Interaction induced photon-number entangled temporal soliton pairs

The quantum fluctuations of two out-of-phase time-separated temporal solitons are calculated. Almost perfect positive correlation between their photon-number fluctuations can be achieved after propgating a certain distance and with suitable initial separation. OCIS codes: (270.5530, 270.6570) Pulse propagation and solitons, Squeezed states. After the first realization of quantum teleportation with coherent states [1], quantum information processing with the continuous variable has attracted a lot of research interest due to its potential for providing an alternative to the single photon schemes. Nowadays, the continuous variable entangled beams have been generated by letting two squeezed fields (squeezed vacuum fields [1] or amplitude squeezed fields [2]) interfere through a beam splitter, which mathematically acts as a Hadamard transformation. In this way, squeezed states become essential parts for generating entangled continuous variables. In addition to the generation of squeezed states by the parametric down-conversion in a sub-threshold optical parametric oscillator [1], one can also generate squeezed states by using optical solitons in nonlinear optical fibers [3]. By utilizing the continuous EPR-like correlations of optical beams, one can also realize quantum key distribution [4] and entanglement swapping [5]. In this paper, we propose a simple scheme for generating continuous variable entangled states without using beam splitters, but through the nonlinear interaction between two temporal solitons. The quantum interaction of the two solitons is described by the quantum Nonlinear Schrödinger Equation (NSE) and the corresponding photon-number quantum correlations can be calculated. Besides the transient multimode correlations induced by cross-phase modulation [6], we also find nearly maximum entanglement between the photon-number fluctuations of the soliton pair. By controlling the initial separations of the two solitons, one can produce positive and almost maximum quantum correlation. The temporal soliton interaction to be studied can be described by the following normalized nonlinear Schrödinger equation: 0 | | 2 1 ) , ( 2 = + + U U U t z iU tt z (1) where z is the propagation distance, t is the retarded time. The input profile of a soliton pair can be given by: θ ρ γ ρ i e t h t h t z U ) ( sec ) ( sec ) , 0 ( − + + = = (2) where the parametersγ , θ , and ρ 2 are the relative amplitude, relative phase and the separation of the initial soliton pair. When the initial relative phase of the soliton pair is in-phase ( 0 = θ ), the two solitons will collide periodically along the propagation. Otherwise they will attract each other within some short propagating distance and then move apart eventually due to the repulsive force between them. One can evaluate the multimode quantum fluctuation structures of quantum solitons by solving the quantum nonlinear Schrödinger equation with the linearization approximation [7]. In the case of two FA3 © 2004 OSA/NLO 2004