We investigate the mean-field ground states of coupled one-dimensional Bose-Einstein condensates subject to a synthetic magnetic field. The resulting interacting coupled-wire model has one continuous and one discrete spatial direction, providing a controlled way to interpolate between the physics of few-leg ladders and extended vortex lattices. For two wires, we study the vortex-like, biased-density, and Meissner-like states, exploring how the finite longitudinal size of the system modifies the transitions between them. Increasing the number of wires, the ground state evolves towards an extended vortex lattice. We find numerically that periodic boundary conditions in the discrete direction can favour staggered arrays of like-signed vortices resembling an Abrikosov lattice, while open boundaries in small finite-size systems confine the vortices into rows near the centre of the synthetic direction. Our results explore how finite size effects and boundary conditions govern the emergence and spatial organisation of vortices in continuous-discrete quantum fluids, with relevance to future experiments in tunnel-coupled atomic wires or with synthetic dimensions.
We investigate the mean-field ground states of coupled one-dimensional Bose-Einstein condensates subject to a synthetic magnetic field. The resulting interacting coupled-wire model has one continuous and one discrete spatial direction, providing a controlled way to interpolate between the physics of few-leg ladders and extended vortex lattices. For two wires, we study the vortex-like, biased-density, and Meissner-like states, exploring how the finite longitudinal size of the system modifies the transitions between them. Increasing the number of wires, the ground state evolves towards an extended vortex lattice. We find numerically that periodic boundary conditions in the discrete direction can favour staggered arrays of like-signed vortices resembling an Abrikosov lattice, while open boundaries in small finite-size systems confine the vortices into rows near the centre of the synthetic direction. Our results explore how finite size effects and boundary conditions govern the emergence and spatial organisation of vortices in continuous-discrete quantum fluids, with relevance to future experiments in tunnel-coupled atomic wires or with synthetic dimensions.
We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [C. L. Kane et al., Phys. Rev. Lett. 88, 036401 (2002)], as well as Meissner phases and vortex phases in double wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e., the Harper-Hofstadter model and the two-leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semicontinuous Harper-Hofstadter model accessible with cold-atom experiments. For the minimal setup of a double wire, we explore how a subwavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in nonplanar geometries such as cylinders, disks, and tori.
We investigate the ground states and rich dynamics of vortices in spin-orbit coupled Bose-Einstein condensates (BEC) subject to position-dependent detuning. Such a detuning plays the role of an effective rotational frequency, causing the generation of a synthetic magnetic field. Through scanning the detuning gradient, we numerically obtain static vortex lattice structures containing 1 to 6 vortices using the coupled Gross-Pitaevskii equations. When quenching detuning gradient below its initial value, the vortex lattices exhibit interesting periodic rotation motion, and their dynamical stability can persist for up to 1000ms. In particular, depending on the detuning gradient, the twin vortices exhibit either a scissors-like rotational oscillation or a clockwise periodic rotation, reflecting the response to the magnetic field gradient experienced by the condensates. We fit the numerical results to quantitatively analyze the relation between rotation dynamics and magnetic field gradients. When quenching the detuning gradient beyond its initial value, additional vortices appear. Our findings may motivate further experimental studies of vortex dynamics in synthetic magnetic fields and offer insights for engineering a BEC-based magnetic field gradiometer.
Synthetic dimensions are a powerful tool for engineering desired quantum systems, based on coupling together sets of states and reinterpreting these as lattice sites along an artificial dimension. Recently, a synthetic dimension of harmonic trap states has been successfully implemented in an ultracold-atom experiment, opening the way for future realizations in this platform of topological lattice models, such as hybrid Harper-Hofstadter (HH) systems, which have one real and one synthetic dimension. However, unlike conventional systems, interparticle interactions along a synthetic dimension of harmonic trap states are inhomogeneous, long ranged and non-state-preserving. Therefore, this setup provides a natural platform for the exploration of the interplay between long-range interactions (including correlated pair tunneling) and magnetic effects. In this paper, we set out to numerically study the effect of such interactions on both a hybrid two-legged HH ladder and a two-dimensional HH model. In the former, we find variants of vortex and Meissner phases familiar from conventional models, while in the latter, we observe the emergence, in small finite systems, of unusual ground states, including a “Meissner stripe” state, which combines counterpropagating Meissner-type currents with strong density variations. This opens up interesting questions, including about the nature of strongly correlated states that would emerge in such a platform.
In this paper, we study the static and dynamic properties of vortices formation in a rotating Bose–Einstein condensate in synthetic magnetic field. The condensate is confined in a harmonic potential and an optical lattice potential. We numerically solve the time-dependent Gross–Pitaevskii equation in two dimensions and compare the vortices formation process with rotating frame method. We derive the two expressions about vortex number N[Formula: see text] and chemical potential [Formula: see text] as a function of rotational frequency [Formula: see text], which show that the number of vortices N[Formula: see text] increases linearly with [Formula: see text], while the chemical potential [Formula: see text] remains nearly unchanged with increasing [Formula: see text]. The analytical results are in qualitative agreement with the numerical ones. Moreover, we also investigate the vortex dynamics. Numerical results indicate that the time spent for the formation of steady state vortices is reduced drastically if the optical lattice is considered. Nevertheless, the synthetic magnetic field approach is still low efficient to generate more vortices.
Soon after its theoretical prediction, striped-density states in the presence of synthetic spin-orbit coupling were realized in Bose-Einstein condensates of ultracold neutral atoms [J.-R. Li et al., Nature 543, 91 (2017)]. The achievement opens avenues to explore the interplay of superfluidity and crystalline order in the search for supersolid features and materials. The system considered is essentially made of two linearly coupled Bose-Einstein condensates, that is, a pseudo-spin-1/2 system, subject to a spin-dependent gauge field ${\ensuremath{\sigma}}_{z}\ensuremath{\hbar}{k}_{\ensuremath{\ell}}$. Under these conditions, the stripe phase is achieved when the linear coupling $\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}/2$ is small against the gauge energy $m\mathrm{\ensuremath{\Omega}}/\ensuremath{\hbar}{k}_{\ensuremath{\ell}}^{2}<1$. The resulting density stripes have been interpreted as a standing-wave interference pattern with approximate wave number $2{k}_{\ensuremath{\ell}}$. Here, we show that the emergence of the stripe phase is induced by an array of Josephson vortices living in the junction defined by the linear coupling. As happens in superconducting junctions subject to external magnetic fields, a vortex array is the natural response of the superfluid system to the presence of a gauge field. Also similar to superconductors, the Josephson currents and their associated vortices can be present as a metastable state in the absence of gauge field. We provide closed-form solutions to the 1D mean-field equations that account for such vortex arrays. The underlying Josephson currents coincide with the analytical solutions to the sine-Gordon equation for the relative phase of superconducting junctions [C. Owen and D. Scalapino, Phys. Rev. 164, 538 (1967)].
We study the ground states of rotating atomic Bose-Einstein condensates with dipolar interactions. We present the results of numerical studies on a periodic geometry which show vortex lattice ground states of various symmetries: triangular and square vortex lattices, ``stripe crystal,'' and ``bubble crystal.'' We present the phase diagram (for systems with a large number of vortices) as a function of the ratio of dipolar to contact interactions and of the chemical potential. We discuss the experimental requirements for observing transitions between vortex lattice ground states via dipolar interactions. We finally investigate the stability of mean-field supersolid phases of a quasi-two-dimensional nonrotating Bose gas with dipolar interactions.