J. Martorell

Dynamic generation of spin-squeezed states in bosonic Josephson junctions

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

Macroscopic self-trapping in Bose-Einstein condensates: Analysis of a dynamical quantum phase transition

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One-dimensional photonic crystals with a sawtooth refractive index: another exactly solvable potential

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.

Bose-Einstein condensates on slightly asymmetric double-well potentials

We consider a Bose-Einstein condensate in a double-well potential undergoing a dynamical transition from the regime of Josephson oscillations to the regime of self-trapping. We analyze the statistical properties of the ground state (or the highest excited state) of the Hamiltonian in these two regimes for attractive (repulsive) interactions. We demonstrate that it is impossible to describe the transition within the mean-field theory. In contrast, the transition proceeds through a strongly correlated delocalized state, with large quantum fluctuations, and spontaneous breaking of the symmetry.

Chapter 9 – Quantum Decay at Long Times

Exact analytical results expressed in terms of Bessel functions for the bandgaps, reflectance and transmittance of one-dimensional photonic crystals with a sawtooth refractive index profile on the period are derived, to our knowledge for the first time. This extends the set of exactly solvable models with periodic refractive indices. Asymptotic approximations to the above exact results have been also obtained.

Enhanced observability of quantum postexponential decay using distant detectors

An analytical insight into the symmetry-breaking mechanisms underlying the transition from Josephson to self-trapping regimes in Bose-Einstein condensates is presented. We obtain expressions for the ground-state properties of the system of a gas of attractive bosons modeled by a two-site Bose-Hubbard Hamiltonian with an external bias. Simple formulas are found relating the appearance of fragmentation in the condensate with the large quantum fluctuations of the population imbalance occurring in the transition from the Josephson to the self-trapped regime.

Fragmented condensation in Bose–Hubbard trimers with tunable tunnelling

Abstract We review the post-exponential decay regime in quantum mechanics, with special attention to potential scattering. The mathematical and physical reasons for this regime are discussed using several techniques. In particular, the possible effects of measurement or interaction with the environment are analyzed. Both general and particular results are provided, along with a history of the attempts to observe post-exponential decay. The chapter ends with an outlook for future research.

Shortcut to adiabaticity in spinor condensates

We study the elusive transition from exponential to postexponential (algebraic) decay of the probability density of a quantum particle emitted by an exponentially decaying source in one dimension. The main finding is that the probability density at the transition time, and thus its observability, increases with the distance of the detector from the source up to a critical distance beyond which exponential decay is no longer observed. Solvable models provide explicit expressions for the dependence of the transition on resonance and observational parameters, facilitating the choice of optimal conditions.

Long-time deviations from exponential decay for inverse-square potentials

We consider a Bose-Hubbard trimer, i.e. an ultracold Bose gas populating three quantum states. The latter can be either different sites of a triple-well potential or three internal states of the atoms. The bosons can tunnel between different states with variable tunnelling strength between two of them. This will allow us to study; i) different geometrical configurations, i.e. from a closed triangle to three aligned wells and ii) a triangular configuration with a

Hybrid synchronization in coupled ultracold atomic gases

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