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Journal of the Optical Society of America B

Squeezing of pulses in a nonlinear interferometer

Masataka Shirasaki, H. A. Haus

Published Jan 1, 1990• 148 citations
Publisher

Abstract

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.

DOI
10.1364/josab.7.000030

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Experiments in our laboratory have arrived at squeezing in a pulse-excited fiber ring. The pulse excitation suppresses stimulated Brillouin scattering, and at the low frequencies used for the measurement, which are made possible by the pump separation, guided acoustic-wave Brillouin scattering is ineffective. It is likely that large squeezing can be realized by using solitons in the same fiber-ring configuration, because solitons assure better squeezing phase profiles. These findings encouraged us to "design" a fiber gyro that performs below the standard quantum limit. It consists of two fiber-ring reflectors; the first acts as a squeezer, and the second acts as a Sagnac interferometer. We use the theory of quantization of solitons.1 The pulse injected into the first fiber ring is a sech adjusted so as to travel as a pair of countertraveling solitons in the squeezing ring.2 The ring acts like a Mach-Zehnder interferometer folded back on itself. The pump is reflected from the pump port, and the vacuum port has squeezed vacuum emerging from it. The pump is recycled in the second Sagnac ring to act as the signal for the rotation sensing. The squeezed vacuum from the first ring is injected into the vacuum port of the Sagnac interferometer. Because practical design considerations dictate fiber lengths on the order of 100 m for both rings, the nonlinearity in the Sagnac ring cannot be neglected. It produces its own squeezing but in the wrong phase for detector noise reduction. However, by proper adjustment of the squeezing in both interferometers, it is possible to counteract the harmful squeezing effect in the Sagnac interferometer and still arrive at a net reduction of the detector noise.

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Squeezed pulse vacuum from fiber-ring interferometer

K. Bergman, H. A. Haus

Squeezing with degenerate parametric amplification sacrifices the power needed for the pump.1 Squeezing by using the third- order nonlinearity does not necessarily sacrifice the pump power, because it remains at the same frequency as the squeezed radiation. Because the third-order nonlinearity is weak, long interaction lengths must be used, i.e., optical fibers. Past experiments with quasi excitation in optical fibers were plagued by stimulated Brillouin scattering (SBS) and guided acoustic wave acoustic Brillouin scattering (GAWBS).2 The use of pulses raises the peak power and the SBS threshold, allowing use of shorter fibers. A Mach-Zehnder interferometer configuration separates the pump from the squeezed vacuum.3 This has two advantages: the pump power can be reused as the local oscillator power, and the squeezed radiation can be measured closer to zero frequency (30 kHz) because the pump fluctuations are absent.

Annual Meeting Optical Society of America•Jan 1, 1990•0 citations
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.
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.
Summary form only given. Several schemes to generate squeezed light by use of the Kerr nonlinearity in optical fibers have been devised. The most recent experiments used asymmetric Sagnac loops to produce amplitude squeezing. In our experiment the Sagnac geometry is "unfolded" into a Mach-Zehnder, wherein the two arms of the interferometer correspond to the polarization modes of a single-mode PM fiber. This setup allows us to switch from an asymmetric to a symmetric interferometer, and gives us full control of the phase and amplitude of the two interfering pulses. With these degrees of freedom, we are able to maximize noise reduction and perform a full measurement of the noise properties of the soliton squeezed pulses.
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.
Experiments in our laboratory have arrived at squeezing in a pulse-excited fiber ring. The pulse excitation suppresses stimulated Brillouin scattering, and at the low frequencies used for the measurement, which are made possible by the pump separation, guided acoustic-wave Brillouin scattering is ineffective. It is likely that large squeezing can be realized by using solitons in the same fiber-ring configuration, because solitons assure better squeezing phase profiles. These findings encouraged us to "design" a fiber gyro that performs below the standard quantum limit. It consists of two fiber-ring reflectors; the first acts as a squeezer, and the second acts as a Sagnac interferometer. We use the theory of quantization of solitons.1 The pulse injected into the first fiber ring is a sech adjusted so as to travel as a pair of countertraveling solitons in the squeezing ring.2 The ring acts like a Mach-Zehnder interferometer folded back on itself. The pump is reflected from the pump port, and the vacuum port has squeezed vacuum emerging from it. The pump is recycled in the second Sagnac ring to act as the signal for the rotation sensing. The squeezed vacuum from the first ring is injected into the vacuum port of the Sagnac interferometer. Because practical design considerations dictate fiber lengths on the order of 100 m for both rings, the nonlinearity in the Sagnac ring cannot be neglected. It produces its own squeezing but in the wrong phase for detector noise reduction. However, by proper adjustment of the squeezing in both interferometers, it is possible to counteract the harmful squeezing effect in the Sagnac interferometer and still arrive at a net reduction of the detector noise.
Squeezing with degenerate parametric amplification sacrifices the power needed for the pump.1 Squeezing by using the third- order nonlinearity does not necessarily sacrifice the pump power, because it remains at the same frequency as the squeezed radiation. Because the third-order nonlinearity is weak, long interaction lengths must be used, i.e., optical fibers. Past experiments with quasi excitation in optical fibers were plagued by stimulated Brillouin scattering (SBS) and guided acoustic wave acoustic Brillouin scattering (GAWBS).2 The use of pulses raises the peak power and the SBS threshold, allowing use of shorter fibers. A Mach-Zehnder interferometer configuration separates the pump from the squeezed vacuum.3 This has two advantages: the pump power can be reused as the local oscillator power, and the squeezed radiation can be measured closer to zero frequency (30 kHz) because the pump fluctuations are absent.