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Journal of the Optical Society of America B

Time-domain analysis of quantum states of light: noise characterization and homodyne tomography

Alessandro Zavatta, Marco Bellini, Pier Luigi Ramazza, Francesco Marin, F. T. Arecchi

Published May 1, 2002• 78 citations
Publisher

Abstract

We measured the time-domain quantum statistics of a pulsed, high-repetition-rate optical field by balanced homodyne detection. The measuring apparatus discriminates the time scales on which intrinsic quantum fluctuations prevail from those scales for which technical noise is overwhelming. A tomographic reconstruction of weak coherent states with various average photon numbers demonstrates the potential ability of the system to measure high-repetition-rate, time-resolved signals. Possible extensions to other physical situations are discussed.

DOI
10.1364/josab.19.001189

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A pulsed, balanced homodyne detector has been developed for precise measurement of the electric field quadratures of pulsed optical quantum states. A high level of common mode suppression (>85 dB) and low electronic noise (730 electrons per pulse) provide a signal-to-noise ratio of 14 dB for measurement of the quantum noise of individual pulses. Measurements at repetition rates as high as 1 MHz are possible. As a test, quantum tomography of the coherent state was performed, and the Wigner function and the density matrix were reconstructed with 99.5% fidelity. The detection system can be used for ultrarsensitive balanced detection in cw mode, e.g., for weak absorption measurements.
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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.
Low-noise, efficient, phase-sensitive time-domain optical detection is essential for foundational tests of quantum physics based on optical quantum states and the realization of numerous applications ranging from quantum key distribution to coherent classical telecommunications. Stability, bandwidth, efficiency, and signal-to-noise ratio are crucial performance parameters for effective detector operation. Here we present a high-bandwidth, low-noise, ultra-stable time-domain coherent measurement scheme based on balanced homodyne detection ideally suited to characterization of quantum and classical light fields in well-defined ultrashort optical pulse modes.