Search results for " Statistical"
showing 10 items of 1649 documents
Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence
2005
We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations will be quantified by a proper convex roof extension of the squared logarithmic negativity (the contangle), satisfying a monogamy relation for multimode Gaussian states, whose proof will be reviewed and elucidated. The residual contangle, emerging from the monog…
GHZ state generation of three Josephson qubits in the presence of bosonic baths
2013
We analyze an entangling protocol to generate tripartite Greenberger-Horne-Zeilinger states in a system consisting of three superconducting qubits with pairwise coupling. The dynamics of the open quantum system is investigated by taking into account the interaction of each qubit with an independent bosonic bath with an ohmic spectral structure. To this end a microscopic master equation is constructed and exactly solved. We find that the protocol here discussed is stable against decoherence and dissipation due to the presence of the external baths.
Phase transition of light on complex quantum networks
2012
Recent advances in quantum optics and atomic physics allow for an unprecedented level of control over light-matter interactions, which can be exploited to investigate new physical phenomena. In this work we are interested in the role played by the topology of quantum networks describing coupled optical cavities and local atomic degrees of freedom. In particular, using a mean-field approximation, we study the phase diagram of the Jaynes-Cummings-Hubbard model on complex networks topologies, and we characterize the transition between a Mott-like phase of localized polaritons and a superfluid phase. We found that, for complex topologies, the phase diagram is non-trivial and well defined in the…
Nonequilibrium critical scaling in quantum thermodynamics
2016
The emerging field of quantum thermodynamics is contributing important results and insights into archetypal many-body problems, including quantum phase transitions. Still, the question whether out-of-equilibrium quantities, such as fluctuations of work, exhibit critical scaling after a sudden quench in a closed system has remained elusive. Here, we take a novel approach to the problem by studying a quench across an impurity quantum critical point. By performing density matrix renormalization group computations on the two-impurity Kondo model, we are able to establish that the irreversible work produced in a quench exhibits finite-size scaling at quantum criticality. This scaling faithfully …
Quantum Criticality in a Bosonic Josephson Junction
2011
In this paper we consider a bosonic Josephson junction described by a two-mode Bose-Hubbard model, and we thoroughly analyze a quantum phase transition occurring in the system in the limit of infinite bosonic population. We discuss the relation between this quantum phase transition and the dynamical bifurcation occurring in the spectrum of the Discrete Self Trapping equations describing the system at the semiclassical level. In particular, we identify five regimes depending on the strength of the effective interaction among bosons, and study the finite-size effects arising from the finiteness of the bosonic population. We devote a special attention to the critical regime which reduces to th…
Uhlmann curvature in dissipative phase transitions
2018
We study the mean Uhlmann curvature in fermionic systems undergoing a dissipative driven phase transition. We consider a paradigmatic class of lattice fermion systems in non-equilibrium steady-state of an open system with local reservoirs, which are characterised by a Gaussian fermionic steady state. In the thermodynamical limit, in systems with translational invariance we show that a singular behaviour of the Uhlmann curvature represents a sufficient criterion for criticalities, in the sense of diverging correlation length, and it is not otherwise sensitive to the closure of the Liouvillian dissipative gap. In finite size systems, we show that the scaling behaviour of the mean Uhlmann curv…
Geometry of quantum phase transitions
2020
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric information in the characterisation of quantum phase transitions, we describe recent developments of geometrical approaches based on mixed-state generalisation of the Berry-phase, i.e. the Uhlmann geometric phase, for the investigation of non-equilibrium steady-state quantum phase transitions (NESS-QPTs ). Equilibrium phase transitions fall invariably into two markedly non-overlapping categories: classical phase transitions and quantum phase transitions, whereas i…
Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
2015
We study transitionless quantum driving in an infinite-range many-body system described by the Lipkin-Meshkov-Glick model. Despite the correlation length being always infinite the closing of the gap at the critical point makes the driving Hamiltonian of increasing complexity also in this case. To this aim we develop a hybrid strategy combining shortcut to adiabaticity and optimal control that allows us to achieve remarkably good performance in suppressing the defect production across the phase transition.
Dynamical bifurcation as a semiclassical counterpart of a quantum phase transition
2011
We illustrate how dynamical transitions in nonlinear semiclassical models can be recognized as phase transitions in the corresponding -- inherently linear -- quantum model, where, in a Statistical Mechanics framework, the thermodynamic limit is realized by letting the particle population go to infinity at fixed size. We focus on lattice bosons described by the Bose-Hubbard (BH) model and Discrete Self-Trapping (DST) equations at the quantum and semiclassical level, respectively. After showing that the gaussianity of the quantum ground states is broken at the phase transition, we evaluate finite populations effects introducing a suitable scaling hypothesis; we work out the exact value of the…
Probing Quantum Frustrated Systems via Factorization of the Ground State
2009
The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physica…