Quantum behaviour of open pumped and damped Bose-Hubbard trimers

We propose and analyse analogs of optical cavities for atoms using three-well inline Bose-Hubbard models with pumping and losses. With one well pumped and one damped, we find that both the mean-field dynamics and the quantum statistics show a qualitative dependence on the choice of damped well. The systems we analyse remain far from equilibrium, although most do enter a steady-state regime. We find quadrature squeezing, bipartite and tripartite inseparability and entanglement, and states exhibiting the EPR paradox, depending on the parameter regimes. We also discover situations where the mean-field solutions of our models are noticeably different from the quantum solutions for the mean fields. Due to recent experimental advances, it should be possible to demonstrate the effects we predict and investigate in this article.Comment: 20 pages, 8 figures, theoretica

Mapping the train model for earthquakes onto the stochastic sandpile model

We perform a computational study of a variant of the ``train'' model for earthquakes [PRA 46, 6288 (1992)], where we assume a static friction that is a stochastic function of position rather than being velocity dependent. The model consists of an array of blocks coupled by springs, with the forces between neighbouring blocks balanced by static friction. We calculate the probability, P(s), of the occurrence of avalanches with a size s or greater, finding that our results are consistent with the phenomenology and also with previous models which exhibit a power law over a wide range. We show that the train model may be mapped onto a stochastic sandpile model and study a variant of the latter for non-spherical grains. We show that, in this case, the model has critical behaviour only for grains with large aspect ratio, as was already shown in experiments with real ricepiles. We also demonstrate a way to introduce randomness in a physically motivated manner into the model.Comment: 14 pages and 6 figures. Accepted in European Physical Journal

Ultracold atomic mode splitter for the entanglement of separated atomic samples

We propose and analyze the use of a three-well Bose-Hubbard model for the creation of two spatially separated entangled atomic samples. Our three wells are in a linear configuration, with all atoms initially in the middle well, which gives some spatial separation of the two end wells. The evolution from the initial quantum state allows for the development of entanglement between the atomic modes in the two end wells. We show how the detected entanglement and the well occupations are time dependent. We propose a method for preserving the en-tanglement by turning off the different interactions when it reaches its first maximum. We analyze the system with both Fock and coherent initial states, showing that the violations of the chosen inequality exist only for initial Fock states and that the collisional nonlinearity degrades them. This system is a preliminary step towards producing entangled atomic samples that can be spatially separated using recently developed methods of potential manipulation and thus help close the locality loophole in tests of quantum mechanics

Quantum correlations in pumped and damped Bose-Hubbard dimers

We propose and analyze two-well Bose-Hubbard models with pumping and losses, finding that these models, with damping and loss able to be added independently to each well, offer a flexibility not found in optical coupled cavity systems. With one well pumped, we find that both the mean-field dynamics and the quantum statistics show a quantitative dependence on the choice of damped well. Both the systems we analyze remain far from equilibrium, preserving good coherence between the wells in the steady state. We find a degree of quadrature squeezing and mode entanglement in these systems. Due to recent experimental advances, it should be possible to demonstrate the effects we investigate and predict

Quantum phase-space analysis of population equilibration in multi-well ultracold atomic systems

We examine the medium time quantum dynamics and population equilibration of two, three and four-well Bose-Hubbard models using stochastic integration in the truncated Wigner phase-space representation. We find that all three systems will enter at least a temporary state of equilibrium, with the details depending on both the classical initial conditions and the initial quantum statistics. We find that classical integrability is not necessarily a good guide as to whether equilibration will occur. We construct an effective single-particle reduced density matrix for each of the systems, using the expectation values of operator moments, and use this to calculate an effective entropy. Knowing the expected maximum values of this entropy for each system, we are able to quantify the different approaches to equilibrium.Comment: 16 pages, 7 figure

Critique of generalised purity as an entanglement measure: Explicit failure in simple separable Bose-Hubbard models

The SU(2) and SU(3) Lie algebras lend themselves naturally to studies of two-and three-well Bose-Einstein condensates, with the group operators being expressed in terms of bosonic annihilation and creation operators at each site. The success of these representations has led to the purities associated with these algebras to be promoted as a measure of entanglement in these systems. In this work, we show that these purities do not provide an unambiguous measure of entanglement between wells, but instead give results which depend on the quantum statistical states of the atomic ensembles in each well. Using the example of totally uncoupled wells where the atoms in one have never interacted with the atoms in the other, we quantify these purities for different states and show that completely separable states can give values which have been claimed to indicate the presence of entanglement. We also consider claims that the generalised purities measure particle rather than mode entanglement, with emphasis on the case of indistinguishable bosons, as found in these systems

Ultrasound-Guided Percutaneous Irrigation of Rotator Cuff Calcific Tendinopathy (US-PICT): Patient Experience

Purpose. To assess patients\u2019experience of ultrasound-guided percutaneous irrigation of rotator cuffcalcific tendinopathy(US-PICT).Methods. Ninety-one patients (58 females; mean age:50:5\ub18:3years) treated by US-PICT (local anesthesia,single-needle lavage, and intrabursal steroid injection) answered to a list of questions regarding their experience of theprocedure before treatment, immediately after treatment, and three months later. The Borg CR10 scale was used toevaluate perceived pain, discomfort during anesthetic injection, and anxiety. The Wilcoxon, Spearman\u2019s rho, linearregression, and chi-square statistics were used.Results. 81/91 patients complained mild discomfort during the injection ofanesthetics (2, 1-2). Pain scores during US-PICT were very low (0, 0-1), with 70% patients having not experienced pain. Aftertreatment, we found a significant reduction of pain (before: 8, 7-8; 3-month: 3, 1-6;p<:001) and anxiety (before: 5, 2-7; duringtreatment: 2, 1-7;p=0:010), with high overall satisfaction (immediately after: 10, 9-10; 3-month: 9, 7-10) and confidence in thepossibility of recovery (immediately after: 9, 8-10; 3-month: 10, 8-10), respectively. Treatments performed before US-PICT werenot statistically associated with pain relief (p=0:389) and clinical improvement (p=0:937). We found a correlation betweensatisfaction immediately postprocedure and confidence in the possibility of recovery (p=0:002) and between satisfaction threemonths after treatment and clinical improvement (p<0:001) and patients\u2019reminds about the description of the procedure(p=0:005) and of the potential complications (p=0:035).Conclusions. US-PICT is a mildly painful, comfortable, andwell-tolerated procedure, regardless of any previous treatments. Patients\u2019satisfaction is correlated with clinical benefit andfull explanation of the procedure and its complications