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Quantum Electronics and Laser Science Conference

Cascaded homodyning for local phase-space sampling

Sascha Wallentowitz, W. Vogel, Z. Kis, T. Kiss, József Janszky, Петер Адам

Published Jan 20, 2003• 0 citations
Publisher

Abstract

Summary form only given. We have shown that the idea of local sampling of phase-space may be experimentally accessible for optical fields by a cascaded homodyne scheme, combining both the advantages of the unbalanced and the balanced scheme. It has been shown that the resulting sampling function is a unique one that does not depend on the phase-space amplitude and whose form is analytically given as a rescaled zero-order pattern function known from balanced-homodyne tomography.

DOI
10.1109/qels.1999.807114

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Summary form only given. We have shown that the idea of local sampling of phase-space may be experimentally accessible for optical fields by a cascaded homodyne scheme, combining both the advantages of the unbalanced and the balanced scheme. It has been shown that the resulting sampling function is a unique one that does not depend on the phase-space amplitude and whose form is analytically given as a rescaled zero-order pattern function known from balanced-homodyne tomography.
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.
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.