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Chinese Physics Letters

Minimum Uncertainty States for Number-Difference-Phase Uncertainty Relation in NFM Operational Phase Description

Fan Hong‐Yi, Zhihu Sun

Published Apr 1, 2000• 0 citations
Publisher

Abstract

For the Noh, Fougères and Mandel (NFM) operational quantum phase description, which is based on an eight-port homodyne-detection, we derive the minimum uncertainty states for the number-difference-phase uncertainty relation. The derivation makes full use of the newly constructed | q , r ⟩ representation which is the common eigenvector of the two-mode photon number-difference a † a - b † b and ( a + b † )( a † + b ).

DOI
10.1088/0256-307x/17/4/002

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For the Noh, Fougères and Mandel (NFM) operational quantum phase description, which is based on an eight-port homodyne-detection, we derive the minimum uncertainty states for the number-difference-phase uncertainty relation. The derivation makes full use of the newly constructed | q , r ⟩ representation which is the common eigenvector of the two-mode photon number-difference a † a - b † b and ( a + b † )( a † + b ).
For the two-mode photon number-difference operator D = a†a -b†b and the Noh, Fougers and Mandel (NFM) operational phase operator [Formula: see text], we introduce the concept of number-difference-phase squeezing. We then find a new minimum-uncertainty state for number-difference-phase squeezing, which turns out to be a special combination of generalized SU(1,1) coherent state. As a by-product, a new orthonormal and complete representation in two-mode Fock space made up of R†n|m, m> is found.
Number-phase minimum uncertainty states and number states are shown to be realized by quantum nondemolition measurements of the photon number. Interphase modulation in a Kerr medium establishes a quantum-mechanical correlation between the signal and probe waves initially in coherent states. State reduction is realized by homodyne detection of a probe quadrature-phase amplitude. The number uncertainty can be arbitrarily reduced by increasing the probe intensity. The minimum uncertainty relation between the number and sine operators approximately holds until a near-number state is realized.