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Journal of Modern Optics

State Reduction for Correlated Photons and Eigenstates of Unitarily and Non-unitarily Displaced Number Operator

A. Lukš, Vlasta Peřinová, J. Křepelka

Published Dec 1, 1994• 20 citations
Publisher

Abstract

The number-quadrature minimum-uncertainty states after rotation and displacement emerge in the parametric down-conversion followed by photon number measurement in the idler mode when the coherent state inputs. Again, the state generated in the signal mode by the reduction is described by the principally measurable quantum-statistical tools.

DOI
10.1080/09500349414552181

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The number-quadrature minimum-uncertainty states after rotation and displacement emerge in the parametric down-conversion followed by photon number measurement in the idler mode when the coherent state inputs. Again, the state generated in the signal mode by the reduction is described by the principally measurable quantum-statistical tools.
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.
Signal and idler waves produced by a nondegenerate parametric amplifier feature strong positive correlation between their photon numbers, or in-phase amplitudes. They feature equally strong negative correlation between their phases, or quadrature-phase amplitudes. These photon twins can produce arbitrarily squeezed states via state reduction by appropriate measurements of an idler wave. When the quadrature amplitude of an idler wave is measured, the signal wave is collapsed to a quadrature-amplitude squeezed state. When the two-quadrature amplitudes of an idler wave are measured simultaneously, the signal wave becomes a coherent state.
The difference between the two nonclassical photon states, i.e., the squeezed state and the number-phase minimum-uncertainty state, is discussed. Four different generation principles for number-phase minimum-uncertainty states (and number states) are described. They are the following: (1) unitary evolution, using self-phase modulation and interference; (2) nonunitary state reduction, using either quantum nondemolition photon-number measurement or parametrically amplified idler-wave photon counting; (3) negative-feedback oscillators, incorporating a correlated photon-pair generator; and (4) pump-amplitude noise-suppressed lasers. A number-phase minimum-uncertainty state with photon-number noise reduced to 1 dB (20%) below the standard quantum limit in a frequency range over 100 MHz was produced by the fourth-generation principle.
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.