Dipolar Bose-Einstein Condensate Research Articles

Superfluid-supersolid phase transition of elongated dipolar Bose-Einstein condensates at finite temperatures

We analyze the finite-temperature phase diagram of a dipolar Bose-Einstein condensate confined in a tubular geometry. The effect of thermal fluctuations is accounted for by means of Bogoliubov theory employing the local density approximation. In the considered geometry, the superfluid-supersolid phase transition can be of first and second order. We discuss how the corresponding transition point is affected by the finite temperature of the system. Published by the American Physical Society 2024

Superfluid fraction tensor of a two-dimensional supersolid

We investigate the superfluid fraction of crystalline stationary states within the framework of mean-field Gross–Pitaevskii theory. Our primary focus is on a two-dimensional Bose–Einstein condensate with a non-local soft-core interaction, where the superfluid fraction is described by a rank-2 tensor. We then calculate the superfluid fraction tensor for crystalline states exhibiting triangular, square, and stripe geometries across a broad range of interaction parameters. Factors leading to an anisotropic superfluid fraction tensor are also considered. We also refine the Leggett bounds for the superfluid fraction of the 2D system. We systematically compare these bounds to our full numerical results, and other results in the literature. This work is of direct relevance to other supersolid systems of current interest, such as supersolids produced using dipolar Bose–Einstein condensates.

Expansion dynamics of a cylindrical-shell-shaped strongly dipolar condensate

A Bose–Einstein condensate (BEC) formed on a curved surface with a distinct topology has been a hot topic of intense research, in search of new phenomena in quantum physics as well as for its possible application in quantum computing. In addition to the study of a spherical-shell-shaped BEC, we studied the formation of a cylindrical-shell-shaped harmonically-trapped dipolar BEC of 164Dy atoms theoretically using an improved mean-field model including a Lee-Huang-Yang-type interaction, meant to stop a collapse at high atom density. To test the robustness of the cylindrical-shell-shaped BEC, here we study its expansion in the same model. We find that as the harmonic trap in the x and y directions are removed, maintaining the axial trap, the cylindrical-shell-shaped BEC expands in the x-y plane without deformation, maintaining its shell-shaped structure. After an adequate radial expansion, the axial trap can be relaxed for a desired axial expansion of the cylindrical-shell-shaped BEC allowing its observation.

Bright solitons in a spin-orbit-coupled dipolar Bose-Einstein condensate trapped within a double-lattice.

By effectively controlling the dipole-dipole interaction, we investigate the characteristics of the ground state of bright solitons in a spin-orbit coupled dipolar Bose-Einstein condensate. The dipolar atoms are trapped within a double-lattice which consists of a linear and a nonlinear lattice. We derive the motion equations of the different spin components, taking the controlling mechanisms of the dipole-dipole interaction into account. An analytical expression of dipole-dipole interaction is derived. By adjusting the dipole polarization angle, the dipole interaction can be adjusted from attraction to repulsion. On this basis, we study the generation and manipulation of the bright solitons using both the analytical variational method and numerical imaginary time evolution. The stability of the bright solitons is also analyzed and we map out the stability phase diagram. By adjusting the long-range dipole-dipole interaction, one can achieve manipulation of bright solitons in all aspects, including the existence, width, nodes, and stability. Considering the complexity of our system, our results will have enormous potential applications in quantum simulation of complex systems.

Non-equilibrium dynamics of dipolar polarons

We study the out-of-equilibrium quantum dynamics of dipolar polarons, i.e., impurities immersed in a dipolar Bose-Einstein condensate, after a quench of the impurity-boson interaction. We show that the dipolar nature of the condensate and of the impurity results in anisotropic relaxation dynamics, in particular, anisotropic dressing of the polaron. More relevantly for cold-atom setups, quench dynamics is strongly affected by the interplay between dipolar anisotropy and trap geometry. Our findings pave the way for simulating impurities in anisotropic media utilizing experiments with dipolar mixtures.

Phonon and maxon instability in Bose–Einstein condensates with parity-time symmetric spin–orbit coupling

Parity-time () symmetry has drawn great research interest in non-Hermitian physics. Recently, there is an emerging model of -symmetric spin–orbit coupling (SOC) which could be realized with spin-1/2 atomic Bose–Einstein condensates (BECs) when the two spin components are respectively subjected to momentum-dependent gain and loss (Qin et al 2022 New J. Phys. 24 063025). In this model, inter-atom interaction has no influence on the -symmetric plane waves. Thus, collective excitation playing the role of fingerprint of inter-atom interaction is investigated in this paper. For the phonon excitation, it is shown that the repulsive interaction between atoms in different spin states, which tends to drive the atoms to populate in only one spin component, can break the -symmetry, and leads to a phonon instability. Whereas, for the case of the phonon-maxon-roton collective excitation spectrum, the repulsive interaction between atoms in different spin states can lead to a maxon instability, which does not occur in Hermitian BEC systems (dipolar BECs or BECs with Raman induced SOC). Simulation of the time evolution of the plane wave solution against small noise shows that the maxon instability can result in the formation of a supersolid-like stripe pattern at the initial stage, but the non-Hermitian nature of the system finally destroys the pattern. The phase diagram of stability shows that the Rabi coupling and repulsive interaction between the atoms in the same spin state can stabilize the system.

A time splitting Chebyshev-Fourier spectral method for the time-dependent rotating nonlocal Schrödinger equation in polar coordinates

In this article, we propose a time splitting Chebyshev-Fourier spectral method to compute the dynamics of rotating nonlocal Schrödinger equation in polar coordinates. Since the rotation term is diagonalizable with Fourier spectral method in azimuthal direction, we split the Hamiltonian into a linear part, i.e., the Laplacian and rotation terms, and the nonlinear part. The linear part is discretized by Chebyshev-Fourier spectral method in space and integrated by Crank-Nicolson or exact matrix exponential. The nonlinear part is solved exactly in physical space, and the nonlocal potential, which is defined as convolution φ:=U⁎|ψ|2 with a singular kernel U, is computed via Kernel Truncation method with spectral accuracy. Then we construct a high order time splitting spectral method. Our scheme is spectrally accurate in space and of second/fourth order in the temporal direction. Extensive numerical results are presented to confirm the accuracy and efficiency for both the nonlocal potential and the wave function, together with one application to a two-component rotating dipolar Bose-Einstein condensates. In addition, we investigate the rotational symmetry preserving performance by a comprehensive comparison with existing scheme.

Spontaneous dipolar Bose-Einstein condensation on the surface of a cylinder

Spontaneous dipolar Bose-Einstein condensation on the surface of a cylinder

Anisotropic inflation in dipolar Bose–Einstein condensates

Early during the era of cosmic inflation, rotational invariance may have been broken, only later emerging as a feature of low-energy physics. This motivates ongoing searches for residual signatures of anisotropic space-time, for example in the power spectrum of the cosmic microwave background. We propose that dipolar Bose–Einstein condensates (BECs) furnish a laboratory quantum simulation platform for the anisotropy evolution of fluctuation spectra during inflation, exploiting the fact that the speed of dipolar condensate sound waves depends on direction. We construct the anisotropic analogue space-time metric governing sound, by linking the time-varying strength of dipolar and contact interactions in the BEC to the scale factors in different coordinate directions. Based on these, we calculate the dynamics of phonon power spectra during an inflation that renders the initially anisotropic Universe isotropic. We find that the expansion speed provides an experimental handle to control and study the degree of final residual anisotropy. Gravity analogues using dipolar condensates can thus provide tuneable experiments for a field of cosmology that was until now confined to a single experiment, our Universe.

Quantum phases of rotating Raman spin–orbit-coupled dipolar Bose–Einstein condensates with Lee–Huang–Yang correction

We investigate the ground-state phases and spin textures of rotating binary dipolar Bose–Einstein condensates with Lee–Huang–Yang (LHY) correction and Raman-induced spin–orbit coupling (SOC) in a harmonic trap. Without rotation and SOC, the enhanced LHY correction can lead to structural phase transitions of the system. In the presence of SOC, a phase diagram as a function of the Raman coupling and LHY correction strengths is given. It is shown that the system exhibits rich and exotic quantum phases including quantum droplet (QD) phase with hidden vortex–antivortex pairs, droplet-stripe coexistence phase with hidden vortex–antivortex cluster, QD phase with visible triangular vortex lattice, annular stripe phase containing Anderson–Toulouse coreless vortex, and annular phase with vortex–antivortex pair necklace. In particular, for the rotation case, with the variation of Raman coupling strength the system displays complicated ground-state structures, such as layered structure of droplet necklaces and annular stripe with hidden layered vortex necklace and antivortex necklace, toroidal stripe phase with hidden antivortex necklace, and composite phase of visible square antivortex lattice and annular stripe. Furthermore, the system sustains fascinating novel spin textures and skyrmion excitations, including triangular half-antiskyrmion lattice, alternating meron-antimeron necklace, double-layer half-skyrmion necklace, and triangular half-skyrmion lattice.

Vortices in dipolar Bose–Einstein condensates

Vortices in dipolar Bose–Einstein condensates

Vortex dynamics of a three-dimensional dipolar Bose–Einstein condensate

By numerically solving the Gross–Pitaevskii equation with phenomenological dissipation term, we study the vortex formation properties of a three-dimensional dipolar Bose–Einstein condensate of 164Dy atoms. We studied the influence of the contact interaction between atoms on the formation mechanism of vortices. We also study how the dipole orientation affects the vortex formation properties and the number of vortices. We find that enhancing the interaction of short-range repulsion interaction or dipolar repulsion interaction can shorten the time to form a stable vortex structure and increase the number of vortices.

Special breathing structures induced by bright solitons collision in a binary dipolar Bose–Einstein condensates

We numerically investigate the breathing dynamics induced by collision between bright solitons in a binary dipolar Bose–Einstein condensates, whose dipole–dipole interaction and contact interaction are attractive. We identify three special breathing structures, such as snakelike special breathing structure, mixed breathing structure, and divide breathing structure. The characteristics of these breathing structures can be described by breathing frequency Ω, maximum breathing amplitude A and lifetime τ, which can be manipulated by atomic number Ni and interspecies scattering length a 12. Meanwhile, the above breathing structures can realize the process of quasi-transition with a reasonable Ni and a 12. Additionally, the collision of two special breathing structures also can bring more abundant breathing dynamics. Our results provide a reference for the study of soliton interactions and deepen the understanding of soliton properties in a binary dipolar Bose–Einstein condensates.

Dipolar Bose–Einstein condensation of 168Er and anisotropic expansion dynamics

We report on the realization of Bose–Einstein condensation (BEC) of 168Er atoms in a crossed optical dipole trap. A magneto-optical trap is realized with just one laser driving the narrow-line transition which increases the phase space density and facilitates the evaporative cooling. A pure BEC with 3 ×104 atoms is achieved by forced evaporative cooling. The complex Feshbach resonance and anisotropic expansion of 168Er are investigated by the loss spectroscopy and controlling the rotating dipoles.

Variational Approaches to Two-Dimensionally Symmetry-Broken Dipolar Bose–Einstein Condensates

It has been shown that quantum fluctuations in dipolar Bose–Einstein condensates (BECs) lead to a stabilisation against collapse, thereby providing access to a range of states with different symmetries. In this paper, we discuss variational approaches to approximately determine the phase diagrams for dipolar BECs that are trapped along the dipolar orientation and otherwise infinite in the perpendicular direction (thermodynamic limit). The two-dimensional symmetry breaking occurs in the plane perpendicular to the polarisation axis. We show in detail how to derive approximate expressions that are valid in a region where modulations to an otherwise unmodulated perfect superfluid emerge gradually with a small modulation amplitude and compare the results to rigorous numerics.

Two-dimensional miscible-immiscible supersolid and droplet crystal state in a homonuclear dipolar bosonic mixture

The recent realization of a binary dipolar Bose-Einstein condensate [A. Trautmann et al., Phys. Rev. Lett. 121, 213601 (2018)] presents new exciting aspects for studying quantum droplets and supersolids in a binary mixture. Motivated by this experiment, we study the ground-state phases and dynamics of a Dy-Dy mixture. The dipolar bosonic mixture exhibits qualitatively novel and rich physics. Relying on the three-dimensional numerical simulations in the extended Gross-Pitaevskii framework, we unravel the ground-state phase diagrams and characterize their different possible phases. The emergent phases include single-droplet (SD), multiple-droplets (MD), doubly supersolid (SS), and superfluid (SF) states in both miscible and immiscible phases. Intriguing mixed ground states are observed for an imbalanced binary mixture, including a combination of SS-SF, SS-MD, and SS-SS phases. We also explore the dynamics across the phase boundaries by linear quenches of interspecies and intraspecies scattering lengths. During these dynamical processes, we observe an abrupt change in phase which initially results in some instability in the system and forms some metastable states in the intermediate timescale. However, the state produced in long-time evolution is similar to our predicted ground state. Although we demonstrate the possible results for a Dy-Dy mixture and for a specific parameter range of intraspecies and interspecies scattering lengths, our results are in general valid for other dipolar mixtures and may become an important benchmark for future experimental scenarios.

Soliton molecules in coupled dipolar Bose–Einstein condensates with spin-orbit coupling

Recent research works on ultra cold quantum gases demonstrated that dipolar Bose–Einstein condensates (BECs) exhibit rich spatiotemporal dynamic where both local and nonlocal interactions are considered. We explore theoretically the possibility of controlling the formation and dynamics of soliton molecules in binary dipolar condensates with spin-orbit coupling (SOC). We exploit the variational technique to derive the new equations of motion for the widths and amplitudes, the effective potential and the oscillation frequency of the molecules. Our study confirms the existence of stable localized bound states in an optical potential. We find that the integrity of the molecules is influenced by the physical parameters, notably the local and nonlocal interactions with the SOC. These parameters are carefully chosen by the Vakhitov–Kolokolov (VK) criterion to ensure the stability of the molecules. We present the results of numerical experiments and confirm the analytical predictions. Moreover, we show the soliton–soliton interaction in each molecule when the local interactions are strong.

Frustration in a dipolar Bose-Einstein condensate introduced by an optical lattice

We study the application of a square perturbing lattice to the naturally forming hexagonal arrays of dipolar droplets in a dipolar Bose-Einstein condensate. We find that the application of the lattice causes spontaneous pattern formation and leads to frustration in some regimes. For certain parameters, the ground state has neither the symmetry of the intrinsic hexagonal supersolid nor the symmetry of the square lattice. These results may give another axis on which to explore dipolar Bose-Einstein condensates and to probe the nature of supersolidity.

Two-dimensional anisotropic vortex–bright soliton and its dynamics in dipolar Bose–Einstein condensates in optical lattice

We study construction and dynamics of two-dimensional (2D) anisotropic vortex–bright (VB) soliton in spinor dipolar Bose–Einstein condensates confined in a 2D optical lattice (OL), with two localized components linearly mixed by the spin–orbit coupling and long-range dipole–dipole interaction (DDI). It is found that the OL and DDI can support stable anisotropic VB soliton in the present setting for arbitrarily small value of norm N. We then present a new method via examining the mean square error of norm share of bright component to implement stability analysis. It is revealed that one can control the stability of anisotropic VB soliton only by adjusting OL depth for a fixed DDI. In addition, the dynamics of the anisotropic VB soliton was studied by applying the kick to them. The mobility of the single kicked VB soliton is Rabbi-like oscillation. However, for the collision dynamics of two kicked anisotropic VB solitons, their properties mainly depend on their initial distance and OL, and they can realize the transition from the bright component to the vortex component. Our work may provide a convenient way to prepare and manipulate anisotropic VB soliton in high-dimensional space.

Generation of higher harmonics in dipolar Bose-Einstein condensates trapped in periodically modulated potentials.

We consider a quasi-one-dimensional Bose-Einstein condensate with contact and long-range dipolar interactions, under the action of the time-periodic modulation applied to the harmonic-oscillator and optical-lattice trapping potentials. The modulation results in generation of a variety of harmonics in oscillations of the condensate's width and centre-of-mass coordinate. These include multiple and combinational harmonics, represented by sharp peaks in the system's spectra. Approximate analytical results are produced by the variational method, which are verified by systematic simulations of the underlying Gross-Pitaevskii equation. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.