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arXiv:1605.02647 · Physical Review A

Coherent emission of atomic soliton pairs by Feshbach-resonance tuning

Humberto Michinel, Ángel Paredes, María Martínez Valado, David Feijoo

Published Jul 16, 2012• 14 citations
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Abstract

We present two simple designs of matter-wave beam splitters in a trapped Bose-Einstein condensate (BEC). In our scheme, identical pairs of atomic solitons are produced by an adequate control---in time and/or space---of the scattering length. Our analysis is performed by numerical integration of the Gross-Pitaevskii equation and supported by several analytical estimates. Our results show that these devices can be implemented in the frame of current BEC experiments. The system has potential applications for the construction of a soliton interferometer.

DOI
10.1103/physreva.86.013620

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We present two simple designs of matter-wave beam splitters in a trapped Bose-Einstein condensate (BEC). In our scheme, identical pairs of atomic solitons are produced by an adequate control---in time and/or space---of the scattering length. Our analysis is performed by numerical integration of the Gross-Pitaevskii equation and supported by several analytical estimates. Our results show that these devices can be implemented in the frame of current BEC experiments. The system has potential applications for the construction of a soliton interferometer.
We discuss the possibility of emitting vector solitons from a two-component elongated BEC by manipulating in time the inter- or intraspecies scattering lengths with Feshbach resonance tuning. We present different situations which do not have an analog in the single species case. In particular, we show vector soliton outcoupling by tuning the interspecies forces, how the evolution in one species is controlled by tuning the dynamics of the other, and how one can implement the so-called supersolitons. The analysis is performed by numerical simulations of the one-dimensional Gross-Pitaevskii equation. Simple analytic arguments are also presented in order to give a qualitative insight.
We present three families of one-soliton solutions for (2+1)-dimensional Gross—Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose—Einstein condensates (BECs) by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments.
We present three families of one-soliton solutions for (2+l)-dimensional Gross-Pitaevskii equation withboth time-dependent scattering length and gain or loss in a harmonic trap.Then we investigate the dynamics of thesesolitons in Bose-Einstein condensates (BECs) by some selected control functions.Our results show that the intensitiesof these solitons first increase rapidly to the condensation peak,then decay very slowly to the background;thus thelifetime of a bright soliton,a train of bright solitons and a dark soliton in BECs can be all greatly extended.Our resultsoffer a useful method for observing matter-wave solitons in BECs in future experiments.
Bright solitons in a quasi-1D Bose–Einstein condensate can be used to enhance precision in matter-wave interferometry, due to their inherent robustness and support against dispersion. Such a soliton interferometer typically relies on a potential barrier used to split a single soliton into two smaller coherent solitons which can then be recombined on the same barrier. In this thesis we examine two extensions to this scheme. Firstly, we investigate a binary BEC system consisting of two bright solitons which are coupled through a mutual nonlinear interaction term. We derive a set of conditions under which the two components can be separated on a potential barrier and use numerical simulations to probe the regimes beyond which this mathematical treatment is applicable. We then use the numerical simulations to look at the effect of the nonlinear coupling on the dynamics of the binary solitons interacting with the barrier. We also look at the interference behaviour found by doubling the simulation time in either a ring trap or a harmonic trapping potential (to ensure recombination on the barrier); as well as the case where the solitons start spatially separated on either side of the barrier in order to find conditions under which the solitons will combine on the barrier. We find a good agreement between the analytical predictions and the results of simulations. Beyond the regions of parameter space where the predictions are expected to hold, we find complex transmission and interference behaviour as a result of nonlinear effects. The second part of this thesis consists of an examination of the prospect of using a subwavelength barrier scheme in a soliton interferometry experiment. This involves using two resonant coupling beams in a Λ-system with a spatially varying intensity. Under certain conditions, this can be used to form an effective potential barrier with a width which is not diffraction-limited. We look at suitable parameter regimes for such a barrier to split and recombine solitons in an interferometer and probe the effects of possible complications such as misalignment in the beams and different scattering lengths in the different states. We simulate the soliton interferometer using the full three component GPE as well as the single component analogue with the effective potential in order to characterise the soliton behaviour and the dependence of the interferometer sensitivity on the system parameters. We find a trend towards an idealised soliton interferometer with a decreasing value of the parameter, w, controlling the barrier characteristics. Also, we demonstrate an agreement between the relevant three component GPE and the analogous single component GPE, in the limit of strong coupling fields.
We demonstrate, through numerical simulations, the controllable emission of matter-wave bursts from a Bose-Einstein condensate in a shallow optical dipole trap. The process is triggered by spatial variations of the scattering length along the trapping axis. In our approach, the outcoupling mechanisms are atom-atom interactions and thus, the trap remains unaltered. Once emitted, the matter wave forms a robust soliton. We calculate analytically the parameters for the experimental implementation of these matter-wave bursts of solitons.