We systematically construct a series of vector solitary waves in harmonically trapped one-dimensional three-, four-, and five-component Bose-Einstein condensates. These stationary states are continued in chemical potentials from the analytically tractable low-density linear limit of respective states, as independent linear quantum harmonic oscillator states, to the high-density nonlinear Thomas-Fermi regime. A systematic interpolation procedure is proposed to achieve this sequential continuation via a trajectory in the multi-dimensional space of the chemical potentials. The Bogolyubov-de Gennes (BdG) spectra analysis shows that all of the states considered herein can be fully stabilized in suitable chemical potential intervals in the Thomas-Fermi regime. Finally, we present some typical $SU(n)$-rotation-induced and driving-induced dynamics. This method can be extended to higher dimensions and shows significant promise for finding a wide range of solitary waves ahead.
A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically. The derived solutions are shown to be unique. The corresponding dispersion relation that generalizes the case of a single-component system shows interesting features.
Multi-component Bose-Einstein condensates exhibit an intriguing variety of nonlinear structures. In recent theoretical work, the notion of magnetic solitons has been introduced. Here we generalize this concept to vector dark-antidark solitary waves in multi-component Bose-Einstein condensates. We first provide concrete experimental evidence for such states in an atomic BEC and subsequently illustrate the broader concept of these states, which are based on the interplay between miscibility and inter-component repulsion. Armed with this more general conceptual framework, we expand the notion of …
We analyse the dynamical properties of three-dimensional solitary waves in cylindrically trapped Bose-Einstein condensates. Families of solitary waves bifurcate from the planar dark soliton and include the solitonic vortex, the vortex ring and more complex structures of intersecting vortex-line known collectively as Chladni solitons. The particle-like dynamics of these guided solitary waves provides potentially profitable features for their implementation in atomtronic circuits, and play a key role in the generation of metastable loop currents. Based on the time-dependent Gross-Pitaevskii equa…
Considering a Bose-Einstein condensed gas confined in one dimension with periodic boundary conditions, we demonstrate that, very generally, solitary-wave and rotational excitations coincide. This exact equivalence allows us to establish connections between a number of effects that are present in these two problems, many of which have been studied using the mean-field approximation.
We study experimentally and theoretically the dynamics of apparent dark soliton stripes in an elongated Bose-Einstein condensate. We show that for the trapping strengths corresponding to our experimental setup, the transverse confinement along one of the tight directions is not strong enough to arrest the formation of solitonic vortices or vortex rings. These solitonic vortices and vortex rings, when integrated along the transverse direction, appear as dark soliton stripes along the longitudinal direction thereby hiding their true character. The latter significantly modifies the interaction dy…
We derive solitary-wave solutions within the mean-field approximation in quasi-one-dimensional binary mixtures of Bose-Einstein condensates under periodic boundary conditions, for the case of an effective repulsive interatomic interaction. The particular gray-bright solutions that give the global energy minima are determined. Their characteristics and the associated dispersion relation are derived. In the case of weak coupling, we diagonalize the Hamiltonian analytically to obtain the full excitation spectrum of "quantum" solitary-wave solutions.
We study the structure, stability, and dynamics of dark solitary waves in parabolically trapped, collisionally inhomogeneous Bose-Einstein condensates (BECs) with spatially periodic variations of the scattering length. This collisional inhomogeneity yields a nonlinear lattice, which we tune from a small-amplitude, approximately sinusoidal structure to a periodic sequence of densely spaced spikes. We start by investigating time-independent inhomogeneities, and we subsequently examine the dynamical response when one starts with a collisionally homogeneous BEC and then switches on an inhomogeneit…
We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bi-chromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions …
Bright solitary waves in a Bose-Einstein condensate contain thousands of identical atoms held together despite their only weakly attractive contact interactions. They nonetheless behave like a compound object, staying whole in collisions, with their collision properties strongly affected by inter-soliton quantum coherence. We show that separate solitary waves decohere due to phase diffusion, dependent on their effective ambient temperature, after which their initial mean-field relative phases are no longer well defined or relevant for collisions. In this situation, collisions occur predominant…
Motivated by recent progress in trapping Bose-Einstein condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schrödinger equation subject to periodic boundary conditions. When the circumference of the ring is much larger than the size of the wave, the density profile is well approximated by that of an infinite ring, however the density and the velocity of propagation cannot vanish simultaneously. When the size of the ring becomes comparable to the size of the wave, the density variation becomes sinusoidal and the velocity of propagation saturates to a cons…
We demonstrate the feasibility of generation of quasi-stable counter-propagating solitonic structures in an atomic Bose-Einstein condensate confined in a realistic toroidal geometry, and identify optimal parameter regimes for their experimental observation. Using density engineering we numerically identify distinct regimes of motion of the emerging macroscopic excitations, including both solitonic motion along the azimuthal ring direction, such that structures remain visible after multiple collisions even in the presence of thermal fluctuations, and snaking instabilities leading to the decay o…
We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates (BECs) subject to strong confinement along the axial direction. Starting from the three-dimensional (3D) Gross-Pitaevskii equation (GPE), we proceed to an effective 2D nonpolynomial Schroeodinger equation (NPSE) derived by means of the integration over the axial coordinate. Results produced by the latter equation are in very good agreement with those obtained from the full 3D GPE, including cases when the formal 2D equation with the cubic nonlinearity is unreliable. The 2D NPSE is used to predict density profi…
Jones-Roberts solitary waves and the onset of rotation in a spherical surface condensate
Kirchhoff-Institut für Physik, Universität Heidelberg（海德堡大学基尔霍夫物理研究所）；School of Engineering, Mathematics and Physics, University of East Anglia（东英吉利大学工程、数学与物理学院）；Centre for Photonics and Quantum Science, University of East Anglia（东英吉利大学光子与量子科学中心）；Institut für Theoretische Physik, Universität Heidelberg（海德堡大学理论物理研究所）；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung（GSI重离子研究中心极端物质研究所EMMI）
Stationary solitary waves are studied in an array of $M$ linearly-coupled one-dimensional Bose-Einstein condensates (BECs) by means of the Gross-Pitaevskii equation. Solitary wave solutions with the character of overlapping dark solitons, Josephson vortex - antivortex arrays, and arrays of half-dark solitons are constructed for $M>2$ from known solutions for two coupled BECs. Additional solutions resembling vortex dipoles and rarefaction pulses are found numerically. Stability analysis of the solitary waves reveals that overlapping dark solitons can become unstable and susceptible to decay int…
We study superfluid (SF) states of strongly interacting Bose-Bose mixtures with equal mass and intra-component interaction in optical lattices both in the presence and absence of a barrier potential (BP). We show that the SF order parameters obey the two-component nonlinear Schroedinger equation (NLSE) with not only cubic but also quintic nonlinearity in the vicinity of the first-order transitions to the Mott insulators with even fillings. In the case of no BP, we analyze solitary-wave (SW) solutions of the cubic-quintic NLSE. When the SF state changes from a ground state to a metastable one, …
A mixture of two distinguishable Bose-Einstein condensates confined in a ring potential has numerous interesting properties under rotational and solitary-wave excitation. The lowest-energy states for a fixed angular momentum coincide with a family of solitary-wave solutions. In the limit of weak interactions, exact diagonalization of the many-body Hamiltonian is possible and permits evaluation of the complete excitation spectrum of the system.
The Bose-stimulated self-organization of a quasi-two dimensional non-equilibrium Bose-Einstein condensate in an in-plane potential is proposed. We obtained the solution of the nonlinear, driven-dissipative Gross-Pitaevskii equation for a Bose-Einstein condensate trapped in an external asymmetric parabolic potential within the method of the spectral expansion. We found that, in sharp contrast to previous observations, the condensate can spontaneously acquire a soliton-like shape for spatially homogenous pumping. This condensate soliton performs oscillatory motion in a parabolic trap and, also, …
We investigate the elastic scattering of Bose-Einstein condensates at shallow periodic and disorder potentials. We show that the collective scattering of the macroscopic quantum object couples to internal degrees of freedom of the Bose-Einstein condensate such that the Bose-Einstein condensate gets depleted. As a precursor for the excitation of the Bose-Einstein condensate we observe wave chaos within a mean-field theory.
We discuss the comment [ arXiv:1102.2943] by E. Kozik about "Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein Condensates [arXiv:1007.4441]".
The dynamics of a Bose-Einstein condensate of atoms having attractive interactions is studied using quantum many-body simulations. The collapse of the condensate by quantum tunneling is numerically demonstrated and the tunneling rate is calculated. The correlation properties of the quantum many-body state are investigated.
We report the formation of Bose-Einstein condensates into non-equilibrium states. Our condensates are much longer than equilibrium condensates with the same number of atoms, show strong phase fluctuations, and have a dynamical evolution similar to that of quadrupole shape oscillations of regular condensates. The condensates emerge in elongated traps as the result of local thermalization when the nucleation time is short compared to the axial oscillation time. We introduce condensate focusing as a powerful method to extract the phase-coherence length of Bose-Einstein condensates.
Synthetic spin-tensor-momentum coupling has recently been proposed to realize in atomic Bose-Einstein condensates. Here we study bright solitons in Bose-Einstein condensates with spin-tensor-momentum coupling and spin-orbit coupling. The properties and dynamics of spin-tensor-momentum-coupled and spin-orbit-coupled bright solitons are identified to be different. We contribute the difference to the different symmetries.
We report explicitly a novel family of exact PT-symmetric solitons and further study their spontaneous PT symmetry breaking, stabilities and collisions in Bose-Einstein condensates trapped in a PT-symmetric harmonic trap and a Hermite-Gaussian gain/loss potential. We observe the significant effects of mean-field interaction by modifying the threshold point of spontaneous PT symmetry breaking in Bose-Einstein condensates. Our scenario provides a promising approach to study PT-related universal behaviors in non-Hermitian quantum system based on the manipulation of gain/loss potential in Bose-Ein…
We show that starting from the Heisenberg equations of motion for Bose annihilation and creation operators and using an appropriate transformation, we can split the Bogoliubov mode into a free particle mode and the amplitude mode. We show this for both the free Bose gas as well as the Bose gas in an optical lattice.
The many-body dissipative flow induced by a mobile aussian impurity harmonically oscillating within a cigar-shaped Bose-Einstein condensate is investigated. For very {small and large driving frequencies} the superfluid phase is preserved. Dissipation is identified, for intermediate driving frequencies, by the non-zero value of the drag force whose abrupt increase {signals the spontaneous downstream emission of an array of gray solitons. After each emission event, typically each of the solitary waves formed decays and splits into two daughter gray solitary waves that are found to be robust prop…
The non-equilibrium spatial dynamics in a two-component Bose-Einstein condensate were excited by controlled miscible-immiscible transition, in which immiscible condensates with domain structures are transferred to the miscible condensates by changing the internal state of 87Rb atoms. The subsequent evolution exhibits the oscillation of spatial structures involving component mixing and separation. We show that the larger total energy of the miscible system results in a higher oscillation frequency. This investigation introduces a new technique to control the miscibility and the spatial degrees …
Dynamics of atomic and molecular bright solitons in a hybrid atom-molecular BEC (Bose Einstein Condensate) system of 85Rb coupled through Magnetic Feshbach Resonance (MFR) has been investigated. By solving the time independent atom-molecular coupled equations, the initial atomic and molecular wavefunctions were obtained and the dynamics of the initial atomic and molecular waves in a spherical one-dimensional trap were studied by solving the time-dependent atom-molecular coupled equations. During evolution two types of induced or stimulated decays of the feshbach molecules were switched on. The…
We study center-of-mass oscillations of a dipolar Bose-Einstein condensate in the vicinity of a superconducting surface. We show that the magnetic field of the magnetic dipoles induces eddy currents in the superconductor, which act back on the Bose-Einstein condensate. This leads to a shift of its oscillation frequency and to an anharmonic coupling of the Bose-Einstein condensate with the superconductor. The anharmonicity creates a coupling to one of the collective modes of the condensate that can be resonantly enhanced, if the parameters of the condensate are chosen properly. This provides a …
We discuss the effect of anomalous quantum-reflection of Bose-Einstein condensates as a screening effect, that is created by the condensate itself. We derive an effective, time-independent single-mode approach, that allows us to define different paths of reflection. We compare our theory with experimental results.
I present an interconversion currents algebra for an atom-molecule Bose-Einstein condensate model and use it to get the quantum dynamics of the currents. For different choices of the Hamiltonian parameters I get different currents dynamics.
Collapsing Bose-Einstein condensates are rich and complex quantum systems for which quantitative explanation by simple models has proved elusive. We present new experimental data on the collapse of high density Rb-85 condensates with attractive interactions and find quantitative agreement with the predictions of the Gross-Pitaevskii equation. The collapse data and measurements of the decay of atoms from our condensates allow us to put new limits on the value of the Rb-85 three-body loss coefficient K_3 at small positive and negative scattering lengths.
The role of complex potentials in single-body Schrődinger equation has been studied intensively. We study the quantum coherence for degenerate Bose gases in complex potentials, when the exchange symmetry of identical bosons is considered. For initially independent Bose-Einstein condensates, it is shown that even very weak imaginary potential can induce perfect quantum coherence between different condensates. The scheme to observe imaginary potential induced quantum coherence is discussed.
We theoretically study macroscopic entanglement between a magnetically trapped Bose-Einstein condensate and a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupling with the magnetic trap to generate macroscopic entanglement. The scheme also provides a platform to investigate interferometry with an entangled Bose Einstein condensate and to explore physics at the quantum-classical interface.
Preparation of molecular quantum gas promises novel applications including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing. Experimental preparation of colder and denser molecular samples, however, is frequently hindered by fast inelastic collisions that heat and deplete the population. Here we report the formation of two-dimensional Bose-Einstein condensates (BECs) of spinning $g-$wave molecules by inducing pairing interactions in an atomic condensate. The trap geometry and the low temperature of the molecules help reducing …
We reveal the connection of the recent numerical observations of Krstulovic and Brachet [arXiv:1007.4441] with the general theory of relaxation kinetics of the strongly non-equilibrium Bose-Einstein condensates.
We describe the transition of $N$ weakly interacting atoms into a Bose-Einstein condensate within a number-conserving quantum master equation theory. Based on the separation of time scales for condensate formation and non-condensate thermalization, we derive a master equation for the condensate subsystem in the presence of the non-condensate environment under the inclusion of all two body interaction processes. We numerically monitor the condensate particle number distribution during condensate formation, and derive a condition under which the unique equilibrium steady state of a dilute, weakl…
The condensate number distribution during the transition of a dilute, weakly interacting gas of N=200 bosonic atoms into a Bose-Einstein condensate is modeled within number conserving master equation theory of Bose-Einstein condensation. Initial strong quantum fluctuations occuring during the exponential cycle of condensate growth reduce in a subsequent saturation stage, before the Bose gas finally relaxes towards the Gibbs-Boltzmann equilibrium.
We calculate the condensate fraction and the condensate and non-condensate spatial and momentum distribution of the Bose-Hubbard model in a trap. From our results, it is evident that using approximate distributions can lead to erroneous experimental estimates of the condensate. Strong interactions cause the condensate to develop pedestal-like structures around the central peak that can be mistaken as non-condensate atoms. Near the transition temperature, the peak itself can include a significant non-condensate component. Using distributions generated from QMC simulations, experiments can map t…
We devise a microscopic scattering approach to probe the excitation spectrum of a Bose-Einstein condensate. We show that the experimentally accessible scattering cross section exhibits universal Ericson fluctuations, with characteristic properties rooted in the underlying classical field equations.
We demonstrate theoretically that analogues of D-branes in string theory can be realized in rotating, phase-separated, two-component Bose-Einstein condensates and that they are observable using current experimental techniques. This study raises the possibility of simulating D-branes in the laboratory.
Bose polarons as relativistic Unruh-DeWitt detectors: Entanglement harvesting from Bose-Einstein condensates
Nordita, KTH Royal Institute of Technology and Stockholm University（诺尔迪塔，皇家理工学院和斯德哥尔摩大学）；Kirchhoff-Institut für Physik, Universität Heidelberg（基希霍夫物理研究所，海德堡大学）
In certain field theoretical models, composite solitons consisting of a domain wall and vortex lines attached to the wall have been referred to as D-brane solitons. We show that similar composite solitons can be realized in phase-separated two-component Bose-Einstein condensates. We discuss the similarities and differences between topological solitons in the Abelian-Higgs model and those in two-component Bose-Einstein condensates. Based on the formulation of gauge theory, we introduce the "boojum charge" to characterize the "D-brane soliton" in Bose-Einstein condensates.
I introduce two family of exactly solvable models for multiatomic hetero-nuclear and homo-nuclear molecular Bose-Einstein condensates through the algebraic Bethe ansatz method. The conserved quantities of the respective models are also showed.
