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arXiv:0907.1964 · Physical Review A

Entanglement measurement of the quadrature components without homodyne detection in the bright, spatially multimode far field

T. Yu. Golubeva, Yu. M. Golubev, K. Samburskaya, Claude Fabre, Nicolas Treps, Mikhail I. Kolobov

Published Jan 27, 2010• 2 citations
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Abstract

We present a procedure for the measurement of quadrature components of an electromagnetic field in the far field as an alternative to the traditional approach based on the homodyne detection (HD) technique. For that we suggest to use coherent sources such as phase-locked lasers or optical parametric oscillators operating above threshold. Then we show how to arrange the detection procedure in the far field that is exactly or partly equivalent to the HD. Our scheme can be applied for both the classical and nonclassical fields. The potential of the procedure is illustrated by an example which utilizes the pixellized sources of the nonclassical light. As an integral part of our investigation we develop a theory of the pixellized source of the spatiotemporally squeezed light.

DOI
10.1103/physreva.81.013831

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We present a procedure for the measurement of quadrature components of an electromagnetic field in the far field as an alternative to the traditional approach based on the homodyne detection (HD) technique. For that we suggest to use coherent sources such as phase-locked lasers or optical parametric oscillators operating above threshold. Then we show how to arrange the detection procedure in the far field that is exactly or partly equivalent to the HD. Our scheme can be applied for both the classical and nonclassical fields. The potential of the procedure is illustrated by an example which utilizes the pixellized sources of the nonclassical light. As an integral part of our investigation we develop a theory of the pixellized source of the spatiotemporally squeezed light.
We present a procedure for the measurement of quadrature components of an electromagnetic field in the far-field as an alternative to the traditional approach based on the homodyne detection (HD) technique. For this we suggest to use coherent sources such as phase-locked lasers or optical parametric oscillators operating above threshold. Then we show how to arrange the detection procedure in the far field that is exactly or partly equivalent to the HD. Our scheme can be applied for both the classical and non-classical fields. The potential of the procedure is illustrated by an example which utilizes the pixellised sources of the non-classical light. As an integral part of our investigation we develop a theory of the pixellised source of the spatio-temporally squeezed light.
We show that spatial entanglement of two twin images obtained by parametric down-conversion is complete, i.e. concerns both amplitude and phase. This is realised through a homodyne detection of these images which allows for measurement of the field quadrature components. EPR correlations are shown to exist between symmetrical pixels of the two images. The best possible correlation is obtained by adjusting the phase of the local oscillator field (LO) in the area of maximal amplification. The results for quadrature components hold unchanged even in absence of any input image i.e. for pure parametric fluorescence. In this case they are not related to intensity and phase fluctuations.
The quantum effects on a cavity mode of the electromagnetic field caused by measuring one of its quadrature components is analyzed. We consider three measurement schemes: an intracavity quantum-nondemolition coupling to another mode, simple homodyne detection, and balanced homodyne detection. It is shown that, for suitable initial conditions, the first scheme has an effect which approaches that of a projective collapse of the state vector for long measurement times. However, the two homodyne schemes (which are shown to be equivalent for large local-oscillator amplitudes) do not approximate a projective measurement in any limit. In particular, it is shown that homodyne measurement cannot produce a squeezed state from a classical initial state. All three schemes are analyzed in terms of ``quantum trajectories'' which link measurement theory with stochastic quantum-jump processes.
A legitimate and easily computable measure of nonclassicality for the pure state of the single-mode electromagnetic field based on the standard deviation in the measurement of the homodyne rotated quadrature operator is proposed. The proposed quantity is an effective nonclassical area projected by the optical tomogram of the quantum state of light on to the optical tomographic plane. It is found that if the nonclassical area projected by the optical tomogram of a pure single-mode quantum state is greater than zero the state is strictly a nonclassical state and it is zero for the classical state. Nonclassical area spanned by the optical tomogram of nonclassical states of light such as Fock states, squeezed states, photon-added coherent states, and even and odd coherent states, have been evaluated theoretically. Nonclassical area projected by the optical tomogram of a quantum state of light may be experimentally tractable using the balanced homodyne detection of the quadrature operator of the field avoiding the reconstruction of density matrix or the quasiprobability distribution of the state.
We show that the spatial entanglement of two twin images obtained by parametric down conversion is complete, i.e., concerns both amplitude and phase. By considering a homodyne detection scheme, which allows comparison of field quadrature components of the two images pixel by pixel, Einstein-Podolsky-Rosen correlations are shown to exist between symmetrical pixels of the two images. The best possible correlation is obtained by adjusting the phase profile of the local oscillator in the amplification area. The results for quadrature components hold even in the absence of any input image, i.e., for pure parametric fluorescence. In this case, they are not related to intensity and phase fluctuations.
Abstract A phase-sensitive detection scheme for optical fields is described, which allows for the simultaneous measurement of orthogonal field quadratures. The recent achievement of -radian cross-phase shifts between a single photon and a second light field has opened the door to quantum computing protocols which utilize photonic quantum bits. Optical phase measurements play an integral role in these schemes. The detection scheme presented here was designed to measure such transient phase shifts of a laser field as it interacts with another light field through a cloud of laser-cooled Rb atoms. In place of conventional spatial interferometry, which is very sensitive to mechanical instabilities, the scheme utilizes beat-note interferometry to improve on the robustness of the measurement. Beat-note interferometry serves to map a signal from a THz-frequency carrier onto a radio-frequency carrier. A variant of 8-port optical homodyne detection, the scheme then uses IQ demodulation, a well-established technique in communications engineering, to extract amplitude information for both the in-phase (I) and quadrature-phase (Q) components of the radio-frequency signal. This IQ data can then be used to extract any amplitude variation and/or phase shifts of the original THz-frequency optical field. The technique is illustrated here by simultaneously measuring the absorption and dispersion experienced by an optical beam as it passes through a cloud of laser-cooled atoms, which have been prepared in a state of electromagnetically-induced transparency. A thorough characterization of the measurement is presented, which identifies the dominant noise sources and illustrates the utility of IQ demodulation in eliminating noise. This scheme has been used to measure rad phase shifts on nanosecond time scales.