33 research outputs found
Controlling spin without magnetic fields -- the Bloch-Rashba rotator
We consider the dynamics of a quantum particle held in a lattice potential,
and subjected to a time-dependent spin-orbit coupling. Tilting the lattice
causes the particle to perform Bloch oscillations, and by suitably changing the
Rashba interaction during its motion, the spin of the particle can be gradually
rotated. Even if the Rashba coupling can only be altered by a small amount,
large spin-rotations can be obtained by accumulating the rotation from
successive oscillations. We show how the time-dependence of the spin-orbit
coupling can be chosen to maximize the rotation per cycle, and thus how this
method can be used to produce a precise and controllable spin-rotator, the
Bloch-Rashba rotator, without requiring an applied magnetic field.Comment: 6 pages, 6 figures. V2: minor changes, added reference
Cat states in a driven superfluid: role of signal shape and switching protocol
We investigate the behavior of a one-dimensional Bose-Hubbard model whose
kinetic energy is made to oscillate with zero time-average. The effective
dynamics is governed by an atypical many-body Hamiltonian where only even-order
hopping processes are allowed. At a critical value of the driving, the system
passes from a Mott insulator to a superfluid formed by a cat-like superposition
of two quasi-condensates with opposite non-zero momenta. We analyze the
robustness of this unconventional ground state against variations of a number
of system parameters. In particular we study the effect of the waveform and the
switching protocol of the driving signal. Knowledge of the sensitivity of the
system to these parameter variations allows us to gauge the robustness of the
exotic physical behavior.Comment: 9 pages, 5 figure
Perturbative analysis of coherent quantum ratchets in cold atom systems
We present a perturbative study of the response of cold atoms in an optical
lattice to a weak time- and space-asymmetric periodic driving signal. In the
noninteracting limit, and for a finite set of resonant frequencies, we show how
a coherent, long lasting ratchet current results from the interference between
first and second order processes. In those cases, a suitable three-level model
can account for the entire dynamics, yielding surprisingly good agreement with
numerically exact results for weak and moderately strong driving.Comment: 8 pages, 6 figure
Fractals on a benchtop: Observing fractal dimension in a resistor network
Our first experience of dimension typically comes in the intuitive Euclidean
sense: a line is one dimensional, a plane is two-dimensional, and a volume is
three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},
systems with a fractional dimension, ``fractals'', now play an important role
in science. The novelty of encountering fractional dimension, and the intrinsic
beauty of many fractals, have a strong appeal to students and provide a
powerful teaching tool. I describe here a low-cost and convenient experimental
method for observing fractal dimension, by measuring the power-law scaling of
the resistance of a fractal network of resistors. The experiments are quick to
perform, and the students enjoy both the construction of the network and the
collaboration required to create the largest networks. Learning outcomes
include analysis of resistor networks beyond the elementary series and parallel
combinations, scaling laws, and an introduction to fractional dimension
Erratum: Location of crossings in the Floquet spectrum of a driven two-level system (vol B 67, art no 165301, 2003)
©2004 The American Physical Society.Depto. de Física de MaterialesFac. de Ciencias FísicasTRUEpu
Directed transport in driven optical lattices by gauge generation.
We examine the dynamics of ultracold atoms held in optical-lattice potentials. By controlling the switching of a periodic driving potential we show how a phase-induced renormalization of the intersite tunneling can be used to produce directed motion and control wave-packet spreading. We further show how this generation of a synthetic gauge potential can be used to split and recombine wave packets, providing an attractive route to implementing quantum computing tasks
Superfluidity from correlations in driven boson systems
We investigate theoretically the superfluidity of a one-dimensional boson
system whose hopping energy is periodically modulated with a zero time average,
which results in the suppression of first-order single-particle hopping
processes. The dynamics of this flat band system is entirely driven by
correlations and described by exotic Hamiltonian and current operators. We
employ exact diagonalization and compare our results with those of the
conventional, undriven Bose-Hubbard system. We focus on the two main
manifestations of superfluidity, the Hess-Fairbank effect and the metastability
of supercurrents, with explicit inclusion of an impurity when relevant. Among
the novel superfluid features, we highlight the presence of a cat-like ground
state, with branches that have opposite crystal momentum but carry the same
flux-dependent current, and the essential role of the interference between the
collective components of the ground-state wave function. Calculation of the
dynamic form factor reveals the presence of an acoustic mode that guarantees
superfluidity in the thermodynamic limit.Comment: 14 pages, 9 figure
Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices
We analyze the dynamics of two strongly interacting fermions moving in two-dimensional lattices under the action of a periodic electric field, both with and without a magnetic flux. Due to the interaction, these particles bind together forming a doublon. We derive an effective Hamiltonian that allows us to understand the interplay between the interaction and the driving, revealing surprising effects that constrain the movement of the doublons. We show that it is possible to confine doublons to just the edges of the lattice and to a particular sublattice if different sites in the unit cell have different coordination numbers. Contrary to what happens in one-dimensional systems, here we observe the coexistence of both topological and Shockley-like edge states when the system is in a nontrivial phase
Effective Josephson dynamics in resonantly driven Bose-Einstein condensates
We show that the orbital Josephson effect appears in a wide range of driven
atomic Bose-Einstein condensed systems, including quantum ratchets, double
wells and box potentials. We use three separate numerical methods:
Gross-Pitaevskii equation, exact diagonalization of the few-mode problem, and
the Multi-Configurational Time-Dependent Hartree for Bosons algorithm. We
establish the limits of mean-field and few-mode descriptions, demonstrating
that they represent the full many-body dynamics to high accuracy in the weak
driving limit. Among other quantum measures, we compute the instantaneous
particle current and the occupation of natural orbitals. We explore four
separate dynamical regimes, the Rabi limit, chaos, the critical point, and
self-trapping; a favorable comparison is found even in the regimes of dynamical
instabilities or macroscopic quantum self-trapping. Finally, we present an
extension of the (t,t')-formalism to general time-periodic equations of motion,
which permits a systematic description of the long-time dynamics of resonantly
driven many-body systems, including those relevant to the orbital Josephson
effect.Comment: 14 pages, 9 figure