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We extend a recent method to shortcut the adiabatic following to internal bosonic Josephson junctions in which the control parameter is the linear coupling between the modes. The approach is based on the mapping between the two-site Bose-Hubbard Hamiltonian and a 1D effective Schrodinger-like equation, valid in the large $N$ (number of particles) limit. Our method can be readily implemented in current internal bosonic Josephson junctions and it improves substantially the production of spin-squeezing with respect to usually employed linear rampings.
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We analyze the effects of the temperature on a bosonic Josephson junction realized with ultracold and dilute atoms in a double-well potential. Starting from the eigenstates of the two-site Bose-Hubbard Hamiltonian, we calculate the coherence visibility and the fluctuation of the on-site occupation number and study them as functions of the temperature. We show that, contrary to naive expectations, when the boson-boson interaction is suitably chosen thermal effects can increase the coherence visibility and reduce the on-site number fluctuation.
We analyze the formation of squeezed states in a condensate of ultracold bosonic atoms confined by a double-well potential. The emphasis is set on the dynamical formation of such states from initially coherent many-body quantum states. Two cases are described: the squeezing formation in the evolution of the system around the stable point, and in the short time evolution in the vicinity of an unstable point. The latter is shown to produce highly squeezed states on very short times. On the basis of a semiclassical approximation to the Bose-Hubbard Hamiltonian, we are able to predict the amount of squeezing, its scaling with $N$ and the speed of coherent spin formation with simple analytical formulas which successfully describe the numerical Bose-Hubbard results. This new method of producing highly squeezed spin states in systems of ultracold atoms is compared to other standard methods in the literature.
We analyze phase interferometry realized with a bosonic Josephson junction made of trapped dilute and ultracold atoms. By using a suitable phase sensitivity indicator we study the zero temperature junction states useful to achieve sub shot-noise precisions. Sub shot-noise phase shift sensitivities can be reached even at finite temperature under a suitable choice of the junction state. We infer a scaling law in terms of the size system (that is, the number of particles) for the temperature at which the shot-noise limit is not overcome anymore
We present an investigation of the fast decompression of a three-dimensional (3D) Bose-Einstein condensate (BEC) at finite temperature using an engineered trajectory for the harmonic trapping potential. Taking advantage of the scaling invariance properties of the time-dependent Gross-Pitaevskii equation, we exhibit a solution yielding a final state identical to that obtained through a perfectly adiabatic transformation, in a much shorter time. Experimentally, we perform a large trap decompression and displacement within a time comparable to the final radial trapping period. By simultaneously monitoring the BEC and the non-condensed fraction, we demonstrate that our specific trap trajectory is valid both for a quantum interacting many-body system and a classical ensemble of non-interacting particles.
We use the Bose-Hubbard Hamiltonian to study quantum fluctuations in canonical equilibrium ensembles of bosonic Josephson junctions at relatively high temperatures, comparing the results for finite particle numbers to the classical limit that is attained as $N$ approaches infinity. We consider both attractive and repulsive atom-atom interactions, with especial focus on the behavior near the T=0 quantum phase transition that occurs, for large enough $N$, when attractive interactions surpass a critical level. Differences between Bose-Hubbard results for small $N$ and those of the classical limit are quite small even when $N sim 100$, with deviations from the limit diminishing as 1/N.
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