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Journal of the Optical Society of America B

Noise reduction in quantum nondemolition measurement with a nonlinear Mach–Zehnder interferometer using squeezed vacuum

Masataka Shirasaki, H. A. Haus

Published Mar 1, 1991• 9 citations
Publisher

Abstract

A quantum nondemolition measurement of photon number taken with a nonlinear Mach–Zehnder interferometer is analyzed. When this interferometer is excited by a coherent input, it shows a large amount of noise, caused by the self-phase modulation. We demonstrate how this noise can be suppressed by applying a squeezed vacuum to the unexcited port of the interferometer.

DOI
10.1364/josab.8.000681

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arXiv:quant-ph/0106102•Physical Review A•Aug 3, 2001•48 citations
A quantum nondemolition measurement of photon number taken with a nonlinear Mach–Zehnder interferometer is analyzed. When this interferometer is excited by a coherent input, it shows a large amount of noise, caused by the self-phase modulation. We demonstrate how this noise can be suppressed by applying a squeezed vacuum to the unexcited port of the interferometer.
Many works have stated that nonlinear interactions can improve phase sensitivity beyond the Heisenberg limit scaling of 1/N1/N1/N with NNN being the mean photon number. This raises some open questions---among them the conclusive sensitivity limits with respect to single-mode inputs. Namely, when one of two inputs is vacuum, is there a shot-noise-style sensitivity bound on a nonlinear Mach-Zehnder interferometer? Within the reach of second-order nonlinear phase shifts, we make an attempt to provide an answer to this question. Based upon phase-averaging approach, this puzzle is partially resolved with careful calculations of the quantum Fisher information regarding three kinds of common inputs: Gaussian states, squeezed number states, and Schrödinger cat states. The results suggest that shot-noise-style sensitivity limit is no longer available, and the ideal candidate is squeezed vacuum.
Noise suppression in an interferometer, employing a nonlinear Mach-Zehnder squeezer, was proposed[1] and experimentally confirmed[2,3]. The noise characteristics of this squeezer were derived for a coherent state input[4]. It may be advantageous to put the squeezer directly into a modelocked laser resonator where higher power pulses may be utilized. In this case the light acquires a large phase uncertainty. Thus, it is of interest to analyze squeezing with an input state of large phase uncertainty. One approach is to expand the input state in terms of coherent states[5]. Another approach is to use number states, which have total phase uncertainty and also present some interesting quantum features.
Summary form only given. Quantum-nondemolition (QND) measurements are those that do not disturb the quantum distribution of the variable being measured. It has been experimentally demonstrated that QND measurement of the photon number an be achieved by use of wavelength-multiplexed soliton collisions. A quantum analysis of the experiment has also been developed. It was found that the phase spreading of the probe as a result of self-phase modulation can contribute significant noises. In this paper we propose a new and better QND scheme using cross-polarized soliton collisions in a fiber loop interferometer. The scheme requires only a single wavelength laser source and can be fully fiber-integrated, and, most importantly, the noise caused by self-phase modulation is automatically suppressed by detection of the squeezed quadrature of the probe soliton.
The output state of a nonlinear Mach-Zehnder interferometer is shown to be an effective number-phase minimum-uncertainty state with reduced photon-number uncertainty. This interferometer includes an optical Kerr medium in one arm with a coherent-state input. Unusual ``crescent''-shaped squeezing which preserves photon number is revealed in the unitary evolution associated with a self-phase-modulation in the Kerr medium. Photon-number uncertainty 〈\ensuremath{\Delta}n${^}^{2}$〉 can be reduced by interference with a coherent-state reference wave. It can be minimized to 〈n^〉1/3{〉}^{1/3}〉1/3, far below the limit 〈n^〉2/3{〉}^{2/3}〉2/3 achieved by an ordinary squeezed state. The increased phase uncertainty due to self-phase-modulation and the reduced photon-number uncertainty still preserve the minimum-uncertainty product 〈\ensuremath{\Delta}n${^}^{2}$〉〈\ensuremath{\Delta}\ensuremath{\Phi}${^}^{2}$〉\ensuremath{\sim}(1/4). .AE