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arXiv:quant-ph/0611190 · Physical Review A

Precision measurement with an optical Josephson junction

H. T. Ng, Keith R. Burnett, Jacob Dunningham

Published Jun 8, 2007• 1 citation
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Abstract

We present a theoretical study of a type of Josephson device, the so-called ``optical Josephson junction'' [Y. Shin et al. Phys. Rev. Lett. 95, 170402 (2005).]. In this device, two condensates are optically coupled through a waveguide by a pair of Bragg beams. This optical Josephson junction differs from the usual Josephson junction where condensates are weakly coupled by tunneling through a barrier. We discuss the use of this optical Josephson junction, for making precision measurements.

DOI
10.1103/physreva.75.063607

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We present a theoretical study of a type of Josephson device, the so-called ``optical Josephson junction'' [Y. Shin et al. Phys. Rev. Lett. 95, 170402 (2005).]. In this device, two condensates are optically coupled through a waveguide by a pair of Bragg beams. This optical Josephson junction differs from the usual Josephson junction where condensates are weakly coupled by tunneling through a barrier. We discuss the use of this optical Josephson junction, for making precision measurements.
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 direct observation of an oscillating atomic current in a one-dimensional array of Josephson junctions realized with an atomic Bose-Einstein condensate. The array is created by a laser standing wave, with the condensates trapped in the valleys of the periodic potential and weakly coupled by the interwell barriers. The coherence of multiple tunneling between adjacent wells is continuously probed by atomic interference. The square of the small-amplitude oscillation frequency is proportional to the microscopic tunneling rate of each condensate through the barriers and provides a direct measurement of the Josephson critical current as a function of the intermediate barrier heights. Our superfluid array may allow investigation of phenomena so far inaccessible to superconducting Josephson junctions and lays a bridge between the condensate dynamics and the physics of discrete nonlinear media.
We consider the far-from-equilibrium quantum transport dynamics in a 1D Josephson junction chain of multimode Bose-Einstein condensates. We develop a theoretical model to examine the experiment of Labouvie et al. [Phys. Rev. Lett. 115, 050601 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.050601], wherein the phenomenon of negative differential conductivity (NDC) was reported in the refilling dynamics of an initially depleted site within the chain. We demonstrate that a unitary c-field description can quantitatively reproduce the experimental results over the full range of tunnel couplings, and requires no fitted parameters. With a view toward atomtronic implementations, we further demonstrate that the filling is strongly dependent on spatial phase variations stemming from quantum fluctuations. Our findings suggest that the interpretation of the device in terms of NDC is invalid outside of the weak coupling regime. Within this restricted regime, the device exhibits a hybrid behavior of NDC and the ac Josephson effect. A simplified circuit model of the device will require an approach tailored to atomtronics that incorporates quantum fluctuations.