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}${10}^{3}$ 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 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}${10}^{3}$ 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 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 ∼5μm/s, ∼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.
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 study the possibility of using dark soliton in quasi one dimensional Bose Einstein condensates to produce two level system (qubits) by exploiting the intrinsic nonlinear and the coherent nature of the matter waves. We calculate the soliton spectrum and the conditions for a qubit to exist. We also compute the coupling between the phonons and the soliton and investigate the emission rate of the qubits in that case. Remarkably, the qubit lifetime is estimated to be of the order of a few seconds, being by the dark soliton "death" due to quantum evaporation.
Dilute atomic Bose-Einstein condensates support intriguing macroscopic excitations in the form of quantized vortices and dark solitons. In this thesis we present extensive quantitative studies of the dynamics of these phenomena in the limit of zero temperature, performed by numerical simulation of the Gross- Pitaevskii equation. We show that vortices and dark solitons are inherently unstable to acceleration through the condensate, leading to the emission of sound waves. Indeed, for a single vortex/soliton, the power emitted is proportional to the square of the local acceleration. However, due to the finite size of the condensate, the vortex/soliton reinteracts with the emitted sound. This coupling has an important effect on the ensuing dynamics, and we illustrate how it can be engineered to induce net decay, stabilise, or even drive energy into the vortex/soliton. Under the harmonic confinement typically employed to trap the condensates, the acceleration-induced decay is stabilised by reabsorption of the emitted sound. However, by modifying the trap geometry, e.g. by adding an inner dimple in which the soliton resides or an optical lattice potential, it is possible to break this equilibrium and so induce a net decay of the vortex/soliton in a controllable manner. The decay rate can be considerable and should be observable under current experimental conditions. The dynamical stability of quantized vortices is also relevant to the field of turbulence in superfluid Helium, where the motion of the vortices is induced by the surrounding distribution of vortices rather than density. We extend these results to this field, and additionally consider the interactions between two and three vortices, which are also found to involve sound emission. By exciting the sound field of the condensate it is possible to drive parametrically energy into a dark soliton. In a real dissipative environment, this can be used to stabilise the soliton decay. Finally, we illustrate the links between dark solitons and vortices: a dark soliton embedded in a three-dimensional system is prone to decay into vortex rings, while a vortex in a quasi-one-dimensional geometry cannot be supported and exists as a hybrid between a vortex and dark soliton, known as a solitonic vortex.
Summary form only given. Bose-Einstein condensates (BEC) of weakly interacting gases allow for the new regime of nonlinear atom optics. Of special interest are macroscopically excited states like dark solitons or vortices. Solitons, as particle like excitations of matter wave fields, provide a link from condensate physics to fluid mechanics, nonlinear optics and fundamental particle physics. Dark solitons in matter waves are characterized by a local density minimum and, a steep phase gradient of the wavefunction at the position of the minimum. We report on experimental and theoretical investigation of dark solitons in BECs of /sup 87/Rb which are produced by the method of phase imprinting. A highly anisotropic confining potential allows us to be close to the (quasi) 1D situation where dark solitons are expected to be dynamically stable. By monitoring the evolution of the density profile we observe the evolution of density minima travelling at a smaller velocity than the speed of sound. By comparison to analytical and numerical solutions of the 3D Gross-Pitaevskii equation for our experimental conditions we identify these density minima to be moving dark solitons. We have studied in detail the creation and the dynamics of dark solitons as a function of evolution time and imprinted phase.
We show that entanglement between two solitary qubits in quasi-one-dimensional Bose-Einstein condensates can be spontaneously generated due to quantum fluctuations. Recently we have shown that dark solitons are an appealing platform for qubits thanks to their appreciable long lifetime. We investigate the spontaneous generation of entanglement between dark-soliton qubits in the dissipative process of spontaneous emission. By driving the qubits with the help of oscillating magnetic field gradients, we observe the formation of long distance steady-state concurrence. Our results suggest that dark-soliton qubits are good candidates for quantum information protocols based purely on matter-wave phononics.