Superpositions in Atomic Quantum Rings

Ultracold atoms are trapped circumferentially on a ring that is pierced at its center by a flux tube arising from a light-induced gauge potential due to applied Laguerre-Gaussian fields. We show that by using optical coherent state superpositions to produce light-induced gauge potentials, we can create a situation in which the trapped atoms are simultaneously exposed to two distinct flux tubes, thereby creating superpositions in atomic quantum rings. We consider the examples of both a ring geometry and harmonic trapping, and in both cases the ground state of the quantum system is shown to be a superposition of counter-rotating states of the atom trapped on the two distinct flux tubes.Comment: 11 pages, 6 figure

Effectively attractive Bose-Einstein condensates in a rotating toroidal trap

We examine an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a rotating toroidal trap, as the magnitude of the coupling constant and the rotational frequency are varied. Using both a variational mean-field approach, as well as a diagonalization technique, we identify the phase diagram between a uniform and a localized state and we describe the system in the two phases.Comment: 4 pages, 4 ps figures, RevTe

Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov Analyses

We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for \emph{metastable states} in \emph{finite size systems}. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear perturbation or Bogoliubov-de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist \emph{two topologically distinct quantum phases}. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is new: one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity, and the phase of the condensate can be continuously wound and unwound

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

We study the rotational properties of an attractively interacting Bose gas in a quadratic + quartic potential. The low-lying modes of both rotational ground state configurations, namely the vortex and the center of mass rotating states, are solved. The vortex excitation spectrum is positive for weak interactions but the lowest modes decrease rapidly to negative values when the interactions become stronger. The broken rotational symmetry involved in the center of mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center of mass rotational state also demonstrate the coupling between the center of mass and relative motions.Comment: 4 pages, 3 eps figures (2 in color) v2: changes in Title, all figures, in text (especially in Sec III) and in Reference

Quantization with Action-Angle Coherent States

For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent states in view to provide a quantization scheme that yields precisely a given observed energy spectrum ${E_n}$ for such a system. This construction is based on a Bayesian approach: each family corresponds to a choice of probability distributions such that the classical energy averaged with respect to this probability distribution is precisely $E_n$ up to a constant shift. The formalism is viewed as a natural extension of the Bohr-Sommerfeld rule and an alternative to the canonical quantization. In particular, it also yields a satisfactory angle operator as a bounded self-adjoint operator

Reflection of a Lieb-Liniger wave packet from the hard-wall potential

Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N particles, can be found by solving an $N$-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta.Comment: revised version, improved notation, Fig. 5 adde

Cavity Optomechanical Sensing and Manipulation of an Atomic Persistent Current

This theoretical work initiates contact between two frontier disciplines of physics, namely, atomic superfluid rotation and cavity optomechanics. It considers an annular Bose-Einstein condensate, which exhibits dissipationless flow and is a paradigm of rotational quantum physics, inside a cavity excited by optical fields carrying orbital angular momentum. It provides the first platform that can sense ring Bose-Einstein condensate rotation with minimal destruction, in situ and in real time, unlike demonstrated techniques, all of which involve fully destructive measurement. It also shows how light can actively manipulate rotating matter waves by optomechanically entangling persistent currents. Our work opens up a novel and useful direction in the sensing and manipulation of atomic superflow

Evolution of the macroscopically entangled states in optical lattices

We consider dynamics of boson condensates in finite optical lattices under a slow external perturbation which brings the system to the unstable equilibrium. It is shown that quantum fluctuations drive the condensate into the maximally entangled state. We argue that the truncated Wigner approximation being a natural generalization of the Gross-Pitaevskii classical equations of motion is adequate to correctly describe the time evolution including both collapse and revival of the condensate.Comment: 14 pages, 10 figures, Discussion of reversibility of entanglement is adde

Diabetic cases controlled with low carbohydrate diet (LCD) and GLP-1 receptor agonist (GLP-1 RA)

Recent treatment for type 2 diabetes mellitus (T2DM) has included glucagon-like peptide-1 receptor agonist (GLP-1 RA), indicating clinical efficacy for better glucose variability. Subjects were seven patients with T2DM associated with the obese tendency. Their average age was 63.8 ± 21.7 years old (5 males, 2 females) who received a new administration of GLP-1 RA (Mean ± standard deviation). For GLP-1 RA, dulaglutide (TRULICITY R, single-dose pen) was administered by subcutaneous injection 0.75 mg once a week. Basal data at 0 month revealed that body weight 76.0 ± 11.6 kg, body mass index (BMI) 29.2 ± 11.6, blood C-peptide immunoreactivity (CPR) 2.68 ± 0.49 ng/mL, respectively. After the intervention of dulaglutide, decreased value of BMI for 3 and 6-9 months was 0.78 ± 0.45 and 1.16 ± 0.85, and HbA1c for 3 and 6-9 months was 1.60 ± 1.52% and 2.01 ± 1.44%, respectively. Though these cases have various complications besides T2DM, they showed clinical effects of weight reduction and lowering blood glucose. Diabetic treatment for current cases would suggest that GLP-1 RA would be effective in various situations such as a super-aged patient, medical practice in the remote area, family care and visiting nursing