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Physical Review A

Quantum correlation and state reduction of photon twins produced by a parametric amplifier

Kimitaka Watanabe, Y. Yamamoto

Published Oct 1, 1988• 43 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.38.3556

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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.
It has been known for a while that coherent high-intensity photon number eigenstate fields can be generated through nonlinear optical parametric processes,1 the same ones that give rise to quadrature squeezing.2,3 In contrast to quadrature squeezing which is essentially a single-mode phenomenon, although it is widely misunderstood that it is a two-mode phenomenon, the generation of single-mode number states through three- or four-wave mixing depends on two separate signal and idler modes that are perfectly correlated in photon numbers, in other words a twin beam. The nature of such twin beams is elucidated in both the Schrodinger and the Heisenberg pictures. In particular, it is shown that strong photon number correlation in a twin beam can still be obtained in an amplifier rather than an oscillator configuration, another widely missed point.
For measurements describable by a discrete set of possibilities, numerous demonstrations of the violation of Bell's inequalities have been reported in optical physics based on observations of polarization correlations for photon pairs. By contrast for observables with a continuous spectrum, there appears to be no general inequalities corresponding to those of Bell and no experimental realization of the original Einstein-Podolsky-Rosen paradox. Following Reid and Drummond,1 we are attempting to demonstrate the EPR paradox in the context of the measurement of continuous quantum variables with a subthreshold optical parametric oscillator operated in a frequency degenerate but polarization nondegenerate mode. In this case, the EPR paradox is formulated in terms of two sets of quadrature phase amplitudes for the spatially separated signal and idler fields. As the parametric gain is increased toward threshold, the quadrature amplitudes of the signal and idler beams become increasingly faithful quantum copies of one another. Our measurements of quadrature amplitudes are carried out using independent balanced homodyne detectors at two sites. When operated for the detection of squeezing at one site, noise reductions of 4 dB relative to the vacuum state limit are observed, which is most encouraging since noise reductions >3 dB in the difference photocurrent from the two sites are sufficient for inference at a distance of a signal observable from a measurement of the corresponding idler variable.
Twin beams generated from a nondegenerate optical parametric amplifier (NOPA) of gaing possess1 an intensity correlation that falls below the quantum limit by (2g – 1). This occurs whenever the input idler to the NOPA is in the vacuum state. Such input is practically advantageous because it makes the NOPA output intensities phase insensitive. When a non-vacuum idler input state is chosen, the NOPA output intensities become phase sensitive. For a proper input state and a suitable pump phase the output intensity correlation falls below the quantum limit by ( g + g − 1 ) 2 , which is 3 dB superior to the vacuum-idler-input result for g >> 1 and is equivalent to the quantum-noise reduction obtainable from a squeezed state generated with the same gain. Thus the sensitivity improvement achievable with NOPA twin beams by using direct detection is equivalent to that obtainable with squeezed states by using homodyne detection. The above equivalence also provides a new scheme for the generation of pulsed squeezed light that, in addition to being simple, automatically generates a matched local oscillator2 for homodyne detection of the squeezed pulses.
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.
The signal and idler beams from a non-degenerate, above threshold, optical parametric oscillator have a strong quantum correlation, which are called twin beams. This correlation arises from the simultaneous generation of the signal and idler photons in the form of twin pairs of photons through the parametric down conversion, and the generated twin beams have exactly the same photon statistics. As a result, the fluctuations on the difference between the intensities of the twin beams are reduced with respect to the shot noise limit, that is, intensity-difference squeezing. We give a comprehensive overview of the generation of twin beams using the optical parametric oscillator, and the applications exploiting the quantum correlation of twin beams are presented.
The bright Einsten-Podolsky-Rosen (EPR) beams with the quantum correlations between the quadrature-phase amplitudes of the spatially separated signal and idler beams have been experimentally generated from a cw nondegenerate optical parametric amplifier injected by seed waves with degenerate frequency but orthogonal polarization. The correlation degree of $0.853\ifmmode\pm\else\textpm\fi{}0.004$ between the quadrature-phase amplitudes of the output entangled beams is directly inferred from the measured quadrature-phase squeezing of the output vacuum squeezed-state light field formed from superposition of the original signal and idler modes. Our theoretical calculation and experimental measurements provide a reliable method to confirm the quadrature phase-squeezing and EPR correlation of bright light field.