Optical weak link between two spatially separated Bose-Einstein condensates

Trapping wave fields in an expulsive potential by means of linear coupling

We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component and an expulsive anti-HO potential acting upon the other. The systems can be implemented in optical and BEC dual-core waveguides. In the 1D linear system, codimension-one solutions are found in an exact form for the ground state (GS) and dipole mode (the first excited state). Generic solutions are produced by means of the variational approximation and are found in a numerical form. Exact codimension-one solutions and generic numerical ones are also obtained for the GS and vortex states in the 2D system (the exact solutions are found for all values of the vorticity). Both the trapped and antitrapped components of the bound states may be dominant ones, in terms of the norm. The localized modes may be categorized as bound states in continuum, as they coexist with delocalized ones. The 1D states, as well as the GS in 2D, are weakly affected and remain stable if the self-attractive or repulsive nonlinearity is added to the system. The self-attraction makes the vortex states unstable against splitting, while they remain stable under the action of the self-repulsion.

Nonlinear Dynamics of Wave Packets in Tunnel-Coupled Harmonic-Oscillator Traps

We consider a two-component linearly coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap acting in both components, we consider Josephson oscillations (JO) initiated by an input in the form of the HO’s ground state (GS) or dipole mode (DM), placed in one component. With the increase of the strength of the self-focusing nonlinearity, spontaneous symmetry breaking (SSB) between the components takes place in the dynamical JO state. Under still stronger nonlinearity, the regular JO initiated by the GS input carries over into a chaotic dynamical state. For the DM input, the chaotization happens at smaller powers than for the GS, which is followed by SSB at a slightly stronger nonlinearity. In the system with the defocusing nonlinearity, SSB does not take place, and dynamical chaos occurs in a small area of the parameter space. In the asymmetric half-trapped system, with the HO potential applied to a single component, we first focus on the spectrum of confined binary modes in the linearized system. The spectrum is found analytically in the limits of weak and strong inter-component coupling, and numerically in the general case. Under the action of the coupling, the existence region of the confined modes shrinks for GSs and expands for DMs. In the full nonlinear system, the existence region for confined modes is identified in the numerical form. They are constructed too by means of the Thomas–Fermi approximation, in the case of the defocusing nonlinearity. Lastly, particular (non-generic) exact analytical solutions for confined modes, including vortices, in one- and two-dimensional asymmetric linearized systems are found. They represent bound states in the continuum.

Damping of Josephson Oscillations in Strongly Correlated One-Dimensional Atomic Gases

We study Josephson oscillations of two strongly correlated one-dimensional bosonic clouds separated by a localized barrier. Using a quantum-Langevin approach and the exact Tonks-Girardeau solution in the impenetrable-boson limit, we determine the dynamical evolution of the particle-number imbalance, displaying an effective damping of the Josephson oscillations which depends on barrier height, interaction strength, and temperature. We show that the damping originates from the quantum and thermal fluctuations intrinsically present in the strongly correlated gas. Because of the density-phase duality of the model, the same results apply to particle-current oscillations in a one-dimensional ring where a weak barrier couples different angular momentum states.

Exciton-polariton Josephson junctions at finite temperatures

We consider finite temperature effects in a non-standard Bose-Hubbard model for an exciton- polariton Josephson junction (JJ) that is characterised by complicated potential energy landscapes (PEL) consisting of sets of barriers and wells. We show that the transition between thermal activation (classical) and tunneling (quantum) regimes exhibits universal features of the first and second order phase transition (PT) depending on the PEL for two polariton condensates that might be described as transition from the thermal to the quantum annealing regime. In the presence of dissipation the relative phase of two condensates exhibits non-equilibrium PT from the quantum regime characterized by efficient tunneling of polaritons to the regime of permanent Josephson or Rabi oscillations, where the tunneling is suppressed, respectively. This analysis paves the way for the application of coupled polariton condensates for the realisation of a quantum annealing algorithm in presently experimentally accessible semiconductor microcavities possessing high (105 and more) Q-factors.

Bosonic Mott insulator with Meissner currents

We introduce a generic bosonic model exemplifying that (spin) Meissner currents can persist in insulating phases of matter. We consider two species of interacting bosons on a lattice. Our model exhibits separation of charge (total density) and spin (relative density): the charge sector is gapped in a bosonic Mott insulator phase with total density one, while the spin sector remains superfluid due to interspecies conversion. Coupling the spin sector to the gauge fields yields a spin Meissner effect reflecting the long-range spin superfluid coherence. We investigate the resulting phase diagram and describe other possible spin phases of matter in the Mott regime possessing chiral currents as well as a spin-density wave phase. The model presented here is realizable in Josephson junction arrays and in cold atom experiments.

Measure synchronization in a two-species bosonic Josephson junction

Measure synchronization (MS) in a two-species bosonic Josephson junction (BJJ) is studied based on semiclassical theory. Six different scenarios for MS, including two in the Josephson oscillation regime (the zero-phase mode) and four in the self-trapping regime (the π-phase mode), are clearly shown. Systematic investigations of the common features behind these different scenarios are performed. We show that the average energies of the two species merge at the MS transition point. The scaling of the power law near the MS transition is verified and the critical exponent is 1/2 for all of the different scenarios for MS. We also illustrate MS in a three-dimensional phase space; from this illustration, more detailed information on the dynamical process can be obtained. In particular, by analyzing the Poincaré sections with changing interspecies interactions, we find that the two-species BJJ exhibits separatrix crossing behavior at the MS transition point and such behavior depicts the general mechanism behind the different scenarios for the MS transitions. The new critical behavior found in a two-species BJJ is expected to be found in real systems of atomic Bose gases.

Dynamics of a tunable superfluid junction

We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.

Adiabatically induced coherent Josephson oscillations of ultracold atoms in an asymmetric two-dimensional magnetic lattice

We propose a new method to create an asymmetric two-dimensional magnetic lattice which exhibits magnetic band gap structure similar to semiconductor devices. The quantum device is assumed to host bound states of collective excitations formed in a magnetically trapped quantum degenerate gas of ultracold atoms such as a Bose-Einstein condensate (BEC) or a degenerate Fermi gas. A theoretical framework is established to describe possible realization of the exciton-Mott to discharging Josephson states oscillations in which the adiabatically controlled oscillations induce ac and dc Josephson atomic currents where this effect can be used to transfer n Josephson qubits across the asymmetric two-dimensional magnetic lattice. We consider second-quantized Hamiltonians to describe the Mott insulator state and the coherence of multiple tunneling between adjacent magnetic lattice sites where we derive the self consistent non-linear Schrödinger equation with a proper field operator to describe the exciton Mott quantum phase transition via the induced Josephson atomic current across the n magnetic bands.

Possible stimulation of nuclear alpha decay by superfluid helium

It is suggested that superfluid helium (condensate of (4)He atoms) may stimulate nuclear alpha decay in a situation when an alpha emitter moves through superfluid helium with fine-tuned velocity, so that the backward-emitted alpha particle is at rest in the laboratory frame. It is shown that the probability of stimulated alpha decay in this case may be sizable enough to be detected.

Non-Abelian Josephson effect between two F=2 spinor Bose-Einstein condensates in double optical traps

We investigate the non-Abelian Josephson effect in F=2 spinor Bose-Einstein condensates with double optical traps. We propose a real physical system which contains non-Abelian Josephson effect and has very different density and spin tunneling characters compared with the Abelian case. We calculate the frequencies of the pseudo Goldstone modes in different phases between two traps, respectively, which are the crucial feature of the non-Abelian Josephson effect. We also give an experimental protocol to observe this novel effect in future experiments.

Interference of Bose-Einstein condensates

A formalism for describing the coherence and interference properties of two atomic clouds of Bose-Einstein condensates (BEC) is presented, which is applicable even in the opposite limits when the BEC clouds are initially coherent and when they are initially independent. First, we develop a mean-field theory wherein one mean-field mode is used, and then, for fragmented (i.e., independent) condensates, we use a mean-field theory with two modes. We then develop a full two-mode field theory, with a field operator composed of a sum of two terms containing matter wave mode functions phi1 and phi2, that multiply the destruction operators of the modes, a1 and a2. When atom-atom interactions are present and when the mode functions overlap, the matter wave mode functions phi1 and phi2 develop components moving to the right and left, and this results in interference fringes in the density. At the many-body level, another source of interference arises from expectation values of the form (a(i)+a(j)) with i double dagger j, which become nonzero due to tunneling and interactions. We detail how these two sources of interference affect the density profile and the density-density correlation functions of Bose-Einstein condensates in the coherent and in the fragmented regimes.

Ultracold bosons in a tilted multilevel double-well potential

The N-body problem in a tilted double well requires new features for macroscopic quantum superposition in ultracold atoms. In particular, one needs to go beyond the single-particle ground state in each well. We provide explicit criteria for when two energy levels are needed to describe the state space. For typical experimental parameters, two levels are indeed required for the creation of macroscopic superposition states. Furthermore, we show that a small tilt causes the collapse of such states. However, partial macroscopic superposition states reappear when the tilt can be compensated by atom-atom interactions.

Preparing and probing atomic number states with an atom interferometer

We describe the controlled loading and measurement of number-squeezed states and Poisson states of atoms in individual sites of a double well optical lattice. These states are input to an atom interferometer that is realized by symmetrically splitting individual lattice sites into double wells, allowing atoms in individual sites to evolve independently. The two paths then interfere, creating a matter-wave double-slit diffraction pattern. The time evolution of the double-slit diffraction pattern is used to measure the number statistics of the input state. The flexibility of our double well lattice provides a means to detect the presence of empty lattice sites, an important and so far unmeasured factor in determining the purity of a Mott state.

Interferences in the density of two Bose-Einstein condensates consisting of identical or different atoms

The density of two initially independent condensates which are allowed to expand and overlap can show interferences as a function of time due to interparticle interaction. Two situations are separately discussed and compared: (1) all atoms are identical and (2) each condensate consists of a different kind of atoms. Illustrative examples are presented.