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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Shock waves in a chain of two-level atoms with exchange and dipole-dipole interactions

V. V. Konotop, Mario Salerno, Sachio Takeno

Published Dec 1, 1997• 14 citations
Publisher

Abstract

We use a small-amplitude multiple scale expansion to investigate the existence of shock waves in a chain of two-level atoms with both exchange and dipole-dipole interactions. We show that the exchange interaction allows the formation of the system of both bright and dark shock waves. Conversely, the dipole-dipole interaction results in the instability of the background and, as a consequence, in the prevention of the formation of shock waves. The analytical results are found to be in good qualitative agreement with a direct numerical integration of the system.

DOI
10.1103/physreve.56.7240

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We use a small-amplitude multiple scale expansion to investigate the existence of shock waves in a chain of two-level atoms with both exchange and dipole-dipole interactions. We show that the exchange interaction allows the formation of the system of both bright and dark shock waves. Conversely, the dipole-dipole interaction results in the instability of the background and, as a consequence, in the prevention of the formation of shock waves. The analytical results are found to be in good qualitative agreement with a direct numerical integration of the system.
Dark and bright soliton solutions (excitons) in one-dimensional chains of two-level atoms with exciton-exciton, dipole-dipole, and exchange interactions are obtained. It is shown that in some limiting cases evolution equations resulting from model Hamiltonians are reduced to the exactly integrable Ablowitz-Ladik model. Bloch oscillations of the excitons in inhomogeneous magnetic field and effects originated by the energy shift are discussed. An example of a multidimensional dark exciton is represented.
We show that the perturbative nonlinearity associated with three-atom interactions, competing with standard two-body repulsive interactions, can change dramatically the evolution of one-dimensional (1D) dispersive shock waves in a Bose-Einstein condensate. In particular, we prove the existence of a rich crossover dynamics, ranging from the formation of multiple shocks regularized by nonlinear oscillations culminating in coexisting dark and antidark matter waves to 1D-soliton collapse. For a given scattering length, all these different regimes can be accessed by varying the density of atoms in the condensate.
Motivated by recent experimental results, we present a systematic theoretical analysis of dark-bright-soliton interactions and multiple-dark-bright-soliton complexes in atomic two-component Bose-Einstein condensates. We study analytically the interactions between two dark-bright solitons in a homogeneous condensate and then extend our considerations to the presence of the trap. We illustrate the existence of robust stationary dark-bright-soliton ``molecules,'' composed of two or more solitons, which are formed due to the competition of the interaction forces between the dark- and bright-soliton components and the trap force. Our analysis is based on an effective equation of motion, derived for the distance between two dark-bright solitons. This equation provides equilibrium positions and characteristic oscillation frequencies of the solitons, which are found to be in good agreement with the eigenfrequencies of the anomalous modes of the system.
We study cooperative effects on the radiation interaction of a pair of two-level atoms with a spatial separation r\ensuremath{\ll}${\ensuremath{\lambda}}_{0}$ much closer than the optical wavelength of the dipole transition. In this regime we allow for charge exchange between the atoms (hybridization), which leads to qualitatively different behavior in contrast to an isolated pair of atoms because of the presence of the monopole Coulomb interaction. The interaction of the atoms with the radiation field and an external classical driving field is treated within a master equation approach. The numerical as well as the analytical results indicate the existence of quantum beats in the radiative decay of the system. In the case of an external driving field the system shows a dark resonance for a fixed detuning independent of the strength of the external field.
We study formation of solitons induced by counterflows of immiscible superfluids. Our setting is based on a quasi-one-dimensional binary Bose-Einstein condensate, composed of two immiscible components with large and small numbers of atoms in them. Assuming that the ``small'' component moves with constant velocity, either by itself, or being dragged by a moving trap, and intrudes into the ``large'' counterpart, the following results are obtained. Depending on the velocity, and on whether the small component moves in the absence or in the presence of the trap, two-component dark-bright solitons, scalar dark solitons, or multiple dark solitons may emerge, the last outcome taking place due to breakdown of the superfluidity. We present two sets of analytical results to describe this phenomenology. In an intermediate velocity regime, where dark-bright solitons form, a reduction of the two-component Gross-Pitaevskii system to an integrable Mel'nikov system is developed, demonstrating that solitary waves of the former are very accurately described by analytically available solitons of the latter. In the high-velocity regime, where the breakdown of the superfluidity induces the formation of dark solitons and multisoliton trains, an effective single-component description, in which a strongly localized wave packet of the ``small'' component acts as an effective potential for the ``large'' one, allows us to estimate the critical velocity beyond which the coherent structures emerge in good agreement with the numerical results.