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Journal of the Optical Society of America B

Noise analysis of Mach-Zehnder squeezer for nonclassical input state

Masataka Shirasaki, Ilya Lyubomirsky, H. A. Haus

Published May 1, 1994• 7 citations
Publisher

Abstract

The squeezing by a nonlinear symmetric Mach–Zehnder interferometer is investigated when the input state of the pump is nonclassical. No linearization approximation is made. The analysis shows that the homodyne noise between the two outputs of the squeezer is suppressed well below the standard quantum limit if the uncertainty of the input photon number is not large. This fact suggests that, even if each output has large phase uncertainty, the two outputs are strongly phase correlated.

DOI
10.1364/josab.11.000857

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IEEE Journal of Quantum Electronics•May 29, 2003•30 citations
The squeezing by a nonlinear symmetric Mach–Zehnder interferometer is investigated when the input state of the pump is nonclassical. No linearization approximation is made. The analysis shows that the homodyne noise between the two outputs of the squeezer is suppressed well below the standard quantum limit if the uncertainty of the input photon number is not large. This fact suggests that, even if each output has large phase uncertainty, the two outputs are strongly phase correlated.
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.
A nonlinear symmetric Mach–Zehnder interferometer is analyzed. It performs squeezing and phase-sensitive amplification through forward degenerate four-wave mixing with automatic phase matching. Since the balanced interferometer is frequency insensitive, the operation is broadband. The squeezing performance is computed numerically by means of the quantum theory without approximation. This result is compared with the squeezing characteristics derived from the linearized representation. It is found that squeezed states can be produced without excess noise. Noise reduction of an interferometric measurement and phase-preserving amplification with this squeezer are also analyzed.
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.
This paper presents the phase precision of a Mach-Zehnder interferometer in the presence of two types of quantum noise. Under the influence of amplitude-damping noise, the precisions of three input cases will gradually decrease and be less than the standard quantum limit. When the quantum states are influenced by bit-phase flip, the precisions for inputs of a coherent state and a squeezed vacuum state and the precision of spin squeezing state decrease at first and then increase with increasing η (parameter characterizing the noise strength) from 0 to 1. Comparing the rates at which the precisions decrease, we found that the precision of the spin squeezing state decreased faster than those of the other two cases in most instances.
The noise figure (NF) of a phase-sensitive parametric amplifier using a nonlinear Mach-Zehnder interferometer (NMZI) with Kerr media is analyzed for amplitude-modulation signals. In the analysis, the distributed loss of the Kerr media and the excess noise of the pump light are taken into account. As for the distributed loss of the Kerr media, the quantum Langevin equation for the NMZI is derived and solved. The results elucidate a simple degradation factor in the NF representation of the amplifier. This factor implies that the NF can be less than the standard quantum limit (SQL) of 3 dB, even if the total loss of the Kerr media exceeds 3 dB. As for the excess noise of the pump light, the semi-classical small signal analysis is utilized. The results clearly indicate that the signal-to-noise ratio of the pump light must be four times higher than that of the input signal in order to realize a low-noise optical amplifier under the SQL of 3 dB.