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Physical Review Letters

Squeezed quantum solitons and Raman noise

S. J. Carter, P. D. Drummond

Published Dec 30, 1991• 55 citations
Publisher

Abstract

The prediction of squeezed optical pulses in single-mode fibers utilizing the Kerr effect has recently been verified for ultrashort solitonlike pulses [M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153 (1991)]. We present a substantial modification of the existing quantum theory to account for Raman quantum noise, which is the limiting factor in generating wide-band squeezing for ultrashort pulses.

DOI
10.1103/physrevlett.67.3757

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The prediction of squeezed optical pulses in single-mode fibers utilizing the Kerr effect has recently been verified for ultrashort solitonlike pulses [M. Rosenbluh and R. M. Shelby, Phys. Rev. Lett. 66, 153 (1991)]. We present a substantial modification of the existing quantum theory to account for Raman quantum noise, which is the limiting factor in generating wide-band squeezing for ultrashort pulses.
Broadband quantum noise suppression of light is required for many applications, including detection of gravitational waves, quantum sensing, and quantum communication. Here, using numerical simulations, we investigate the possibility of polarization squeezing of ultrashort soliton pulses in an optical fiber with an enlarged mode field area, such as large-mode area or multicore fibers (to scale up the pulse energy). Our model includes the second-order dispersion, Kerr and Raman effects, quantum noise, and optical losses. In simulations, we switch on and switch off Raman effects and losses to find their contribution to squeezing of optical pulses with different durations (0.1–1 ps). For longer solitons, the peak power is lower and a longer fiber is required to attain the same squeezing as for shorter solitons, when Raman effects and losses are neglected. In the full model, we demonstrate optimal pulse duration (~0.4 ps) since losses limit squeezing of longer pulses and Raman effects limit squeezing of shorter pulses.
A source of quantum noise in a non-linear optical medium is the coupling of photons with thermal phonons, called the Raman effect. This noise source sets the lower limit of squeezing in the polarisation variables for ultrashort pulses. Increasing the soliton pulse width reduces the coupling between photons and phonons by decreasing the overlap of the pulse spectrum and the Raman frequency response, which is specific to the medium. We investigate the dependence of squeezing on the soliton pulse width, to determine if improvements in squeezing result from longer pulses. We numerically solve a stochastic nonlinear Schrodinger equation with extra nonlinear terms for Raman effect (derived within the truncated Wigner approach), for a 3M FS-PM 7811 silica fibre using the pde solver XMDS 2.0. Computational efficiency was improved by use of a single-Lorentzian approximation for the Raman gain profile. Results show that squeezing can be improved for longer pulse widths. However, there is a tradeoff between the Raman effects and the classical phase noise due to guided acoustic wave Brillouin scattering.
A source of quantum noise in a non-linear optical medium is the coupling of photons with thermal phonons, called the Raman effect. This noise source sets the lower limit of squeezing in the polarisation variables for ultrashort pulses. Increasing the soliton pulse width reduces the coupling between photons and phonons by decreasing the overlap of the pulse spectrum and the Raman frequency response, which is specific to the medium. We investigate the dependence of squeezing on the soliton pulse width, to determine if improvements in squeezing result from longer pulses. We numerically solve a stochastic nonlinear Schrödinger equation with extra nonlinear terms for Raman effect (derived within the truncated Wigner approach), for a 3M FS-PM7811 silica fibre using the pde solver XMDS 2.0. Computational efficiency was improved by use of a single-Lorentzian approximation for the Raman gain profile. Results show that squeezing can be improved for longer pulse widths. However, there is a tradeoff between the Raman effects and the classical phase noise due to guided acoustic wave Brillouin scattering.
Generation of light with nonclassical properties, such as squeezed light, has gathered a lot of attention because of possible uses in such areas as quantum state engineering, quantum imaging, continuous variable quantum computing, and detection of gravitational waves. Squeezed light is generally produced by transporting light through a nonlinear medium. One such media is Kerr-nonlinear optical fibres. We aim to find the parameters for a fibre polarization squeezing setup by studying the dependencies of quantum noise suppression on the duration of the pulse and the input power. This is performed by modeling the light field propagation using the split-step Fourier method to numerically solve the stochastic nonlinear Schrödinger equation obtained by using the Wigner representation. This equation includes such physical effects as damping, quantum loss noise, dispersion, Kerr and Raman nonlinearities, and stochastic Raman noise.
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.
Comparing stochastic simulations and experimental measurements, we study the quantum dynamics of polarisation squeezing in optical fibres. Squeezing of -6.8 dB is measured, with Raman effects limiting squeezing for higher pulse energies and longer fibres. Depolarising GAWBS phase-noise adversely affects squeezing at low pulse energies. Third-order dispersion is also accounted for in the simulations, and this has an effect on pulses with more than the soliton energy. We theoretically determine the optimal pulse energy and fibre length for the best squeezing.