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arXiv:quant-ph/9704034 · Physics Letters A

Added noise in homodyne measurement of field observables

Giacomo Mauro D’Ariano, Matteo G. A. Paris

Published Aug 1, 1997• 18 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(97)00424-6

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We study the effects of phase-insensitive noise on homodyne measurements of a radiation density matrix. We prove that this noise has an effect equivalent to a non-unit quantum efficiency at detectors. The overall effective quantum efficiency η∗ of the measurement is evaluated in terms of the quantum efficiency at detectors and of the average number of noise photons added to the radiation field. For pure Gaussian-displacement noise, we show that half a photon of noise is enough to prevent the homodyne measurement of the density matrix.
Quantum synchronization has been a central topic in quantum nonlinear dynamics. Despite the rapid development in this field, very few have studied how to efficiently boost synchronization. Homodyne measurement emerges as one of the successful candidates for this task but preferably in the semiclassical regime. In our work, we focus on the phase synchronization of a harmonic-driven quantum Stuart-Landau oscillator and show that the enhancement induced by homodyne measurement persists into the quantum regime. Interestingly, optimal two-photon damping rates exist when the oscillator and driving are at resonance and with a small single-photon damping rate. We also report noise-induced enhancement in quantum synchronization when the single-photon damping rate is sufficiently large. Apart from these results, we discover that adding a squeezing Hamiltonian can further boost synchronization, especially in the semiclassical regime. Furthermore, the addition of squeezing causes the optimal two-photon pumping rates to shift and converge.
The fundamental and simplest kind of squeezing (broadband squeezing) is produced by pumping a nonlinear medium at a single frequency. The observables squeezed are the electric-field quadrature phases defined relative to the pump frequency. Their measurement requires homodyning against an optical-frequency (the pump frequency) local oscillator. When the medium is pumped at several different frequencies (equally spaced), different kinds of observables exhibit squeezing. Their measurement requires further homodyning, against a radio-frequency (the pump frequency spacing) local oscillator, and, for four or more pump frequencies, against subsequent lower-frequency local oscillators. For a given total pump power, it is possible to achieve greater squeezing by distributing the pump power over several (at least three) different pump frequencies than by pumping at a single frequency. The drawback is that a more sophisticated detection scheme is required (i.e., further homodyning) to measure the maximum squeezing (less squeezing is produced in more easily measured observables, such as the electric-field quadrature phases). The required further homodyning at rf and lower frequencies is straightforward to accomplish, however, and the advantages of using lower pump powers at each optical frequency can be substantial, especially in mediums such as optical fibers, where large pump powers bring with them substantial added noise sources.