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Journal of the Optical Society of America B

Squeezing performance of a nonlinear symmetric Mach–Zehnder interferometer using forward degenerate four-wave mixing

Masataka Shirasaki

Published Mar 1, 1991• 11 citations
Publisher

Abstract

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.

DOI
10.1364/josab.8.000672

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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.
A symmetric nonlinear Mach–Zehnder interferometer containing a Kerr medium performs the operation of squeezing. The operation is performed by the interference of cotraveling waves, and the pump wave is removed. This mechanism is broadband. We analyze the operation of the interferometer and determine the degree of shot-noise reduction achieved in a balanced detector. A modification of the interferometer into a fiber ring reflector is described that accomplishes the squeezing and the pump separation.
Degenerate four-wave mixing (DFWM) in optical fibres can be used to obtain gain and to generate squeezed states, by utilizing a balanced Mach-Zehnder fibre interferometer (MZFI) with two non-linear arms, which behaves as a degenerate parametric amplifier. In a classical derivation for the optical gain; pump depletion and propagation loss are considered. Maximum achievable gain is calculated in the presence of loss. A numerical study compares the signal gain under different input pump-to-signal field ratios and its limit (undepleted pump), which is the assumption for the derivation of squeezing. Pump depletion and fibre loss hinder the validity of using large non-linear phase shifts to generate squeezed states. A semiclassical derivation provides the correct expression for the degree of squeezing in the absence of loss and pump depletion. Quantum-mechanical solutions provide the same result. The squeezing limitation due to loss is studied by a lumped-parameter model.
A nonlinear Mach-Zehnder fiber-optic interferometer as shown in Fig. 1 can be used for light squeezing1 and amplification.2 The mechanism can be viewed either as the Kerr effect,1 or degenerate four-wave mixing (DFWM).2 Using the classical DFWM approach, one finds that if fields of the same frequency with phasors E s and E p (′signal′ and ′pump′) are fed into the inputs, then one output phasor is given by where the nonlinear phase shift is given by δφnl= QL |E S E p | cosδ, Q is the fiber nonlinear coefficient, L is the fiber length, and δ is the phase difference between the inputs.
A simple way of realizing a phase-sensing interferometer for quantum noise reduction is to use a squeezed vacuum for the usually unused port.1 We previously proposed a simple way to generate an approximately squeezed vacuum.2 Our method is based on degenerate forward four-wave mixing, and it is advantageous because the phase-matching condition between the signal and the pump is automatically satisfied, and the operation is broadband. We also expect that the noise of a phase-sensing interferometer following our squeezer will be reduced.
We review our recent experimental progress in quantum technology employing amplification effect of four-wave mixing in a rubidium vapor. We have produced an intensity difference squeezed light source at frequencies as low as 1.5 kHz which is so far the lowest frequency at which squeezing has been observed in an atomic system. Moreover, we find that the bandwidth of our squeezed light source can be controlled with light intensity pumping. Using our non-classical light source, we have further developed a nonlinear Mach-Zehnder (MZ) interferometer, for which the maximum fringe intensity depends quadratically on the intensity of the phase-sensing field at the high-gain regime, leading to much better sensitivity than a linear MZ interferometer in which the beam splitters have the same phase-sensing intensity. The quantum technologies developed by our group could have great potential in areas such as precision measurement and quantum information.