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Optics Letters

Perturbation theory of quantum solitons:?continuum evolution and optimum squeezing by spectral filtering

Dmitry Levandovsky, Michael Vasilyev, Prem Kumar

Published Jan 1, 1999• 49 citations
Publisher

Abstract

We study the quantum-noise properties of spectrally filtered solitons in optical fibers. Perturbation theory, including a quantum description of the continuum, is used to derive a complete analytical expression for the second-order correlator of the amplitude quadrature. This correlator is subsequently used to optimize the frequency response of the filter numerically in order to achieve the minimum photon-number noise. For propagation distances up to three soliton periods, the length at which the best noise reduction occurs, a square filter is found to be approximately optimum. For longer distances, more-complicated filter shapes are predicted for the best noise reduction.

DOI
10.1364/ol.24.000043

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We study the quantum-noise properties of spectrally filtered solitons in optical fibers. Perturbation theory, including a quantum description of the continuum, is used to derive a complete analytical expression for the second-order correlator of the amplitude quadrature. This correlator is subsequently used to optimize the frequency response of the filter numerically in order to achieve the minimum photon-number noise. For propagation distances up to three soliton periods, the length at which the best noise reduction occurs, a square filter is found to be approximately optimum. For longer distances, more-complicated filter shapes are predicted for the best noise reduction.
We study the time-domain quantum-noise properties of solitons in optical fibers. Perturbation theory, including quantum description of the continuum, is used to derive a complete analytical expression for the second-order correlator of the amplitude quadrature in time domain. This correlator is subsequently used to calculate the photon-number noise reduction below the standard quantum limit by means of a time-gating filter. For propagation distances up to three soliton periods, the length at which the best noise reduction occurs, a square band-reject time filter is found to produce approximately 3.2 dB of squeezing.
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.
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.
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.