169 research outputs found
Atomic quantum gases in periodically driven optical lattices
Time periodic forcing in the form of coherent radiation is a standard tool
for the coherent manipulation of small quantum systems like single atoms. In
the last years, periodic driving has more and more also been considered as a
means for the coherent control of many-body systems. In particular, experiments
with ultracold quantum gases in optical lattices subjected to periodic driving
in the lower kilohertz regime have attracted a lot of attention. Milestones
include the observation of dynamic localization, the dynamic control of the
quantum phase transition between a bosonic superfluid and a Mott insulator, as
well as the dynamic creation of strong artificial magnetic fields and
topological band structures. This article reviews these recent experiments and
their theoretical description. Moreover, fundamental properties of periodically
driven many-body systems are discussed within the framework of Floquet theory,
including heating, relaxation dynamics, anomalous topological edge states, and
the response to slow parameter variations.Comment: Review, accepted for publication as Colloquium in Reviews of Modern
Physic
High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective
We derive a systematic high-frequency expansion for the effective Hamiltonian
and the micromotion operator of periodically driven quantum systems. Our
approach is based on the block diagonalization of the quasienergy operator in
the extended Floquet Hilbert space by means of degenerate perturbation theory.
The final results are equivalent to those obtained within a different approach
[Phys.\ Rev.\ A {\bf 68}, 013820 (2003), Phys.\ Rev.\ X {\bf 4}, 031027 (2014)]
and can also be related to the Floquet-Magnus expansion [J.\ Phys.\ A {\bf 34},
3379 (2000)]. We discuss that the dependence on the driving phase, which
plagues the latter, can lead to artifactual symmetry breaking. The
high-frequency approach is illustrated using the example of a periodically
driven Hubbard model. Moreover, we discuss the nature of the approximation and
its limitations for systems of many interacting particles.Comment: 48 pages, 7 figure
Interband heating processes in a periodically driven optical lattice
We investigate multi-"photon" interband excitation processes in an optical
lattice that is driven periodically in time by a modulation of the lattice
depth. Assuming the system to be prepared in the lowest band, we compute the
excitation spectrum numerically. Moreover, we estimate the effective coupling
parameters for resonant interband excitation processes analytically, employing
degenerate perturbation theory in Floquet space. We find that below a threshold
driving strength, interband excitations are suppressed exponentially with
respect to the inverse driving frequency. For sufficiently low frequencies,
this leads to a rather sudden onset of interband heating, once the driving
strength reaches the threshold. We argue that this behavior is rather generic
and should also be found in lattice systems that are driven by other forms of
periodic forcing. Our results are relevant for Floquet engineering, where a
lattice system is driven periodically in time in order to endow it with novel
properties like the emergence of a strong artificial magnetic field or a
topological band structure. In this context, interband excitation processes
correspond to detrimental heating.Comment: 11 pages, 4 figure
Orbital-driven melting of a bosonic Mott insulator in a shaken optical lattice
In order to study the interplay between localized and dispersive orbital
states in a system of ultracold atoms in an optical lattice, we investigate the
possibility to coherently couple the lowest two Bloch bands by means of
resonant periodic forcing. Considering bosons in one dimension, it is shown
that a strongly interacting Floquet system can be realized, where at every
lattice site two (and only two) near-degenerate orbital states are relevant. By
smoothly tuning both states into resonance we find that the system can undergo
an orbital-driven Mott-insulator-to-superfluid transition. As an intriguing
consequence of the kinetic frustration in the system, this transition can be
either continuous or first-order, depending on parameters such as lattice depth
and filling.Comment: 7 pages, 3 figure
Quantum crystal growing: Adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity
We theoretically study the adiabatic preparation of an antiferromagnetic
phase in a mixed Mott insulator of two bosonic atom species in a
one-dimensional optical lattice. In such a system one can engineer a tunable
parabolic inhomogeneity by controlling the difference of the trapping
potentials felt by the two species. Using numerical simulations we predict that
a finite parabolic potential can assist the adiabatic preparation of the
antiferromagnet. The optimal strength of the parabolic inhomogeneity depends
sensitively on the number imbalance between the two species. We also find that
during the preparation finite size effects will play a crucial role for a
system of realistic size. The experiment that we propose can be realized, for
example, using atomic mixtures of Rubidium 87 with Potassium 41 or Ytterbium
168 with Ytterbium 174.Comment: 25 pages, 6 figure
Avoided level crossing spectroscopy with dressed matter waves
We devise a method for probing resonances of macroscopic matter waves in
shaken optical lattices by monitoring their response to slow parameter changes,
and show that such resonances can be disabled by particular choices of the
driving amplitude. The theoretical analysis of this scheme reveals far-reaching
analogies between dressed atoms and time-periodically forced matter waves.Comment: 4 pages, 3 figure
The optimal frequency window for Floquet engineering in optical lattices
The concept of Floquet engineering is to subject a quantum system to
time-periodic driving in such a way that it acquires interesting novel
properties. It has been employed, for instance, for the realization of
artificial magnetic fluxes in optical lattices and, typically, it is based on
two approximations. First, the driving frequency is assumed to be low enough to
suppress resonant excitations to high-lying states above some energy gap
separating a low energy subspace from excited states. Second, the driving
frequency is still assumed to be large compared to the energy scales of the
low-energy subspace, so that also resonant excitations within this space are
negligible. Eventually, however, deviations from both approximations will lead
to unwanted heating on a time scale . Using the example of a
one-dimensional system of repulsively interacting bosons in a shaken optical
lattice, we investigate the optimal frequency (window) that maximizes .
As a main result, we find that, when increasing the lattice depth,
increases faster than the experimentally relevant time scale given by the
tunneling time , so that Floquet heating becomes suppressed.Comment: 11 pages, 8 figure
Bath-induced decay of Stark many-body localization
We investigate the relaxation dynamics of an interacting Stark-localized
system coupled to a dephasing bath, and compare its behavior to the
conventional disorder-induced many body localized system. Specifically, we
study the dynamics of population imbalance between even and odd sites, and the
growth of the von Neumann entropy. For a large potential gradient, the
imbalance is found to decay on a time scale that grows quadratically with the
Wannier-Stark tilt. For the non-interacting system, it shows an exponential
decay, which becomes a stretched exponential decay in the presence of finite
interactions. This is different from a system with disorder-induced
localization, where the imbalance exhibits a stretched exponential decay also
for vanishing interactions. As another clear qualitative difference, we do not
find a logarithmically slow growth of the von-Neumann entropy as it is found
for the disordered system. Our findings can immediately be tested
experimentally with ultracold atoms in optical lattices
Tomography of band insulators from quench dynamics
We propose a simple scheme for tomography of band-insulating states in one-
and two-dimensional optical lattices with two sublattice states. In particular,
the scheme maps out the Berry curvature in the entire Brillouin zone and
extracts topological invariants such as the Chern number. The measurement
relies on observing---via time-of-flight imaging---the time evolution of the
momentum distribution following a sudden quench in the band structure. We
consider two examples of experimental relevance: the Harper model with
-flux and the Haldane model on a honeycomb lattice. Moreover, we
illustrate the performance of the scheme in the presence of a parabolic trap,
noise, and finite measurement resolution.Comment: v2: 5+5 pages, 3+5 figures; added analytical and numerical results
for the presence of a harmonic confinement. v3: Minor changes; as accepted in
PR
A unified theory for excited-state, fragmented, and equilibrium-like Bose condensation in pumped photonic many-body systems
We derive a theory for Bose condensation in nonequilibrium steady states of
bosonic quantum gases that are coupled both to a thermal heat bath and to a
pumped reservoir (or gain medium), while suffering from loss. Such a scenario
describes photonic many-body systems such as exciton-polariton gases. Our
analysis is based on a set of kinetic equations for a gas of noninteracting
bosons. By identifying a dimensionless scaling parameter controlling the boson
density, we derive a sharp criterion for which system states become selected to
host a macroscopic occupation. We show that with increasing pump power, the
system generically undergoes a sequence of nonequilibrum phase transitions. At
each transition a state either becomes or ceases to be Bose selected (i.e. to
host a condensate): The state which first acquires a condensate when the
pumping exceeds a threshold is the one with the largest ratio of pumping to
loss. This intuitive behavior resembles simple lasing. In the limit of strong
pumping, the coupling to the heat bath becomes dominant so that eventually the
ground state is selected, corresponding to equilibrium(-like) Bose
condensation. For intermediate pumping strengths, several states become
selected giving rise to fragmented nonequilibrium Bose condensation. We compare
these predictions to experimental results obtained for excitons polaritons in a
double-pillar structure [Phys. Rev. Lett. 108, 126403 (2012)] and find good
agreement. Our theory, moreover, predicts that the reservoir occupation is
clamped at a constant value whenever the system hosts an odd number of Bose
condensates
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