Squeezing of quantum noise in optical solitons
One of the most beautiful manifestations of optical nonlinearity is propagation of solitons in optical fiber. Despite the presence of chromatic dispersion, the solitons preserve their pulse shape by balancing the phase shift due to dispersion with the one due to Kerr nonlinearity. This property, as well as the ability of the solitons to re-adjust themselves in response to external perturbations have been utilized in all-optical regeneration and high-capacity ultra-long-haul transmission experiments.The focus of our theoretical and experimental studies in this area has been on using solitons in the fiber to generate non-classical states of light (e.g. sub-Poissonian or squeezed light) with photon-number or quadrature fluctuations well below the standard quantum level of coherent-state light. For continuous-wave (single-mode) field, quantum noise reduction is well known (Fig. 1), but is not very productive because of significant parasitic effects arising from Brillouin scattering in the necessarily long length of fiber. Thus, short-pulse approach is preferred, since it requires much shorter fiber, and the solitons are particularly advantageous because they can overcome the pulse spreading due to dispersion.
Fig. 1. Evolution of electric field under nonlinear propagation in Kerr medium. Gray area represents the uncertainty due to quantum zero-point fluctuations. After the propagation, the electric field phasor is rotated by the amount of nonlinear phase shift, so that positive fluctuations of the amplitude lead to larger rotation angle, and vice versa. The resulting uncertainty area becomes elliptical (squeezed), with reduced fluctuations along the minor axis positioned at an angle with the output field.
The soliton noise squeezing necessarily involves multimode treatment and can be described by several approaches. The most physically intuitive is the one based on soliton perturbation theory, which projects the perturbations onto the eigenfunctions of the linearized Shrodinger equation. These eigenfunctions correspond to four parameters associated with the propagating soliton pulse (photon number, phase, time, and frequency) and a continuous spectrum of modes representing the dispersive radiation shed by pulse transforming into the soliton. The perturbative method was first applied to the quantum noise of solitons by Haus and Lai [1] who considered the four discrete modes of the soliton. We extended this approach by developing the complete perturbation theory of quantum solitons, with full account for the modes of the soliton continuum [2,3]. The effect of the soliton continuum turned out to be important in the several experimentally-important situations described below:
Amplitude noise squeezing by spectral filtering of the solitons
Soliton noise squeezing in asymmetric nonlinear-optical loop mirror
Soliton squeezing in nonlinear Mach-Zehnder interferometer [4]
Optimum detection of the solitons
References
- H. A. Haus and Y. Lai, "Quantum theory of soliton squeezing: a linearized approach," J. Opt. Soc. Am. B 7, 386 (1990).
- D. Levandovsky, M. Vasilyev, and P. Kumar, "Perturbation theory of quantum solitons: continuum evolution and optimum squeezing by spectral filtering," Opt. Lett. 24, 43 (1999).
- D. Levandovsky, M. Vasilyev, and P. Kumar, "Soliton squeezing in a highly transmissive nonlinear optical loop mirror," Opt. Lett. 24, 89 (1999).
- M. Fiorentino, J. E. Sharping, P. Kumar, D. Levandovsky, and M. Vasilyev, "Soliton squeezing in a Mach-Zehnder fiber interferometer," Phys. Rev. A 6403, 1801 (2001).
