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arXiv:1601.07889 · New Journal of Physics

Matter-wave soliton interferometer based on a nonlinear splitter

Hidetsugu Sakaguchi, Boris A. Malomed

Published Feb 22, 2016• 71 citations
arXivHTMLPDF

Abstract

We elaborate a model of the interferometer which, unlike previously studied ones, uses a local ( δ -functional) nonlinear repulsive potential, embedded into a harmonic-oscillator trapping potential, as the splitter for the incident soliton. An estimate demonstrates that this setting may be implemented by means of the localized Feshbach resonance controlled by a focused laser beam. The same system may be realized as a nonlinear waveguide in optics. Subsequent analysis produces an exact solution for scattering of a plane wave in the linear medium on the δ -functional nonlinear repulsive potential, and an approximate solution for splitting of the incident soliton when the ambient medium is nonlinear. The most essential result, obtained by means of systematic simulations, is that the use of the nonlinear splitter provides the sensitivity of the soliton-based interferometer to the target, inserted into one of its arms, which is much higher than the sensitivity provided by the usual linear splitter.

DOI
10.1088/1367-2630/18/2/025020

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We elaborate a model of the interferometer which, unlike previously studied ones, uses a local ( δ -functional) nonlinear repulsive potential, embedded into a harmonic-oscillator trapping potential, as the splitter for the incident soliton. An estimate demonstrates that this setting may be implemented by means of the localized Feshbach resonance controlled by a focused laser beam. The same system may be realized as a nonlinear waveguide in optics. Subsequent analysis produces an exact solution for scattering of a plane wave in the linear medium on the δ -functional nonlinear repulsive potential, and an approximate solution for splitting of the incident soliton when the ambient medium is nonlinear. The most essential result, obtained by means of systematic simulations, is that the use of the nonlinear splitter provides the sensitivity of the soliton-based interferometer to the target, inserted into one of its arms, which is much higher than the sensitivity provided by the usual linear splitter.
We consider a matter-wave bright soliton interferometer composed of a harmonic potential trap with a Rosen-Morse barrier at its center on which an incident soliton collides and splits into two solitons. These two solitons recombine after a dipole oscillation in the trap at the position of the barrier. We focus on the characterization of the splitting process in the case in which the reflected and transmitted solitons have the same number of atoms. We obtain that the velocity of the split solitons strongly depends on the nonlinearity and on the width of the barrier and that the reflected soliton is in general slower than the transmitted one. Also, we study the phase difference acquired between the two solitons during the splitting and we fit semianalytically the main dependences with the velocity of the incident soliton, the nonlinearity, and the width of the barrier. The implementation of the full interferometer sequence is tested by means of the phase imprinting method.
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 introduce a new method to achieve long-lived Bloch oscillations and dynamical localization of matter wave gap solitons in optical lattices. The method is based on the time-dependent modulations of the nonlinearity which can be experimentally implemented by means of the Feshbach resonance technique. In particular, we show that the width of the wavepacket is preserved if the time modulations of the nonlinearity are taken proportional to the curvature of the linear band spectrum which for most typical experimental settings are well approximated by harmonic time modulations of proper frequencies.
Solitons are long-lived wavepackets that propagate without dispersion and exist in a wide range of one-dimensional (1D) nonlinear systems. A Bose-Einstein condensate trapped in a quasi-1D waveguide can support bright-solitary-matter waves (3D analogues of solitons) when interatomic interactions are sufficiently attractive that they cancel dispersion. Solitary-matter waves are excellent candidates for a new generation of highly sensitive interferometers, as their non-dispersive nature allows them to acquire phase shifts for longer times than conventional matter-waves interferometers. However, such an interferometer is yet to be realised experimentally. In this work, we demonstrate the splitting and recombination of a bright-solitary-matter wave on a narrow repulsive barrier, which brings together the fundamental components of an interferometer. We show that both interference-mediated recombination and classical velocity filtering effects are important, but for a sufficiently narrow barrier interference-mediated recombination can dominate. We reveal the extreme sensitivity of interference-mediated recombination to the experimental parameters, highlighting the potential of soliton interferometry.
We investigate the nonlinearity-assisted quantum tunnelling and formation of nonlinear collective excitations in a matter-wave interferometer, which is realized by the adiabatic transformation of a double-well potential into a single-well harmonic trap. In contrast to the linear quantum tunnelling induced by the crossing (or avoided crossing) of neighbouring energy levels, the quantum tunnelling between different nonlinear eigenstates is assisted by the nonlinear mean-field interaction. When the barrier between the wells decreases, the mean-field interaction aids quantum tunnelling between the ground and excited nonlinear eigenstates. The resulting non-adiabatic evolution depends on the input states. The tunnelling process leads to the generation of dark solitons, and the number of the generated dark solitons is highly sensitive to the matter-wave nonlinearity. The results of the numerical simulations of the matter-wave dynamics are successfully interpreted with a coupled-mode theory for multiple nonlinear eigenstates.
We present the first realization of a solitonic atom interferometer. A Bose-Einstein condensate of 1×10(4) atoms of rubidium-85 is loaded into a horizontal optical waveguide. Through the use of a Feshbach resonance, the s-wave scattering length of the 85Rb atoms is tuned to a small negative value. This attractive atomic interaction then balances the inherent matter-wave dispersion, creating a bright solitonic matter wave. A Mach-Zehnder interferometer is constructed by driving Bragg transitions with the use of an optical lattice colinear with the waveguide. Matter-wave propagation and interferometric fringe visibility are compared across a range of s-wave scattering values including repulsive, attractive and noninteracting values. The solitonic matter wave is found to significantly increase fringe visibility even compared with a noninteracting cloud.