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Physical Review A

Physical realization of an environment with squeezed quantum fluctuations via quantum-nondemolition-mediated feedback

P. Tombesi, David Vitali

Published Nov 1, 1994• 62 citations
Publisher

Abstract

We show how a squeezed environment can be obtained by means of a suitable feedback of the output signal corresponding to a quantum-nondemolition (QND) measurement of an observable. As an example we show how the variance of a field quadrature of a cavity mode subject to QND-mediated feedback can be squeezed below the standard quantum limit and that this actually means that applying feedback is equivalent to coupling the mode to a squeezed environment.

DOI
10.1103/physreva.50.4253

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We show how a squeezed environment can be obtained by means of a suitable feedback of the output signal corresponding to a quantum-nondemolition (QND) measurement of an observable. As an example we show how the variance of a field quadrature of a cavity mode subject to QND-mediated feedback can be squeezed below the standard quantum limit and that this actually means that applying feedback is equivalent to coupling the mode to a squeezed environment.
We present the quantum theory of optical cavity feedback mediated by homodyne detection, with an arbitrary time delay. We apply this theory to a system with nonclassical dynamics, a sub-Poissonian pumped laser. By using the feedback to phase lock the laser it is possible to produce output light which exhibits perfect quadrature squeezing on resonance, rather than just sub-Poissonian intensity statistics. However, we also show that feedback mediated by homodyne detection (or any other extracavity measurement) cannot produce nonclassical light unless the cavity dynamics can do so without feedback. Furthermore, in systems which already exhibit squeezing, such feedback can only degrade the squeezing in the output. With feedback mediated by an intracavity measurement, these theorems do not apply. We show that an (admittedly unrealistic) intracavity quantum nondemolition quadrature measurement allows arbitrary squeezing to be produced by controlling the amplitude of a coherent driving field.
A new scheme for generating an amplitude-squeezed state is proposed. The photon-flux fluctuation of a semiconductor-laser output wave is measured with a quantum nondemolition (QND) detector, and is negatively fed back to the laser pumping current. The operator Langevin equations are derived by combining the quantum-mechanical analyses on the laser internal-external field fluctuations, the quantum nondemolition detector based on an optical Kerr effect, and a negative-feedback circuit. The output wave features a reduced photon number noise below the standard quantum limit, 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉^〉, and an enhanced phase noise above that, 〈(\ensuremath{\Delta}\ensuremath{\psi}^)2{)}^{2})2〉>(1/4)〈n^${〉}^{\mathrm{\ensuremath{-}}1}$, while the minimum uncertainty product is still preserved. The observed photoelectron statistics in a negative-feedback GaAs laser diode using a conventional p-i-n photodiode (not a QND detector) are shown to exhibit sub-Poissonian statistics with the variance 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉apeq20.26〈n^〉. The measured photocurrent fluctuation spectral density is also indicated to be below the standard quantum limit by a factor of 0.2 (=-7 dB). The experimental results also confirm that such amplitude squeezing is only observed inside the feedback loop and cannot be extracted from the loop unless a quantum nondemolition detector is used.
We suggest an interferometric scheme assisted by squeezing and linear feedback to realize the whole class of field-quadrature quantum nondemolition measurements, from Von Neumann projective measurement to a fully nondestructive noninformative one. In our setup, the signal under investigation is mixed with a squeezed probe in an interferometer and, at the output, one of the two modes is revealed through homodyne detection. The second beam is then amplitude-modulated according to the outcome of the measurement, and finally squeezed according to the transmittivity of the interferometer. Using strongly squeezed or antisqueezed probes respectively, one achieves either a projective measurement, i.e., homodyne statistics arbitrarily close to the intrinsic quadrature distribution of the signal, and conditional outputs approaching the corresponding eigenstates, or a fully nondestructive one, characterized by an almost uniform homodyne statistics, and by an output state arbitrarily close to the input signal. By varying the squeezing between these two extremes, or simply by tuning the internal phase shift of the interferometer, the whole set of intermediate cases may also be obtained. In particular, an optimal quantum nondemolition measurement of quadrature may be achieved, which minimizes the information gain versus state disturbance tradeoff.
A quantum nondemolition measurement based on a three-mode interaction mediated by a second-order nonlinear susceptibility is discussed. All three modes are treated quantum mechanically. The signal field is taken as one of the three modes and the probe field is the combined field in the other two modes. If the probe system is initially in a number state, the interaction between the signal and probe is equivalent to that between a harmonic oscillator and an angular momentum system. Photon counting on the probe field realizes a quantum nondemolition measurement of the square of a quadrature phase amplitude of the signal, and thus provides a direct measurement of second-order squeezing.