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

Analysis of the conditional mutual information in ballistic and diffusive non-equilibrium steady-states

The conditional mutual information (CMI) $\mathcal{I}(A\! : \! C|B)$ quantifies the amount of correlations shared between $A$ and $C$ \emph{given} $B$. It therefore functions as a more general quantifier of bipartite correlations in multipartite scenarios, playing an important role in the theory of quantum Markov chains. In this paper we carry out a detailed study on the behavior of the CMI in non-equilibrium steady-states (NESS) of a quantum chain placed between two baths at different temperatures. These results are used to shed light on the mechanisms behind ballistic and diffusive transport regimes and how they affect correlations between different parts of a chain. We carry our study for the specific case of a 1D bosonic chain subject to local Lindblad dissipators at the boundaries. In addition, the chain is also subject to self-consistent reservoirs at each site, which are used to tune the transport between ballistic and diffusive. As a result, we find that the CMI is independent of the chain size $L$ in the ballistic regime, but decays algebraically with $L$ in the diffusive case. Finally, we also show how this scaling can be used to discuss the notion of local thermalization in non-equilibrium steady-states

An eccentrically perturbed Tonks-Girardeau gas

We investigate the static and dynamic properties of a Tonks-Girardeau gas in a harmonic trap with an eccentric $\delta$-perturbation of variable strength. For this we first find the analytic eigensolution of the single particle problem and use this solution to calculate the spatial density and energy profiles of the many particle gas as a function of the strength and position of the perturbation. We find that the crystal nature of the Tonks state is reflected in both the lowest occupation number and momentum distribution of the gas. As a novel application of our model, we study the time evolution of the the spatial density after a sudden removal of the perturbation. The dynamics exhibits collapses and revivals of the original density distribution which occur in units of the trap frequency. This is reminiscent of the Talbot effect from classical optics.Comment: Comments and suggestions are welcom

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)

Orthogonality catastrophe as a consequence of qubit embedding in an ultra-cold Fermi gas

We investigate the behaviour of a single qubit coupled to a low-dimensional, ultra-cold Fermi gas. The scattering between the system and the fermions leads to the loss of any coherence in the initial state of the qubit and we show that the exact dynamics of this process is strongly influenced by the effect of the orthogonality catastrophe within the gas. We highlight the relationship between the Loschmidt echo and the retarded Green's function - typically used to formulate the dynamical theory of the catastrophe - and demonstrate that the effect can be triggered and characterized via local operations on the qubit. We demonstrate how the expected broadening of the spectral function can be observed using Ramsey interferometry on the qubit.Comment: 4 and a bit pages, 3 figures. Updated versio

Charging a quantum battery with linear feedback control

Energy storage is a basic physical process with many applications. When considering this task at the quantum scale, it becomes important to optimise the non-equilibrium dynamics of energy transfer to the storage device or battery. Here, we tackle this problem using the methods of quantum feedback control. Specifically, we study the deposition of energy into a quantum battery via an auxiliary charger. The latter is a driven-dissipative two-level system subjected to a homodyne measurement whose output signal is fed back linearly into the driving field amplitude. We explore two different control strategies, aiming to stabilise either populations or quantum coherences in the state of the charger. In both cases, linear feedback is shown to counteract the randomising influence of environmental noise and allow for stable and effective battery charging. We analyse the effect of realistic control imprecisions, demonstrating that this good performance survives inefficient measurements and small feedback delays. Our results highlight the potential of continuous feedback for the control of energetic quantities in the quantum regime.Comment: v1: 10 pages, 8 figures. Comments welcome! v2: Final versio

Association between health insurance literacy and avoidance of health care services owing to cost

Importance: Navigating health insurance and health care choices requires considerable health insurance literacy. Although recommended preventive services are exempt from out-of-pocket costs under the Affordable Care Act, many people may remain unaware of this provision and its effect on their required payment. Little is known about the association between individuals\u27 health insurance literacy and their use of preventive or nonpreventive health care services. Objective: To assess the association between health insurance literacy and self-reported avoidance of health care services owing to cost. Design, Setting, and Participants: In this survey study, a US national, geographically diverse, nonprobability sample of 506 US residents aged 18 years or older with current health insurance coverage was recruited to participate in an online survey between February 22 and 23, 2016. Main Outcomes and Measures: The validated 21-item Health Insurance Literacy Measure (HILM) assessed individuals\u27 self-rated confidence in selecting and using health insurance (score range, 0-84, with higher scores indicating greater levels of health insurance literacy). Dependent variables included delayed or foregone preventive and nonpreventive services in the past 12 months owing to perceived costs, and preventive and nonpreventive use of services. Covariates included age, sex, race/ethnicity, income, educational level, high-deductible health insurance plan, health literacy, numeracy, and chronic health conditions. Analyses included descriptive statistics and bivariate and multivariable logistic regression. Results: A total of 506 of 511 participants who began the survey completed it (participation rate, 99.0%). Of the 506 participants, 339 (67.0%) were younger than 35 years (mean [SD] age, 34 [10.4] years), 228 (45.1%) were women, 406 of 504 who reported race (80.6%) were white, and 245 (48.4%) attended college for 4 or more years. A total of 228 participants (45.1%) had 1 or more chronic health condition, 361 of 500 (72.2%) who responded to the survey item had seen a physician in the outpatient setting in the past 12 months, and 446 of the 501 (89.0%) who responded to the survey item had their health insurance plan for 12 or more months. One hundred fifty respondents (29.6%) reported having delayed or foregone care because of cost. The mean (SD) HILM score was 63.5 (12.3). In multivariable logistic regression, each 12-point increase in HILM score was associated with a lower likelihood of both delayed or foregone preventive care (adjusted odds ratio [aOR], 0.61; 95% CI, 0.48-0.78) and delayed or foregone nonpreventive care (aOR, 0.71; 95% CI, 0.55-0.91). Conclusions and Relevance: This study\u27s findings suggest that lower health insurance literacy may be associated with greater avoidance of both preventive and nonpreventive services. It appears that to improve appropriate use of recommended health care services, including preventive health services, clinicians, health plans, and policymakers may need to communicate health insurance concepts in accessible ways regardless of individuals\u27 health insurance literacy. Plain language communication may be able to improve patients\u27 understanding of services exempt from out-of-pocket costs

Thermodynamics of precision in quantum nanomachines

Fluctuations strongly affect the dynamics and functionality of nanoscale thermal machines. Recent developments in stochastic thermodynamics have shown that fluctuations in many far-from-equilibrium systems are constrained by the rate of entropy production via so-called thermodynamic uncertainty relations. These relations imply that increasing the reliability or precision of an engine's power output comes at a greater thermodynamic cost. Here we study the thermodynamics of precision for small thermal machines in the quantum regime. In particular, we derive exact relations between the power, power fluctuations, and entropy production rate for several models of few-qubit engines (both autonomous and cyclic) that perform work on a quantized load. Depending on the context, we find that quantum coherence can either help or hinder where power fluctuations are concerned. We discuss design principles for reducing such fluctuations in quantum nanomachines and propose an autonomous three-qubit engine whose power output for a given entropy production is more reliable than would be allowed by any classical Markovian model