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ABSTRACT: We present three types of dark solitons in quasi-one-dimensional spin-orbit
coupled repulsive Bose-Einstein condensates. Among these families, two are
always stable, while the third one is only stable sufficiently close to the
linear regime. The solitons' excitation spectra reveal the potential existence
of a second anomalous mode. While the first such mode describes the soliton
oscillatory motion in a parabolic trap, the second, when present, reflects the
double well structure of the underlying single-particle spectrum. This novel
mode results in moving density stripes in the vicinity of the soliton core, or
in an out-of-phase oscillation of the constituent components, with little
effect on the nearly stationary striped total density of the composite soliton.
04/2013;
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ABSTRACT: We introduce the concept of parity symmetry in restricted spatial domains—local parity—and explore its impact on the stationary transport properties of generic, one-dimensional aperiodic potentials of compact support. It is shown that, in each domain of local parity symmetry of the potential, there exists an invariant quantity in the form of a nonlocal current, in addition to the globally invariant probability current. For symmetrically incoming states, both invariant currents vanish if weak commutation of the total local parity operator with the Hamiltonian is established, leading to local parity eigenstates. For asymmetrically incoming states which resonate within locally symmetric potential units, the complete local parity symmetry of the probability density is shown to be necessary and sufficient for the occurrence of perfect transmission. We connect the presence of local parity symmetries on different spatial scales to the occurrence of multiple perfectly transmitting resonances, and we propose a construction scheme for the design of resonant transparent aperiodic potentials. Our findings are illustrated through application to the analytically tractable case of piecewise constant potentials.
Physical Review A 03/2013; 87:032113. · 2.88 Impact Factor
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ABSTRACT: We demonstrate the emergence of criticality due to power-law cross correlations in an ensemble of noninteracting particles propagating in an infinite Lorentz channel. The origin of these interparticle long-range correlations is the intermittent dynamics associated with the ballistic corridors in the single particle phase space. This behavior persists dynamically, even in the presence of external driving, provided that the billiard's horizon becomes infinite at certain times. For the driven system, we show that Fermi acceleration permits the synchronization of the particle motion with the periodic appearance of the ballistic corridors. The particle ensemble then acquires characteristics of self-organization as the weight of the phase space regions leading to critical behavior increases with time. The Lorentz gas (LG) [1] acts in the theory of dynamical systems as a paradigm allowing us to address fundamental issues of statistical mechanics, for instance, ergodicity and mixing [2–4], as well as transport processes, such as diffu-sion in the configuration space [5–9]. The static periodic LG comprises a regular lattice of circular fixed scatterers and an ensemble of noninteracting particles traveling freely be-tween collisions and scattering elastically off the circular obstacles. The transport properties of such a system are determined by the billiard's geometry, that is the specific lattice symmetry and the lattice constant. If the maximum free path length is not bounded from above, then the setup possesses a so-called infinite horizon (IH) and the diffusion in configuration space is anomalous [10,11]. For a more compact packing of the scatterers, i.e., finite horizon (FH), arbitrarily long flights are not possible and the system exhibits normal diffusion [6]. From a dynamical point of view, if the system has FH, then it is fully hyperbolic. However, in the case of the IH geometry, the chaoticity weakens and an ordered portion of phase space emerges, due to the existence of ballistic corridors, leading to an intermittent behavior [12]. Alternatively, chaoticity can be reduced also by using different scatterer geometry as in Ref. [13] where algebraically decaying autocorrelations have been observed, although the corresponding horizon is finite. Time-dependent generalizations of the original periodic Lorentz gas model have been introduced, in which the scatterers are allowed to oscillate [14–16], rendering the study of diffusion in momentum space possible. This pro-cess is intimately linked to Fermi acceleration [17], which is considered a fundamental acceleration mechanism in many areas of physics [18]. The mechanism consists in the indefinite increase of the mean energy of particles as a result of random collisions with moving scatterers. In this Letter, we show the emergence of power-law (critical) cross correlations between noninteracting particles propagating in the LG with IH in a channel geometry. To reveal these cross correlations, a spatially coarse grained description of the dynamics is employed. The dynamically infinite horizon (DIH) is introduced as a property of driven extended billiards for which ballistic corridors open up and close periodically in time, i.e., exist only for certain time intervals. The development of Fermi acceleration then en-ables the particles to synchronize their motion with the periodic appearance of the ballistic corridors, such that they can perform free flights of arbitrary length, which, in turn, gives rise to intermittent dynamics and the appearance of critical correlations. In this sense, it is shown that Fermi acceleration can act as an effective driving force to steer an ensemble of propagating particles towards a critical state, imparting to the system's dynamics characteristics of self-organized criticality. This work adds to the recent intensive efforts to clarify the interrelation between intermittency, criticality, and self-organization [19–22]. The device investigated is an infinite strip of a periodic LG, known as Lorentz channel (LC) [23–25], consisting in hard circular scatterers placed on a semi-infinite triangular lattice as shown in Fig. 1. The central disks of the device with radii b can oscillate with amplitude A and angular frequency !. Without loss of generality, provided that the flat segments between the static discs are small enough to prohibit bouncing orbits in the y direction [26], we choose the radii of the static semi-circles a=w ¼ 0:48, where w is the lattice constant. In the following, distance and time is measured in units of w and 1=!, respectively. Statistical aspects of the transport properties of the static Lorentz gas, have been modeled by a suitable hopping process, either as a two-dimensional completely uncorre-lated random walk [5] or by taking into account correla-tions between jumps [8,27,28]. Inspired by these studies, we introduce here, a coarse grained description of the dynamics in the driven LC by integrating out the motion of the particle inside a unit cell [marked by dashed blue
Physical Review Letters 09/2012; · 7.37 Impact Factor
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ABSTRACT: Employing Monte-Carlo simulation techniques we investigate the statistical
properties of equally charged particles confined in a one-dimensional box trap
and detect a crossover from a crystalline to a cluster phase with increasing
temperature. The corresponding transition temperature depends separately on the
number of particles N and the box size L, implying non-extensivity due to the
long-range character of the interactions. The probability density of the
spacing between the particles exhibits at low temperatures an accumulation of
discrete peaks with an overall asymmetric shape. In the vicinity of the
transition temperature it is of a Gaussian form whereas in the high temperature
regime an exponential decay is observed. The high temperature behaviour shows a
cluster phase with a mean cluster size that first increases with the
temperature and then saturates. The crossover is clearly identifiable also in
the non-linear behaviour of the heat capacity with varying temperature. The
influence of the trapping potential on the observed results as well as possible
experimental realizations are briefly addressed.
08/2012;
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ABSTRACT: A semi-analytical approach to atomic waveguide scattering for harmonic
confinement is developed taking into account all partial waves. As a
consequence $\ell$-wave confinement-induced resonances are formed being coupled
to each other due to the confinement. The corresponding resonance condition is
obtained analytically using the $K$-matrix formalism. Atomic scattering is
described by transition diagrams which depict all relevant processes the atoms
undergo during the collision. Our analytical results are compared to
corresponding numerical data and show very good agreement.
07/2012;
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ABSTRACT: We introduce the concept of parity symmetry in restricted spatial domains --
local parity -- and explore its impact on the transport properties of generic,
one-dimensional aperiodic potentials of compact support. It is shown that, in
each domain of local parity symmetry of the potential, there exists a conserved
quantity in the form of a non-local current, in addition to the globally
conserved probability current. For symmetrically incoming states, both
conserved currents vanish if weak commutation of the total local parity
operator with the Hamiltonian is established, leading to local parity
eigenstates. For asymmetrically incoming states, the local parity symmetry of
the probability density is shown to be necessary and sufficient for the
occurrence of perfect transmission in completely locally symmetric potentials.
We connect the presence of local parity symmetries on different spatial scales
to the occurrence of multiple perfectly transmitting resonances and propose a
construction scheme for the design of resonant transparent aperiodic
potentials. Our findings are illustrated through application to the
analytically tractable case of piecewise constant potentials.
07/2012;
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ABSTRACT: The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein
condensates through bifurcations from suitable eigenstates of the underlying
linear system is examined. These dipoles can have their bright solitary
structures be in phase (symmetric) or out of phase (anti-symmetric). The
dynamical robustness of each of these two possibilities is considered and the
out-of-phase case is found to exhibit an intriguing symmetry-breaking
instability that can in turn lead to tunneling of the bright wavefunction
between the two vortex "wells". We interpret this phenomenon by virtue of a
vortex-induced double well system, whose spontaneous symmetry breaking leads to
asymmetric vortex-bright dipoles, in addition to the symmetric and
anti-symmetric ones. The theoretical prediction of these states is corroborated
by detailed numerical computations.
07/2012;
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ABSTRACT: A field-theoretical approach to the scattering off an oscillating quantum system is developed. As a key ingredient it employs the adiabatic eigenstate basis and consists of a perturbative scheme for the calculation of the geometric phases influencing the transmission through the time-dependent potential landscape. The main advantage is the identification of basic diagrams which allow for an immediate interpretation of the underlying elementary physical processes contributing to the scattering and transmission behavior. We apply our method to the simple, but prototypical, problem of transmission through an one-dimensional oscillating δ potential and demonstrate how it enables a deeper understanding of the relevant physical processes.
Physical Review A 06/2012; 85(6):062110. · 2.88 Impact Factor
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ABSTRACT: A field-theoretical approach to the scattering off an oscillating quantum system is developed. As a key ingredient it employs the adiabatic eigenstate basis and consists of a perturbative scheme for the calculation of the geometric phases influencing the transmission through the time-dependent potential landscape. The main advantage is the identification of basic diagrams which allow for an immediate interpretation of the underlying elementary physical processes contributing to the scattering and transmission behavior. We apply our method to the simple, but prototypical, problem of transmission through an one-dimensional oscillating δ potential and demonstrate how it enables a deeper understanding of the relevant physical processes.
Phys. Rev. A. 06/2012; 85(6).
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ABSTRACT: We study vortex excitations in one-component Bose-Einstein condensates, with
a special emphasis on the role of anisotropic confinement for the existence,
stability and dynamical properties of vortices and particularly few-vortex
clusters. Symmetry breaking features are pervasive within this system even in
its isotropic installment, where cascades of symmetry breaking bifurcations
give rise to the multi-vortex clusters, but also within the anisotropic realm
which naturally breaks the rotational symmetry of the multi-vortex states. Our
first main tool for analyzing the system consists of a weakly nonlinear
(bifurcation) approach which starts from the linear states of the problem and
examines their continuation and bifurcation into novel symmetry-broken
configurations in the nonlinear case. This is first done in the isotropic limit
and the modifications introduced by the anisotropy are subsequently presented.
The second main tool concerns the highly nonlinear regime where the vortices
can be considered as individual topologically charged "particles" which precess
within the parabolic trap and interact with each other, similarly to fluid
vortices. The conclusions stemming from both the bifurcation and the
interacting particle picture are corroborated by numerical computations which
are also used to bridge the gap between these two opposite-end regimes.
03/2012;
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ABSTRACT: We show the existence of ultra-long-range giant dipole molecules formed by a neutral alkali ground state atom that is bound to the decentered electronic wave function of a giant dipole atom. The adiabatic potential surfaces emerging from the interaction of the ground state atom with the giant dipole electron possess a rich topology depending on the degree of electronic excitation. Binding energies and the vibrational motion in the energetically lowest surfaces are analyzed by means of perturbation theory and exact diagonalization techniques. The resulting molecules are truly giant with internuclear distances up to several μm. Finally, we demonstrate the existence of intersection manifolds of excited electronic states that potentially lead to a vibrational decay of the ground state atom dynamics.
EPL (Europhysics Letters) 02/2012; 97(4):43001. · 2.17 Impact Factor
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ABSTRACT: We explore the external electric field control of a species of
ultralong-range molecules that emerge from the interaction of a ground state
polar molecule with a Rydberg atom. The external field mixes the Rydberg
electronic states and therefore strongly alters the electric field seen by the
polar diatomic molecule due to the Rydberg electron. As a consequence, the
adiabatic potential energy curves responsible for the molecular binding can be
tuned in such a way that an intersection with neighboring curves occurs. The
latter leads to admixture of s-wave character in the Rydberg wave function and
will substantially facilitate the experimental preparation and realization of
this particular class of Rydberg molecule species.
01/2012;
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ABSTRACT: We explore the effective long-range interaction of charged particles confined to a curved low-dimensional manifold using the example of a helical geometry. Opposite to the Coulomb interaction in free space the confined particles experience a force which is oscillating with the distance between the particles. This leads to stable equilibrium configurations and correspondingly induced bound states whose number is tunable with the parameters of the helix. We demonstrate the existence of a plethora of equilibria of few-body chains with different symmetry character that are allowed to freely move. An outline concerning the implications on many-body helical chains is provided.
EPL (Europhysics Letters) 08/2011; 95(5):50005. · 2.17 Impact Factor
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ABSTRACT: We study dark-bright ring solitons in two-component Bose-Einstein
condensates. In the limit of large densities of the dark component, we describe
the soliton dynamics by means of an equation of motion for the ring radius. The
presence of the bright, "filling" species is demonstrated to have a stabilizing
effect on the ring dark soliton. Near the linear limit, we discuss the
symmetry-breaking bifurcations of dark-bright soliton stripes and vortex-bright
soliton clusters from the dark-bright ring and relate the stabilizing effect of
filling to changes in the bifurcation diagram. Finally, we show that
stabilization by means of a second component is not limited to the radially
symmetric structures, but can also be observed in a cross-like dark-bright
soliton configuration.
07/2011;
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ABSTRACT: We present a systematic theoretical analysis of the motion of a pair of
straight counter-rotating vortex lines within a trapped Bose-Einstein
condensate. We introduce the dynamical equations of motion, identify the
associated conserved quantities, and illustrate the integrability of the
ensuing dynamics. The system possesses a stationary equilibrium as a special
case in a class of exact solutions that consist of rotating guiding-center
equilibria about which the vortex lines execute periodic motion; thus, the
generic two-vortex motion can be classified as quasi-periodic. We conclude with
an analysis of the linear and nonlinear stability of these stationary and
rotating equilibria.
06/2011;
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ABSTRACT: We analyze the quantum dynamics of the time-dependent elliptical billiard
using the example of a certain breathing mode. A numerical method for the
time-propagation of an arbitrary initial state is developed, based on a series
of transformations thereby removing the time-dependence of the boundary
conditions. The time-evolution of the energies of different initial states is
studied. The maximal and minimal energy that is reached during the
time-evolution shows a series of resonances as a function of the applied
driving frequency. At these resonances, higher (or lower) lying states are
periodically populated, leading to the observed change in energy. The
resonances occur when the driving frequency or a multiple of it matches exactly
the mean energetic difference between the two involved states. This picture is
confirmed by a few-level Rabi-like model with periodic couplings, reproducing
the key results of our numerical study.
06/2011;
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ABSTRACT: We present experimental results and a systematic theoretical analysis of
dark-br ight soliton interactions and multiple-dark-bright soliton complexes in
atomic t wo-component Bose-Einstein condensates. We study analytically the
interactions b etween two-dark-bright solitons in a homogeneous condensate and,
then, extend ou r considerations to the presence of the trap. An effective
equation of motion is derived for the dark-bright soliton center and the
existence and stability of stationary two-dark-bright soliton states is
illustrated (with the bright components being either in- or out-of-phase). The
equation of motion provides the characteristic oscillation frequencies of the
solitons, in good agreement with the eigenfrequencies of the anomalous modes of
the system.
04/2011;
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ABSTRACT: A quantized vortex dipole is the simplest vortex molecule, comprising two
counter-circulating vortex lines in a superfluid. Although vortex dipoles are
endemic in two-dimensional superfluids, the precise details of their dynamics
have remained largely unexplored. We present here several striking observations
of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a
vortex-particle model that generates vortex line trajectories that are in good
agreement with the experimental data. Interestingly, these diverse trajectories
exhibit essentially identical quasi-periodic behavior, in which the vortex
lines undergo stable epicyclic orbits.
04/2011;
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ABSTRACT: We explore the non-equilibrium escape dynamics of long-range interacting ions in one-dimensional traps. The phase space of the few ion setup and its impact on the escape properties are studied. As the main result, we show that an instantaneous reduction of the trap's potential depth leads to the synchronized emission of a sequence of ion pairs if the initial configurations are close to the crystalline ionic configuration. The corresponding time intervals of the consecutive pair emission as well as the number of emitted pairs can be tuned by changing the final trap depth. Correlations between the escape times and kinetic energies of the ions are observed and analyzed.
New Journal of Physics 02/2011; 13(2):023006. · 4.18 Impact Factor
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ABSTRACT: The internal electric field of a Rydberg atom electron can bind a polar
molecule to form a giant ultralong-range stable polyatomic molecule. Such
molecules not only share their properties with Rydberg atoms, they possess huge
permanent electric dipole moments and in addition allow for coherent control of
the polar molecule orientation. In this work, we include additional Rydberg
manifolds which couple to the nearly degenerate set of Rydberg states employed
in [S. T. Rittenhouse and H. R. Sadeghpour, Phys. Rev. Lett. 104, 243002
(2010)]. The coupling of a set of $(n+3)s$ Rydberg states with the $n(l>2)$
nearly degenerate Rydberg manifolds in alkali metal atoms leads to pronounced
avoided crossings in the Born-Oppenheimer potentials. Ultimately, these avoided
crossings enable the formation of the giant polyatomic Rydberg molecules with
standard two-photon laser photoassociation techniques.
01/2011;
