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Journal of Physics Conference Series

Quantum Control of the States of Light in a Mach-Zehnder Interferometer

Z Blanco-Garcia

Published May 26, 2017• 1 citation
Publisher

Abstract

The experiment proposed by Elitzur and Vaidman is modified by replacing the fully absorbing obstacle (the 'bomb') with a non-linear optical medium. In this form the involved Mach-Zehnder interferometer works as a quantum beam splitter that produces NOON states which can be controlled if the input is the appropriate linear combination of two-mode Fock states.

DOI
10.1088/1742-6596/839/1/012021

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The experiment proposed by Elitzur and Vaidman is modified by replacing the fully absorbing obstacle (the 'bomb') with a non-linear optical medium. In this form the involved Mach-Zehnder interferometer works as a quantum beam splitter that produces NOON states which can be controlled if the input is the appropriate linear combination of two-mode Fock states.
The familiar input-output relations for an optical beam splitter are generalized to allow for linear absorption by the medium forming the mirror. Beam-splitter losses generally affect the noise levels detectable in experiments involving nonclassical light. When employed to investigate two-photon interference effects, a lossy beam splitter can lead to apparent nonlinear absorption, which, in the most extreme case, leads to either both or neither of the photons being absorbed. The degree of second-order coherence of antibunched light can be maintained on transmission through the beam splitter but any amplitude squeezing in the incident light is degraded.
NOON states (states of the form ∣N>a∣0>b+∣0>a∣N>b|N>_{a}|0>_{b}+|0>_{a}|N>_{b}∣N>a​∣0>b​+∣0>a​∣N>b​ where aaa and bbb are single particle states) have been used for predicting violations of local realism (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state Bose-Einstein condensates as sources in a modified Mach-Zehnder interferometer can lead to the creation of the NOON state in which aaa and bbb refer to arms of the interferometer and NNN is a subset of the total number of particles in the two condensates. The modification of the interferometer involves making {}"side" measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter if the phase states are orthogonal. When they are not orthogonal, a {}"feedforward" correction circuit is shown to convert them into proper form so a NOON results. We apply the NOON to the measurement of phase. Here the NOON experiment is equivalent to one in which a large molecule passes through two slits. The NOON components can be recombined in a final beam splitter to show interference.
States of the form $|N\ensuremath{\rangle}{}_{a}|0\ensuremath{\rangle}{}_{b}+|0\ensuremath{\rangle}{}_{a}|N\ensuremath{\rangle}{}_{b}$, where aaa and bbb are single-particle states---i.e., NOON states---have been used for predicting violations of local realism (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock-state Bose-Einstein condensates as sources in a modified Mach-Zehnder interferometer can lead to creation of the NOON state in which aaa and bbb refer to arms of the interferometer and NNN is a subset of the total number of particles in the two condensates. The modification of the interferometer involves making ``side'' measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter if the phase states are orthogonal. When they are not orthogonal, a ``feed-forward'' correction circuit is shown to convert them into proper form so that a NOON results. We apply the NOON to the measurement of phase. Here the NOON experiment is equivalent to one in which a large molecule passes through two slits. The NOON components can be recombined in a final beam splitter to show interference.