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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Fabry-Perot resonators for matter-wave solitons

V. Ahufinger, Boris A. Malomed, G. Birkl, R. Corbalán, Anna Sanpera

Published Jun 1, 2009• 0 citations
Publisher

Abstract

The interaction of a MW GS with a double-barrier potential resembling a Fabry- Perot cavity formed by two potential barriers. The behaviour of the incident soliton hitting the first barrier remains as described above, i.e., an abrupt transition from perfect transmission to perfect reflection occurs. Nevertheless, when the height of the barriers is close to this transition, and the length of the cavity is larger than the size of the soliton, the soliton which has passed the first barrier may get trapped in the cavity, in a state of oscillatory motion. Thus, three scenarios are identified in the interaction of the incident soliton with the double- barrier structure: complete reflection, complete transmission, and trapping into the oscillatory state. It is relevant to note that the GS may be trapped in the cavity entirely, without losses.

DOI
10.1109/cleoe-eqec.2009.5192422

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The interaction of a MW GS with a double-barrier potential resembling a Fabry- Perot cavity formed by two potential barriers. The behaviour of the incident soliton hitting the first barrier remains as described above, i.e., an abrupt transition from perfect transmission to perfect reflection occurs. Nevertheless, when the height of the barriers is close to this transition, and the length of the cavity is larger than the size of the soliton, the soliton which has passed the first barrier may get trapped in the cavity, in a state of oscillatory motion. Thus, three scenarios are identified in the interaction of the incident soliton with the double- barrier structure: complete reflection, complete transmission, and trapping into the oscillatory state. It is relevant to note that the GS may be trapped in the cavity entirely, without losses.
We investigate collisions of solitons of the gap type, supported by a lattice potential in repulsive Bose-Einstein condensates, with an effective double-barrier potential that resembles a Fabry-Perot cavity. We identify conditions under which the trapping of the entire incident soliton in the cavity is possible. Collisions of the incident soliton with an earlier trapped one are considered too. In the latter case, many outcomes of the collisions are identified, including merging, release of the trapped soliton with or without being replaced by the incoming one, and trapping of both solitons.
The interaction of matter–wave solitons with a potential barrier is a fundamentally important problem, and the splitting and subsequent recombination of the soliton by the barrier is the essence of soliton matter–wave interferometry. We demonstrate the three-dimensional (3D) character of the interactions in the case relevant to ongoing experiments, where the number of atoms in the soliton is relatively close to the collapse threshold. We examine the soliton dynamics in the framework of the effectively one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE), which admits the collapse in a modified form, and in parallel we use the full 3D Gross–Pitaevskii equation (GPE). Both approaches produce similar results, which are, however, quite different from those produced in recent work that used the 1D cubic GPE. Basic features, produced by the NPSE and the 3D GPE alike, include (a) an increase in the first reflection coefficient for increasing barrier height and decreasing atom number; (b) large variation of the secondary reflection/recombination probability versus barrier height; (c) pronounced asymmetry in the oscillation amplitudes of the transmitted and reflected fragments; and (d) enhancement of the transverse excitations as the number of atoms is increased. We also explore effects produced by variations of the barrier width and outcomes of the secondary collision upon phase imprinting on the fragment in one arm of the interferometer.
We study the possibility of implementing a quantum switch and a quantum memory using matter-wave lattice solitons and making them interact with 'effective' potentials (barrier/well) corresponding to defects of the optical lattice. In the case of interaction with an 'effective' potential barrier, the bright lattice soliton experiences an abrupt transition from complete transmission to complete reflection (quantum switch) for a critical height of the barrier. The trapping of the soliton in an 'effective' potential well and its release on demand, without losses, shows the feasibility of using the system as a quantum memory. The inclusion of defects as a way of controlling the interactions between two solitons is also reported.
The interaction of matter-wave solitons with a potential barrier is a fundamentally important problem, and the splitting and subsequent recombination of the soliton by the barrier is the essence of soliton matter-wave interferometry. We demonstrate the three-dimensional (3D) character of the interactions in the case relevant to ongoing experiments, where the number of atoms in the soliton is sufficiently large that the soliton is close to collapse. The mean-field description is quite accurate, but the proximity to the collapse threshold makes the use of the 1D Gross-Pitaevskii equation (GPE) irrelevant. We examine the soliton dynamics in the framework of the effectively 1D nonpolynomial Schr{\\"{o}}dinger equation (NPSE), which admits the collapse in a modified form, and in parallel we use the full 3D GPE. Both approaches produce results which are very different from those produced in recent work which used the 1D cubic GPE. The features observed in both the NPSE and the 3D GPE include (a) an increase in the first reflection coefficient for increasing barrier height and decreasing atom number; (b) strong modulation in the secondary reflection/recombination probability vs. barrier height; (c) a pronounced asymmetry in the oscillation amplitudes of the transmitted and reflected fragments; (d) an enhancement of the transverse excitations as the number of atoms is increased. We also explore effects produced by variations of the barrier width and outcomes of the secondary collision upon phase imprinting on the fragment in one arm of the interferometer.
We study the possibility of implementing a quantum switch and a quantum memory using matter-wave lattice solitons and making them interact with 'effective' potentials (barrier/well) corresponding to defects of the optical lattice. In the case of interaction with an 'effective' potential barrier, the bright lattice soliton experiences an abrupt transition from complete transmission to complete reflection ( quantum switch) for a critical height of the barrier. The trapping of the soliton in an 'effective' potential well and its release on demand, without losses, shows the feasibility of using the system as a quantum memory. The inclusion of defects as a way of controlling the interactions between two solitons is also reported.
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.