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arXiv:1412.1014 · Physical Review A

Tunneling dynamics of bosonic Josephson junctions assisted by a cavity field

Gergely Szirmai, G. Mazzarella, Luca Salasnich

Published Feb 3, 2015• 15 citations
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Abstract

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 solutions with finite imbalance and at the same time find a lack of self-trapping solutions due to the emergence of a new separatrix resulting from enhanced tunneling.

DOI
10.1103/physreva.91.023601

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We study the influence of photons on the dynamics and the ground state of the atoms in a bosonic Josephson junction inside an optical resonator. The system is engineered in such a way that the atomic tunneling can be tuned by changing the number of photons in the cavity. In this setup the cavity photons are a means of control, which can be utilized both in inducing self-trapping solutions and in driving the crossover of the ground state from an atomic coherent state to a Schr\"odinger cat state. This is achieved, for suitable setup configurations, with interatomic interactions weaker than those required in the absence of a cavity. This is corroborated by the study of the entanglement entropy. In the presence of a laser, this quantum indicator attains its maximum value (which marks the formation of the catlike state and, at a semiclassical level, the onset of self-trapping) for attractions smaller than those of the bare junction.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.
We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the nthn\mathrm{th}nth LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.
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.
We explore the interplay between tunneling and interatomic interactions in the dynamics of a bosonic Josephson junction. We tune the scattering length of an atomic ^{39}K Bose-Einstein condensate confined in a double-well trap to investigate regimes inaccessible to other superconducting or superfluid systems. In the limit of small-amplitude oscillations, we study the transition from Rabi to plasma oscillations by crossing over from attractive to repulsive interatomic interactions. We observe a critical slowing down in the oscillation frequency by increasing the strength of an attractive interaction up to the point of a quantum phase transition. With sufficiently large initial oscillation amplitude and repulsive interactions, the system enters the macroscopic quantum self-trapping regime, where we observe coherent undamped oscillations with a self-sustained average imbalance of the relative well population. The exquisite agreement between theory and experiments enables the observation of a broad range of many body coherent dynamical regimes driven by tunable tunneling energy, interactions and external forces, with applications spanning from atomtronics to quantum metrology.
An atomic Josephson junction realized with dipolar bosons in a double-well potential can be described by an extended Bose-Hubbard model in which dipolar interactions generate an effective on-site interaction and nearest-neighbor pair tunneling. Using mean-field theory and exact diagonalization, we investigate how this correlated process affects zero-temperature equilibrium and dynamical properties of the system. In equilibrium, we show that pair tunneling induces ground-state parity modulations and significantly reshapes the phase diagram, producing qualitative changes in the quantum phase transitions toward NOON and phase-NOON states, as well as quantitative shifts of the critical points. Out of equilibrium, we demonstrate that it modifies the conditions for macroscopic quantum self-trapping, and assess its impact by comparing mean-field and fully quantum evolution, including the emergence of dynamical quantum phase transitions.