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Physical Review A

Generation of nonclassical photon states using correlated photon pairs and linear feedforward

Gunnar G. Bjork, Y. Yamamoto

Published Jun 1, 1988• 33 citations
Publisher

Abstract

It is shown that nonclassical photon states can be produced by generating correlated photon pairs, measuring the idler mode, and manipulating the signal mode using feedforward and linear attenuators, amplifiers, or phase modulators. The minimum achievable Fano factor for such schemes is (2/\ensuremath{\pi}〈n〉${)}^{1/2}$, where 〈n〉 is the mean output photon number. A nondegenerate parametric oscillator followed by linear manipulators can reach this limit. A nondegenerate parametric amplifier followed by linear phase manipulation can produce phase-squeezed states. The minimum achievable phase noise is a factor 1/2G below that of a coherent state, where G is the amplifier gain. The advantages with these schemes are wavelength tunability, potentially very high squeezing bandwidth, and relative simplicity.

DOI
10.1103/physreva.37.4229

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It is shown that nonclassical photon states can be produced by generating correlated photon pairs, measuring the idler mode, and manipulating the signal mode using feedforward and linear attenuators, amplifiers, or phase modulators. The minimum achievable Fano factor for such schemes is (2/\ensuremath{\pi}〈n〉)1/2{)}^{1/2})1/2, where 〈n〉 is the mean output photon number. A nondegenerate parametric oscillator followed by linear manipulators can reach this limit. A nondegenerate parametric amplifier followed by linear phase manipulation can produce phase-squeezed states. The minimum achievable phase noise is a factor 1/2G below that of a coherent state, where G is the amplifier gain. The advantages with these schemes are wavelength tunability, potentially very high squeezing bandwidth, and relative simplicity.
We analyze an intensity feedforward scheme to produce a sub-Poissonian (amplitude-squeezed) light beam from the intensity-correlated twin beams generated by a nondegenerate parametric amplifier. Photon-number measurement of the idler beam at the output of the parametric amplifier is linearly fed forward onto the output signal beam using an amplitude modulator. The minimum available Fano factor is shown to be 1/(2g-1), where g is the parametric amplifier gain, and is equal to the nonclassical intensity-noise-reduction factor of the twin beams at the output of the parametric amplifier. By changing the frequency of the input-signal beam, tunable sub-Poissonian light can be generated with this scheme for application in precision absorption spectroscopy.
We analyze an optical-phase feed-forward scheme to produce a squeezed-light beam from intensity-correlated twin beams generated by nondegenerate parametric amplification. The quadrature measurement of the idler beam at the output of the parametric amplifier is linearly fed forward onto the output signal beam with an electro-optic phase modulator. The minimum available squeezing factor is shown to be 1/(2g - 1), where g is the parametric amplifier gain, and is equal to the nonclassical intensity-noise reduction factor of the original twin beams at the output of the parametric amplifier. By changing the frequency of the input signal beam, one can generate tunable squeezed light with this scheme for application in precision spectroscopy.
Noise spectra of the in-phase and quadrature-phase components of the signal and idler fields of a nondegenerate optical parametric amplifier are calculated. It is shown that, as is suggested by the operator Manley-Rowe relations, the external in-phase (amplitude) fluctuations of the signal and idler fields are correlated in the frequency region lower than the signal and idler cavity bandwidths. If the idler photon flux is continuously measured and the photocurrent fluctuations are fed back to control the pump intensity, the signal output will feature an amplitude noise spectral density reduced to below the standard quantum limit (amplitude squeezing) in the frequency region below the feedback loop and signal and idler cavity bandwidths. An all-optical realization of such a negative-feedback parametric oscillator is presented. It is also shown that a nondegenerate parametric amplifier with idler measurement feedback can add a fixed number of photons to a photon-number state.
We show that a continuous range of nonclassical states of light can be generated using conditional measurements on the idler mode of an optical parametric amplifier. The output state is prepared by introducing a coherent state in the signal mode of the amplifier with a single photon in the idler mode, followed by a conditional measurement of a single photon in the output idler mode. By varying the gain of the amplifier, this approach can produce a coherent state, a photon-added state, a displaced number state, or a continuous range of other nonclassical states with intermediate properties. We note that this approach can generate a photon-added state even though the postselected amplifier does not add any photons to the signal or idler modes. The ability to generate a continuous range of nonclassical states may have practical applications in quantum information processing.
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.
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.