Array Of Bose-Einstein Condensates Research Articles

Unlocked-relative-phase states in arrays of Bose-Einstein condensates

Phase engineering techniques are used to control the dynamics of long-bosonic-Josephson-junction arrays built by linearly coupling Bose-Einstein condensates. Just at the middle point of the underlying discrete energy band of the system, unlocked-relative-phase states are shown to be stationary along with the locked-relative-phase Bloch waves. In finite, experimentally-feasible systems, such states find ranges of dynamical stability that depend on the ratio of coupling to interaction energy. The same ratio determines different decay regimes, which include the recurrence of staggered-soliton trains in the condensates around Josephson loop currents at the junctions. These transient solitons are also found in their stationary configurations, which provide striped-density states by means of either dark-soliton or bright-soliton trains. Additionally, the preparation of maximally out-of-phase (or splay) states is demonstrated to evolve into an oscillation of the uniform density of the condensates that keeps constant the total density of the system and robust against noise at low coupling.

Strongly interacting array of Bose-Einstein condensates trapped in a one-dimensional optical lattice

We study a strongly interacting array of Bose-Einstein condensates trapped in a one-dimensional (1D) optical lattice. The system is described by a nonstandard 1D Bose-Hubbard model in which both the tunneling matrix element and the on-site atomic interaction depend on the lattice site due to the interaction broadening of the local wave function and the system inhomogeneity. We quantitatively compare theoretical analyses based on the Gutzwiller approximation with experimental observations obtained using ytterbium atoms. We show that atomic states are highly number squeezed owing to strong interatomic interactions as the lattice potential becomes deeper. Furthermore, the calculated inhomogeneous collisional broadening of spectroscopic line shapes agrees well with high-resolution spectra measured by using the ultranarrow magnetic quadrupole ${}^{1}{S}_{0}{\ensuremath{-}}^{3}{P}_{2}$ transition.

Spectroscopy of superradiant scattering from an array of Bose-Einstein condensates

We theoretically study the superradiant gain and the direction of this coherent radiant for an array of Bose-Einstein condensates in an optical lattice. We find that the density grating is formed to amplify the scattering light with the phase-matching condition. The scattering spectroscopy in the momentum space can provide a method to measure the overlap of wave functions of neighboring sites, which is related to the inner-site and intersite coherences.

Interference between a large number of independent Bose-Einstein condensates

We study theoretically the interference patterns produced by the overlap of an array of Bose-Einstein condensates that have no phase coherence among them. We show that density-density correlations at different quasimomenta, which play an important role in two-condensate interference, become negligible for large $N$, where $N$ is the number of overlapping condensates. In order to understand the physics of this phenomenon, it is sufficient to consider the periodicity of the lattice and the statistical probability distribution of a random-walk problem. The average visibility of such interference patterns decreases as ${N}^{\ensuremath{-}1∕2}$ for large $N$.

Spatiotemporal dynamics of circular flow modes in a ring array of Bose-Einstein condensates

We numerically investigate the spatiotemporal dynamics of a circular flow mode in a ring array of Bose-Einstein condensates, which consists of $M$ identical Bose-Einstein condensates that couple to the nearest-neighbor sites by tunneling. Introducing a rotational potential in the Gross-Pitaevskii equation, a series of circular flow modes is resonantly excited. For the initial conditions with uniform density and one-round phase difference of $2\ensuremath{\pi}\ensuremath{\ell}\phantom{\rule{0.3em}{0ex}}(l=0,1,\dots{},M\ensuremath{-}1)$, two circular flow modes are excited for each circulation-quantized number $l$. It is shown that these circular flow modes periodically appear in time in the presence of the rotational field and persistently survive with a constant shape even after the external potential is removed, the transitions between the circular flow modes with different quantized number $l$ can be realized by applying the phase-imprinting optical pulses, and the rotational velocity of the circular flow mode can be continuously modulated by adiabatically tuning the scattering length in a magnetic field, i.e., by use of the Feshbach resonance.

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length (``Feshbach-resonance management, FRM'') is investigated. The cases of both slow and rapid modulation, in comparison with the tunneling frequency, are considered. We employ a discrete variational approach for the analysis of the system. The existence of nonlinear resonances and chaos is predicted at special values of the driving frequency. Soliton splitting is observed in numerical simulations. In the case of the rapid modulation, we derive an averaged equation, which is a generalized discrete nonlinear Schroedinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions. Thus the predicted discrete FRM solitons are a direct matter-wave analog of recently investigated discrete diffraction-managed optical solitons.

Nonlinear excitations in arrays of Bose-Einstein condensates

The dynamics of localized excitations in an array of Bose-Einstein condensates (BECs) is investigated in the framework of the nonlinear lattice theory. The existence of temporarily stable ground states displaying an atomic population distribution localized on very few lattice sites (intrinsic localized modes), as well as atomic population distributions involving many lattice sites (envelope solitons), is studied both numerically and analytically. The origin and properties of these modes are shown to be inherently connected with the interplay between macroscopic quantum tunneling and nonlinearity-induced self-trapping of atoms in coupled BECs. The phenomenon of Bloch oscillations of these excitations is studied both for zero and nonzero backgrounds. We find that in a definite range of parameters, homogeneous distributions can become modulationally unstable. We also show that bright solitons and excitations of shock-wave type can exist in BEC arrays even in the case of positive scattering length. Finally, we argue that a BEC array with negative scattering length in the presence of linear potentials can display collapse.