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Physical Review A

Conditional generation of special states using continuous measurements

Vlasta Peřinová, A. Lukš, J. Křepelka

Published Jul 1, 1996• 6 citations
Publisher

Abstract

The theory of continuous measurement of the photon number has been applied to a two-mode light field and it has been assumed that the second mode is being measured. An entanglement of the two-mode state has been supposed. The destructive and nondemolition continuous photon-number measurements have been compared according to their response in the first mode to the parameters of the quantum correlation and the detection time. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.821

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The theory of continuous measurement of the photon number has been applied to a two-mode light field and it has been assumed that the second mode is being measured. An entanglement of the two-mode state has been supposed. The destructive and nondemolition continuous photon-number measurements have been compared according to their response in the first mode to the parameters of the quantum correlation and the detection time. \textcopyright{} 1996 The American Physical Society.
A continuous photon-number measurement has been assumed in the idler mode output from parametric down-conversion for an initial coherent state. The states generated in the signal mode due to the mode entanglement and the effects of both the destructive and the ideal reduction are described in terms of a quasidistribution of the complex field amplitude as well as of the density-matrix elements. The resulting near-number states in the ideal case are suitable for the study of the dynamics of phase and quadrature distributions rotated by the actual preferred phase. These states exhibit both number and quadrature squeezing. \textcopyright{} 1996 The American Physical Society.
This paper presents a general theory for a continuous quantum-nondemolition measurement of photon number. This theory treats a time-distributed measurement as a sequence of measurements in which at most one photon can be detected in an infinitesimal time, and shows that the average number of photons remaining in the measured field increases when a photon is detected and decreases when no photon is detected. The state of the measured system evolves nonunitarily and reduces continuously to a nunber state whose eigenvalue is uniquely determined by the average rate of photodetection and whose probability distribution coincides with the initial photon-number distribution. Applying the general theory to typical quantum states---coherent, thermal, and squeezed states---shows that the continuous-state reduction towards a number state depends strongly on the initial photon statistics. Despite the nonunitarity of state evolution, an initially pure state keeps its purity: the initial density operator becomes diagonalized only if the readout information is discarded.
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.
A sufficient condition for entanglement in two-mode continuous systems is constructed with the interference visibility and the uncertainty of the total particle number. The observables to be measured (particle numbers and particle number variances) are relatively easily accessible experimentally. The method may be used to detect entanglement in light fields or in Bose-Einstein condensates. In contrast to the standard approach based on entanglement witnesses, the condition is expressed in terms of an inequality which is nonlinear in expectation values. The condition is constructed using uncertainty relations with the particle number and the destruction operators.