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arXiv:1701.08965 · Physical Review Letters

Anomalous Quantum Correlations of Squeezed Light

B. Kühn, W. Vogel, Martin Mráz, S. Köhnke, Boris Hage

Published Apr 10, 2017• 18 citations
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Abstract

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.

DOI
10.1103/physrevlett.118.153601

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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.
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.
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.
Information carried by an optical beam of light can usually be conveyed in the form of a temporal modulation of the intensity, phase, frequency or the polarization of the constituent mode(s). In that regard, homodyne detection is one of the most popular and standard method to measure the quantum mechanical properties of light Yuen & Shapiro (1978); Yuen et al. (1979); Yuen & Shapiro (1980); Yurke (1985). The quantum theory of homodyne detection originated principally from the works of Yuen and Shapiro et al. Yuen & Shapiro (1978); Yuen et al. (1979). In this method, a weak signal field is combined with a strong local oscillator field at a beam splitter, and the resulting signal is measured as a photocurrent. With the homodyne detection method, the quantum state of the signal field, such as the quadrature amplitude of the squeezed state, is easily measured Slusher et al. (1985); Wu et al. (1986 ); Polzik et al. (1992), and the quasiprobability distribution function can be measured by using the so-called optical homodyne tomography Smithey et al. (1993); Banaszek & W’odkiewicz (1996); Wallentowitz & Vogel (1996); Youn et al. (2001). Furthermore, optical homodyne detection is used to eavesdrop on the quantum key in quantum cryptography Hirano et al. (2000).
Nonclassical effects exhibited by the homodyned field when light from an optical parametric oscillator (OPO) is mixed with coherent light from a local oscillator are discussed. Calculations are carried out exactly without making the strong local oscillator approximation. It is found that, depending upon the local oscillator phase and the parameters characterizing the light from the OPO, the second order intensity correlation function of the superposed field violates various classical inequalities g(2)(0) ≥ 1, g(2)(0) ≥g(2)(τ), and |g(2)(0) –1| ≥ | g(2)(τ)–1|. Thus we can see sub-Poissonian or super-Poissonian statistics and bunching or antibunching. We express the fields at the beam splitter in terms of independent real Gaussian stochastic processes with coherent component. Using these properties of the dynamical field variables, we derive analytic expressions for quantities directly measurable in photon counting experiments. It is found that the waiting time distribution shows two extrema at nonzero times. The second order intensity correlation function is found to vanish at nonzero time in violation of a classical inequality.
We develop a multimode theory of direct homodyne measurements of quantum optical quasidistribution functions. We demonstrate that unbalanced homodyning with appropriately shaped auxiliary coherent fields allows one to sample point-by-point different phase-space representations of the electromagnetic field. Our analysis includes practical factors that are likely to affect the outcome of a realistic experiment, such as nonunit detection efficiency, imperfect mode matching, and dark counts. We apply the developed theory to discuss feasibility of observing a loophole-free violation of Bell's inequalities by measuring joint two-mode quasidistribution functions by photon counting under locality conditions. We determine the range of parameters of the experimental setup that enable violation of Bell's inequalities for two states exhibiting entanglement in the Fock basis: a one-photon Fock state divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced in the process of nondegenerate parametric down-conversion.