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Journal of the Optical Society of America B

Quantum-nondemolition measurement of optical solitons

H. A. Haus, Kimitaka Watanabe, Y. Yamamoto

Published Jun 1, 1989• 59 citations
Publisher

Abstract

Quantization of optical solitons is discussed, using the nonlinear Fourier-transform (inverse-scattering) method. A quantum soliton is described in terms of two sets of conjugate variables such as the photon number and the phase, and the momentum and the center position. The theory of a soliton collision is extended to describe the quantum-nondemolition measurement of soliton photon number and momentum. These two variables are indeed quantum-nondemolition observables and can be measured by means of the phase and the center position of the probe soliton. It is demonstrated that the measurement error and backaction noise on the conjugate variable satisfy an uncertainty product.

DOI
10.1364/josab.6.001138

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Quantization of optical solitons is discussed, using the nonlinear Fourier-transform (inverse-scattering) method. A quantum soliton is described in terms of two sets of conjugate variables such as the photon number and the phase, and the momentum and the center position. The theory of a soliton collision is extended to describe the quantum-nondemolition measurement of soliton photon number and momentum. These two variables are indeed quantum-nondemolition observables and can be measured by means of the phase and the center position of the probe soliton. It is demonstrated that the measurement error and backaction noise on the conjugate variable satisfy an uncertainty product.
A fully quantum-mechanical Heisenberg description of the quantum-nondemolition measurements via soliton collision in an optical fiber is provided. Solutions to the equations of motion for meaningful soliton collective operators such as photon number, phase, position, and frequency (momentum) are applied to quantifying the error of inference of photon number and frequency of the signal soliton by performing a measurement on the probe soliton. A detection method based on measuring a four-component quadrature amplitude is proposed and proved to give the best accuracy.
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.
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.
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.
Quantum mechanics allows quantum nondemolition (QND) variables to be measured without being changed. This requires QND variables to be initially in an eigenstate and measurement backaction noise to be directed into conjugate variables. Experimental demonstrations thus require two measurements: the first to collapse variables toward an eigenstate and the second to show results identical to the first. Here, we report results from two successive soliton-collision QND measurements that optical correlation measurements show to be nearly identical.