Interspecies Interaction Strength Research Articles

Correlation induced localization of lattice trapped bosons coupled to a Bose–Einstein condensate

We investigate the ground state properties of a lattice trapped bosonic system coupled to a Lieb–Liniger type gas. Our main goal is the description and in depth exploration and analysis of the two-species many-body quantum system including all relevant correlations beyond the standard mean-field approach. To achieve this, we use the multi-configuration time-dependent Hartree method for mixtures (ML-MCTDHX). Increasing the lattice depth and the interspecies interaction strength, the wave function undergoes a transition from an uncorrelated to a highly correlated state, which manifests itself in the localization of the lattice atoms in the latter regime. For small interspecies couplings, we identify the process responsible for this cross-over in a single-particle-like picture. Moreover, we give a full characterization of the wave function’s structure in both regimes, using Bloch and Wannier states of the lowest band, and we find an order parameter, which can be exploited as a corresponding experimental signature. To deepen the understanding, we use an effective Hamiltonian approach, which introduces an induced interaction and is valid for small interspecies interaction. We finally compare the ansatz of the effective Hamiltonian with the results of the ML-MCTDHX simulations.

A distinguishable single excited-impurity in a Bose–Einstein condensate

We investigate the properties of a distinguishable single excited state impurity pinned in the center of a trapped Bose–Einstein condensate in a one-dimensional harmonic trapping potential by changing the bare mass of the impurity and its interspecies interaction strength with the Bose–Einstein condensate. We model our system by using two coupled differential equations for the condensate and the single excited-impurity wave function, which we solve numerically. For equilibrium, we find that an excited-impurity induces two bumps or dips on the condensate for the attractive- or repulsive-interspecies coupling strengths, respectively. Afterwards, we show that the excited-impurity induced imprint upon the condensate wave function remains present during a time-of-flight expansion after having switched off the harmonic confinement. We also investigate shock-waves or gray-solitons by switching off the interspecies coupling strength in the presence of harmonic trapping potential. During this process, we found that the generation of gray bi-soliton or gray quad-solitons (four-solitons) depend on the bare mass of the excited-impurity in a harmonic trap.

Solvable model of a generic trapped mixture of interacting bosons: reduced density matrices and proof of Bose–Einstein condensation

A mixture of two kinds of identical bosons, species 1 with N1 bosons of mass m1 and species 2 with N2 bosons of mass m2, held in a harmonic potential of frequency ω and interacting by harmonic intra-species and inter-species particle-particle interactions of strengths , , and is discussed. This is an exactly-solvable model of a generic mixture of trapped interacting bosons which allows one to investigate and determine analytically properties of interest. To start, closed form expressions for the frequencies, ground-state energy, and wave-function of the mixture are obtained and briefly analyzed as a function of the masses, numbers of particles, and strengths and signs of interactions. To prove Bose–Einstein condensation of the mixture three steps are needed. First, we integrate the all-particle density matrix, employing a four-parameter matrix-recurrence relations, down to the lowest-order intra-species and inter-species reduced density matrices of the mixture. Second, the coupled Gross–Pitaevskii (mean-field) equations of the mixture are solved analytically. Third, we analyze the mixture’s reduced density matrices in the limit of an infinite number of particles of both species 1 and 2 (when the interaction parameters, i.e. the products of the number of particles times the intra-species and inter-species interaction strengths, are held fixed) and prove that: (i) both species 1 and 2 are 100% condensed; (ii) the inter-species reduced density matrix per particle is separable and given by the product of the intra-species reduced density matrices per particle; and (iii) the mixture’s energy per particle, and reduced density matrices and densities per particle all coincide with the Gross–Pitaevskii quantities. Finally, when the infinite-particle limit is taken with respect to, say, species 1 only (with interaction parameters held fixed) we prove that: (iv) only species 1 is 100% condensed and its reduced density matrix and density per particle, as well as the mixture’s energy per particle, coincide with the Gross–Pitaevskii quantities of species 1 alone; and (v) the inter-species reduced density matrix per particle is nonetheless separable and given by the product of the intra-species reduced density matrices per particle. The results are compared and discussed with respect to the recent work by Bouvrie et al (2014 Eur. Phys. J. D 68 346) who found for attractive mixtures vanishing bipartite entanglement between the two species and between a single particle (of either kind) and the remaining particles in the mixture. Implications are briefly discussed.

Solvable model of a trapped mixture of Bose–Einstein condensates

A mixture of two kinds of identical bosons held in a harmonic potential and interacting by harmonic particle–particle interactions is discussed. This is an exactly-solvable model of a mixture of two trapped Bose–Einstein condensates which allows us to examine analytically various properties. Generalizing the treatments in Cohen and Lee (1985) and Osadchii and Muraktanov (1991), closed form expressions for the mixture’s frequencies and ground-state energy and wave-function, and the lowest-order densities are obtained and analyzed for attractive and repulsive intra-species and inter-species particle–particle interactions. A particular mean-field solution of the corresponding Gross–Pitaevskii theory is also found analytically. This allows us to compare properties of the mixture at the exact, many-body and mean-field levels, both for finite systems and at the limit of an infinite number of particles. We discuss the renormalization of the mixture’s frequencies at the mean-field level. Mainly, we hereby prove that the exact ground-state energy per particle and lowest-order intra-species and inter-species densities per particle converge at the infinite-particle limit (when the products of the number of particles times the intra-species and inter-species interaction strengths are held fixed) to the results of the Gross–Pitaevskii theory for the mixture. Finally and on the other end, we use the mixture’s and each species’ center-of-mass operators to show that the Gross–Pitaevskii theory for mixtures is unable to describe the variance of many-particle operators in the mixture, even in the infinite-particle limit. The variances are computed both in position and momentum space and the respective uncertainty products compared and discussed. The role of the center-of-mass separability and, for generically trapped mixtures, inseparability is elucidated when contrasting the variance at the many-body and mean-field levels in a mixture. Our analytical results show that many-body correlations exist in a trapped mixture of Bose–Einstein condensates made of any number of particles. Implications are briefly discussed.

Phase separation and dynamics of two-component Bose-Einstein condensates

The miscibility of two interacting quantum systems is an important testing ground for the understanding of complex quantum systems. Two-component Bose-Einstein condensates enable the investigation of this scenario in a particularly well controlled setting. In a homogeneous system, the transition between mixed and separated phases is fully characterised by a `miscibility parameter', based on the ratio of intra- to inter-species interaction strengths. Here we show, however, that this parameter is no longer the optimal one for trapped gases, for which the location of the phase boundary depends critically on atom numbers. We demonstrate how monitoring of damping rates and frequencies of dipole oscillations enables the experimental mapping of the phase diagram by numerical implementation of a fully self-consistent finite-temperature kinetic theory for binary condensates. The change in damping rate is explained in terms of surface oscillation in the immiscible regime, and counterflow instability in the miscible regime, with collisions becoming only important in the long time evolution.

Numerical study of localized impurity in a Bose-Einstein condensate

Motivated by recent experiments, we investigate a single $^{133}\text{Cs}$ impurity in the center of a trapped $^{87}\text{Rb}$ Bose-Einstein condensate. Within a zero-temperature mean-field description we provide a one-dimensional physical intuitive model which involves two coupled differential equations for the condensate and the impurity wave function, which we solve numerically. With this we determine within the equilibrium phase diagram spanned by the intra- and inter-species coupling strength, whether the impurity is localized at the trap center or expelled to the condensate border. In the former case we find that the impurity induces a bump or dip on the condensate for an attractive or a repulsive Rb-Cs interaction strength, respectively. Conversely, the condensate environment leads to an effective mass of the impurity which increases quadratically for small interspecies interaction strength. Afterwards, we investigate how the impurity imprint upon the condensate wave function evolves for two quench scenarios. At first we consider the case that the harmonic confinement is released. During the resulting time-of-flight expansion it turns out that the impurity-induced bump in the condensate wave function starts decaying marginally, whereas the dip decays with a characteristic time scale which decreases with increasing repulsive impurity-BEC interaction strength. Secondly, once the attractive or repulsive interspecies coupling constant is switched off, we find that white-shock waves or bi-solitons emerge which both oscillate within the harmonic confinement with a characteristic frequency.

Structure of two-component Bose-Einstein condensates with respective vortex-antivortex superposition states

We investigate the phase structure of two-component Bose-Einstein condensates (BECs) with repulsive intra- and interspecies interactions in the presence of respective vortex-antivortex superposition states (VAVSSs). We show that different winding numbers of the vortex and antivortex and different intra- and interspecies interaction strengths may lead to different phase configurations, such as fully separated phases, inlaid separated phases, asymmetric separated phases, and partially mixed phases, where the density profile of each component displays a petal-like (or modulated petal-like) structure. A phase diagram is given for the case of equal unit winding numbers of the vortex and antivortex in the respective components, and it is shown that the conventional criterion for phase separation of two-component BECs is not applicable for the present system due to the VAVSSs. In addition, our nonlinear stability analysis indicates that the typical phase structures of two-component BECs with VAVSSs allow them to be detected in experiments. Moreover, for the case of unequal winding numbers of the vortex and antivortex in the respective components, we find that each component in any of the possible phase structures is in a cluster state of vortices and antivortices, where the topological defects appear in the form of a singly quantized visible vortex, or a hidden vortex, or a ghost vortex, depending on the specific parameters of the system. Finally, a general relationship between the vortex-antivortex cluster state and the winding numbers of vortex and antivortex is revealed.

Correlated phases of population imbalanced Fermi-Fermi mixtures on an optical lattice

We study a two-species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with onsite interspecies repulsive interaction. Such a model can be realized in a cold-atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable interspecies interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities for the minority species, we find that several correlated phases emerge as the ground state, including a spin density wave state, a charge density wave state with stripe structure, and various $p$-wave BCS pairing states for both species. We study this system using a functional renormalization group method, determine its phase diagram at weak coupling, discuss the origin and characteristics of each phase, and provide estimates for the critical temperatures.

Large-Napproximation for one- and two-component dilute Bose gases

We discuss the mean-field theories obtained from the leading order in a large-$N$ approximation for one- and two- component dilute Bose gases. For a one-component Bose gas this approximation has the following properties: the Bose-Einstein condensation (BEC) phase transition is second order but the critical temperature $T_c$ is not shifted from the non-interacting gas value $T_0$. The spectrum of excitations in the BEC phase resembles the Bogoliubov dispersion with the usual coupling constant replaced by the running coupling constant which depends on both temperature and momentum. We then study two-component Bose gases with both inter- and intra- species interactions and focus on the stability of the mixture state above $T_c$. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the inter-species interaction strength to the intra-species interaction strength (assuming equal strength for both species) exceeds a critical value. At high temperature this is a structural transition and the global translational symmetry is broken. Our work complements previous studies on the instability of the mixture phase in the presence of BEC.

Combined periodic wave and solitary wave solutions in two-component Bose-Einstein condensates

In this paper, the Jacobi elliptic function expansion method provides an effective approach to obtain the exact periodic wave solutions of two-component Bose-Einstein condensates. Exact combined bright-bright and dark-dark soliton wave solutions can be achieved in their limit conditions. We also obtain the different formation regions of combined solitons. Our results show that the intraspecies (interspecies) interaction strengths clearly affect the formation of dark-dark, bright-bright and dark-bright soliton solutions in different regions.

Disordered One-Dimensional Bose-Fermi Mixtures: The Bose-Fermi Glass

We analyze an interacting Bose-Fermi mixture in a 1D disordered potential by using a combination of renormalization group and variational methods. We obtain the complete phase diagram in the incommensurate case as a function of bosonic and interspecies interaction strengths, in the weak disorder limit. We find that the system is characterized by several phase transitions between superfluid and various glassy insulating states, including a new Bose-Fermi glass phase, where both species are coupled and localized. We show that the dynamical structure factor, as measured through Bragg scattering experiments, can distinguish between the various localized phases and probe their dynamics.

Formation of combined solitons in two-component Bose–Einstein condensates

We investigate the combined soliton solutions of two-component Bose–Einstein condensates with external potential. The “phase diagram" is obtained for the formation regions of different combined solitons. Our results show that the intraspecies (interspecies) interaction strengths and the external trapped potential clearly affect the formation of dark-dark, bright-bright, and dark–bright soliton solutions in different regions. Especially, we find that the bright–bright (dark–dark) soliton can exist in the case of both repulsive (attractive) intraspecies interaction strengths in the presence of external potential. This novel phenomenon is completely different from the formation of soliton solution of one-component Bose–Einstein condensates without external potential, and it will be useful for the study of two-component Bose–Einstein condensates.

Collective dynamics of two-species Bose-Einstein-condensate mixtures in a double-well potential

By employing a binary mixture of Bose-Einstein condensates in a symmetric double-well potential we study the collective dynamics of a two-coupled-Hamiltonian system. There we find three interesting collective dynamic regimes. Besides measure synchronization, phase synchronization and nonlocal measure synchronization have been found. We demonstrate that by varying the interspecies interaction strength, the transitions between different regimes can be found clearly. A diagram of dynamic regimes with experimentally adjustable parameters has also been presented.

Dynamical Structure Factor and Spin-Density Separation for a Weakly Interacting Two-Component Bose Gas

We show that spin-density separation in a Bose gas is not restricted to 1D but also occurs in higher dimensions. The ratio (alpha) of the intraspecies atom-atom interaction strength to the interspecies interaction strength strongly influences the dynamics of spin-density separation and the elementary excitations. The density wave is phononlike for all values of alpha. For alpha < 1, the spin wave is also phononlike. The spin waves have a quadratic dispersion in the alpha=1 coupling regime, while in the phase separated regime (alpha > 1) the spin waves are found to be damped. The dynamical structure factor reveals two distinct peaks corresponding to the density and spin waves for alpha < or =1. For alpha > 1 there is only one dynamical structure factor peak corresponding to the density wave.

Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution

We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly on the population densities of all species resident in the community. New species are introduced through mutation. Both models are amenable to exact linear stability analysis, and we compare the analytic results with large-scale kinetic Monte Carlo simulations, obtaining the population size as a function of an average interspecies interaction strength. Over time, the models self-optimize through mutation and selection to approximately maximize a community potential function, subject only to constraints internal to the particular model. If the interspecies interactions are randomly distributed on an interval including positive values, the system evolves toward self-sustaining, mutualistic communities. In contrast, for the predator-prey case the matrix of interactions is antisymmetric, and a nonzero population size must be sustained by an external resource. Time series of the diversity and population size for both models show approximate 1/f noise and power-law distributions for the lifetimes of communities and species. For the mutualistic model, these two lifetime distributions have the same exponent, while their exponents are different for the predator-prey model. The difference is probably due to greater resilience toward mass extinctions in the food-web like communities produced by the predator-prey model.

Superfluid-insulator transitions of two-species bosons in an optical lattice

We consider a realization of the two-species bosonic Hubbard model with variable interspecies interaction and hopping strength. We analyze the superfluid-insulator (SI) transition for the relevant parameter regimes and compute the ground state phase diagram for odd filling at commensurate densities. We find that in contrast to the even commensurate filling case, the superfluid-insulator transition occurs with (a) simultaneous onset of superfluidity of both species or (b) coexistence of Mott insulating state of one species and superfluidity of the other or, in the case of unit filling, (c) complete depopulation of one species. The superfluid-insulator transition can be first order in a large region of the phase diagram. We develop a variational mean-field method which takes into account the effect of second order quantum fluctuations on the superfluid-insulator transition and corroborate the mean-field phase diagram using a quantum Monte Carlo study.

Generation of Bell states in two-component Bose–Einstein condensates

We examine analytically the generation of Bell state in Bose condensates of two interacting species trapped in a double well configuration. The density of probability for finding the entangled Bell state is given. The effect of the tunnelling rate and the interspecies interaction strength on the generation of Bell state is discussed. We find that the oscillation amplitude of the density of probability for finding the entangled Bell state becomes greater as the tunnelling rate Ω increases and the self-interaction strength of the component A(B) has no effect on it.

Structure of vortex lattices in rotating two-component Bose–Einstein condensates

We investigate numerically the structure of vortex lattices in rotating two-component Bose–Einstein condensates with equal intraspecies interaction strengths g 11= g 22. The stationary solutions of the coupled Gross–Pitaevskii equations with a centrifugal term show various non-trivial patterns of vortex lattices, depending on the interspecies interaction strength g 12. For g 11g 22 >g 12 the vortices in each condensate form a vortex lattice, and one lattice is shifted from the other to reduce the overlap of the condensates. For g 11g 22 <g 12 when the phase separation of the condensate occurs, the vortex lattices are destroyed, forming the vortex sheet structure. The dynamics of vortex lattice formation is also discussed.

Dynamically turning off interactions in a two-component condensate

We propose a mechanism to change the interaction strengths of a two component condensate. It is shown that the application of pi/2 pulses allows to alter the effective interspecies interaction strength as well as the effective interaction strength between particles of the same kind. This mechanism provides a simple method to transform spatially stable condensates into unstable once and vice versa. It also provides a means to store a squeezed spin state by turning off the interaction for the internal states and thus allows to gain control over many body entangled states.

“Stability Signature” in Two-Species Dilute Bose-Einstein Condensates

We identify an eigenvalue associated with a dilute two-species Bose-Einstein condensate as the determiner of condensate stability. It plays the same role as the sign of scattering length in a one-species condensate. We predict that there is a range of interspecies interaction strength in which a sodium-rubidium mixture can be stable in a harmonic trap. {copyright} {ital 1997} {ital The American Physical Society}