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.
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.
Experimental demonstration of more than 50% photon-number squeezing obtained using microstructure fibers (MFs) , of which zero-dispersion wavelength locates at 820 nm, in a spectral filtering scheme with 40-fs laser pulses at /spl lambda/ = 810 nm is reported. The highest photon-number squeezing of -4.6 dB is obtained when a soliton-like Stokes Raman pulse, which broke up from the main pulse, exhibiting a self-frequency shift toward the longer wavelength, is preserved by low-pass spectral filtering from the white-light spectrum generated from the 30-cm MF.
Quantum correlations of photon numbers in different spectral components of ultrashort optical solitons have been observed experimentally. These correlations are crucial for the understanding and characterization of the internal quantum structure of soliton pulses and contribute significantly to soliton squeezing by spectral filtering. The accessible information on the nonclassical state of the correlated spectral components is discussed with the example of two modes. The method may be generalized to obtain a complete quantum description of a multimode field.
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.
Intrapulse quantum spectral correlation of photon numbers of a femtosecond optical pulse, which propagates a 5-m-long optical fiber, is presented in a matrix format for quantum noise study by numerical calculation. The calculation includes the higher-order optical effects such as intrapulse-stimulated Raman scattering and self-steepening effects, as well as self-phase modulation and group velocity dispersion. The quantum correlations between spectral components (spectral resolution of 0.7 nm) which evolve with the pulse energy are provided in a matrix format at soliton orders including the low orders,
N=0.1 to 1.0 (a 0.1 step), to give the detailed properties of spectral correlation evolutions in the matrix format. It is shown that the photon-number correlations between spectral components near the pulse spectrum center form strong correlations of a square shape in the matrix, at a soliton order
N ($\ensuremath{\le}$0.4), and then are redistributed into those between spectral components near the spectrum wings such that the cross-shaped correlation pattern in the matrix begin to be visible at
N=0.5 before their further redistribution as $N\ensuremath{\rightarrow}1.0$. In addition, significant anticorrelations can be increasingly extended to be found between spectral components near the spectrum center as $N\ensuremath{\rightarrow}1.0$, leading to the expectation that the degree of photon-number squeezing by spectral filtering for subsolitons can be lower than that for solitons. Intrapulse-stimulated Raman scattering that starts to become visible at around
N=0.6 produces an asymmetric correlation structure with respect to the spectrum center in the correlation matrices while the relevant pulse self-frequency shift becomes visible at $N\ensuremath{\ge}0.8$. The calculation presented indicates that the measurement of nonlinear effects which are not detectable distinctly at the classical level is possible at the quantum level.