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Springer series in chemical physics

Spectrally-Resolved, DC-Balanced Homodyne Detection for Ultrafast, Multimode, Quantum Field State Measurement

Ian A. Walmsley, Chris Iaconis, Rick P. Trebino

Published Jan 1, 1996• 0 citations
Publisher
DOI
10.1007/978-3-642-80314-7_72

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Ultimately the properties of all optical fields are contained in the density matrix that specifies their quantum mechanical state. It has only recently been demonstrated that it is possible to actually reconstruct this density matrix from measured data, and to do so with temporal resolution of a few hundred femtoseconds.[1] This technique, known as Optical Homodyne Tomography (OHT), is unfortunately restricted to the measurement of only single mode radiation. In fact it selects out from the test field only those components which overlap temporally with the local oscillator pulse mode.
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.
We investigate reconstruction of moments of creation and annihilation operators of multimode traveling light field from data recorded in multimode balanced homodyne detection with a single homodyne detector. We derive sampling functions whose average over the measured quadrature statistics provides the estimates of the moments. We show that detection losses may be compensated by a simple rescaling of the sampling functions. We also show that all moments of given order can be reconstructed from the statistics of a finite number of quadratures.