Activated transport in the exciton condensate at balanced and imbalanced densities measured in drag and counter-flow configuration

We observe the total filling factor ν_T=1 exciton condensate in independently contacted bilayer two-dimensional electron systems in samples with minute tunnel coupling. At balanced electron densities in the layers, we find for both drag and counter-flow current configurations, thermally activated transport with a monotonic increase of the activation energy for d/ℓ_B<1.65 with activation energies up to 0.4 K. In the imbalanced system the activation energies show a striking asymmetry around the balance point, implying that the gap to charge excitations is considerably different in the separate layers that form the bilayer condensate. This indicates that the measured activation energy is neither the binding energy of the excitons, nor their condensation energy.     

Phase transition of Bose–Einstein condensate under decoherence

The effect of decoherence on the phase transition of a Bose-Einstein condensate in a symmetric double-well potential is determined by the mean atom number difference. It still has two phases, the tunneling phase and the self-trapping phase, even under decoherence. The density matrix and the operator fidelity also show very different behaviors in the two phases. This suggests that operator fidelity can be used to characterize the phase transition of this Bose-Einstein condensate model, even under decoherence.     

Manipulating nonclassical quantum statistical properties of light field by an f-deformed Bose–Einstein condensate

We consider the interaction between an f-deformed Bose–Einstein condensate and a single-mode quantized light field. By using the Gardiner’s phonon operators, we find that there exists a natural deformation in the model which modifies the Bogoliubov approximation under the condition of large but finite number of particles in condensate. This approach introduces an intrinsically deformed Bose–Einstein condensate, where the deformation parameter, well-defined by the particle number N in condensate, controls the strength of the associated nonlinearity. By introducing the deformed Gardiner’s phonon operators we modify the very dilute-gas approximation through including atomic collisions in condensate. The rate of atomic collisions κ, as a new deformation parameter in the deformed Bose–Einstein condensate, controls the nonlinearity related to the atomic collisions. We show that by controlling the nonlinearities in the f-deformed atomic condensate through the two atomic parameters N and κ, it is possible to generate and manipulate the nonclassical quantum statistical properties of radiation field, such as, the sub-Poissonian photon statistics and quadrature squeezing. Also, it is possible to control the collapses and revivals phenomena in the average number of photons by atomic parameters N and κ.     

Manifestation of a gap due to the exchange energy in a spinor condensate

We investigate the dynamic response of population transfer between two components of a finite temperature spinor Bose condensed gas to a time-dependent coupling potential. Comparison between the results obtained in the Bogoliubov–Popov approximation (BPA) and in the generalized random phase approximation (GRPA) shows noticeable discrepancies. In particular, the inter-component current response function calculated in the GRPA displays a gapped spectrum due to the exchange interaction energy whereas the corresponding density response function is gapless. We verify that, contrary to the BPA, the GRPA preserves the SU(2) symmetry and the f-sum rule associated to the spinor gas. In order to validate the approximation, we propose an experimental setup that allows the observation of the predicted gap.     

Coherent state approach to the cross-collisional effects in the population dynamics of a two-mode Bose–Einstein condensate

We reanalyze the non-linear population dynamics of a Bose–Einstein condensate (BEC) in a double well trap considering a semiclassical approach based on a time dependent variational principle applied to coherent states associated to SU(2) group. Employing a two-mode local approximation and hard sphere type interaction, we show in the Schwinger’s pseudo-spin language the occurrence of a fixed point bifurcation that originates a separatrix of motion on a sphere. This separatrix corresponds to the borderline between two dynamical regimes of Josephson oscillations and mesoscopic self-trapping. We also consider the effects of interaction between particles in different wells, known as cross-collisions. Such terms are usually neglected for traps sufficiently far apart, but recently it has been shown that they contribute to the effective tunneling constant with a factor growing linearly with the particle number. This effect changes considerably the effective tunneling of the system for sufficiently large number of trapped atoms, in perfect accord with experimental data. Finally, we identify analytically the transition parameter associated to the bifurcation in the generalized phase space of the model with cross-collision terms, and show how the dynamical regime depends on the initial conditions of the system and the collisional parameters values.     

Nonlinear resonance phenomenon of one-dimensional Bose–Einstein condensate under periodic modulation

We investigate the effect of an external periodic modulation on the one-dimensional （1D） Bose-Einstein conden- sate with harmonic trapping potential. By numerically solving the Gross-Pitaevskii equation with symplectic algorithm, the nonlinear resonance phenomenon is shown and the corresponding Fourier spectrum is given. The autoresonance phe- nomenon is also presented under almost periodic external modulation, and it shows that the condensate eventually evolves into quasi-periodic oscillation.     

Investigations on finite ideal quantum gases

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose–Einstein condensation are discussed.     

A continuation BSOR-Lanczos–Galerkin method for positive bound states of a multi-component Bose–Einstein condensate

We develop a continuation block successive over-relaxation (BSOR)-Lanczos–Galerkin method for the computation of positive bound states of time-independent, coupled Gross–Pitaevskii equations (CGPEs) which describe a multi-component Bose–Einstein condensate (BEC). A discretization of the CGPEs leads to a nonlinear algebraic eigenvalue problem (NAEP). The solution curve with respect to some parameter of the NAEP is then followed by the proposed method. For a single-component BEC, we prove that there exists a unique global minimizer (the ground state) which is represented by an ordinary differential equation with the initial value. For a multi-component BEC, we prove that m identical ground/bound states will bifurcate into m different ground/bound states at a finite repulsive inter-component scattering length. Numerical results show that various positive bound states of a two/three-component BEC are solved efficiently and reliably by the continuation BSOR-Lanczos–Galerkin method.     

Nonlinear dissipative dynamics of a two-component atomic condensate coupling with a continuum

We investigate the nonlinear dissipative coherence bifurcation and population dynamics of a two-component atomic Bose-Einstein condensate coupling with a continuum. The coupling between the two-component condensates and the continuum brings effective dissipations to the two-component condensates. The steady states and the coherence bifurcation depend on both dissipation and the nonlinear interaction between condensed atoms. The coherence among condensed atoms may be even enhanced by the effective dissipations. The combination of dissipation and nonlinearity allows one to control the switching between different self-trapped states or the switching between a self-trapped state and a non-self-trapped state.     

Resonant energy transfer in Bose–Einstein condensates

We consider the dynamics of a dilute, magnetically-trapped one-dimensional Bose–Einstein condensate whose scattering length is periodically modulated with a frequency that linearly increases in time. We show that the response frequency of the condensate locks to its eigenfrequency for appropriate ranges of the parameters. The locking sets in at resonance, i.e., when the effective frequency of driving field is equal to the eigenfrequency, and is accompanied by a sudden increase of the oscillations amplitude due to resonant energy transfer. We show that the dynamics of the condensate is given, to leading order, by a driven harmonic oscillator on the time-dependent part of the width of the condensate. This equation captures accurately both the locking and the resonant energy transfer as it is evidenced by comparison with direct numerical simulations of original Gross–Pitaevskii equation.     

A Dicke Type Model for Equilibrium BEC Superradiance

We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier paper we considered the problem for two simple models showing the cooperative effect between Bose–Einstein condensation and superradiance. In this paper we formalize the model suggested by Ketterle et al. in which the Bose condensate particles have a two level structure. We present a soluble microscopic Dicke type model describing a thermodynamically stable system. We find the equilibrium states of the system and compute the thermodynamic functions giving explicit formulæ expressing the cooperative effect between Bose–Einstein condensation and superradiance.     

Controlling Decoherence Speed Limit of a Single Impurity Atom in a Bose–Einstein‐Condensate Reservoir

The decoherence speed limit (DSL) of a single impurity atom immersed in a Bose‐Einstein‐condensed (BEC) reservoir when the impurity atom is in a double‐well potential is studied. It is demonstrated how the DSL of the impurity atom can be manipulated by engineering the BEC reservoir and the impurity potential within experimentally realistic limits. It is shown that the DSL can be controlled by changing key parameters such as the condensate scattering length, the effective dimension of the BEC reservoir, and the spatial configuration of the double‐well potential imposed on the impurity. The physical mechanisms of controlling the DSL at root of the spectral density of the BEC reservoir are uncovered.     

Micro traps for quantum information processing and precision force sensing

We review recent experimental progress towards quantum information processing and precision force sensing using neutral atoms in micro traps. Microscopic potential structures as generated by optical or electronic microstructures (micro traps) allow for a versatile manipulation of quantum states of atoms and of ultracold atomic quantum gases. Most recent experimental results include the implementation of single‐qubit‐operations in both, optical and magnetic micro traps, as well as in the demonstration of matter‐wave interferometer using Bose‐Einstein condensates coherently split in micro traps.     

Renormalized dispersion of elementary excitations in spinor polariton condensates

We analyse the polarization of spinor polariton condensates and corresponding dispersions of elementary excitations. We have considered the effects of magnetic field induced splitting in circular polarizations and residual splitting in linear polarizations in the ground state provided by the cavity asymmetry. We show that anisotropic polariton–polariton interactions fully compensate the Zeeman splitting in circular polarizations below the critical magnetic field, thus leading to the spin-Meissner effect for the polariton condensates. We also analyzed the effect of polariton–polariton interactions on the stability of the gap in linear polarizations characteristic for anisotropic microcavities. It was shown that in realistic systems this gap increases with concentration of the particles, thus contributing to the stability of the pinning of linear polarization of photoemission in semiconductor microcavities for pump intensities above the stimulation threshold.     

Integrable Limits of Dynamics in Trapped Bose-Condensates

The dynamics of quasiparticles in Bose condensates at zero temperature, confined in harmonic potentials, are studied using the Bogoliubov-theory. The Hamiltonian of the Bogoliubov-theory, appearing in the semiclassical limit is investigated in detail. The classical motion given by this Hamiltonian is generally chaotic already for axially symmetric traps. But, in certain parameter regions the motion becomes quasi-integrable. Integrable regions are studied classically, and the experimentally accessible low-energy region quantum mechanically.     

Bose–Einstein Condensation for Homogeneous Interacting Systems with a One-Particle Spectral Gap

We prove rigorously the occurrence of zero-mode Bose–Einstein condensation for a class of continuous homogeneous systems of boson particles with superstable interactions. This is the first example of a translation invariant continuous Bose-system, where the existence of the Bose–Einstein condensation is proved rigorously for the case of non-trivial two-body particle interactions, provided there is a large enough one-particle excitations spectral gap. The idea of proof consists of comparing the system with specially tuned soluble models.     

Black Holes in Bose–Einstein Condensates

It is shown that there exist both dynamically stable and unstable dilute-gas Bose–Einstein condensates that, in the hydrodynamic limit, exhibit a behavior completely analogous to that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models. We have also simulated the creation of a stable sonic black hole by solving the Gross–Pitaevskii equation numerically for a condensate subject to a trapping potential that is adiabatically deformed. A sonic black hole could in this way be created experimentally with state-of-the-art or planned technology.     

Wannier–Stark chaos of a Bose–Einstein condensate in 1D optical lattices

Using the idea of the macroscopic quantum wave function and the definition of the Melnikov chaos, we investigate the spatially chaotic features of a Bose–Einstein condensate (BEC) in a Wannier–Stark potential for the trivial phase and the non-trivial phase cases. The perturbed chaotic solutions are constructed, and the chaotic and unstable regions on the parameter space are illustrated. Numerical calculations to the spatial evolutions of the atomic number density and the energy density demonstrate the analytical results and exhibit the chaotic spatial distribution and energy distribution of the BEC atoms.     

Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.