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arXiv:1112.3509 · Physical Review Letters

Bosonic Josephson Junction Controlled by a Single Trapped Ion

R. Gerritsma, Antonio Negretti, H. Doerk, Zbigniew Idziaszek, Tommaso Calarco, Ferdinand Schmidt‐Kaler

Published Aug 22, 2012• 57 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.109.080402

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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.
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.
We analyze theoretically the dynamics of an atomic double-well system with a single ion trapped in its center. We find that the atomic tunneling rate between the wells depends both on the spin of the ion via the short-range spin-dependent atom-ion scattering length and on its motional state with tunneling rates reaching hundreds of hertz. A protocol is presented that could transport an atom from one well to the other, depending on the motional (Fock) state of the ion within a few milliseconds. This phonon-atom coupling is of interest for creating atom-ion entangled states and may form a building block in constructing a hybrid atom-ion quantum simulator. We also analyze the effect of imperfect ground-state cooling of the ion and the role of micromotion when the ion is trapped in a Paul trap. Due to the strong nonlinearities in the atom-ion interaction, the micromotion can cause couplings to high-energy atom-ion scattering states, preventing accurate state preparation and complicating the double-well dynamics. We conclude that the effects of micromotion can be reduced by choosing ion-atom combinations with a large mass ratio and by choosing large interwell distances. The proposed double-well system may be realized in an experiment by combining either optical traps or magnetic microtraps for atoms with ion trapping technology.
We consider a degenerate Bose gas confined in a double-well potential in interaction with a trapped ion in one dimension and investigate the impact of two relevant sources of imperfections in experiments on the system dynamics: ion motion and thermal excitations of the bosonic ensemble. Particularly, their influence on the entanglement generation between the spin state of the moving ion and the atomic ensemble is analyzed. We find that the detrimental effects of the ion motion on the entanglement protocol can be mitigated by properly choosing the double-well parameters as well as timings of the protocol. Furthermore, thermal excitations of the bosons affect significantly the system's tunneling and self-trapping dynamics at moderate temperatures; i.e., thermal occupation of a few double-well quanta reduces the protocol performance by about 10%. Hence, we conclude that finite temperature is the main source of decoherence in such junctions and we demonstrate the possibility to entangle the condensate motion with the ion vibrational state.
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 study an atomic Josephson junction (AJJ) in the presence of two interacting Bose–Einstein condensates (BECs) confined in a double-well trap. We assume that bosons of different species interact with each other. The macroscopic wavefunctions of the two components obey a system of two 3D coupled Gross–Pitaevskii equations (GPEs). We write the Lagrangian of the system, and from this we derive a system of coupled ordinary differential equations (ODEs), for which the coupled pendula represent the mechanical analogues. These differential equations control the dynamical behaviour of the fractional imbalance and of the relative phase of each bosonic component. We perform the stability analysis around the points which preserve the symmetry and get an analytical formula for the oscillation frequency around the stable points. Such a formula could be used as an indirect measure of the inter-species s-wave scattering length. We also study the oscillations of each fractional imbalance around zero and nonzero—the macroscopic quantum self-trapping (MQST)—time averaged values. For different values of the inter-species interaction amplitude, we carry out this study both by directly solving the two GPEs and by solving the corresponding coupled pendula equations. We show that, under certain conditions, the predictions of these two approaches are in good agreement. Moreover, we calculate the crossover value of the inter-species interaction amplitude which signals the onset of MQST.
In this work, we have studied the tunneling of a single atom in a double-well. The atom is interacting with a single ion in a simple harmonic trap placed in the center of the double-well. The tunneling of the atom is controlled by the spin and/or motional state of the ion. Considering a model potential, we have shown that it is possible to generate an entangled state between the spatial state of the ion and the atomic wavefunction. By employing the optimal control method, the quantum speed limit of generating this entangled process has been explored. This system can be used as qubit in quantum computers.