Quantum Self-trapping Research Articles

Symmetry-breaking and symmetry-restoring dynamics of a mixture of Bose-Einstein condensates in a double well

We study the coherent nonlinear tunneling dynamics of a binary mixture of Bose-Einstein condensates in a double-well potential. We demonstrate the existence of a type of mode associated with the ``swapping'' of the two species in the two wells of the potential. In contrast to the symmetry-breaking macroscopic quantum self-trapping (MQST) solutions, the swapping modes correspond to the tunneling dynamics that preserves the symmetry of the double-well potential. As a consequence of two distinct types of broken-symmetry MQST phases where the two species localize in different potential wells or coexist in the same well, the corresponding symmetry-restoring swapping modes result in dynamics where the two species either avoid or chase each other. In view of the possibility to control the interaction between the species, the binary mixture offers a very robust system to observe these novel effects as well as the phenomena of Josephson oscillations and $\ensuremath{\pi}$ modes.

Exact coherent control to two weakly coupled Bose–Einstein condensates

We investigate the exact ac control of two periodically driven and weakly coupled Bose–Einstein condensates in a double-well trap. By employing two balance conditions we construct new exact Floquet solutions with the degenerate Floquet energy, and give the balance region on the parameter space. It is revealed that for some different parameters in the balance region the Floquet solutions exactly describe the macroscopic quantum self-trapping, nonlinear coherent construction and destruction of quantum tunneling, respectively. Therefore, we can accurately perform the coherent control by suitably adjusting the system parameters.

Fock-space WKB method for the boson Josephson model describing a Bose-Einstein condensate trapped in a double-well potential

We develop a Fock-space WKB method for a Bose-Einstein condensate (BEC) in a double-well trap, using an analogy with a single particle of either positive or negative mass in a quantum potential. The usual mean-field approach is the classical limit, and the inverse number of atoms plays the role of Planck constant. The ground state of positive-mass particles corresponds to the mean-field fixed point of lower energy, while that of negative mass to the excited fixed point. In the case of attractive BECs above the threshold for symmetry breaking, the ground state is the Schr\"odinger cat state and we relate this to the double-well shape of the potential in Fock space. In the repulsive case, we identify the quantum states corresponding to the mean-field macroscopic self-trapping phenomenon. In particular, the phase-locked ($\ensuremath{\pi}$ phase) macroscopic quantum self-trapping of BECs is related to the double-well shape of the potential in Fock space. The running-phase macroscopic quantum self-trapping state is found to be subject to quantum collapses and revivals. The phase dispersion grows exponentially, reaching the absolute maximum just before the first collapse of the running phase, which may explain the growth of the phase fluctuations seen in the experiment on macroscopic quantum self-trapping.

Josephson dynamics for coupled polariton modes under the atom–field interaction in the cavity

We consider a new approach to the problem of Bose–Einstein condensation (BEC) of polaritons for atom–field interaction under the strong coupling regime in the cavity. We investigate the dynamics of two macroscopically populated polariton modes corresponding to the upper and lower branch energy states coupled via Kerr-like nonlinearity of atomic medium. We found out the dispersion relations for new type of collective excitations in the system under consideration. Various temporal regimes like linear (nonlinear) Josephson transition and/or Rabi oscillations, macroscopic quantum self-trapping (MQST) dynamics for population imbalance of polariton modes are predicted. We also examine the switching properties for time-averaged population imbalance depending on initial conditions, effective nonlinear parameter of atomic medium and kinetic energy of low-branch polaritons.

Effect of decoherence on the dynamics of Bose-Einstein condensates in a double-well potential

We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to environments. Two kinds of coupling are taken into account. With the first kind of coupling dominated, the decoherence can enhance the self-trapping by increasing the damping of the oscillations in the dynamics, while the decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.

Tunneling dynamics between two-component Bose–Einstein condensates

We present a mean-field model to study the tunneling dynamics between initially separated two-component Bose condensates in a time-dependent double-well potential. We solve the model in terms of a completely numerical procedure. In contrast to the usual Josephson effect between two coherently separated single-component condensates, we find that this system sustains a macroscopic quantum self-trapping even for sufficiently weak interatomic interactions and small initial population imbalance far below the critical value.

Atomic population oscillations between two coupled Bose–Einstein condensates with time-dependent nonlinear interaction

The atomic population oscillations between two Bose–Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system's steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping (MQST). In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.

Stability and chaotic behavior of a two-component Bose–Einstein condensate

We investigate the stability and chaotic behavior of a periodically driven Bose–Einstein condensate (BEC) with two hyperfine states. The effects of the population transfer K and relative energy fluctuation γ between the two hyperfine states are demonstrated analytically and numerically. The stability analysis shows that the steady-state relative population will appear the tuning-fork bifurcation, when the physical parameters are changed to some critical values. Meanwhile, the dependence of the macroscopic quantum self-trapping (MQST) on the initial conditions, the population transfer and the relative energy is revealed, and the stationary, periodical and chaotic MQSTs are found. Finally, we illustrate that the relative population oscillation can undergo a process from order to chaos, through a series of period-doubling bifurcations.

Dynamic chaos and stability of a weakly open Bose-Einstein condensate in a double-well trap

We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.

Dynamics of dipolar spinor condensates

We study the semiclassical dynamics of a spinor condensate with the magnetic dipole–dipole interaction included. The time evolution of the population imbalance and the relative phase among different spin components depend greatly on the relative strength of interactions as well as on the initial conditions. The interplay of spin-exchange and dipole–dipole interaction makes it possible to manipulate the atomic population on different components, leading to the phenomena of spontaneous magnetization and macroscopic quantum self-trapping. A simple estimate demonstrates that these effects are accessible and controllable by modifying the geometry of the trapping potential.

Direct Observation of Tunneling and Nonlinear Self-Trapping in a Single Bosonic Josephson Junction

We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the predicted nonlinear generalization of tunneling oscillations in superconducting and superfluid Josephson junctions. Additionally, we confirm a novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations.

Adiabatic vibrational excitons: Amide I states in α-helices as an example

Based on a correct quantum dynamical description, exciton formation and self-trapping in α-helical polypeptides is reinvestigated. The studies are focused on the amide I high-frequency vibration of the peptide group and account for their modulation by longitudinal helix vibrations. First, the adiabatic single- and two-exciton states are analyzed for a chain of 10 peptide units, whereby the presence of two types of self-trapped amide I two-exciton states is confirmed. In a second step, by using the multi-configuration time-dependent Hartree method an exact quantum description is achieved for the complete exciton helix-vibrational states. The computational approach incorporating up to nine helix coordinates is used to calculate the infrared linear absorbance. Moreover, excitation energy motion through the chain is characterized.

Three-body recombination in two coupled Bose–Einstein condensates

We investigate the dynamics of two Bose–Einstein condensates (BECs) tunnel coupled by a double-well potential. In the case of attractive interatomic interaction, the effects of the three-body recombination losses and the feeding of the condensates from the thermal cloud are studied by using a two-mode approximation. It is shown that the stability region of the parameter space could be enlarged by increasing the three-body losses or the tunnelling coefficient. The numerical results also reveal some interesting motion characteristics of the BECs for different s-wave scattering lengths, including macroscopic quantum self-trapping of non-stationary state BECs, and periodic oscillation of the population whose phase orbit tends to a stable limit cycle.

Influence of quantum entanglement on quantum tunnelling between two atomic Bose–Einstein condensates

We investigate the influence of quantum entanglement (QE) on an atomic tunnelling process in two Bose–Einstein condensates (BECs) with tunnelling interaction. We show that through changing the initial QE one can control macroscopic quantum self-trapping (MQST) and the atomic tunnelling current (ATC). We also show that the QE can enhance and suppress the MQST and ATC significantly under certain conditions. It is indicated that the maximal entanglement between two BECs can induce an equal-population stationary state. It is found that the distribution of the Shapiro-like steps of the ATC is equal-distant, and the size of each step can be controlled through changing the amount of entanglement.

Tunneling Dynamics of the Halves of a Double-Well Trap Containing a Bose-Einstein Condensate

In this paper, we have studied tunneling dynamics of the halves of a double-well trap containing a Bose–Einstein condensate. It is found that there exist step structure and macroscopic quantum self-trapping of population difference of atoms, and exist Shapiro-like steps of atomic tunneling current. Both the population difference and the atomic tunneling current depend strongly on the total number of atoms and the initial phase difference.

Coexisting Condensates of Weakly Interacting Bose Gas in a Harmonic Trap

We study particles in a vortex state driven to a core state with lower energy and zero angular momentum by the trap potential asymmetries. We find that at when the role of the thermal gas can be ignored, there will be coexisting condensates. We also calculate the fluctuation of the number difference and argue that in certain range of the parameters the state of the whole system is the macroscopic quantum self-trapping in the Josephson tunnelling regime.

Dynamics of a period-3 pattern-loaded Bose-Einstein condensate in an optical lattice

We discuss the dynamics of a Bose-Einstein condensate initially loaded into every third site of an optical lattice using a description based upon the discrete nonlinear Schrodinger equation. An analytic solution is developed for the case of a periodic initial condition and is compared with numerical simulations for more general initial configurations. We show that mean field effects in this system can cause macroscopic quantum self-trapping, a phenomenon already predicted for double well systems. In the presence of a uniform external potential, the atoms exhibit generalized Bloch oscillations which can be interpreted in terms of the interference of three different Bloch states. We also discuss how the momentum distribution of the system can be used as experimental signature of the macroscopic self trapping effect.

Tunneling Dynamics of Two-Species Bose–Einstein Condensates**The project supported in part by National Natural Science Foundation of China

We have studied the tunneling dynamics of two-species Bose–Einstein condensates. It is shown that the population difference and the Josephson-like tunneling current between the two condensates exhibit oscillation behaviors and there exists macroscopic quantum self-trapping, which strongly depends on the initial state, interatomic nonlinear self-interaction, interspecies nonlinear interaction, and the total number of atoms in the two condensates.

Quantum coherence of double-well Bose-Einstein condensates: An SU(2) coherent-state path-integral approach

Macroscopic quantum coherence of Bose gas in a double-well potential is studied, based on an SU(2) coherent-state path-integral approach. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.

Atomic Tunnelling Dynamics of Two Squeezed Bose–Einstein Condensates**The project supported in part by the National “973” Research Plan, the National Natural Science Foundation, and the EYTF of the Educational Department of China

In this paper, tunnelling dynamics of squeezed Bose–Einstein condensates (BEC's) in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunnelling interaction is investigated by using the second quantization approach. The influence of BEC squeezing on macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunnelling is analyzed in detail. It is shown that the MQST and coherent atomic tunnelling between two squeezed BEC's can be manipulated through changing squeezing amplitude and squeezing phase of BEC squeezed states.