Bosonic Josephson Junction Research Articles

Formula omitted]-coherence vs. [formula omitted]-coherence: An alternative route to the Gross–Pitaevskii equation

We show how a candidate mean-field amplitude can be constructed from the exact wave function of an externally forcedN-Boson system. The construction makes use of subsidiary (N−1)-particle states which are propagated in time in addition to the true N-particle state, but does not involve spontaneous breaking of the U(1) symmetry associated with particle number conservation. Provided the flow in Fock space possesses a property which we call maximum stiffness, or t-coherence, the candidate amplitude actually satisfies the time-dependent Gross–Pitaevskii equation, and then serves as macroscopic wave function of the forced N-particle system. The general procedure is illustrated in detail by numerical calculations performed for the model of a driven bosonic Josephson junction, which allows one to keep track of all contributions which usually are subject to uncontrolled assumptions. These calculations indicate that macroscopic wave functions can persist even under conditions of strong forcing, but are rapidly destroyed upon entering a regime of chaotic dynamics. Our results provide a foundation for future attempts to manipulate, and actively control, macroscopic wave functions by means of purposefully designed force protocols.

Stability and tunneling dynamics of a dark-bright soliton pair in a harmonic trap

We consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright (DB) solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a Bosonic Josephson Junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.

Tunneling dynamics of bosonic Josephson junctions assisted by a cavity field

We study the interplay between the dynamics of a Bose-Einstein condensate in a double-well potential and that of an optical cavity mode. The cavity field is superimposed to the double-well potential and affects the atomic tunneling processes. The cavity field is driven by a laser red detuned from the bare cavity resonance; the dynamically changing spatial distribution of the atoms can shift the cavity in and out of resonance. At resonance the photon number is hugely enhanced and the atomic tunneling becomes amplified. The Josephson junction equations are revisited and the phase diagram is calculated. We find new solutions with finite imbalance and at the same time a lack of self-trapping solutions due to the emergence of a new separatrix resulting from enhanced tunneling.

Critical exponents for an impurity in a bosonic Josephson junction: Position measurement as a phase transition

A model of an atomic impurity immersed in a BEC trapped in a double-well potential is presented and the concept of fidelity susceptibility is used to calculate the critical exponents of the phase transition from a balanced to an imbalanced number of particles in either the left- or right-hand well.

Quasiparticle tunneling in a periodically driven bosonic Josephson junction

A resonantly driven bosonic Josephson junction supports stable collective excitations, or quasiparticles, which constitute analogs of the Trojan wave packets previously explored with Rydberg atoms in strong microwave fields. We predict a quantum beating effect between such symmetryrelated many-body Trojan states taking place on time scales which are long in comparison with the driving period. Within a mean-field approximation, this quantum beating can be regarded as a manifestation of dynamical tunneling. On the full N-particle level, the beating phenomenon leads to an experimentally feasible, robust strategy for probing highly entangled mesoscopic states.

Fluctuations of the order parameter of a mesoscopic Floquet condensate

We suggest that nonequilibrium Bose-Einstein condensates may occur in time-periodically driven interacting Bose gases. Employing the model of a periodically forced bosonic Josephson junction, we demonstrate that resonance-induced ground-state-like many-particle Floquet states possess an almost perfect degree of coherence, as corresponding to a mesoscopically occupied, explicitly time-dependent single-particle orbital. In marked contrast to the customary time-independent Bose-Einstein condensates, the order parameter of such systems is destroyed by violent fluctuations when the particle number becomes too large, signaling the nonexistence of a proper mean-field limit.

Trojan quasiparticles

We argue that a time-periodically driven bosonic Josephson junction supports stable, quasiparticle-like collective response modes which are N-particle analogs of the nonspreading Trojan wave packets known from microwave-driven Rydberg atoms. Similar to their single-particle counterparts, these collective modes, dubbed ‘flotons’, are well described by a Floquet–Mathieu approximation, and possess a well-defined discrete set of excitations. In contrast to other, ‘chaotic’ modes of response, the nonheating Trojan modes conform to a mean-field description, and thus may be of particular interest for the more general question under which conditions the reduction of quantum N-particle dynamics to a strongly simplified mean-field evolution is feasible. Our reasoning is supported by phase-space portraits which reveal the degree of correspondence beween the N-particle dynamics und the mean-field picture in an intuitive manner.

Effect of a laser dip in the semiclassical dynamics of bosonic Josephson junctions

We consider the standard double-well setup extended with a laser beam in the center to create a ``triple-well'' potential. The beam in the center is much narrower than the barrier, and it creates a tunable depth well which can support a localized state in the middle. We show that the presence of the localized state in the central well changes the sign of tunneling between the left and the right wells and therefore controls the fixed-point dynamics of the bosonic Josephson junction.

Impurity in a bosonic Josephson junction: Swallowtail loops, chaos, self-trapping, and Dicke model

We study a model describing $N$ identical bosonic atoms trapped in a double-well potential together with a single impurity atom, comparing and contrasting it throughout with the Dicke model. As the boson-impurity coupling strength is varied, there is a symmetry-breaking pitchfork bifurcation which is analogous to the quantum phase transition occurring in the Dicke model. Through stability analysis around the bifurcation point, we show that the critical value of the coupling strength has the same dependence on the parameters as the critical coupling value in the Dicke model. We also show that, like the Dicke model, the mean-field dynamics go from being regular to chaotic above the bifurcation and macroscopic excitations of the bosons are observed. Overall, the boson-impurity system behaves like a poor man's version of the Dicke model.

Universality of fragmentation in the Schrödinger dynamics of bosonic Josephson junctions

The many-body Schr\"odinger dynamics of a one-dimensional bosonic Josephson junction is investigated for up to 10 000 bosons and long times. The initial states are fully condensed and the interaction strength is weak. We report on a universal fragmentation dynamics on the many-body level: systems consisting of different numbers of particles fragment to the same value at constant mean-field interaction strength. The phenomenon manifests itself in observables such as the correlation functions of the system. We explain this universal fragmentation dynamics analytically based on the Bose-Hubbard model. We thereby show that the extent to which many-body effects become important at later times depends crucially on the initial state. Even for arbitrarily large particle numbers and arbitrarily weak interaction strength the dynamics is many-body in nature and the fragmentation universal. There is no weakly interacting limit where the Gross-Pitaevskii mean field is valid for long times.

Coherent control of quantum collapse in a Bosonic Josephson junction by modulation of the scattering length

By means of a temporal-periodic modulation of the s-wave scattering length, a procedure to control the evolution of an initial atomic coherent state associated with a bosonic Josephson junction is presented. The scheme developed has a remarkable advantage of avoiding the quantum collapse of the state due to phase and number diffusion. This kind of control could prove useful for atom interferometry using BECs, where the interactions limit the evolution time stage within the interferometer, and where the modulation can be induced via magnetic Feshbach resonances as recently experimentally demonstrated.

Shortcut to adiabaticity in internal bosonic Josephson junctions

We extend a recent method to shortcut the adiabatic following to internal bosonic Josephson junctions in which the control parameter is the linear coupling between the modes. The approach is based on the mapping between the two-site Bose-Hubbard Hamiltonian and a one-dimensional effective Schr\"odinger-like equation, valid in the large-$N$ (number of particles) limit. Our method can be readily implemented in current internal bosonic Josephson junctions and it substantially improves the production of spin squeezing with respect to the usually employed linear rampings.

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.

Quantum and thermal fluctuations in bosonic Josephson junctions

We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in canonical equilibrium ensembles of bosonic Josephson junctions at relatively high temperatures, comparing the results for finite particle numbers to the classical limit that is attained as $N$ approaches infinity. We consider both attractive and repulsive atom-atom interactions, with especial focus on the behavior near the T=0 quantum phase transition that occurs, for large enough $N$, when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small $N$ and those of the classical limit are quite small even when $N \sim 100$, with deviations from the limit diminishing as 1/N.

Berezinskii–Kosterlitz–Thouless transition in two-dimensional arrays of Josephson coupled Bose–Einstein condensates

Abstract We study the phase transition occurring in Bose–Einstein condensates placed in an optical lattice where the system is arranged in a form of a two-dimensional bosonic Josephson junction array. It is shown that the Josephson interaction between adjacent condensates (trapped in the valleys of the periodic lattice potential) can trigger Berezinskii–Kosterlitz–Thouless transition at a finite temperature T KT to the ordered state composed of bound vortex–antivortex phase-field configurations of individual condensates. Using a lattice model of the bosonic Josephson junction array, we derive the effective phase-only Hamiltonian and calculate the critical temperature T KT . Finally, we discuss the results in the context of system parameters and possible experiments.

Effects of Quantum Correction on Dynamical Phase Transition in a Single Species Bosonic Josephson Junction

In this paper, by employing Bogliubov backreaction method, we investigate quantum correction effects on dynamical phase transition in a single species bosonic Josephson junction induced by increasing nonlinear interaction. Compared with mean field theory results, we find that the transition point is shifted. The dynamical phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point of the mean field theory.

Temporal fluctuations in the bosonic Josephson junction as a probe for phase space tomography

We study the long-time dynamics of the reduced one-particle Bloch vector S of a two-mode Bose–Hubbard model in the Josephson interaction regime, as a function of the relative phase and occupation imbalance of an arbitrary coherent preparation. We find that the variance of the long-time fluctuations of S can be factorized as a product of the inverse participation number 1/M that depends only on the preparation, and a semiclassical function C(E) that reflects the phase space characteristics of the pertinent observable. Temporal fluctuations can thus be used as a sensitive probe for phase space tomography of quantum many-body states.

POINCARÉ SECTION ANALYSIS TO MEASURE SYNCHRONIZATION IN COUPLED HAMILTONIAN SYSTEMS

As a novel synchronization phenomenon, measure synchronization (MS) in Hamiltonian systems is characterized by a commonly shared phase space that has invariant measure. Although there has been some discussions of the underlying mechanism, a general explanation of MS is still lacking. In this paper, we reveal the essence of MS by using Poincaré section analysis. A two coupled Bosonic Josephson junction model is employed to perform the analysis as an illustration. It is shown that coupled Hamiltonian systems exhibit separatrix crossing behavior at quasiperiodic MS transition. Moreover, using this analysis method we find that chaotic MS is the result of separatrix chaos. It is concluded that the Poincaré section technique is a general method to explain MS, and the direct correspondence between separatrix behavior and the MS transition is a universal property in coupled Hamiltonian systems.

Fast generation of spin-squeezed states in bosonic Josephson junctions

We describe methods for fast production of highly coherent-spin-squeezed many-body states in bosonic Josephson junctions (BJJs). We start from the known mapping of the two-site Bose-Hubbard (BH) Hamiltonian to that of a single effective particle evolving according to a Schr\"odinger-like equation in Fock space. Since, for repulsive interactions, the effective potential in Fock space is nearly parabolic, we extend recently derived protocols for shortcuts to adiabatic evolution in harmonic potentials to the many-body BH Hamiltonian. The best scaling of the squeezing parameter for large number of atoms N is \xi^2_S ~ 1/N.

QUANTUM INTERFEROMETRY AT ZERO AND FINITE TEMPERATURE WITH TWO-MODE BOSONIC JOSEPHSON JUNCTIONS

We analyze phase interferometry realized with a bosonic Josephson junction (BJJ) made of trapped dilute and ultracold atoms. By using a suitable phase sensitivity indicator we study the zero temperature junction-states useful to achieve sub shot-noise precisions. Sub shot-noise phase shift sensitivities can be reached even at finite temperature under a suitable choice of the junction state. We infer a scaling law in terms of the size system (that is, the number of particles) for the temperature at which the shot-noise limit is not overcome anymore.