We present a theory to describe domain formation observed very recently in a quenched Rb-87 gas, a typical ferromagnetic spinor Bose system. An overlap factor is introduced to characterize the symmetry breaking of M_F=\pm 1 components for the F=1 ferromagnetic condensate. We demonstrate that the domain formation is a co-effect of the quantum coherence and the thermal relaxation. A thermally enhanced quantum-oscillation is observed during the dynamical process of the domain formation. And the spatial separation of domains leads to significant decay of the M_F=0 component fraction in an initial M_F=0 condensate.
A quantum phase transition between the symmetric (polar) phase and the phase with broken symmetry can be induced in a ferromagnetic spin-1 Bose-Einstein condensate in space (rather than in time). We consider such a phase transition and show that the transition region in the vicinity of the critical point exhibits scalings that reflect a compromise between the rate at which the transition is imposed (i.e., the gradient of the control parameter) and the scaling of the divergent healing length in the critical region. Our results suggest a method for the direct measurement of the scaling exponent …
A spin-1 ferromagnetic Bose-Einstein condensate subject to a certain magnetic field exhibits a broken-axisymmetry phase in which the magnetization tilts against the applied magnetic field due to the competition between ferromagnetism and linear and quadratic Zeeman effects. The Bogoliubov analysis shows that in this phase two Goldstone modes associated with U(1) and SO(2) symmetry breakings exist, in which phonons and magnons are coupled to restore the two broken symmetries.
Motivated by recent experiments involving the non-destructive imaging of magnetization of a spin-1 87Rb Bose gas (Higbie et al., cond-mat/0502517), we address the question of how the spontaneous magnetization of a ferromagnetic BEC occurs in a spin-conserving system. Due to competition between the ferromagnetic interaction and the total spin conservation, various spin structures such as staggered magnetic domains, and helical and concentric ring structures are formed, depending on the geometry of the trapping potential.
Properties of spin-1 Bose gases with ferromagnetic interaction in the presence of a nonzero magnetic field are studied. The equation of state and thermodynamic quantities are worked out with the help of a mean-field approximation. The phase diagram besides Bose-Einstein condensation contains a first order transition where two values of the magnetization coexist. The dynamics is investigated with the help of the Random Phase Approximation. The soft mode corresponding to the critical point of the magnetic phase transition is found to behave like in conventional theory.
We discuss dynamics of a slow quantum phase transition in a spin-1 Bose-Einstein condensate. We determine analytically the scaling properties of the system magnetization and verify them with numerical simulations in a one dimensional model.
We investigate the dynamics of the one-dimensional strongly repulsive spin-1/2 Bose-Hubbard model for filling $ν\le1.$ While at $ν=1$ the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at $ν<1$ it is a ferromagnetic liquid with complex spin dynamics. We find that close to the insulator-liquid transition the system admits for a complete separation of spin and density degrees of freedom valid at {\it all} energy and momentum scales within the $t-J$ approximation. This allows us to derive the propagator of transverse spin waves and the shape of t…
The achievement in cooling alkali atomic gases, such as $^{87}$Rb, $^{23}$Na and $^{7}$Li, to quantum degeneracy opens up a way to study magnetism in spinor bosons, because these constituent atoms usually have a hyperfine spin degree of freedom. This article reviews several basic problems related to the ferromagnetic phase transition in spinor atomic Bose gases from a theoretical perspective. After a brief discussion on various possible origins of the ferromagnetic interaction, the phase diagram of the ferromagnetically coupled spinor bosons is investigated. It is found that the ferromagnetic …
We investigate the propagation of spin excitations in a one-dimensional (1D) ferromagnetic Bose gas. While the spectrum of longitudinal spin waves in this system is sound-like, the dispersion of transverse spin excitations is quadratic making a direct application of the Luttinger Liquid (LL) theory impossible. By using a combination of different analytic methods we derive the large time asymptotic behavior of the spin-spin dynamical correlation function for strong interparticle repulsion. The result has an unusual structure associated with a crossover from the regime of trapped spin wave to an…
The spin vortices are shown to be created through the Kibble-Zurek (KZ) mechanism in a quantum phase transition of a spin-1 ferromagnetic Bose-Einstein condensate, when the applied magnetic field is quenched below a critical value. It is shown that the magnetic correlation functions have finite correlation lengths, and magnetizations at widely separated positions grow in random directions, resulting in spin vortices. We numerically confirm the scaling law that the winding number of spin vortices is proportional to the square root of the length of the closed path, and for slow quench, proportio…
We study the dynamics of the quantum phase transition of a ferromagnetic spin-1 Bose-Einstein condensate from the polar phase to the broken-axisymmetry phase by changing magnetic field, and find the spontaneous formation of spinor domain walls followed by the creation of polar-core spin vortices. We also find that the spin textures depend very sensitively on the initial noise distribution, and that an anisotropic and colored initial noise is needed to reproduce the Berkeley experiment [Sadler et al., Nature 443, 312 (2006)]. The dynamics of vortex nucleation and the number of created vortices …
We show that a spin-1 Bose-Einstein condensate with ferromagnetic interactions spontaneously generates a topological spin texture, in which the m = \pm 1 components of the magnetic sublevels form vortices with opposite circulations. This phenomenon originates from an interplay between ferromagnetic interactions and spin conservation.
We study the temperature dependence of single-particle and pair coherent condensate densities for a Bose liquid with a "depleted" single-particle Bose-Einstein condensate (BEC) at $T \neq 0$. Our investigations were based on the field-theoretical Green's functions. On the basis of the use of empirical data about the speeds of the first and second sounds is described superfluid state at $T \neq 0$. It is studied the structure of superfluid state taking into account appearance with the different from zero temperatures of normal component and taking into account the branch of the second sound, wh…
Considering a two-component Bose-Einstein condensate in a double-well potential, a method to generate a Bell state consisting of two spatially separated condensates is suggested. For repulsive interactions, the required tunnelling control is achieved numerically by varying the amplitude of a sinusoidal potential difference between the wells. Both numerical and analytical calculations reveal the emergence of a highly entangled mesoscopic state.
We study the dynamic structure factor of two coherent bright solitary waves in attractive Bose- Einstein condensates confined in a harmonic trap. We demonstrate that the wave function of the two solitary waves with a fixed relative phase shows interference in momentum space. The fringes are shifted depending on the values of the phase. This momentum interference can be extracted from the dynamic structure factor of the system using stimulated two-photon Bragg scattering. Thus our method provides a way to measure the relative phase directly.
We study, both experimentally and theoretically, short-time modifications of the decay of excitations in a Bose-Einstein Condensate (BEC) embedded in an optical lattice. Strong enhancement of the decay is observed compared to the Golden Rule results. This enhancement of decay increases with the lattice depth. It indicates that the description of decay modifications of few-body quantum systems also holds for decay of many-body excitations of a BEC.
The possibility of Bose-Einstein condensation of excitations has been discussed for a long time. The phenomenon of the phase-coherent precession of magnetization in superfluid 3He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different states of coherent precession has been observed in 3He-B: homogeneously precessing domain (HPD); persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of the coherent precession in compressed aerogel. In compressed aer…
Reviewing the ideas developed in, the ground state life time of a finite size atomic Bose Einstein condensate is studied for coherent, squeezed coherent and thermal coherent ground states. Ground state evolution of coherent and squeezed coherent states in a double well potential is studied. Effects of thin spectrum on Bose-Einstein condensates is discussed and quasiparticle excitation lifetimes are calculated. It is shown that the effect of the states we use on the free energy vanishes in the thermodynamic limit. Possible extension to a double well potential and effect of a second broken symme…
We study the energetic and dynamic stability of coreless vortices in nonrotated spin-1 Bose-Einstein condensates, trapped with a three-dimensional optical potential and a Ioffe-Pritchard field. The stability of stationary vortex states is investigated by solving the corresponding Bogoliubov equations. We show that the quasiparticle excitations corresponding to axisymmetric stationary states can be taken to be eigenstates of angular momentum in the axial direction. Our results show that coreless vortex states can occur as local or global minima of the condensate energy or become energetically o…
We model the off-resonant superradiant Raman scattering of light from a cigar-shaped atomic Bose-Einstein condensate. Absorption images of transmitted light serve as a direct probe of long range coherence in the condensate. Our multimode theory is in good agreement with the time-dependent spatial features observed in recent experiments, and the inclusion of quantum fluctuations in the initial stages of the superradiant emission accounts well for shot-to-shot fluctuations.
We create atom-molecule superpositions in a Bose-Fermi mixture of Rb-87 and K-40 atoms. The superpositions are generated by ramping an applied magnetic field near an interspecies Fano-Feshbach resonance to coherently couple atom and molecule states. Rabi- and Ramsey-type experiments show oscillations in the molecule population that persist as long as 150 microseconds and have up to 50% contrast. The frequencies of these oscillations are magnetic-field dependent and consistent with the predicted molecule binding energy. This quantum superposition involves a molecule and a pair of free particles…
We study the behavior of a Bose-Einstein condensate held in an optical lattice. We first show how a self-trapping transition can be induced in the system by either increasing the number of atoms occupying a lattice site, or by raising the interaction strength above a critical value. We then investigate how applying a periodic driving potential to the self-trapped state can be used to coherently control the emission of a precise number of correlated bosons from the trapping-site. This allows the formation and transport of entangled bosonic states, which are of great relevance to novel technolog…
We studied the static and dynamic domain wall solutions of spinor Bose-Einstein condensates trapped in an optical lattice. The single and double domain wall solutions are constructed analytically. Our results show that the magnetic field and light-induced dipolar interactions play an important role for both the formation of different domain walls and the adjusting of domain wall width and velocity. Moreover, these interactions can drive the motion of domain wall of Bose ferromagnet systems similar to that driven by the external magnetic field or the spin-polarized current in fermion ferromagne…
We study soliton solutions for the Gross--Pitaevskii equation of the spinor Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses are made in two ways: by assuming single-mode amplitudes and by generalizing Hirota's direct method for multi-components. We obtain one-solitons of single-peak type in the ferromagnetic, polar and cyclic states, respectively. Moreover, twin-peak type solitons both in the ferromagnetic and the polar state are found.
We discuss how to engineer the phase and amplitude of a complex order parameter using localized dissipative perturbations. Our results are applied to generate and control various types of atomic nonlinear matter waves (solitons) by means of localized dissipative defects.
We discuss the dynamics of a Bose-Einstein condensate of atoms which is suddenly coupled to a condensate of molecules by an optical or magnetic Feshbach resonance. Three limiting regimes are found and can be understood from the transient dynamics occuring for each pair of atoms. This transient dynamics can be summarised into a time-dependent shift and broadening of the molecular state. A simple Gross-Pitaevskii picture including this shift and broadening is proposed to describe the system in the three regimes. Finally, we suggest how to explore these regimes experimentally.
We report the phase coherent splitting of Bose-Einstein condensates by means of a phase grating produced near the surface of a micro-electronic chip. A lattice potential with a period of $4μ$m is generated by the superposition of static and oscillating magnetic fields. Precise control of the diffraction is achieved by controlling the currents in the integrated conductors. The interference of overlapping diffraction orders is observed after 8ms of propagation in a harmonic trap and subsequent ballistic expansion of the atomic ensemble. By analyzing the interference pattern we show a reproducibl…
Collisions in a thermal gas are perceived as random or incoherent as a consequence of the large numbers of initial and final quantum states accessible to the system. In a quantum gas, e.g. a Bose-Einstein condensate or a degenerate Fermi gas, the phase space accessible to low energy collisions is so restricted that collisions be-come coherent and reversible. Here, we report the observation of coherent spin-changing collisions in a gas of spin-1 bosons. Starting with condensates occupying two spin states, a condensate in the third spin state is coherently and reversibly created by atomic collis…
We experimentally investigate the collapse dynamics of dipolar Bose- Einstein condensates of chromium atoms in different harmonic trap geometries, from prolate to oblate. The evolutions of the condensates in the unstable regime are compared to three-dimensional simulations of the Gross-Pitaevskii equation including three-body losses. In order to probe the phase coherence of collapsed condensates, we induce the collapse in several condensates simultaneously and let them interfere.
For a weakly interacting Bose-Einstein condensate in a double well, an appropriate time-dependent modulation of the trapping potential counter-acts the "self-trapping" effects of the interactions, thereby allowing tunneling between the wells. It is demonstrated numerically that this modulation can be employed for transferring the condensate from one well to the other in a controlled way. Moreover it allows the production of mesoscopic entangled states on short time scales.
We study quantum transport of an interacting Bose-Einstein condensate in a two-dimensional disorder potential. In the limit of vanishing atom-atom interaction, a sharp cone in the angle-resolved density of the scattered matter wave is observed, arising from constructive interference between amplitudes propagating along reversed scattering paths. Weak interaction transforms this coherent backscattering peak into a pronounced dip, indicating destructive instead of constructive interference. We reproduce this result, obtained from the numerical integration of the Gross-Pitaevskii equation, by a d…
We study an atomic quantum dot representing a single hyperfine "impurity" atom which is coherently coupled to two well-separated Bose-Einstein condensates, in the limit when the coupling between the dot and the condensates dominates the inter-condensate tunneling coupling. It is demonstrated that the quantum dot by itself can induce large-amplitude Josephson-like oscillations of the particle imbalance between the condensates, which display a two-frequency behavior. For noninteracting condensates, we provide an approximate solution to the coupled nonlinear equations of motion which allows us to…
We theoretically study the structure of a stationary soliton in the polar phase of spin-1 Bose--Einstein condensate in the presence of quadratic Zeeman effect at zero temperature. The phase diagram of such solitons is mapped out by finding the states of minimal soliton energy in the defining range of polar phase. The states are assorted into normal, anti-ferromagnetic, broken-axisymmetry, and ferromagnetic phases according to the number and spin densities in the core. The order of phase transitions between different solitons and the critical behaviour of relevant continuous transitions are pro…
Coherent optical information storage capacity of an atomic Bose-Einstein condensate is examined. Theory of slow light propagation in atomic clouds is generalized to short pulse regime by taking into account group velocity dispersion. It is shown that the number of stored pulses in the condensate can be optimized for a particular coupling laser power, temperature and interatomic interaction strength. Analytical results are derived for semi-ideal model of the condensate using effective uniform density zone approximation. Detailed numerical simulations are also performed. It is found that axial d…
We study dark soliton solutions of a multi-component Gross--Pitaevskii equation for hyperfine spin F=1 spinor Bose--Einstein condensate. The interactions are supposed to be inter-atomic repulsive and anti-ferromagnetic ones of equal magnitude. The solutions are obtained from those of an integrable $2\times 2$ matrix nonlinear Schrödinger equation with nonvanishing boundary conditions. We investigate the one-soliton and two-soliton solutions in detail. One-soliton is classified into two kinds. The ferromagnetic state has wavefunctions of domain-wall shape and its total spin is nonzero. The pola…
