187 research outputs found
Efficient reverse engineering of one-qubit filter functions with dynamical invariants
We derive an integral expression for the filter-transfer function of an
arbitrary one-qubit gate through the use of dynamical invariant theory and
Hamiltonian reverse engineering. We use this result to define a cost functional
which can be efficiently optimized to produce one-qubit control pulses that are
robust against specified frequency bands of the noise power spectral density.
We demonstrate the utility of our result by generating optimal control pulses
that are designed to suppress broadband detuning and pulse amplitude noise. We
report an order of magnitude improvement in gate fidelity in comparison with
known composite pulse sequences. More broadly, we also use the same theoretical
framework to prove the robustness of nonadiabatic geometric quantum gates under
specific error models and control constraints
A general T-matrix approach applied to two-body and three-body problems in cold atomic gases
We propose a systematic T-matrix approach to solve few-body problems with
s-wave contact interactions in ultracold atomic gases. The problem is generally
reduced to a matrix equation expanded by a set of orthogonal molecular states,
describing external center-of-mass motions of pairs of interacting particles;
while each matrix element is guaranteed to be finite by a proper
renormalization for internal relative motions. This approach is able to
incorporate various scattering problems and the calculations of related
physical quantities in a single framework, and also provides a physically
transparent way to understand the mechanism of resonance scattering. For
applications, we study two-body effective scattering in 2D-3D mixed dimensions,
where the resonance position and width are determined with high precision from
only a few number of matrix elements. We also study three fermions in a
(rotating) harmonic trap, where exotic scattering properties in terms of mass
ratios and angular momenta are uniquely identified in the framework of
T-matrix.Comment: 14 pages, 4 figure
Bound Chains of Tilted Dipoles in Layered Systems
Ultracold polar molecules in multilayered systems have been experimentally
realized very recently. While experiments study these systems almost
exclusively through their chemical reactivity, the outlook for creating and
manipulating exotic few- and many-body physics in dipolar systems is
fascinating. Here we concentrate on few-body states in a multilayered setup. We
exploit the geometry of the interlayer potential to calculate the two- and
three-body chains with one molecule in each layer. The focus is on dipoles that
are aligned at some angle with respect to the layer planes by means of an
external eletric field. The binding energy and the spatial structure of the
bound states are studied in several different ways using analytical approaches.
The results are compared to stochastic variational calculations and very good
agreement is found. We conclude that approximations based on harmonic
oscillator potentials are accurate even for tilted dipoles when the geometry of
the potential landscape is taken into account.Comment: 10 pages, 6 figures. Submitted to Few-body Systems special issue on
Critical Stability, revised versio
Dimers, Effective Interactions, and Pauli Blocking Effects in a Bilayer of Cold Fermionic Polar Molecules
We consider a bilayer setup with two parallel planes of cold fermionic polar
molecules when the dipole moments are oriented perpendicular to the planes. The
binding energy of two-body states with one polar molecule in each layer is
determined and compared to various analytic approximation schemes in both
coordinate- and momentum-space. The effective interaction of two bound dimers
is obtained by integrating out the internal dimer bound state wave function and
its robustness under analytical approximations is studied. Furthermore, we
consider the effect of the background of other fermions on the dimer state
through Pauli blocking, and discuss implications for the zero-temperature
many-body phase diagram of this experimentally realizable system.Comment: 18 pages, 10 figures, accepted versio
Cavitation of Electrons Bubbles in Liquid Helium Below saturation Pressure
We have used a Hartree-type electron-helium potential together with a density
functional description of liquid He and He to study the explosion of
electron bubbles submitted to a negative pressure. The critical pressure at
which bubbles explode has been determined as a function of temperature. It has
been found that this critical pressure is very close to the pressure at which
liquid helium becomes globally unstable in the presence of electrons. It is
shown that at high temperatures the capillary model overestimates the critical
pressures. We have checked that a commonly used and rather simple
electron-helium interaction yields results very similar to those obtained using
the more accurate Hartree-type interaction. We have estimated that the
crossover temperature for thermal to quantum nucleation of electron bubbles is
very low, of the order of 6 mK for He.Comment: 22 pages, 9 figure
Condensed Matter Theory of Dipolar Quantum Gases
Recent experimental breakthroughs in trapping, cooling and controlling
ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the
way toward the investigation of highly tunable quantum systems, where
anisotropic, long-range dipolar interactions play a prominent role at the
many-body level. In this article we review recent theoretical studies
concerning the physics of such systems. Starting from a general discussion on
interaction design techniques and microscopic Hamiltonians, we provide a
summary of recent work focused on many-body properties of dipolar systems,
including: weakly interacting Bose gases, weakly interacting Fermi gases,
multilayer systems, strongly interacting dipolar gases and dipolar gases in 1D
and quasi-1D geometries. Within each of these topics, purely dipolar effects
and connections with experimental realizations are emphasized.Comment: Review article; submitted 09/06/2011. 158 pages, 52 figures. This
document is the unedited author's version of a Submitted Work that was
subsequently accepted for publication in Chemical Reviews, copyright American
Chemical Society after peer review. To access the final edited and published
work, a link will be provided soo
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