are among those that may be measured with one-atom interaction, and squeezed states and ‚Schrödinger cats‘ are among those that may be measured with a two-atom interaction.
The photon number parity is a binary observable playing an important role in the description of the non-classical features of light. In microwave experiments, this observable can be measured by using a single Rydberg atom evolving in a two dimension space and interacting dispersively with a field stored in one or two cavities. The procedure, based on atomic interferometry, maps the field parity (+ 1 or − 1) onto the states of the two-level atom. By performing repeated measurements of the field parity, it is possible to observe field quantum jumps, to reconstruct the complete Wigner function of an arbitrary field and to study how it evolves due to decoherence.