Quasi One-dimensional Bose-Einstein Condensate Research Articles

Phononic phase gate with dark-soliton qubit

We investigate a single as well as two dark-soliton qubits in a quasi one-dimensional Bose–Einstein condensates, surrounded by a dilute set of impurities. The qubits are driven externally with the help of oscillating magnetic field gradient, to observe the decay of populated states. The existence of Dicke superradiance and subradiance phenomenon, resulting from phonon-mediated coupling between dark-soliton qubit, enables to build a quantum phase gate. This is the first study on quantum gates mediated by phonons in dark-soliton qubit.

Gap solitons and their stabilities in a quasi one-dimensional Bose-Einstein condensate under three-body interaction

We study the gap solitons and their stability properties in a Bose-Einstein condensation (BEC) under three-body interaction loaded in a Jacobian elliptic sine potential, which can be described by a cubic-quintic Gross-Pitaevskii equation (GPE) in the mean-field approximation. Firstly, the GPE is transformed into a stationary cubic-quintic nonlinear Schrödinger equation (NLSE) by the multi-scale method. A class of analytical solution of the NLSE is presented to describe the gap solitons. It is shown analytically that the amplitude of the gap soliton decreases as the two-body or three-body interaction strength increases. Secondly, many kinds of gap solitons, including the fundamental soliton and the sub-fundamental soliton, are obtained numerically by the Newton-Conjugate-Gradient (NCG) method. There are two families of fundamental solitons: one is the on-site soliton and the other is the off-site soliton. All of them are bifurcated from the Bloch band. Both in-phase and out-phase dipole solitons for off-site solitons do exist in such a nonlinear system. The numerical results also indicate that the amplitude of the gap soliton decreases as the nonlinear interaction strength increases, which accords well with the analytical prediction. Finally, long-time dynamical evolution for the GPE is performed by the time-splitting Fourier spectrum method to investigate the dynamical stability of gap solitons. It is shown that the on-site solitons are always dynamically stable, while the off-site solitons are always unstable. However, both stable and unstable in-phase or out-phase dipole solitons, which are not bifurcated from the Bloch band, indeed exist. For a type of out-phase soliton, there is a critical value <inline-formula><tex-math id="M1">\begin{document}$ q_c$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191278_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191278_M1.png"/></alternatives></inline-formula> when the chemical potential <i>μ</i> is fixed. The solitons are linearly stable as <inline-formula><tex-math id="M2">\begin{document}$ q>q_c$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191278_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191278_M2.png"/></alternatives></inline-formula>, while they are linearly unstable for <inline-formula><tex-math id="M3">\begin{document}$ q<q_c$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191278_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20191278_M3.png"/></alternatives></inline-formula>. Therefore, the modulus <i>q</i> plays an important role in the stability of gap solitons. One can change the dynamical behavior of gap solitons by adjusting the modulus of external potential in experiment. We also find that there exists a kind of gap soliton, in which the soliton is dynamically unstable if only the two-body interaction is considered, but it becomes stable when the three-body interaction is taken into account. This indicates that the three-body interaction has influence on the stability of gap solitons.

Evanescent modes and step-like acoustic black holes

We consider a model of an acoustic black hole formed by a quasi-one dimensional Bose–Einstein condensate with a step-like horizon. This system is analyzed by solving the corresponding Bogoliubov–de Gennes equation with an appropriate matching condition at the jump. When the step is between a subsonic and supersonic flow, a sonic horizon develops and in addition to the scattering coefficients we compute the distribution of the accompanying analogue Hawking radiation. Additionally, in response to the abrupt variation in flow and non-linear Bogoliubov dispersion relation, evanescent solutions of the Bogoliubov–de Gennes equation also appear and decay out from the horizon. We bound this decay length and show that these modes produce a modulation of observables outside the event horizon by their interference with outgoing Hawking flux. We go further and find specific superpositions of ingoing eigenmodes which exhibit coherent cancellation of the Hawking flux outside the horizon but nevertheless have evanescent support outside the black hole. We conclude by speculating that when quasiparticle interactions are included, evanescent modes may yield a leakage of information across the event horizon via interactions between the real outgoing Hawking flux and the virtual evanescent modes, and that we may expect this as a generic feature of models which break Lorentz invariance at the UV (Planck) scale.

Slow sound in matter-wave dark soliton gases

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 $\sim 5$ $\mu$m/s, $\sim 10^3$ 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.

Momentum correlations as signature of sonic Hawking radiation in Bose-Einstein condensates

We study the two-body momentum correlation signal in a quasi one dimensional Bose-Einstein condensate in the presence of a sonic horizon. We identify the relevant correlation lines in momentum space and compute the intensity of the corresponding signal. We consider a set of different experimental procedures and identify the specific issues of each measuring process. We show that some inter-channel correlations, in particular the Hawking quantum-partner one, are particularly well adapted for witnessing quantum non-separability, being resilient to the effects of temperature and/or quantum quenches.

Statics and dynamics of quasi one-dimensional Bose–Einstein condensate in harmonic and dimple trap

We investigate a quasi one-dimensional Bose–Einstein condensate in a harmonic trap with an additional dimple trap (dT) in the center. Within a zero-temperature Gross–Pitaevskii mean-field description we provide a one-dimensional physical intuitive model, which we solve by both a time-independent variational approach and numerical calculations. With this we obtain at first equilibrium results for the emerging condensate wave function which reveal that a dimple trap potential induces a bump or a dip in case of a red- or a blue-detuned Gaussian laser beam, respectively. Afterwards, we investigate how this dT induced bump/dip-imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the generic case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the dT induced bump in the condensate wave function remains present, whereas the dip starts decaying after a characteristic time scale which decreases with increasing blue-detuned dT depth. Secondly, once the red- or blue-detuned dT is switched off, we find that bright shock-waves or gray/dark bi-soliton trains emerge which oscillate within the harmonic confinement with a characteristic frequency.

Quasi one-dimensional Bose–Einstein condensate in a gravito-optical surface trap

We study both static and dynamic properties of a weakly interacting Bose–Einstein condensate (BEC) in a quasi one-dimensional gravito-optical surface trap, where the downward pull of gravity is compensated by the exponentially decaying potential of an evanescent wave. First, we work out approximate solutions of the Gross–Pitaevskii equation for both a small number of atoms using a Gaussian ansatz and a larger number of atoms using the Thomas–Fermi limit. Then we confirm the accuracy of these analytical solutions by comparing them to numerical results. From there, we numerically analyze how the BEC cloud expands non-ballistically, when the confining evanescent laser beam is shut off, showing agreement between our theoretical and previous experimental results. Furthermore, we analyze how the BEC cloud expands non-ballistically due to gravity after switching off the evanescent laser field in the presence of a hard-wall mirror which we model by using a blue-detuned far-off-resonant sheet of light. There we find that the BEC shows significant self-interference patterns for a large number of atoms, whereas for a small number of atoms, a revival of the BEC wave packet with few matter-wave interference patterns is observed.

Shock waves in quasi one-dimensional Bose-Einstein condensate

We study analytically and numerically the generation of shock waves in a quasi one-dimensional Bose-Einstein condensate (BEC) made of dilute and ultracold alkali-metal atoms. For the BEC we use an equation of state based on a 1D nonpolynomial Schrodinger equation (1D NPSE), which takes into account density modulations in the transverse direction and generalizes the familiar 1D Gross-Pitaevskii equation (1D GPE). Comparing 1D NPSE with 1D GPE we find quantitative differences in the dynamics of shock waves regarding the velocity of propagation, the time of formation of the shock, and the wavelength of after-shock dispersive ripples.

Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability

We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown, that these phenomena are related to a depletion of the Floquet-Bogoliubov states and a decoherence of the condensate in the many-particle description. Three different types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability, and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.

The dynamics of bright matter wave solitons in a quasi one-dimensionalBose–Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensionalBose–Einstein condensate (BEC) with a periodically rapidly varying time trap isconsidered. The governing equation is based on averaging the fast modulations ofthe Gross–Pitaevskii (GP) equation. This equation has the form of a GP equationwith an effective potential of a more complicated structure than an unperturbedtrap. In the case of an inverted (expulsive) quadratic trap corresponding to anunstable GP equation, the effective potential can be stable. For the boundedspace trap potential it is showed that bifurcation exists, i.e. the single-wellpotential bifurcates to the triple-well effective potential. The stabilization of aBEC cloud on-site state in the temporary modulated optical lattice is found. Thisphenomenon is analogous to the Kapitza stabilization of an inverted pendulum.The analytical predictions of the averaged GP equation are confirmed bynumerical simulations of the full GP equation with rapid perturbations.

Stability of gap solitons in a Bose-Einstein condensate

We analyze the dynamical stability of gap solitons formed in a quasi one-dimensional Bose-Einstein condensate in an optical lattice. Using two different numerical methods we show that, under realistic assumptions for experimental parameters, a gap soliton is stable only in a truly one-dimensional situation. In two and three dimensions resonant transverse excitations lead to dynamical instability. The time scale of the decay is numerically calculated and shown to be large compared to the characteristic time scale of solitons for realistic physical parameters.