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Physical Review A

Ultrafast photon-number correlations from dual-pulse, phase-averaged homodyne detection

D. F. McAlister, Michael G. Raymer

Published Mar 1, 1997• 70 citations
Publisher

Abstract

We propose and demonstrate a method for determining the two-time photon-number correlations of an optical field on ultrafast time scales. The method, which uses dual-pulse, phase-averaged, balanced-homodyne detection, is sensitive at the single-photon level and can have a quantum efficiency approaching 100%. Using this method we have determined the two-time, photon-number correlations on subpicosecond time scales of emission from a semiconductor optical amplifier.

DOI
10.1103/physreva.55.r1609

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We propose and demonstrate a method for determining the two-time photon-number correlations of an optical field on ultrafast time scales. The method, which uses dual-pulse, phase-averaged, balanced-homodyne detection, is sensitive at the single-photon level and can have a quantum efficiency approaching 100%. Using this method we have determined the two-time, photon-number correlations on subpicosecond time scales of emission from a semiconductor optical amplifier.
We prove that the photon-number distribution of an arbitrary single-mode optical state can be calculated directly from the phase-averaged quadrature amplitude distribution, measured using optical homodyne detection. We experimentally demonstrate the application of this result by measuring the ultrafast (subpicosecond), time-resolved photon-number statistics of a weak field from a pulsed diode laser. Also presented is a numerical calculation of the photon-number distribution of a quadrature-squeezed vacuum state.
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.
A theoretical treatment is given which establishes dual-mode balanced-homodyne detection as a practical and well characterized technique for measuring optical field correlations, photon-number correlations, or the full quantum state of a pair of optical modes. The definition of modes used includes temporal wave packets, Gaussian or other beam profiles, or two-frequency fields. The proposed method allows the measurement of two-time correlations on sub-picosecond scales, the disentangling of the statistics of signal light in two spatially overlapping modes, and the measurement of field correlations, such as squeezing, over 100 THz bandwidths. We show how to estimate from the data the statistical errors on the measured correlations and the density matrix arising from finite data sets, and the errors introduced by using finite numbers of phases and relative amplitudes of the two local oscillator fields.
A balanced homodyne detection scheme with nanosecond time resolution and sub-shot-noise sensitivity has been developed and successfully tested yielding an efficient detection scheme for high-speed quantum-optical measurements and communication protocols, for example, quantum cryptography. The parameters of the detector and its precise balancing allow complete characterization of quantum states created by femtosecond light pulses that include the measurement of photon number, optical phase, and statistical properties with a high signal-to-noise ratio for the whole bandwidth from DC to several tens of megahertz. The electronic part of the detector is based on a commercially available amplifier that provides ease of construction and use while yielding good performance.
Abstract We demonstrated an ultrafast time-resolved measurement method operating at the single-photon level and employing a two-color comb-based asynchronous optical sampling (ASOPS) setup. We harnessed the two-color ASOPS photon counting approach to achieve long-term averaging of the ultralow intensity signal with a synchronized optical trigger signal, which minimizes residual timing jitter between the two combs. A pulse-width limited picosecond cross-correlation signal was successfully obtained with a power level of <1 photon/pulse. This approach enables the thorough study of ultrafast time-resolved detection of entangled photon pairs, quantum mechanical correlations in the time-frequency domain and finds wide use in optical quantum technology.