The pinning quantum phase transition in a Tonks Girardeau gas: diagnostics by ground state fidelity and the Loschmidt echo

We study the pinning quantum phase transition in a Tonks-Girardeau gas, both in equilibrium and out-of-equilibrium, using the ground state fidelity and the Loschmidt echo as diagnostic tools. The ground state fidelity (GSF) will have a dramatic decrease when the atomic density approaches the commensurate density of one particle per lattice well. This decrease is a signature of the pinning transition from the Tonks to the Mott insulating phase. We study the applicability of the fidelity for diagnosing the pinning transition in experimentally realistic scenarios. Our results are in excellent agreement with recent experimental work. In addition, we explore the out of equilibrium dynamics of the gas following a sudden quench with a lattice potential. We find all properties of the ground state fidelity are reflected in the Loschmidt echo dynamics i.e., in the non equilibrium dynamics of the Tonks-Girardeau gas initiated by a sudden quench of the lattice potential

Ion induced density bubble in a strongly correlated one dimensional gas

We consider a harmonically trapped Tonks-Girardeau gas of impenetrable bosons in the presence of a single embedded ion, which is assumed to be tightly confined in a RF trap. In an ultracold ion-atom collision the ion's charge induces an electric dipole moment in the atoms which leads to an attractive $r^{-4}$ potential asymptotically. We treat the ion as a static deformation of the harmonic trap potential and model its short range interaction with the gas in the framework of quantum defect theory. The molecular bound states of the ionic potential are not populated due to the lack of any possible relaxation process in the Tonks-Girardeau regime. Armed with this knowledge we calculate the density profile of the gas in the presence of a central ionic impurity and show that a density \textit{bubble} of the order of a micron occurs around the ion for typical experimental parameters. From these exact results we show that an ionic impurity in a Tonks gas can be described using a pseudopotential, allowing for significantly easier treatment.Comment: Accepted for publication in Physical Review A (Rapid Communications)

Non-Markovianity, Loschmidt echo and criticality: a unified picture

A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo is established, holding for a two-level system (qubit) undergoing pure dephasing due to a coupling with a many-body environment. We show that the Loschmidt echo is intimately related to the information flowing out from and occasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. In particular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context, the information flux between system and environment is strongly affected by the environmental criticality; the qubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore non-Markovianity is an indicator of criticality in the model considered here

Bridging the gap through Rényi divergences

The work performed on or extracted from a nonautonomous quantum system described by means of a two-point projective-measurement approach is a stochastic variable. We show that the cumulant generating function of work can be recast in the form of quantum Rényi-α divergences, and by exploiting the convexity of this cumulant generating function, derive a single-parameter family of bounds for the first moment of work. Higher order moments of work can also be obtained from this result. In this way, we establish a link between quantum work statistics in stochastic approaches and resource theories for quantum thermodynamics, a theory in which Rényi-α divergences take a central role. To explore this connection further, we consider an extended framework involving a control switch and an auxiliary battery, which is instrumental to reconstructing the work statistics of the system. We compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource-theoretic settings

An ITPR1 gene deletion causes SCA15 and 16; a genetic, clinical and radiological description

Spinocerebellar ataxia (SCA) 15/16 is an autosomal dominantly inherited, almost pure cerebellar ataxia, which shows slow or no progression. (It has been designated variably SCA15 and SCA 16; we refer to it here as SCA15/16 to avoid confusion). Deletions in the inositol 1, 4, 5-triphosphate receptor 1 (ITPR1) on chromosome 3 have been shown to cause SCA15/16 in six families worldwide to date, with one further Japanese family identified as having an ITPR1 point mutation. We present a previously unreported SCA15/16 kindred. We describe the clinical phenotype of the family in detail; affected subjects display a remarkably slow, almost pure cerebellar syndrome. We also present genetic analyses for all subjects and longitudinal MRI data for one affected subject. Genetic analysis shows a deletion of 346,487bp in ITPR1 (the second largest ITPR1 deletion reported to date), suggesting SCA15 is due to a loss of ITPR1 function, and western blotting of lymphoblastoid cell line protein confirms reduced ITPR1 protein levels. Serial MRIs show progressive midline cerebellar atrophy with mild inferior parietal and temporal cortical volume loss in the absence of clinical disease progression. We believe that genetic testing for SCA15/16 should become a routine DNA screen available in all Neurogenetics clinics, which is likely to lead to an increased rate of the diagnosis. Familiarity with the phenotype is therefore important for all neurologists

On defining the Hamiltonian beyond quantum theory

Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories, a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories.Comment: Authors' accepted manuscript for inclusion in the Foundations of Physics topical collection on Foundational Aspects of Quantum Informatio

Second law, entropy production, and reversibility in thermodynamics of information

We present a pedagogical review of the fundamental concepts in thermodynamics of information, by focusing on the second law of thermodynamics and the entropy production. Especially, we discuss the relationship among thermodynamic reversibility, logical reversibility, and heat emission in the context of the Landauer principle and clarify that these three concepts are fundamentally distinct to each other. We also discuss thermodynamics of measurement and feedback control by Maxwell's demon. We clarify that the demon and the second law are indeed consistent in the measurement and the feedback processes individually, by including the mutual information to the entropy production.Comment: 43 pages, 10 figures. As a chapter of: G. Snider et al. (eds.), "Energy Limits in Computation: A Review of Landauer's Principle, Theory and Experiments

Teleportation of a quantum state of a spatial mode with a single massive particle

Mode entanglement exists naturally between regions of space in ultra-cold atomic gases. It has, however, been debated whether this type of entanglement is useful for quantum protocols. This is due to a particle number superselection rule that restricts the operations that can be performed on the modes. In this paper, we show how to exploit the mode entanglement of just a single particle for the teleportation of an unknown quantum state of a spatial mode. We detail how to overcome the superselection rule to create any initial quantum state and how to perform Bell state analysis on two of the modes. We show that two of the four Bell states can always be reliably distinguished, while the other two have to be grouped together due to an unsatisfied phase matching condition. The teleportation of an unknown state of a quantum mode thus only succeeds half of the time.Comment: 12 pages, 1 figure, this paper was presented at TQC 2010 and extends the work of Phys. Rev. Lett. 103, 200502 (2009

Eigenvectors under a generic perturbation: non-perturbative results from the random matrix approach

We consider eigenvectors of the Hamiltonian H0 perturbed by a generic perturbation V modelled by a random matrix from the Gaussian Unitary Ensemble (GUE). Using the super-symmetry approach we derive analytical results for the statistics of the eigenvectors, which are non-perturbative in V and valid for an arbitrary deterministic H0. Further we generalise them to the case of a random H0, focusing, in particular, on the Rosenzweig-Porter model. Our analytical predictions are confirmed by numerical simulations

Quantum work statistics and resource theories: bridging the gap through Renyi divergences

The work performed on or extracted from a non-autonomous quantum system described by means of a two-point projective-measurement approach takes the form of a stochastic variable. We show that the cumulant generating function of work can be recast in the form of quantum Renyi divergences, and by exploiting convexity of this cumulant generating function, derive a single-parameter family of bounds for the first moment of work. Higher order moments of work can also be obtained from this result. In this way, we establish a link between quantum work statistics in stochastic approaches on the one hand and resource theories for quantum thermodynamics on the other hand, a theory in which Renyi divergences take a central role. To explore this connection further, we consider an extended framework involving a control switch and an auxiliary battery, which is instrumental to reconstruct the work statistics of the system. We compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource theoretic settings.Comment: 8 pages, minor changes, references adde