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New Journal of Physics

Local sampling of the quantum phase-space distribution of a continuous-wave optical beam

Sascha Wallentowitz, Birger Seifert, S Godoy

Published Oct 19, 2012• 4 citations
Publisher

Abstract

It is shown how the quantum phase-space distribution of a continuous-wave (cw) optical beam can be obtained independently at each point in phase space by a combination of unbalanced homodyne and balanced-heterodyne techniques. The unbalanced homodyning allows for the local sampling of phase space, whereas the heterodyne part, although introducing a loss of detection efficiency, provides a highly efficient reduction of 1/ f excess noise that is required for the sampling of cw fields. The method complements well-known techniques for light pulses by providing a robust method for cw optical beams.

DOI
10.1088/1367-2630/14/10/105019

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It is shown how the quantum phase-space distribution of a continuous-wave (cw) optical beam can be obtained independently at each point in phase space by a combination of unbalanced homodyne and balanced-heterodyne techniques. The unbalanced homodyning allows for the local sampling of phase space, whereas the heterodyne part, although introducing a loss of detection efficiency, provides a highly efficient reduction of 1/ f excess noise that is required for the sampling of cw fields. The method complements well-known techniques for light pulses by providing a robust method for cw optical beams.
Balanced homodyning, heterodyning, and unbalanced homodyning are three well-known sampling techniques used in quantum optics to characterize photonic sources in the continuous-variable regime. We show that for all quantum states and all observable-parameter tomography schemes, which includes reconstructions of arbitrary operator moments and phase-space quasidistributions, localized sampling with unbalanced homodyning is always tomographically more powerful (gives more accurate estimators) than delocalized sampling with heterodyning. The latter is recently known to often give more accurate parameter reconstructions than conventional marginalized sampling with balanced homodyning. This result also holds for realistic photodetectors with subunit efficiency. With examples from first- through fourth-moment tomography, we demonstrate that unbalanced homodyning can outperform balanced homodyning when heterodyning fails to do so. This new benchmark takes us one step towards optimal continuous-variable tomography with conventional photodetectors and minimal experimental components.
Multichannel unbalanced homodyning is proposed for measuring the density matrix of a single-mode optical field in the photon-number representation. Combining the signal beam and the local oscillator by a hightransmittance beam splitter, the interfering field is detected using multichannel photocounting. The density matrix is determined by direct statistical sampling of the coincident events recorded for various values of the local-oscillator phase. The usefulness of the method is demonstrated by computer simulations of measurements including error estimations.
We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.
The technique of dc-balanced, pulsed homodyne detection for the purpose of determining optical-field statistics on short time scales is analyzed theoretically. Such measurements provide photon-number and phase distributions associated with a repetitive signal light field in a short time window. Time- and space-varying signal and local-oscillator pulses are treated, thus generalizing earlier treatments of photoelectron difference statistics in homodyne detection. Experimental issues, such as the effects of imperfect detector balancing on (time-integrated) dc detection and the consequences of background noise caused by non-mode-matched parts of the multimode signal field, are analyzed. The Wigner, or joint, distribution for the two field-quadrature amplitudes during the sampling time window can be directly determined by tomographic inversion of the measured photoelectron distributions. It is pointed out that homodyne detection provides a new method for the simultaneous measurement of temporal and spectral information. Although the theory is generally formulated, with both signal and local-oscillator fields being quantized, emphasis is placed on the limit of a strong, coherent local-oscillator field, making semiclassical interpretation possible.