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Physical Review A

Homodyne detection for the enhancement of antibunching

Reeta Vyas, Changxin Wang, Surendra Singh

Published Sep 1, 1996• 9 citations
Publisher

Abstract

We propose a scheme based on homodyne detection for enhancing antibunching in second-harmonic generation and multiatom optical bistability. We show that depending on the reflectivity of the beam splitter, relative field strengths, and relative phase it is possible to achieve perfect antibunching in the superposed field. We also discuss other nonclassical effects exhibited by the superposed field and present curves to illustrate the behavior. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2391

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Photon antibunching in intracavity second-harmonic generation and intracavity atomic absorption inside a high-Q optical cavity is discussed. A linearized description of quantum dynamics in the weak-field limit is used because the system size, as characterized by the number of photons n0{\mathit{n}}_{0}n0​ needed to probe the nonlinearity of the system, is often quite large for realistic parameters. In both cases standard results are recalled that demonstrate that antibunching is a small effect given by g(2){\mathit{g}}^{(2)}g(2)(0)-1\ensuremath{\approxeq}-1/n0{\mathit{n}}_{0}n0​ for large values of n0{\mathit{n}}_{0}n0​. We show that when higher-order terms that are usually ignored in linearized treatments are retained, g(2){\mathit{g}}^{(2)}g(2)(0) satisfies the lower bound g(2){\mathit{g}}^{(2)}g(2)(0)\ensuremath{\ge}0 even for small values of n0{\mathit{n}}_{0}n0​. It is further shown that by employing a high-Q cavity to suppress the coherent part of the spectrum of field fluctuations, perfect antibunching can be achieved even for large systems. Conditions under which this is possible are derived and curves are presented to illustrate the behavior.
The familiar input-output relations for an optical beam splitter are generalized to allow for linear absorption by the medium forming the mirror. Beam-splitter losses generally affect the noise levels detectable in experiments involving nonclassical light. When employed to investigate two-photon interference effects, a lossy beam splitter can lead to apparent nonlinear absorption, which, in the most extreme case, leads to either both or neither of the photons being absorbed. The degree of second-order coherence of antibunched light can be maintained on transmission through the beam splitter but any amplitude squeezing in the incident light is degraded.
Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.
The dynamics of a two-mode Bose-Einstein condensate trapped in a double-well potential results approximately in an effective Rabi oscillation regime of exchange of population between both wells for sufficiently strong overlap between the modes functions and sufficiently large condensates. Facing the effective Rabi oscillation as a temporal atomic beam splitter we propose a nondestructive measurement process allowing an atomic homodyne detection, thus yielding indirect relative phase information about one of the two-mode condensates. This proposal is achieved through a secondary optical homodyne detection, in which the field is allowed to dispersively interact with one of the condensate modes inside an optical cavity.
We present a simple protocol to purify a coherent state superposition from a statistical mixture of a superposed states and coherent states. The scheme constitutes only a single beam splitter and a homodyne detector, and thus experimentally feasible. In practice, a superposition of coherent states is transformed into such a mixture by linear loss, which is usually the dominant decoherence mechanism in optical systems. We also address the possibility of producing a larger amplitude superposition state from decohered states, and show that in most cases the decoherence of the states are amplified along with the amplitude.
A different way of producing antibunched light was experimentally demonstrated in which the production process is difficult to understand by a naive photon picture. A degenerate beam of down-converted photon pairs from a nonlinear crystal pumped by pulsed light was mixed with coherent local oscillator pulses by a beam splitter, and the intensity autocorrelation of one of the output beams was measured. It showed two-photon interference fringes as the phase difference of the two input fields was varied, and showed antibunching when the interference was destructive. \textcopyright{} 1996 The American Physical Society.