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arXiv:2302.10386

Controlling dark solitons on the healing length scale

Ling-Zheng Meng, Li-Chen Zhao, Thomas Busch, Yongping Zhang

Published Feb 21, 2023• 0 citations
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Abstract

While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose-Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton can be obtained by just driving the impurity atoms. By controlling the driving force on the impurity, one can therefore fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.

DOI
10.48550/arxiv.2302.10386

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•Oct 25, 2018•0 citations
While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose-Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton can be obtained by just driving the impurity atoms. By controlling the driving force on the impurity, one can therefore fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.
Abstract While usually the optical diffraction limit is setting a limit for the lengthscales on which a typical alkali Bose–Einstein condensate can be controlled, we show that in certain situations control via matter waves can achieve smaller resolutions. For this we consider a small number of impurity atoms which are trapped inside the density dip of a dark soliton state and show that any grey soliton state can be obtained by selectively driving the impurity atoms. This allows to fully control the position and velocity of the dark soliton, and also study controlled collisions between these non-linear objects.
We propose a new method of creating solitons in elongated Bose-Einstein condensates (BECs) by sweeping three laser beams through the BEC.If one of the beams is in the first order (TEM10) Hermite-Gaussian mode, its amplitude has a transversal π phase slip which can be transferred to the atoms creating a soliton.Using this method it is possible to circumvent the restriction set by the diffraction limit inherent to conventional methods such as phase imprinting.The method allows one to create multicomponent (vector) solitons of the dark-bright form as well as the dark-dark combination.In addition it is possible to create in a controllable way two or more dark solitons with very small velocity and close to each other for studying their collisional properties.
Dilute atomic Bose-Einstein condensates are inherently nonlinear systems and support solitary wave solutions. An important distinction from optical systems is the inhomogeneous background density, which results from the traps used to confine the atoms. As in optical systems, dark solitary waves in three-dimensional geometries are unstable to transverse excitations, which lead to a bending of the dark soliton plane and decay into vortex rings. Highly elon-gated geometries can now be achieved experimentally, in which the condensate dynamics are effectively one-dimensional, and the motion of the dark soliton is governed by the inhomogeneous longitudinal density. We show that a dark soliton is fundamentally unstable to such a changing background density, by means of numerical simulations of the soliton under various potentials (e.g. steps, ramps, harmonic traps, and optical lattices). This leads to the emission of radiation in the form of sound waves. The power emitted is found to be proportional to the square of the soliton acceleration. The latter quantity is shown to be proportional to the deformation of the apparent soliton profile, arising from the sound field in the region of the soliton. We demonstrate that the ensuing interactions between the soliton and sound field, and therefore the dynamics of the soliton, can be controlled experimentally via manipulation of the emitted sound, achieved by modifying the trap geometry. In this manner, it is possible to induce a rapid decay of the soliton, stabilise the soliton, or even pump energy into the soliton by means of parametric driving. 1
We demonstrate the possibility of drastically reducing the velocity of phonons in quasi-one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark soliton ``gas'' that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of qutrits (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter-wave phononics, in analogy with the electromagnetically induced transparency effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to \ensuremath{\sim}5 $\ensuremath{\mu}\mathrm{m}$/s, \ensuremath{\sim}103{10}^{3}103 times lower than the condensate sound speed. This is a value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of ``stopped-sound''-based quantum information protocols.
We examine the spectral properties of single and multiple matter-wave dark solitons in Bose–Einstein condensates confined in parabolic traps, where the scattering length is periodically modulated. In addition to the large density limit picture previously established for homogeneous nonlinearities, we explore a perturbative analysis in the vicinity of the linear limit, which provides good agreement with the observed spectral modes. Between these two analytically tractable limits, we use numerical computations to fill in the relevant intermediate regime. We find that the scattering length modulation can cause a variety of features absent for homogeneous nonlinearities. Among them, we note the potential oscillatory instability even of the single dark soliton, the potential absence of instabilities in the immediate vicinity of the linear limit for two dark solitons, and the existence of an exponential instability associated with the in-phase motion of three dark solitons.
We demonstrate the possibility of drastically reducing the velocity of phonons in quasi one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark-soliton gas that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of {\it qutrits} (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter wave phononics, in analogy with the electric induced transparency (EIT) effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to ∼5\sim 5∼5 μ\muμm/s, ∼103\sim 10^3∼103 times lower than the condensate sound speed. This is a record value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of stopped-sound based quantum information protocols.