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

New spin squeezing and other entanglement tests for two mode systems of identical bosons

For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrization principle (SP) and conform to super-selection rules (SSR) that prohibit coherences between differing total particle numbers. Here we consider bi-partitite states for massive bosons, where both the system and sub-systems are modes (or sets of modes) and particle numbers for quantum states are determined from the mode occupancies. Defining non-entangled or separable states as those prepared via local operations (on the sub-systems) and classical communication processes, the sub-system density operators are also required to satisfy the SP and conform to the SSR, in contrast to some other approaches. Whilst in the presence of this additional constraint the previously obtained sufficiency criteria for entanglement, such as the sum of the ˆSx and ˆSy variances for the Schwinger spin components being less than half the mean boson number, and the strong correlation test of |haˆm (bˆ†)ni|2 being greater than h(aˆ†)maˆm (bˆ†)nbˆni(m, n = 1, 2, . . .) are still valid, new tests are obtained in our work. We show that the presence of spin squeezing in at least one of the spin components ˆSx , ˆSy and ˆSz is a sufficient criterion for the presence of entanglement and a simple correlation test can be constructed of |haˆm (bˆ†)ni|2 merely being greater than zero.We show that for the case of relative phase eigenstates, the new spin squeezing test for entanglement is satisfied (for the principle spin operators), whilst the test involving the sum of the ˆSx and ˆSy variances is not. However, another spin squeezing entanglement test for Bose–Einstein condensates involving the variance in ˆSz being less than the sum of the squared mean values for ˆSx and ˆSy divided by the boson number was based on a concept of entanglement inconsistent with the SP, and here we present a revised treatment which again leads to spin squeezing as an entanglement test

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

Quantum entanglement for systems of identical bosons: II. Spin squeezing and other entanglement tests

These two accompanying papers are concerned with entanglement for systems of identical massive bosons and the relationship to spin squeezing and other quantum correlation effects. The main focus is on two mode entanglement, but multi-mode entanglement is also considered. The bosons may be atoms or molecules as in cold quantum gases. The previous paper I dealt with the general features of quantum entanglement and its specific definition in the case of systems of identical bosons. Entanglement is a property shared between two (or more) quantum sub-systems. In defining entanglement for systems of identical massive particles, it was concluded that the single particle states or modes are the most appropriate choice for sub-systems that are distinguishable, that the general quantum states must comply both with the symmetrization principle and the super-selection rules (SSR) that forbid quantum superpositions of states with differing total particle number (global SSR compliance). Further, it was concluded that (in the separable states) quantum superpositions of sub-system states with differing sub-system particle number (local SSR compliance) also do not occur. The present paper II determines possible tests for entanglement based on the treatment of entanglement set out in paper I. Several inequalities involving variances and mean values of operators have been previously proposed as tests for entanglement between two sub-systems. These inequalities generally involve mode annihilation and creation operators and include the inequalities that define spin squeezing. In this paper, spin squeezing criteria for two mode systems are examined, and spin squeezing is also considered for principle spin operator components where the covariance matrix is diagonal. The proof, which is based on our SSR compliant approach shows that the presence of spin squeezing in any one of the spin components requires entanglement of the relevant pair of modes. A simple Bloch vector test for entanglement is also derived. Thus we show that spin squeezing becomes a rigorous test for entanglement in a system of massive bosons, when viewed as a test for entanglement between two modes. In addition, other previously proposed tests for entanglement involving spin operators are considered, including those based on the sum of the variances for two spin components. All of the tests are still valid when the present concept of entanglement based on the symmetrization and SSR criteria is applied. These tests also apply in cases of multi-mode entanglement, though with restrictions in the case of sub-systems each consisting of pairs of modes. Tests involving quantum correlation functions are also considered and for global SSR compliant states these are shown to be equivalent to tests involving spin operators. A new weak correlation test is derived for entanglement based on local SSR compliance for separable states, complementing the stronger correlation test obtained previously when this is ignored. The Bloch vector test is equivalent to one case of this weak correlation test. Quadrature squeezing for single modes is also examined but not found to yield a useful entanglement test, whereas two mode quadrature squeezing proves to be a valid entanglement test, though not as useful as the Bloch vector test. The various entanglement tests are considered for well-known entangled states, such as binomial states, relative phase eigenstates and NOON states—sometimes the new tests are satisfied while than those obtained in other papers are not. The present paper II then outlines the theory for a simple two mode interferometer showing that such an interferometer can be used to measure the mean values and covariance matrix for the spin operators involved in entanglement tests for the two mode bosonic system. The treatment is also generalized to cover multi-mode interferometry. The interferometer involves a pulsed classical field characterized by a phase variable and an area variable defined by the time integral of the field amplitude, and leads to a coupling between the two modes. For simplicity the center frequency was chosen to be resonant with the inter-mode transition frequency. Measuring the mean and variance of the population difference between the two modes for the output state of the interferometer for various choices of interferometer variables is shown to enable the mean values and covariance matrix for the spin operators for the input quantum state of the two mode system to be determined. The paper concludes with a discussion of several key experimental papers on spin squeezing

Direct detection of bound ammonium ions in the selectivity filter of ion channels by solid-state NMR.

The flow of ions across cell membranes facilitated by ion channels is an important function for all living cells. Despite the huge amount of structural data provided by crystallography, elucidating the exact interactions between the selectivity filter atoms and bound ions is challenging. Here, we detect bound 15 N-labeled ammonium ions as a mimic for potassium ions in ion channels using solid-state NMR under near-native conditions. The non-selective ion channel NaK showed two ammonium peaks corresponding to its two ion binding sites, while its potassium-selective mutant NaK2K that has a signature potassium- selective selectivity filter with four ion binding sites gave rise to four ammonium peaks. Ions bound in specific ion binding sites were identified based on magnetization transfer between the ions and carbon atoms in the selectivity filters. Magnetization transfer between bound ions and water molecules revealed that only one out of four ions in the selectivity filter of NaK2K is in close contact with water, which is in agreement with the direct knock-on ion conduction mechanism where ions are conducted through the channel by means of direct interactions without water molecules in between. Interestingly, the potassium-selective ion channels investigated here (NaK2K and, additionally, KcsA-Kv1.3) showed remarkably different chemical shifts for their bound ions, despite having identical amino acid sequences and crystal structures of their selectivity filters. Molecular dynamics simulations show similar ion binding and conduction behavior between ammonium and potassium ions and identify the origin of the differences between the investigated potassium channel

Sports Under Quarantine: A Case Study of Major League Baseball in 2020

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This case study entailed a Twitter content analysis to address the pandemic-delayed start to Major League Baseball (MLB) in the shortened 2020 season. This case study helps address the overarching objective to investigate how the sports world, especially fans, responded to MLB played during the 2020 COVID-19 pandemic. The methods investigated the common themes and determined who used predetermined Twitter hashtags. We recorded how many times external links, photos, emojis, and the 30 MLB teams were mentioned in the 779 tweets obtained during 39 days of data retrieval. Results showed that the most common category of tweeted content concerned news reports. Comparable numbers of positive and negative responses to the start of the MLB season were recognized, with a fraction of tweets highlighting COVID-19 impacts on health and modification of play (e.g., cardboard fans). The majority of Twitter users were from media and layperson categories. More inferred males tweeted using the selected hashtags. In exploratory analyses, results indicated that 50.2% of the sample included a link or a photo, and 2.2% of the sample used an emoji. The three most mentioned teams were the Cardinals (N = 51), Marlins (N = 49), and the Yankees (N = 48). The results confirmed the value of social media analysis as a research approach and revealed patterns emerging during a unique pandemic sports and media era

Regulating CCTV? : We can't solve problems by using the same kind of thinking we used when we created them

Peer reviewedPostprin

An ITPR1 Gene Deletion Causes Spinocerebellar Ataxia 15/16: A Genetic, Clinical and Radiological Description

The purpose of this study was to characterise a novel family with very slowly progressive pure spinocerebellar ataxia (SCA) caused by a deletion in the inositol 1,4,5-triphosphate receptor 1 (ITPR1) gene on chromosome 3. This is a detailed clinical, genetic, and radiological description of the genotype. Deletions in ITPR1 have been shown to cause SCA15/SCA16 in six families to date. A further Japanese family has been identified with an ITPR1 point mutation. The exact prevalence is as yet unknown, but is probably higher than previously thought. The clinical phenotype of the family is described, and videotaped clinical examinations are presented. Serial brain magnetic resonance imaging studies were carried out on one affected individual, and genetic analysis was performed on several family members. Protein analysis confirmed the ITPR1 deletion. Affected subjects display a remarkably slow, almost pure cerebellar syndrome. Serial magnetic resonance imaging shows moderate cerebellar atrophy with mild inferior parietal and temporal cortical volume loss. Genetic analysis shows a deletion of 346,487 bp in ITPR1 (the second largest ITPR1 deletion reported to date), suggesting SCA15 is due to a loss of ITPR1 function. Western blotting of lymphoblastoid cell line protein confirms reduced ITPR1 protein levels. SCA15 is a slowly or nonprogressive pure cerebellar ataxia, which appears to be caused by a loss of ITPR1 function and a reduction in the translated protein. Patients with nonprogressive or slowly progressive ataxia should be screened for ITPR1 defects

Structure and interactions of ultracold Yb ions and Rb atoms

In order to study ultracold charge-transfer processes in hybrid atom-ion traps, we have mapped out the potential energy curves and molecular parameters for several low lying states of the Rb, Yb$^+$ system. We employ both a multi-reference configuration interaction (MRCI) and a full configuration interaction (FCI) approach. Turning points, crossing points, potential minima and spectroscopic molecular constants are obtained for the lowest five molecular states. Long-range parameters, including the dispersion coefficients are estimated from our {\it ab initio} data. The separated-atom ionization potentials and atomic polarizability of the ytterbium atom ($\alpha_d=128.4$ atomic units) are in good agreement with experiment and previous calculations. We present some dynamical calculations for (adiabatic) scattering lengths for the two lowest (Yb,Rb$^+$) channels that were carried out in our work. However, we find that the pseudo potential approximation is rather limited in validity, and only applies to nK temperatures. The adiabatic scattering lengths for both the triplet and singlet channels indicate that both are large and negative in the FCI approximation.Comment: 8 pages, 3 figures, 5 table

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