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Quantum Optoelectronics

Squeezing With Input State of Large Phase Uncertainty

Ilya Lyubomirsky, Masataka Shirasaki, H. A. Haus

Published Jan 1, 1993• 0 citations
Publisher

Abstract

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.

DOI
10.1364/qo.1993.qwc.2

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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.
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
We have studied the sensitivity of four different phase shift measurement schemes with a Mach-Zehnder interferometer. The input light is considered to be in a coherent state and the detectors are assumed to be ideal with the quantum efficiency of unity. It is shown by direct calculation of the operators corresponding to the measurement schemes that the uncertainty of the phase-shift measurement is limited to the classical one 1m\frac{1}{\sqrt{m}}m​1​ (m is the average number of the photons in the input state) regardless of the phase-shift measurement schemes.
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.