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Physical Review A

Detection of squeezed states by cross correlation

Z. Y. Ou, C. K. Hong, L. Mandeļ

Published Jul 1, 1987• 30 citations
Publisher

Abstract

A new method for detecting a squeezed state by coincidence counting or cross correlation of the signals from two photodetectors is proposed. The two light beams falling on the two detectors are obtained from the two outputs of a homodyne beam splitter, whose inputs are the squeezed light and the local oscillator beam. With fast detectors the squeezing gives rise to excess photon coincidence counts. When a spectral analysis of the photoelectric currents is made, squeezing shows up as a positive cross correlation between the two signals, whereas unsqueezed light always produces negative correlations. Although the technique does not always cause the effects of local oscillator fluctuations to cancel out, as does the method of Yuen and Chan [Opt. Lett. B8R, 177 (1983)], they cancel in special cases, and the method has the advantage of being largely unaffected by detector after-pulsing. A simple combination of autocorrelation and cross-correlation measurements yields the degree of squeezing.

DOI
10.1103/physreva.36.192

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A new method for detecting a squeezed state by coincidence counting or cross correlation of the signals from two photodetectors is proposed. The two light beams falling on the two detectors are obtained from the two outputs of a homodyne beam splitter, whose inputs are the squeezed light and the local oscillator beam. With fast detectors the squeezing gives rise to excess photon coincidence counts. When a spectral analysis of the photoelectric currents is made, squeezing shows up as a positive cross correlation between the two signals, whereas unsqueezed light always produces negative correlations. Although the technique does not always cause the effects of local oscillator fluctuations to cancel out, as does the method of Yuen and Chan [Opt. Lett. B8R, 177 (1983)], they cancel in special cases, and the method has the advantage of being largely unaffected by detector after-pulsing. A simple combination of autocorrelation and cross-correlation measurements yields the degree of squeezing.
Based on proposals to measure squeezing by homodyne cross correlation [Ou, Hong, and Mandel, Phys. Rev. A 36, 192 (1987)] and by homodyne intensity correlation measurements with a weak local oscillator [Vogel, Phys. Rev. Lett. 67, 2450 (1991)], the method of homodyne correlation measurements is considered in detail for the case of weak local oscillators. Aside from the feasibility of measuring squeezing in low efficiency detection, it appears possible to record the correlation of the noise of two noncommuting observables, namely, the intensity and the electric field strength of the signal field. The separation of the different contributions to the measured correlations is considered and spectral correlation measurements are analyzed. Local oscillator noise, which is not balanced out in such a scheme, is found to be attenuated effectively by decreasing the local oscillator field. In particular, in the homodyne cross correlation scheme, it is of interest to use a beam splitter that significantly differs from a 50%:50% partition.
Certain two-time correlation functions of squeezed optical fields and their Fourier conjugates are investigated. These functions are related to the autocorrelation function and the spectral density of the photoelectric current that appears in measurements made of the squeezed light by a homodyne technique. Because the field is often assumed to contain a monochromatic carrier, it is only quasi-stationary, and modified quantum correlation functions, specially constructed to be time independent, are used to describe its properties. The symmetries of the corresponding conjugate spectral functions, which are not always spectral densities, are investigated. The concepts of homogeneous squeezing, inhomogeneous squeezing, and spectral component squeezing are introduced, and it is shown that the condition for cross-spectral purity, when satisfied, leads to homogeneous squeezing. A frequency-dependent parameter called the degree of squeezing, which lies between 0 and −1 for a squeezed state and is simply related to photoelectric measurements, is introduced. These ideas are then applied to the squeezing produced in resonance fluorescence, in parametric downconversion, and in four-wave mixing, and the degrees of squeezing under different conditions are compared.
Three different noise moments of field strength, intensity, and their correlations are simultaneously measured. For this purpose a homodyne cross-correlation measurement [1] is implemented by superimposing the signal field and a weak local oscillator on an unbalanced beam splitter. The relevant information is obtained via the intensity noise correlation of the output modes. Detection details like quantum efficiencies or uncorrelated dark noise are meaningless for our technique. Yet unknown insight in the quantumness of a squeezed signal field is retrieved from the anomalous moment, correlating field strength with intensity noise. A classical inequality including this moment is violated for almost all signal phases. Precognition on quantum theory is superfluous, as our analysis is solely based on classical physics.
We discuss homodyne and heterodyne statistics when squeezed light from a parametric oscillator is mixed with coherent light from a local oscillator. We also consider the case where the fields or the intensities of the two nondegenerate beams from a parametric oscillator are combined. By using a dynamic model of these beams we discuss photon sequences underlying these beams in terms of photoelectric pulse sequences recorded by a detector. Analytic expressions for quantities directly measurable in photon counting experiments are derived, using the method developed in our earlier investigations.1
Cross correlation heterodyne detectors exhibit the potential for suppression of the detection quantum noise below shot noise without use of optical squeezing for capturing weak optical signals in low frequency bands. To understand the underlying mechanism, we develop a quantum theory to describe the noise performance of cross correlation heterodyne detectors. By calculating the cross spectral density (CSD) of the photocurrent fluctuations from a cross correlation heterodyne detector, we prove that its noise performance can break the shot noise limit and exceed that of a regular heterodyne detector for detection of coherent light. When the detected light signal is in a squeezed state, we show that the corresponding CSD value is negative and discuss how a negative CSD may be explored to improve the output signal-to-noise ratio of the detector contaminated by classical noises through tuning the parameter of the degree of squeezing. This work may find itself useful in space-based gravitational wave searching and a variety of other scientific research activities, such as observation of vacuum magnetic birefringence and telecommunications.