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arXiv:quant-ph/0406102 · Journal of Optics B Quantum and Semiclassical Optics

Vacuum fluctuations and the conditional homodyne detection of squeezed light

H. J. Carmichael, Hyunchul Nha

Published Jul 28, 2004• 4 citations
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Abstract

Conditional homodyne detection of quadrature squeezing is compared with standard nonconditional detection. Whereas the latter identifies nonclassicality in a quantitative way, as a reduction of the noise power below the shot noise level, conditional detection makes a qualitative distinction between vacuum state squeezing and squeezed classical noise. Implications of this comparison for the realistic interpretation of vacuum fluctuations (stochastic electrodynamics) are discussed.

DOI
10.1088/1464-4266/6/8/004

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Conditional homodyne detection of quadrature squeezing is compared with standard nonconditional detection. Whereas the latter identifies nonclassicality in a quantitative way, as a reduction of the noise power below the shot noise level, conditional detection makes a qualitative distinction between vacuum state squeezing and squeezed classical noise. Implications of this comparison for the realistic interpretation of vacuum fluctuations (stochastic electrodynamics) are discussed.
Measurement of the squeezed fluctuations of an optical field by the method of conditional homodyne detection is discussed. It is shown that conditional homodyne detection is able to distinguish qualitatively between vacuum-state squeezing and squeezed classical noise. Whereas for conventional squeezed-light detection, only a quantitative distinction can be made, based on the setting of the shot-noise level, under conditional detection, the presence of classical noise changes the actual shape of the measured correlation function. The correlations show a positive peak due to the unsqeezed classical noise frequencies, set inside the negative dip associated with the squeezed fluctuations. The width in time of the positive peak is the larger of the detector response time and the inverse of the classical noise bandwidth. The fundamental distinction between vacuum-state squeezing and squeezed classical noise is that there is no positive peak, even in the limiting form of a delta-function, when the unsqueezed frequencies correspond to vacuum state modes. Implications for the literal interpretation of vacuum fluctuations, such as is adopted in stochastic electrodynamics, are discussed. The ideas are presented in general terms and illustrated by an example which treats the generation and detection of broadband squeezed light, including finite-bandwidth classical noise, within the framework of the quantum trajectory theory of cascaded open systems.
This chapter is a short summary of recent developments concerning quantum noise. A quantum state is said to be squeezed when the fluctuations of one observable have been reduced below that of the vacuum state, that is, the ‘shot-noise’ level of the coherent state. Squeezed states are detected using the technique known as balanced homodyne detection. The chapter reviews the reductions in phase and amplitude fluctuations of a squeezed state and discusses their use in interferometry and spectroscopy. The phase-dependent nature of the squeezed field results in line-narrowing of the incoherent spectrum for particular phase choices while other choices of phase result in line-broadening. Interferometry with squeezed light as well as quantum non-demolition measurements are attempting to assess quantum measurement limits in order to further extend the experimental manipulation of light.
A simple scheme for conditional generation of nonclassical light with sub-Poissonian photon-number statistics is proposed. The method utilizes entanglement of signal and idler modes in a two-mode squeezed vacuum state generated in an optical parametric amplifier. A quadrature component of the idler mode is measured in the balanced homodyne detector and the signal mode is accepted only if the absolute value of the measured idler quadrature lies inside a certain chosen interval of quadratures. It is shown that the conditionally generated state of the signal mode can exhibit reduction of photon-number fluctuations below the coherent-state level.
Squeezed states of the electromagnetic field are characterized by a reduction of fluctuations for one of two quadrature phase amplitudes below the level of fluctuations for the vacuum state. This reduction is a manifestly quantum or nonclassical feature which is of great interest in its own right but also potentially important for precision measurement with sensitivity beyond the shot-noise or vacuum-state limit. We describe three different experiments in which squeezed light has been generated in our laboratory involving parametric downconversion, intracavity frequency doubling, and optical bistability with two-state atoms. By employing the squeezed light produced by a subthreshold optical parametric oscillator, we have achieved improvements in sensitivity beyond the vacuum-state limit for the detection of both phase and amplitude changes of the electromagnetic field. An alternate route to sensitivity beyond the vacuum-state limit is through quantum nondemolition measurement, where we have suggested and are implementing a scheme involving parametric conversion and polarization mixing.