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Journal of the Optical Society of America B

Reduction of quantum noise in soliton propagation by phase-sensitive amplification

Ivan Deutsch, Izo I. Abram

Published Nov 1, 1994• 48 citations
Publisher

Abstract

We study the possibility of employing phase-sensitive parametric amplifiers to compensate for losses incurred by solitons propagating in optical fibers. As phase-sensitive amplification is free from the excess spontaneous noise associated with laser amplifiers, the only quantum noise source in such a system arises from the fiber losses. In addition, under phase-sensitive amplification, fluctuations in the soliton frequency are squeezed to one half of the vacuum level, thus producing a negligible contribution to the fluctuations in the soliton arrival time. This greatly reduces the Gordon–Haus jitter of the solitons. The performance of the phase-sensitive amplifier is compared with that of alternative noise-reduction schemes employing phase-insensitive amplifiers and spectral filters as well as with the limits on long-distance data transmission imposed by quantum mechanics.

DOI
10.1364/josab.11.002303

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We study the possibility of employing phase-sensitive parametric amplifiers to compensate for losses incurred by solitons propagating in optical fibers. As phase-sensitive amplification is free from the excess spontaneous noise associated with laser amplifiers, the only quantum noise source in such a system arises from the fiber losses. In addition, under phase-sensitive amplification, fluctuations in the soliton frequency are squeezed to one half of the vacuum level, thus producing a negligible contribution to the fluctuations in the soliton arrival time. This greatly reduces the Gordon–Haus jitter of the solitons. The performance of the phase-sensitive amplifier is compared with that of alternative noise-reduction schemes employing phase-insensitive amplifiers and spectral filters as well as with the limits on long-distance data transmission imposed by quantum mechanics.
Recently we have shown that stable soliton-like pulse propagation over ultra-long distances is possible in a nonlinear fiber line in which linear loss is balanced by periodic phase-sensitive (parametric) amplification.1 In such a line the length scale over which pulse evolution occurs is significantly increased beyond a soliton period because of the attenuation of phase variations across the pulse’s profile by the amplifiers. Here we examine the effects of quantum noise in the context of a storage ring for a bit stream of soliton-like pulses. We show that the one’s (soliton pulses) are asymptotically stable and the noise on the zero’s of the bit stream (absence of a soliton) is bounded. Moreover, we present evidence that the soliton-soliton interaction and Raman self-frequency shift are efficiently suppressed by the phase-sensitive amplifiers (PSA’s). The effects of direct timing noise and cubic dispersion in the fiber could also be decreased by using a pulsed pump (gain modulation) for the PSA’s.
Optical solitons are pulses that propagate in optical fibers without temporal or spectral distortion, owing to balancing of the second-order dispersion of the refractive index by nonlinear self-phase modulation induced by the intensity-dependent refractive index. Classically, this stationary distortion-free propagation only requires the proper choice of pulse width and shape for a given pulse energy. However, quantum fluctuations do not undergo stationary propagation but rather evolve due to dispersion and self-phase modulation. As a soliton pulse propagates, zero-point or vacuum noise associated with the pulse evolves into squeezed noise. Vacuum fluctuations are responsible for the fundamental detector noise floor known as the shot noise limit. Reduction of the noise in the detection of squeezed soliton pulses has achieved a noise level 34% below this limit. In optical fibers, thermal fluctuation of the refractive index limit the noise reduction that can be achieved by adding phase fluctuations in excess of the vacuum noise. At low frequencies thermal noise originates from local structural dynamics of fused silica which produces a 1/f power spectrum and from guided acoustic wage Brillouin scattering which modulates the refractive index at frequencies characteristic of the fiber structure. The bandwidth of these fluctuations is ~2 GHz; and for soliton pulses with spectral bandwidth much >2 GHz, we have shown that this noise can be made insignificant. For very short pulses, however, noise from Raman scattering must be considered. Recent calculations incorporating this noise mechanism are compared with experiment.
Quantum fluctuations in an optical amplifier are of fundamental as well as technological significance and lead to basic limitations on noise performance. It is well-known that the signal-to-noise ratio (SNR) of an injected signal is degraded in the amplification process due to added noise from thermal or (at best) vacuum fluctuations of the internal modes of the amplifier.[1] However, if the internal modes are coupled to a squeezed vacuum, the added noise in amplification can be reduced.[2] With this motivation, we have constructed a nondegenerate parametric amplifier whose idler mode is itself coupled to a squeezed vacuum, which is generated by a second parametric amplifier. Phase-sensitive noise amplification of a vacuum input to the signal mode is observed with the minimum amplified noise level 0.5dB below the usual phase-insensitive amplified noise level for the amplified signal of the same amplifier but with the idler mode coupled to a vacuum state. Prospects for improvement by increasing the squeezing that is coupled into the idler mode of the amplifier beyond the current level of 2dB as well as surprising results from our theoretical analysis which includes losses will be discussed.
The sensitivity of future gravitational wave interferometers is expected to be limited throughout the detection band by quantum vacuum fluctuations, which can be reduced by applying quantum optics techniques such as squeezed vacuum injection. However, decoherence caused by optical losses in the readout chain will severely limit the effectiveness of such schemes. It was proposed that effect of losses in the final stage of detection can be mitigated by a phase-sensitive amplifier placed in between the output port of the interferometer and the photodetector. In this paper we propose to implement such amplification using an optomechanical device, study some of its practical limitations, and discuss its applicability to next-generation gravitational-wave detectors.