Photon trapping and transfer with solitons

Abstract

We show, numerically, that a single photon trapped by a soliton in a Kerr nonlinear medium can be transferred from one soliton to another when the captor soliton undergoes collision with a second soliton. Soliton collisions can also be used in this way to realize a beam splitter, as well as a mode-separating beam splitter, analogous to the usual polarizing beam splitter. We discuss briefly the feasibility of an optical fiber implementation and possible applications to quantum-information processing. DOI: 10.1103/PhysRevA.79.021802 PACS number͑s͒: 42.65.Tg, 42.50.Ex, 42.65.Jx, 42.79.Fm An optical soliton in a homogeneous medium such as a fiber is characterized, ideally, by undistorted propagation and elastic collisions. It arises because of an intensity-dependent change in the fiber's refractive index. For a temporal soliton, this refractive index change creates a traveling potential, which can serve as a waveguide for another optical pulse ͑the probe͒. Similarly, a spatial soliton imprints a waveguide in the medium, an effect that has been confirmed in both Kerr ͓1͔ and photorefractive media ͓2-5͔. In this Rapid Communication we show that when a soliton ͑the pump͒ collides with another soliton, the corresponding probe wave can be transferred almost perfectly from one soliton to another, or, depending on the conditions, split between two solitons, in perfect analogy to a beam splitter.In the quantum limit where the probe wave represents a single photon, these effects may find application to the storage, transport, and routing of qubits. Its delivery by a soliton means that a single photon will be subject to reduced dispersion compared with unguided transmission; its arrival time will be known more precisely and timing jitter reduced. This may be beneficial in quantum-communication applications as bit rates and propagation distances increase. Beyond this, the proposed implementation of a mode-splitting beam splitter suggests application to quantum computing using linear optics ͓6͔. Pittman et al. ͓7͔ show, in fact, that a polarizing beam splitter completely analogous to the mode-splitting beam splitter described here can be used to realize a controlled-NOT gate. Soliton-guided photons-in a fiber, for example-may thus provide a natural medium for optical quantum gate implementation.Following Manassah ͓8,9͔, de la Fuente and Barthelemy ͓1͔, and Ostrovskaya et al. ͓10͔ we model the system of interest with two coupled wave equations, the first being a standard cubic nonlinear Schrödinger equation for the pump, and the second a linear wave equation for the probe signal, which is assumed to be very much weaker than the pump. Thus, the propagation of the pump signal P͑z , t͒ is governed bywhere t is local time, z is propagation distance, ␤ 2p represents the group velocity dispersion of the pump, and ␥ p is a nonlinearity parameter. We neglect higher-order dispersion and assume a lossless medium with an instantaneous electronic response. We would like to use the exact two-soliton solution given in ͓11͔. To this end we...

Computing in Verotoxin

“…[2] Significantr esults haveb eeno btainedi nc ollision-basedc omputingw iths olitons, [3][4][5][6] includingc onstructiono ff unctionally completes etso f logic gates, [7] information transferb etween colliding solitons, [8] computationv ia phase coding, [1] quantum computingv ia the entanglement of solitons in theF renkel-Kontorova model. [9] Gliders in cellular automataare discretephenomenological analogieso fs olitons.…”

Soliton-guided phase shifter and beam splitter

“…This paper focuses on controlling the phase of light wave packets captured by solitons, extending the work reported in [1]. We propose, analyze, and study numerically a phase shifter, and we study in some detail both phase and magnitude characteristics of the operator determined by a soliton-guided nonpolarizing beam splitter.…”

“…As in [1] we adopt the formulation in [2,[7][8][9]: two coupled wave equations. The large-signal pump, P (z, t), is described by the standard cubic nonlinear Schrödinger equation; the probe signal, u(z, t), which is assumed to be very much smaller than the pump, is described by a linear wave equation; and the pump determines the potential seen by the probe:…”

“…For the purposes of this paper, we choose the simplest groundstate solution, m = = 1, and, as in [1], determine β 2s from the other parameters to make this so. The eigenvalue E = k 2 R β 2s /2, and u(t) = sech(k R t).…”

“…This waveguide can be used to capture an electromagnetic wave [2][3][4][5][6]. It was shown in [1] that soliton collisions can be used to transfer the captured wave, or probe, from one soliton to another and, when the transfer is incomplete, split the wave as in a beam splitter. We next review the model.…”