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International Journal of Physical Research

Quantum non-demolition measurement in the interferometer

Dmitri L. Khokhlov

Published Jan 1, 2021• 1 citation
Publisher

Abstract

The schemes of the arrangements based on the Mach-Zehnder interferometer and the interferometer with two polarizing beam splitters are considered. The interferometers in both the schemes are equipped with some devices, creating a Kerr medium, to perform the quantum non-demolition measurement of a single photon. Such a device gives which way information of the photon while preserving the work of the interferometer.

DOI
10.14419/ijpr.v9i1.31243

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The schemes of the arrangements based on the Mach-Zehnder interferometer and the interferometer with two polarizing beam splitters are considered. The interferometers in both the schemes are equipped with some devices, creating a Kerr medium, to perform the quantum non-demolition measurement of a single photon. Such a device gives which way information of the photon while preserving the work of the interferometer.
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We have theoretically and experimentally studied how a Mach-Zehnder interferometer with an additional mirror transforms a light beam composed of the second lowest transverse modes, HG10,{\mathrm{HG}}_{10},HG10​, HG01,{\mathrm{HG}}_{01},HG01​, LG01,{\mathrm{LG}}_{01},LG01​, and ${\mathrm{LG}}_{0\ensuremath{-}1}$ (HG denotes Hermite-Gaussian mode; LG denotes Laguerre-Gaussian mode). In certain conditions, the interferometer divides the incident beam into the HG10{\mathrm{HG}}_{10}HG10​ and HG01{\mathrm{HG}}_{01}HG01​ components as a transverse-mode beam splitter. We propose a practical device involving the two interferometers for quantum cryptography, in which a photon carries two bits corresponding to the polarization and the transverse mode.
Abstract The superposition states, allowed by quantum theory, are dramatically diverse with respect to classical states and represent the true quantum states. By using a Mach-Zehnder interferometer we experimentally show how a single photon in a polarization superposition state can produce interference. The experimental setup includes a strongly attenuated laser source, polarizing beam splitters, half-waveplates, polarizers and single-photon detectors. The experimental activity has been performed with high-school students and teachers in several different contexts.
The role of decoherence of an electromagnetic field in the process of quantum nondemolition measurement of the number of photons using a nonlinear Mach-Zehnder interferometer is investigated. This decoherence is caused by distributed losses in a Kerr medium. A long interaction time between the field and the medium is required to achieve a high accuracy in the photon number measurement. The losses in the Kerr medium accompanying the resonance four-wave interaction between the measured and the probe fields lead to a measurement error close to unity at γτ ≫1 (γ is the rate of losses in the medium, and τ is the time of interaction between the field and the medium); consequently, nondemolition quantum measurement turns out to be impossible in the scheme considered. Under these conditions, an increase in the intensity of the probe field does not result in achievement of the required measurement accuracy.
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.