49,325 research outputs found
Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
We propose a general method by which experiments on ultracold gases can be
used to determine the topological properties of the energy bands of optical
lattices, as represented by the map of the Berry curvature across the Brillouin
zone. The Berry curvature modifies the semiclassical dynamics and hence the
trajectory of a wave packet undergoing Bloch oscillations. However, in two
dimensions these trajectories may be complicated Lissajous-like figures, making
it difficult to extract the effects of Berry curvature in general. We propose
how this can be done using a "time-reversal" protocol. This compares the
velocity of a wave packet under positive and negative external force, and
allows a clean measurement of the Berry curvature over the Brillouin zone. We
discuss how this protocol may be implemented and explore the semiclassical
dynamics for three specific systems: the asymmetric hexagonal lattice, and two
"optical flux" lattices in which the Chern number is nonzero. Finally, we
discuss general experimental considerations for observing Berry curvature
effects in ultracold gases.Comment: 12 page
Edge excitations and Topological orders in rotating Bose gases
The edge excitations and related topological orders of correlated states of a
fast rotating Bose gas are studied. Using exact diagonalization of small
systems, we compute the energies and number of edge excitations, as well as the
boson occupancy near the edge for various states. The chiral Luttinger-liquid
theory of Wen is found to be a good description of the edges of the bosonic
Laughlin and other states identified as members of the principal Jain sequence
for bosons. However, we find that in a harmonic trap the edge of the state
identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An
experimental way of detecting these correlated states is also discussed.Comment: Results extended to larger systems. Improved presentatio
Periodically-driven quantum matter: the case of resonant modulations
Quantum systems can show qualitatively new forms of behavior when they are
driven by fast time-periodic modulations. In the limit of large driving
frequency, the long-time dynamics of such systems can often be described by a
time-independent effective Hamiltonian, which is generally identified through a
perturbative treatment. Here, we present a general formalism that describes
time-modulated physical systems, in which the driving frequency is large, but
resonant with respect to energy spacings inherent to the system at rest. Such a
situation is currently exploited in optical-lattice setups, where superlattice
(or Wannier-Stark-ladder) potentials are resonantly modulated so as to control
the tunneling matrix elements between lattice sites, offering a powerful method
to generate artificial fluxes for cold-atom systems. The formalism developed in
this work identifies the basic ingredients needed to generate interesting flux
patterns and band structures using resonant modulations. Additionally, our
approach allows for a simple description of the micro-motion underlying the
dynamics; we illustrate its characteristics based on diverse dynamic-lattice
configurations. It is shown that the impact of the micro-motion on physical
observables strongly depends on the implemented scheme, suggesting that a
theoretical description in terms of the effective Hamiltonian alone is
generally not sufficient to capture the full time-evolution of the system.Comment: 16 pages, 3 figures; includes a new Section III dedicated to the
strong-driving regim
Variational Ansatz for PT-Symmetric Quantum Mechanics
A variational calculation of the energy levels of a class of PT-invariant
quantum mechanical models described by the non-Hermitian Hamiltonian H= p^2 -
(ix)^N with N positive and x complex is presented. Excellent agreement is
obtained for the ground state and low lying excited state energy levels and
wave functions. We use an energy functional with a three parameter class of
PT-symmetric trial wave functions in obtaining our results.Comment: 9 pages -- one postscript figur
Robustness of Fractional Quantum Hall States with Dipolar Atoms in Artificial Gauge Fields
The robustness of fractional quantum Hall states is measured as the energy
gap separating the Laughlin ground-state from excitations. Using thermodynamic
approximations for the correlation functions of the Laughlin state and the
quasihole state, we evaluate the gap in a two-dimensional system of dipolar
atoms exposed to an artificial gauge field. For Abelian fields, our results
agree well with the results of exact diagonalization for small systems, but
indicate that the large value of the gap predicted in [Phys. Rev. Lett. 94,
070404 (2005)] was overestimated. However, we are able to show that the small
gap found in the Abelian scenario is dramatically increased if we turn to
non-Abelian fields squeezing the Landau levels
Fragmentation pathways of [Re₂(μ-OR)₃(CO)₆]– (R = H, Me) and ligand exchange reactions with oxygen donor ligands, investigated by electrospray mass spectrometry
The rhenium hydroxy and methoxy carbonyl complexes [Re₂(μOR)₃(CO)₆]⁻ (R = H or Me) have been studied by negative-ion electrospray mass spectrometry (ESMS). The complexes undergo facile exchange reactions with protic compounds, including alcohols and phenols. With dimethyl malonate, ester hydrolysis occurs giving carboxylate-containing complexes, and with H₂O₂ or ButOOH, oxidation to ReO₄⁻occurs. The feasibility and extent of these reactions can conveniently, rapidly, and unambiguously be determined by electrospray mass spectrometry, and is dependent on the acidity and steric bulk of the protic compound. The results also suggest that the complexes can be used as versatile starting materials for the synthesis of a wide range of analogous [Re₂(μ-OR)₃(CO)₆]⁻ complexes by simple reaction with an excess of the appropriate alcohol. By varying the applied cone voltage the fragmentation pathways have been investigated; the hydroxy complex undergoes dehydration followed by CO loss, whereas for the methoxy complex -hydride elimination (and CO loss) is observed, with confirmation provided by deuterium labelling studies. Under ESMS conditions, the neutral complexes [Re₂(μ-OR)₂(μ-dppf )(CO)₆] [R = H or Me; dppf = 1,1 -bis(diphenylphosphino)ferrocene] undergo substantial solvolysis and hydrolysis to give mainly mononuclear species; simple parent ions (e.g. [M + H]⁺) are not formed in appreciable abundance, probably due to the lack of an efficient ionisation pathway
Single vortex states in a confined Bose-Einstein condensate
It has been demonstrated experimentally that non-axially symmetric vortices
precess around the centre of a Bose-Einstein condensate. Two types of single
vortex states have been observed, usually referred to as the S-vortex and the
U-vortex. We study theoretically the single vortex excitations in spherical and
elongated condensates as a function of the interaction strength. We solve
numerically the Gross-Pitaevskii equation and calculate the angular momentum as
a function of precession frequency. The existence of two types of vortices
means that we have two different precession frequencies for each angular
momentum value. As the interaction strength increases the vortex lines bend and
the precession frequencies shift to lower values. We establish that for given
angular momentum the S-vortex has higher energy than the U-vortex in a rotating
elongated condensate. We show that the S-vortex is related to the solitonic
vortex which is a nonlinear excitation in the nonrotating system. For small
interaction strengths the S-vortex is related to the dark soliton. In the
dilute limit a lowest Landau level calculation provides an analytic description
of these vortex modes in terms of the harmonic oscillator states
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