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Journal of Modern Optics

Enhancement of detection efficiencies in homodyne measurements Comparison between squeezing signal fields and squeezing local oscillator fields

M. S. Kim

Published Aug 1, 1997• 1 citation
Publisher

Abstract

It is known that squeezing the signal field can enhance the detection efficiency in Wigner function measurements using optical tomography. There exists an equivalence between squeezing the signal field and squeezing the local oscillator state when the detection efficiency is unity. We compare the cases of squeezing the local oscillator field and squeezing the signal field in the light of improving the detection efficiency in homodyne measurements.

DOI
10.1080/09500349708230748

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It is known that squeezing the signal field can enhance the detection efficiency in Wigner function measurements using optical tomography. There exists an equivalence between squeezing the signal field and squeezing the local oscillator state when the detection efficiency is unity. We compare the cases of squeezing the local oscillator field and squeezing the signal field in the light of improving the detection efficiency in homodyne measurements.
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).
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 novel experimental scheme is proposed that allows us to avoid the deterioration of homodyne detection measurements due to nonideal detectors. The basic idea is to "preamplify" the signal by means of antisqueezing. Experimentally, we would employ a squeezer, e.g., a degenerate optical parametric amplifier, that squeezes just the nonobserved quadrature component of the electric field while antisqueezing the conjugate component which is measured. It is shown that for sufficiently strong antisqueezing one achieves the same measurement accuracy as with perfectly efficient detectors. In particular, in this way the actual Wigner function can be reconstructed in cptical homodyne tomography.
Summary form only given. Considerable interest is growing around self homodyne techniques. Such techniques allow to avoid nonunitary detection efficiencies due to inefficient mode matching of the local oscillator. As proposed by Galatola et al. [1991], one possible scheme of self homodyne detection of a field with a strong coherent component involves the use of a Fabry-Perot cavity with a high reflecting rear mirror. Using this setup we are able to perform a tomographic measure of the Wigner function of the field emitted by a laser diode.
An analysis of the homodyne tomography process that is often used to determine the Wigner functions of quantum optical states is performed to consider the effects of the spatiotemporal degrees of freedom. The homodyne tomography process removes those parts of the input state that are not associated with the mode of the local oscillator by tracing out those degrees of freedom. Using a functional approach to incorporate all the spatiotemporal degrees of freedom, we find that this reduction in the degrees of freedom introduces distortions in the observed Wigner function. The analysis also shows how the homodyne tomography process introduces a scaling caused by the efficiency and a resolution that depends on the strength of the local oscillator. As examples, we consider coherent states, Fock states, and squeezed vacuum states.