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Physical Review A

Asymmetric Rosen-Zener–like transition through a soliton–surface-plasmon photonic Josephson junction with spatially varying coupling

Güneş Aydındoğan, Kaan Güven

Published Nov 1, 2017• 2 citations
Publisher

Abstract

The transition dynamics of photons between an optical soliton in a nonlinear dielectric waveguide and a spatially coupled surface-plasmon excitation on a parallel flat metal surface can be formulated in analogy to that of a Josephson junction of two-level (double-well) Bose-Einstein condensates, albeit with a nonlinear coupling that inherently depends on the population imbalance of the levels. The present work demonstrates that asymmetric Rosen-Zener--like transitions can be obtained through this optical Josephson junction, by turning on and off the coupling across a hyperbolically varying separation between the soliton and the surface-plasmon. The transitions can generate full population transfer, population splitting, or merging between the quasistationary initial and final states, which are defined by a fixed population imbalance in the decoupled limit. Transitions from a pure soliton or pure surface-plasmon initial state are found to be robust against the relative phase, whereas the transitions from an initial state with mixed population depend strongly on the relative phase. The soliton--surface-plasmon system also bears similarities to the spatially coupled optical waveguides which are introduced further as the classical analogs of the spatial adiabatic passage and stimulated Raman adiabatic passage mechanisms in quantum and atom optics.

DOI
10.1103/physreva.96.053802

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The transition dynamics of photons between an optical soliton in a nonlinear dielectric waveguide and a spatially coupled surface-plasmon excitation on a parallel flat metal surface can be formulated in analogy to that of a Josephson junction of two-level (double-well) Bose-Einstein condensates, albeit with a nonlinear coupling that inherently depends on the population imbalance of the levels. The present work demonstrates that asymmetric Rosen-Zener--like transitions can be obtained through this optical Josephson junction, by turning on and off the coupling across a hyperbolically varying separation between the soliton and the surface-plasmon. The transitions can generate full population transfer, population splitting, or merging between the quasistationary initial and final states, which are defined by a fixed population imbalance in the decoupled limit. Transitions from a pure soliton or pure surface-plasmon initial state are found to be robust against the relative phase, whereas the transitions from an initial state with mixed population depend strongly on the relative phase. The soliton--surface-plasmon system also bears similarities to the spatially coupled optical waveguides which are introduced further as the classical analogs of the spatial adiabatic passage and stimulated Raman adiabatic passage mechanisms in quantum and atom optics.
We examine the quantum dynamics of surface plasmons weakly coupled to optical soliton photons in a metal-dielectric-nonlinear Kerr medium interface. We consider a photon-number-dependent coupling model which is a heuristic extension of the classical soliton excitation of surface plasmons in the quantum limit. The coupling coefficient additionally depends on the distance between the dielectric and the metal. We propose a practical scheme to control the number of surface plasmons using a Gaussian variation of the metal-dielectric spatial separation. Our numerical simulations show that the curvature of the Gaussian distance profile can be used for controlling the number of surface plasmons.
We show that the transfer of matter-wave solitons and half-vortex solitons in a spin-orbit coupled Bose-Einstein condensate between two (or more) arbitrarily chosen sites of an optical lattice can be implemented using the adiabatic passage. The underlying linear Hamiltonian has a flat band in its spectrum, so that even sufficiently weak interatomic interactions can sustain well-localized Wannier solitons which are involved in the transfer process. The adiabatic passage is assisted by properly chosen spatial and temporal modulations of the Rabi frequency. Within the framework of a few-mode approximation, the mechanism is enabled by a dark state created by coupling the initial and target low-energy solitons with a high-energy extended Bloch state, like in the conventional stimulated Raman adiabatic passage used for the coherent control of quantum states. In real space, however, the atomic transfer between initial and target states is sustained by the current carried by the extended Bloch state, which remains populated during the whole process. The full description of the transfer is provided by the Gross-Pitaevskii equation. Protocols for the adiabatic passage are described for one- and two-dimensional optical lattices, as well as for splitting and subsequent transfer of an initial wave packet simultaneously to two different target locations. Published by the American Physical Society 2024
Transition dynamics have been studied widely in two-mode Bose–Einstein condensate systems with linear coupling effects. Nonlinear interaction between atoms would induce a nonlinear Josephson oscillation, which admits an oscillation form different from the classical Josephson oscillation. Similar extensions for the Rosen–Zener transition and the Landau–Zener transition also suggest that a strong nonlinear strength would induce nonlinear-type transition dynamics, which is in sharp contrast to the linear process. Interestingly, here we show a standard Josephson oscillation that has a constant linear coupling strength, no matter how great the nonlinear interaction strength is. This characteristic is in sharp contrast to the nonlinear Josephson oscillation reported before in nonlinear coupled systems. By manipulating the linear coupling strength with the RF field, we demonstrate that the Rosen–Zener transition particles, with an invariant distribution profile, can be managed well under exponential and periodic forms. The nonlinear interaction strength is found to have no effect on the transition rate between atoms in the two components for the case where the inter- and intra-atomic interaction strengths are equal. Furthermore, we test the robustness of the transition dynamics against parameter deviations and noises in the initial condition. These results are helpful for controllable quantum state preparations.
We consider a generalization of a recently proposed non-Hermitian model for resonant cavities coupled by a chiral mirror by taking into account number non-conservation and nonlinear interactions. We analyze non-Hermitian quantum dynamics of populations and entanglement of the cavity modes. We find that the interplay between initial coherence and non-Hermitian coupling leads to a counterintuitive population transfer. While an initially coherent cavity mode is depleted, the other empty cavity can be populated more than or less than the initially filled one. Moreover, the presence of nonlinearity yields population collapse and revival as well as bipartite entanglement of the cavity modes. In addition to coupled cavities, we point out that similar models can be found in -symmetric Bose-Hubbard dimers of Bose-Einstein condensates or in coupled soliton-plasmon waveguides. We specifically illustrate the quantum dynamics of populations and entanglement in a heuristic model that we propose for a soliton-plasmon system with soliton amplitude-dependent asymmetric interaction. Degree of asymmetry, nonlinearity and coherence are examined to control plasmon excitations and soliton-plasmon entanglement. Relations to -symmetric lasers and Jahn-Teller systems are pointed out.
We investigate the dynamics of Einstein-Podolsky-Rosen steering in a soliplasmonic system where the asymmetrical coupling between linear solitons and nonlinear plasmons is controlled by the weak soliton amplitude. We employ non-Hermitian quantum dynamics to evaluate quantum steering witnesses for different coupling strengths. Quantum steering is examined for an initially Fock state and we briefly discuss Einstein-Podolsky-Rosen entanglement for initially coherent states. We numerically investigate the adjustability of the witnessing periods of quantum steering via tunable coupling strength of soliton-plasmon interaction and discuss the possibility of the nonlinear soliplasmonic systems as a robust platform for implementing one-sided quantum key distributions.
We study the Rosen-Zener transition (RZT) in a nonlinear two-level system in which the level energies depend on the occupation of the levels, representing a mean-field type of interaction between the particles. We find that the nonlinearity could affect the quantum transition dramatically. At certain nonlinearity the 100% population transfer between two levels is observed and found to be robust over a very wide range of external parameters. On the other hand, the quantum transition could be completely blocked by a strong nonlinearity. In the sudden and adiabatic limits we have derived analytical expressions for the transition probability. Numerical explorations are made for a wide range of parameters of the general case. Possible applications of our theory to Bose-Einstein condensates (BECs) and solid-state physics are discussed.