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      Macroscopic quantum self-trapping and Josephson oscillations of exciton-polaritons

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          Abstract

          A textbook example of quantum mechanical effects is the coupling of two states through a tunnel barrier. In the case of macroscopic quantum states subject to interactions, the tunnel coupling gives rise to Josephson phenomena including Rabi oscillations, the a.c. and d.c. effects, or macroscopic self-trapping depending on whether tunnelling or interactions dominate. Non-linear Josephson physics, observed in superfluid helium and atomic condensates, has remained inaccessible in photonic systems due to the required effective photon-photon interactions. We report on the observation of non-linear Josephson oscillations of two coupled polariton condensates confined in a photonic molecule etched in a semiconductor microcavity. By varying both the distance between the micropillars forming the molecule and the condensate density in each micropillar, we control the ratio of coupling to interaction energy. At low densities we observe coherent oscillations of particles tunnelling between the two micropillars. At high densities, interactions quench the transfer of particles inducing the macroscopic self-trapping of the condensate in one of the micropillars. The finite lifetime of polaritons results in a dynamical transition from self-trapping to oscillations with pi phase. Our results open the way to the experimental study of highly non-linear regimes in photonic systems, such as chaos or symmetry-breaking bifurcations.

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          The a.c. and d.c. Josephson effects in a Bose–Einstein condensate

          The alternating- and direct-current (a.c. and d.c.) Josephson effects were first discovered in a system of two superconductors, the macroscopic wavefunctions of which are weakly coupled via a tunnelling barrier. In the a.c. Josephson effect, a constant chemical potential difference (voltage) is applied, which causes an oscillating current to flow through the barrier. Because the frequency is proportional to the chemical potential difference only, the a.c. Josephson effect serves as a voltage standard. In the d.c. Josephson effect, a small constant current is applied, resulting in a constant supercurrent flowing through the barrier. In a sense, the particles do not 'feel' the presence of the tall tunnelling barrier, and flow freely through it with no driving potential. Bose-Einstein condensates should also support Josephson effects; however, while plasma oscillations have been seen in a single Bose-Einstein condensate Josephson junction, the a.c. Josephson effect remains elusive. Here we observe the a.c. and d.c. Josephson effects in a single Bose-Einstein condensate Josephson junction. The d.c. Josephson effect has been observed previously only in superconducting systems; in our study, it is evident when we measure the chemical potential-current relation of the Bose-Einstein condensate Josephson junction. Our system constitutes a trapped-atom interferometer with continuous readout, which operates on the basis of the a.c. Josephson effect. In addition, the measured chemical potential-current relation shows that the device is suitable for use as an analogue of the superconducting quantum interference device, which would sense rotation.
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            Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates

            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 inter-well 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 non-linear BEC tunneling dynamics sustains a self-maintained population imbalance: a novel "macroscopic quantum self-trapping effect".
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              Direct Observation of Tunneling and Nonlinear Self-Trapping in a single Bosonic Josephson Junction

              , , (2004)
              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 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.
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                Author and article information

                Journal
                21 December 2012
                Article
                10.1038/nphys2609
                1212.5467
                94a72e0c-353e-4189-8813-0307f326a44d

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Nature Physics 9, 275 (2013)
                cond-mat.mes-hall cond-mat.quant-gas

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