Spontaneous symmetry breaking and collapse in bosonic Josephson junctions

We investigate an attractive atomic Bose-Einstein condensate (BEC) trapped by a double-well potential in the axial direction and by a harmonic potential in the transverse directions. We obtain numerically, for the first time, a quantum phase diagram which includes all the three relevant phases of the system: Josephson, spontaneous symmetry breaking (SSB), and collapse. We consider also the coherent dynamics of the BEC and calculate the frequency of population-imbalance mode in the Josephson phase and in the SSB phase up to the collapse. We show that these phases can be observed by using ultracold vapors of 7Li atoms in a magneto-optical trap.Comment: 5 pages, 4 figures, to be published in Phys. Rev.

Consensus for quantum networks: from symmetry to gossip iterations

This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different generalizations of classical consensus states. This new viewpoint can be directly used to study consensus for probability distributions, as these can be seen as a particular case of quantum statistical states: in this light, our analysis is also relevant for classical problems. We then extend the gossip consensus algorithm to the quantum setting and prove it converges to symmetric states while preserving the expectation of permutation-invariant global observables. Applications of the framework and the algorithms to estimation and control problems on quantum networks are discussed

Quantum correlations of few dipolar bosons in a double-well trap

We consider $N$ interacting dipolar bosonic atoms at zero temperature in a double-well potential. This system is described by the two-space-mode extended Bose-Hubbard (EBH) Hamiltonian which includes (in addition to the familiar BH terms) the nearest-neighbor interaction, correlated hopping and bosonic-pair hopping. For systems with $N=2$ and $N=3$ particles we calculate analytically both the ground state and the Fisher information, the coherence visibility, and the entanglement entropy that characterize the correlations of the lowest energy state. The structure of the ground state crucially depends on the correlated hopping $K_c$. On one hand we find that this process makes possible the occurrence of Schr\"odinger-cat states even if the onsite interatomic attraction is not strong enough to guarantee the formation of such states. On the other hand, in the presence of a strong onsite attraction, sufficiently large values of $|K_c|$ destroys the cat-like state in favor of a delocalized atomic coherent state.Comment: 21 pages, 10 figures. This paper has been accepted for publication in a festschrift issue of Journal of Low Temperature Physics in honor of Prof. Flavio Toigo on the occasion of his 70th birthday. The paper extends our previous results, which can be found in arXiv:1410.5321, obtained in the absence of dipolar interactio

Superfluid hydrodynamics of polytropic gases:dimensional reduction and sound velocity

Motivated by the fact that two-component confined fermionic gases in Bardeen-Cooper-Schrieffer-Bose-Einstein condensate (BCS-BEC) crossover can be described through an hydrodynamical approach, we study these systems - both in the cigar-shaped configuration and in the disk-shaped one - by using a polytropic Lagrangian density. We start from the Popov Lagrangian density and obtain, after a dimensional reduction process, the equations that control the dynamics of such systems. By solving these equations we study the sound velocity as a function of the density by analyzing how the dimensionality affects this velocityComment: Accepted for publication in J. Phys. A: Math. Theo

Asymmetric Architecture for Heralded Single Photon Sources

Single photon source represent a fundamental building block for optical implementations of quantum information tasks ranging from basic tests of quantum physics to quantum communication and high-resolution quantum measurement. In this paper we investigate the performance of a multiplexed system based on asymmetric configuration of multiple heralded single photon sources. {To compare the effectiveness of different designs we introduce a single-photon source performance index that is based on the value of single photon probability required to achieve a guaranteed signal to noise ratio.} The performance and scalability comparison with both currently existing multiple-source architectures and faint laser configurations reveals an advantage the proposed scheme offers in realistic scenarios. This analysis also provides insights on the potential of using such architectures for integrated implementation.Comment: 11 pages, 13 figure

Consensus for Quantum Networks: Symmetry from Gossip Interactions

This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different generalizations of classical consensus states. This new viewpoint can be directly used to study consensus for probability distributions, as these can be seen as a particular case of quantum statistical states: in this light, our analysis is also relevant for classical problems. We then extend the gossip consensus algorithm to the quantum setting and prove it converges to symmetric states while preserving the expectation of permutationinvariant global observables. Applications of the framework and the algorithms to estimation and control problems on quantum networks are discussed

Symmetrizing dynamics: from classical to quantum applications

Among the issues regarding networked systems, the “consensus problem” and the related algorithms have received a significant share of attention during the last ten years. In this problem the network agents asymptotically have to attain agreement on the value of some objective variable under local communication constraints. A number of algorithms have been developed to address this problem, among which the celebrated gossip algorithm. The latter relays on switching dynamics and, under rather weak assumptions, exhibits robust convergence under variations in the interaction constraints, i.e. the network topology. In this dissertation we reinterpret the goal of the consensus problem as a symmetrisation problem, and we address it by a switching-type dynamics based on convex combinations of actions of a finite group. In order to study the convergence of our class of algorithms we lift the dynamics to an abstract, group-theoretic level that allow us to derive general conditions for convergence. Such conditions, in fact, are independent of the particular group action, and focus only on the group itself and the way the iterations are selected. Convergence is guaranteed provided that some mild assumptions on the selection rule for the iterations are fulfilled. Furthermore, this class of algorithms retains the robustness features and unsupervised character of the consensus algorithm. Our reformulation allow to devise algorithms for application as diverse as randomized discrete Fourier transform and random state generation. We pose a special emphasis on the extension of the consensus problem to the quantum domain. In this setting we highlight how, due to the richer mathematical structure over which the internal state is encoded, the definition of the consensus goal admits various extensions, each of them exhibiting different features. We also propose a suitable dissipative dynamics enacting the symmetrising gossip interactions and then use our general result on convergence to prove it ensures asymptotic convergence. Beside the technical results, one of the main contributions of our work is a new, generalized view point on consensus, which allows us to extend the robustness of consensus-inspired algorithms to new problems in apparently unrelated fields. This reinforces the role of consensus algorithms as fundamental tools for distributed computing, both in the classical and the quantum setting

Nonlinear quantum model for atomic Josephson junctions with one and two bosonic species

We study atomic Josephson junctions (AJJs) with one and two bosonic species confined by a double-well potential. Proceeding from the second quantized Hamiltonian, we show that it is possible to describe the zero-temperature AJJs microscopic dynamics by means of extended Bose-Hubbard (EBH) models, which include usually-neglected nonlinear terms. Within the mean-field approximation, the Heisenberg equations derived from such two-mode models provide a description of AJJs macroscopic dynamics in terms of ordinary differential equations (ODEs). We discuss the possibility to distinguish the Rabi, Josephson, and Fock regimes, in terms of the macroscopic parameters which appear in the EBH Hamiltonians and, then, in the ODEs. We compare the predictions for the relative populations of the Bose gases atoms in the two wells obtained from the numerical solutions of the two-mode ODEs, with those deriving from the direct numerical integration of the Gross-Pitaevskii equations (GPEs). Our investigations shows that the nonlinear terms of the ODEs are crucial to achieve a good agreement between ODEs and GPEs approaches, and in particular to give quantitative predictions of the self-trapping regime.Comment: Accepted for the publication in J. Phys. B: At. Mol. Opt. Phy