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Bose-Einstein Condensates in a Single Double Well Potential

Rudolf Gati

Published Jan 1, 2007• 9 citations
Publisher

Abstract

The subject of this work is the experimental implementation of a single bosonic Josephson junction and the discussion of the performed investigations. To generate this new kind of Josephson junction a 87-Rubidium Bose-Einstein condensate is split in a double well potential into two matter wave packets, which are coupled coherently to each other via quantum mechanical tunneling of atoms through the barrier. The state of the system can be described by two dynamical variables, the population imbalance of the two wells and their phase difference. The investigation of the dynamical response of the Josephson junction shows, that two dynamical regimes can be identified, the plasma oscillation regime, where atoms tunnel back and forth between the wells, and the self trapping regime, where no tunneling is found. Furthermore, the investigation at finite temperature reveals, that the relative phase in steady state is not locked to zero but fluctuates according to its temperature and the tunneling coupling. By measuring the fluctuations and calculating the tunneling coupling it is possible to deduce the temperature of the atomic cloud. With this a new method for thermometry is realized, which also works in a regime, where the standard methods can not be applied.

DOI
10.11588/heidok.00007293

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The subject of this work is the experimental implementation of a single bosonic Josephson junction and the discussion of the performed investigations. To generate this new kind of Josephson junction a 87-Rubidium Bose-Einstein condensate is split in a double well potential into two matter wave packets, which are coupled coherently to each other via quantum mechanical tunneling of atoms through the barrier. The state of the system can be described by two dynamical variables, the population imbalance of the two wells and their phase difference. The investigation of the dynamical response of the Josephson junction shows, that two dynamical regimes can be identified, the plasma oscillation regime, where atoms tunnel back and forth between the wells, and the self trapping regime, where no tunneling is found. Furthermore, the investigation at finite temperature reveals, that the relative phase in steady state is not locked to zero but fluctuates according to its temperature and the tunneling coupling. By measuring the fluctuations and calculating the tunneling coupling it is possible to deduce the temperature of the atomic cloud. With this a new method for thermometry is realized, which also works in a regime, where the standard methods can not be applied.
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 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 study quantum dynamical properties of a spin-1 atomic Bose-Einstein condensate in a double-well potential. Adopting a mean field theory and single spatial mode approximation, we characterize our model system as two coupled spins. For certain initial states, we find full magnetization oscillations between wells not accompanied by mass (or atom numbers) exchange. We identify dynamic regimes of collective spin variables arising from nonlinear self-interactions that are different from the usual Josephson oscillations. We also discuss magnetization beats and incomplete oscillations of collective spin variables other than the magnetization. Our study points to an alternative approach to observe coherent tunnelling of a condensate through a (spatial) potential barrier.
We theoretically investigate the properties of a double-well bosonic Josephson junction coupled to a single trapped ion. We find that the coupling between the wells can be controlled by the internal state of the ion, which can be used for studying mesoscopic entanglement between the two systems and to measure their interaction with high precision. As a particular example we consider a single ^{87}Rb atom and a small Bose-Einstein condensate controlled by a single 171Yb+ ion. We calculate interwell coupling rates reaching hundreds of Hz, while the state dependence amounts to tens of Hz for plausible values of the currently unknown s-wave scattering length between the atom and the ion. The analysis shows that it is possible to induce either the self-trapping or the tunneling regime, depending on the internal state of the ion. This enables the generation of large scale ion-atomic wave packet entanglement within current technology.
We present an experimental study on the nonequilibrium tunnel dynamics of two coupled one-dimensional Bose-Einstein quasicondensates deep in the Josephson regime. Josephson oscillations are initiated by splitting a single one-dimensional condensate and imprinting a relative phase between the superfluids. Regardless of the initial state and experimental parameters, the dynamics of the relative phase and atom number imbalance shows a relaxation to a phase-locked steady state. The latter is characterized by a high phase coherence and reduced fluctuations with respect to the initial state. We propose an empirical model based on the analogy with the anharmonic oscillator to describe the effect of various experimental parameters. A microscopic theory compatible with our observations is still missing.
We study the coherent atomic tunneling between two zero-temperature Bose-Einstein condensates (BEC) confined in a double-well magnetic trap. Two Gross-Pitaevskii equations for the self-interacting BEC amplitudes, coupled by a transfer matrix element, describe the dynamics in terms of the interwell phase difference and population imbalance. In addition to the anharmonic generalization of the familiar ac Josephson effect and plasma oscillations occurring in superconductor junctions, the nonlinear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel ``macroscopic quantum self-trapping'' effect.