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Physical Review Letters

Observation of Optical Soliton Photon-Number Squeezing

Stephen R. Friberg, S. Machida, M. J. Werner, Amikam Levanon, Takaaki Mukai

Published Oct 28, 1996• 149 citations
Publisher

Abstract

We report the photon-number squeezing of optical solitons. 2.7 ps pulses were launched as solitons down a 1.5 km optical fiber. For energies slightly above that of fundamental solitons, they broadened spectrally due to self-phase modulation caused by ${\ensuremath{\chi}}^{(3)}$ nonlinearities. Filtering away outlying components of the broadened spectra squeezed the soliton's photon-number fluctuations to 2.3 dB (41%) below the shot-noise limit. Accounting for losses, this corresponds to 3.7 dB (57%) photon-number squeezing. A quantum field-theoretic model shows that the outlying spectral components have large energy fluctuations, so that their removal causes squeezing.

DOI
10.1103/physrevlett.77.3775

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Physical Review Letters•Sep 21, 1998•149 citations
We report the photon-number squeezing of optical solitons. 2.7 ps pulses were launched as solitons down a 1.5 km optical fiber. For energies slightly above that of fundamental solitons, they broadened spectrally due to self-phase modulation caused by \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3) nonlinearities. Filtering away outlying components of the broadened spectra squeezed the soliton's photon-number fluctuations to 2.3 dB (41%) below the shot-noise limit. Accounting for losses, this corresponds to 3.7 dB (57%) photon-number squeezing. A quantum field-theoretic model shows that the outlying spectral components have large energy fluctuations, so that their removal causes squeezing.
Photon number squeezing of spectrally filtered optical solitons has been observed in the sub-picosecond regime, where the Raman effect changes the internal quantum structure of each pulse. 160 fs pulses were propagated down a 10 m optical fibre of anomalous group velocity dispersion. At energies below the soliton energy subsequent spectral filtering with an optical band-pass squeezed the directly detected photocurrent fluctuations to 3.2 ± 0.1 dB (52%) below the shot-noise limit. This implies 4.5 dB (65%) of soliton photon number squeezing, if detection losses are taken into account. Using a spectral edge filter the spectral components of the pulses are shown to contribute asymmetrically to the squeezing due to stimulated Raman scattering.
Summary form only given.Spectral filtering of optical solitons has been demonstrated to squeeze their photon-number uncertainty up to a measured value of 3.8 dB. The squeezing has been explained in terms of an uneven spectral distribution of photon-number noise caused by the Kerr nonlinearity of the fiber. Some indication for correlations among different frequency components has been found in a numerical analysis. We present the first experimental evidence for such spectral correlations. The experimental setup is shown. Pulses of 130 fs centered at 1.5 /spl mu/m are launched into a 2.9-m polarization-presenting single-mode optical fiber with energies close to the fundamental soliton energy.
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 requires only the proper choice of pulse width and shape for a given pulse energy. However, quantum mechanical zero-point fluctuations of the amplitude and phase of the optical pulse limit the precision with which this pulse shape can be produced. These quantum fluctuations do not undergo stationary propagation but, rather, evolve because of dispersion and self-phase modulation, As a soliton pulse propagates, this zero-point or vacuum noise associated with the pulse evolves into squeezed noise owing to self-phase modulation in the fiber.1,2
We present new results on photon number squeezing of spectrally filtered solitons in fibers. The impact of frequency low-, high-, and bandpass filtering on noise reduction has been measured as a function of fiber length for 130-fs pulses close to the soliton energy. For short fibers our results agree qualitatively with theoretical predictions. For longer fibers, however, the measured squeezing increases to an unexpectedly large value. Filtering out the long-wavelength components of strongly Raman-shifted, higher energy pulses squeezed the directly detected photocurrent fluctuations down to 3.8+/-0,2 dB (59%) below the shot noise level. The measured noise reductions are broadband from 5 to 90 MHz.
Summary form only given.We describe numerical and experimental investigations of the use of soliton spectral filtering in the spatial domain. As is well known, the nonlinear Schrodinger equation description of optical soliton propagation in single-mode fibers applies equally well to spatial solitons in nonlinear planar waveguides. Therefore, we can expect that the photon-number squeezing methods that work for temporal solitons in optical fibers apply equally well to spatial solitons. The spatial-soliton equivalent of spectral filtering is to use a spatial slit to remove the edge portions of the spatial soliton after it emerges from the planar waveguide. To optimize the experimental configuration, we have modeled the spatial-soliton propagation using a numerical quantum propagation code. Our results show that optimal squeezing is obtained at propagation distances of several soliton periods for solitons with the order N/spl sim/1.2. To experimentally demonstrate photon number squeezing by spatial filtering of spatial solitons, we have fabricated an AlGaAs planar waveguide that is 1.5 /spl mu/m thick and 1-3 cm long. For our device, the bandgap is in the vicinity of 0.8 /spl mu/m, so by using short pulses from a color-center laser tuned to 1.5- to 1.6-/spl mu/m wavelengths, we can excite reasonably large nonlinearities due to two-photon and three-photon resonances in the bandgap. This allows us to create spatial solitons. Spatial solitons created by color-center laser pulses are spatially windowed by slits at the output of the planar waveguide. The spatially filtered pulses are transmitted to a balanced mixer-detector arrangement that allows measurement of the noise of the windowed pulses relative to the shot-noise level.
Direct photon-number squeezing is demonstrated, for the first time to our knowledge, in a nonlinear fiber-optic interferometer. Launching 126-fs solitons into a highly asymmetric Sagnac loop, the maximum photocurrent noise reduction was $3.9\ifmmode\pm\else\textpm\fi{}0.2\mathrm{dB}$ below shot noise, corresponding to $6.0\ifmmode\pm\else\textpm\fi{}0.9\mathrm{dB}$, when corrected for linear losses. The loop is a model system for squeezing generated by the interference of two pulses after nonlinear propagation through a fiber.