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Journal of Experimental and Theoretical Physics

Quantum nondemolition measurements of the phase and polarization Stokes parameters of optical fields

A. P. Alodzhants, Sergei M Arakelyan

Published Apr 1, 1998• 4 citations
Publisher

Abstract

We propose a new method for performing continuous quantum nondemolition measurements (QNDM) of the polarization characteristics of light, the signal photon number, and the Stokes parameters of light. For devices that implement such measurements we take cubically nonlinear double-filament optical fibers with tunnel coupling of the filaments. Such a system employs a four-mode mixing of the waves (two probe modes and two signal modes). Linear optical elements needed for preliminary and subsequent conversion of the Stokes parameters are also used. We show that measurements of one Stokes parameter can be used for QNDM of the phase difference between the two initial modes. Here the accuracy of such measurements is determined by the initial fluctuations of the Stokes parameters of the probe modes and by the size of the nonlinear mode conversion coefficient in the optical fibers.

DOI
10.1134/1.558525

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We propose a new method for performing continuous quantum nondemolition measurements (QNDM) of the polarization characteristics of light, the signal photon number, and the Stokes parameters of light. For devices that implement such measurements we take cubically nonlinear double-filament optical fibers with tunnel coupling of the filaments. Such a system employs a four-mode mixing of the waves (two probe modes and two signal modes). Linear optical elements needed for preliminary and subsequent conversion of the Stokes parameters are also used. We show that measurements of one Stokes parameter can be used for QNDM of the phase difference between the two initial modes. Here the accuracy of such measurements is determined by the initial fluctuations of the Stokes parameters of the probe modes and by the size of the nonlinear mode conversion coefficient in the optical fibers.
A possibility of formation of nonclassical polarization states of light in the case of interaction of two orthogonally polarized modes in a spatio-inhomogeneous nonlinear medium is considered. A procedure of the quantum nondemolition (QND) measurement both of the Stokes parameters and the phase difference of two orthogonally polarized modes of optical field is presented and analyzed for the first time. We also introduce a new nonlinear parameter to describe the light polarization (depolarization) in quantum optics. The general approach to the measurement procedure under study allows to propose the new scheme for the QND-measurement of the angular momentum of atomic system as well.
The analysis of formation of chaotic quantum states for two (or four) orthogonally polarized modes in a tunnelly-coupled optical fiber (TCOF) has been carried out. A special attention is devoted both to the structure of arising polarization instabilities and to the possibility to control of such a quantum state by procedure of quantum nondemolition measurements. New effect of polarization switching is obtained. A new method of generating correlated fluctuations in optical field, based on Raman-Nath diffraction by a fine grating, is discussed. A nonclassical effect is predicted: a suppression of quantum fluctuations below the level of full coherence in the sum of difference photon numbers for the transmitted and scattered waves. The physics of this phenomenon involves a correlation of quantum fluctuations in the intensities of two modes that are coupled nonlinearly. This correlation is most effective in the limit of parametric interaction between the waves in the medium.
In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.
The analysis of formation of chaotic quantum states for two (or four) orthogonally polarized modes in a tunnelly-coupled optical fiber has been carried out. A special attention is devoted both to the structure of arising polarization instabilities and to the possibility to control of such a quantum state by procedure of quantum nondemolition measurements. New effect of polarization switching is obtained and we discuss the problem of both coding of information and construction of quantum logical elements for quantum computing. The optical schemes to realize the quantum AND (NOT-AND), OR (NOT-OR) and controlled-NOT gates with quantum nondemolition filtering of the signal are proposed.
The collision of two optical solitons, one a probe and the other a signal, writes out the energy of the signal soliton as a phase shift of the probe soliton. Consequently, a readout of the probe phase shift gives the photon number of the signal soliton. If the collision takes place in a low-loss optical fiber with the usual Kerr nonlinearity, the photon number of the signal soliton is preserved, and the measurement can be a quantum nondemolitional (QND) measurement. We describe experimental progress towards soliton collision QND measurements. We have collided two solitons at 1.460 nm (probe) and 1.463 nm (signal) and with the help of a delayed reference soliton (identical to the probe) in a homodyne detector system, we have measured the resulting probe soliton phase shifts. Toward a QND measurement, we correlate the shot noise fluctuations of the signal soliton with the corresponding phase noise fluctuations written on the probe. We present our current results.
We report the quantum-nondemolition measurement of the photon number of an optical soliton. Taking advantage of the conservation properties of quantum solitons, we were able to read out the photon number of a ``signal'' soliton via the phase of a ``probe'' soliton after a soliton collision in a single-mode low-loss optical fiber. Subsequent noise measurements showed the photon number fluctuations of the signal soliton at the shot-noise limit to be correlated to the phase fluctuations of the probe soliton, signifying a backaction-evading measurement of the photon number.