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Journal of Modern Optics

Phase Destruction and Quantum Non-demolition Measurement of Photon Number by Atomic Beam Deflection

Ulrike Herzog, Th. Richter

Published Mar 1, 1994• 5 citations
Publisher

Abstract

It is found by computer simulation that in the atomic beam deflection experiment proposed by Holland et al. to perform a quantum non-demolition measurement of the photon number, the rate of entropy decrease owing to the transition to a Fock state depends in a quasi-periodic way on the interaction parameter. Moreover, a simple analytic expression is derived for the decay of the off-diagonal field density matrix elements. With the help of this expression the phase destruction of the field due to the measurement process is investigated.

DOI
10.1080/09500349414550531

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It is found by computer simulation that in the atomic beam deflection experiment proposed by Holland et al. to perform a quantum non-demolition measurement of the photon number, the rate of entropy decrease owing to the transition to a Fock state depends in a quasi-periodic way on the interaction parameter. Moreover, a simple analytic expression is derived for the decay of the off-diagonal field density matrix elements. With the help of this expression the phase destruction of the field due to the measurement process is investigated.
The decay of the off-diagonal elements of the density matrix for the field that accompanies the quantum non-demolition measurement, recently proposed by Brune et al (Phys. Rev. Lett., vol.65, p.976, 1990) of the number of photons present in a microwave cavity, is studied. Averaging over the time of flight of the atoms, a simple estimate of the number of atoms needed for a precise measurement, is found. It agrees well with the result obtained by Brune et al by numerically simulating the measurement, and, moreover, allows a determination, in a systematic manner, of the optimum values for the relevant physical parameters.
When atoms are illuminated by an off-resonant field, the AC Stark effect will lead to phase shifts in atomic states. The phase shifts are proportional to the photon number of the off-resonant illuminating field. By measuring the atomic phase with newly developed atom-light hybrid interferometers, we can achieve quantum non-demolition measurement of the photon number of the optical field. In this paper, we analyze theoretically the performance of this QND measurement scheme by using the QND measurement criteria established by Holland et al [Phys. Rev. A 42, 2995 (1990)]. We find the quality of the QND measurement depends on the phase resolution of the atom-light hybrid interferometers. We apply this QND measurement scheme to a twin-photon state from parametric amplifier to verify the photon correlation in the twin beams. Furthermore, a sequential QND measurement procedure is analyzed for verifying the projection property of quantum measurement and for the quantum information tapping. Finally, we discuss the possibility for single-photon-number-resolving detection via QND measurement.
We consider the deflection of a resonant two-level atom by a quantized electromagnetic field using the Jaynes-Cummings Hamiltonian. We show that a joint measurement of the atomic momentum and an appropriate field variable allows us to reconstruct the original photon statistics even for this demolition Hamiltonian. We demonstrate that the momentum distribution of atoms scattered at the nodes of the standing wave also follows the original photon statistics of the field. In this sense a recent experiment on the optical Stern-Gerlach effect [T. Sleator et al., Phys. Rev. Lett. 68, 1996 (1992)] measures the intensity fluctuations of the standing wave.
This paper proposes a realistically feasible experiment, within the realm of existing technology and proved techniques, to measure the mean photon number of a coherent source by means of a quantum non-demolition scheme, exploiting the parametric amplification of correlated photons in χ (2) media. We deduce the number of photons of an input source interacting with a high-intensity pump field in a nonlinear crystal, using as the probe the shift in the quadrature amplitude of the pump beam induced by the source under measurement. We perform a theoretical evaluation of the noise level associated with this measurement and compare it with the quantum limit. We explore the possible implications of this method for radiometry.
We discuss some theoretical and experimental aspects of quantum non-demolition (QND) measurements in the optical domain. The efficiency of a QND measurement can be characterized using three criteria, which describe respectively the quality of the quantum measurement, the non-destruction of the signal, and the conditional variance of the output signal beam, given the output meter beam (quantum-state-preparation criterion). Quantitative limits can be defined with respect to these criteria, delimiting "classical" and "quantum" domains of operation. We describe the implementation of two experiments which fulfill these criteria, using either three-level atoms inside a doubly-resonant optical cavity, or semiconductors emitters and receivers.