29 research outputs found
Anderson localization of a Rydberg electron along a classical orbit
Anderson localization is related to exponential localization of a particle in
the configuration space in the presence of a disorder potential. Anderson
localization can be also observed in the momentum space and corresponds to
quantum suppression of classical diffusion in systems that are classically
chaotic. Another kind of Anderson localization has been recently proposed, i.e.
localization in the time domain due to the presence of {\it disorder} in time.
That is, the probability density for the detection of a system at a fixed
position in the configuration space is localized exponentially around a certain
moment of time if a system is driven by a force that fluctuates in time. We
show that an electron in a Rydberg atom, perturbed by a fluctuating microwave
field, Anderson localizes along a classical periodic orbit. In other words the
probability density for the detection of an electron at a fixed position on an
orbit is exponentially localized around a certain time moment. This phenomenon
can be experimentally observed.Comment: version accepted for publication in Phys. Rev.
Time crystal platform: from quasi-crystal structures in time to systems with exotic interactions
Time crystals are quantum many-body systems which, due to interactions
between particles, are able to spontaneously self-organize their motion in a
periodic way in time by analogy with the formation of crystalline structures in
space in condensed matter physics. In solid state physics properties of space
crystals are often investigated with the help of external potentials that are
spatially periodic and reflect various crystalline structures. A similar
approach can be applied for time crystals, as periodically driven systems
constitute counterparts of spatially periodic systems, but in the time domain.
Here we show that condensed matter problems ranging from single particles in
potentials of quasi-crystal structure to many-body systems with exotic
long-range interactions can be realized in the time domain with an appropriate
periodic driving. Moreover, it is possible to create molecules where atoms are
bound together due to destructive interference if the atomic scattering length
is modulated in time.Comment: misprints correcte
Many-body localization caused by temporal disorder
The many-body localization (MBL) is commonly related to a strong spatial
disorder. We show that MBL may alternatively be generated by adding a temporal
disorder to periodically driven many-body systems. We reach this conclusion by
mapping the evolution of such systems on the dynamics of the time-independent,
disordered, Hubbard-like models. Our result opens the way to experimental
studies of MBL in systems that reveal crystalline structures in the time
domain. In particular, we discuss two relevant setups which can be implemented
in experiments on ultra-cold atomic gases.Comment: 6 pages, 2 figures, version accepted for publication in Phys. Rev. B
as a Rapid Communicatio
Time crystals: analysis of experimental conditions
Time crystals are quantum many-body systems which are able to self-organize
their motion in a periodic way in time. Discrete time crystals have been
experimentally demonstrated in spin systems. However, the first idea of
spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms
bouncing on an oscillating mirror, still awaits experimental demonstration.
Here, we perform a detailed analysis of the experimental conditions needed for
the realization of such a discrete time crystal. Importantly, the considered
system allows for the realization of dramatic breaking of discrete time
translation symmetry where a symmetry broken state evolves with a period tens
of times longer than the driving period. Moreover, atoms bouncing on an
oscillating mirror constitute a suitable system for the realization of
dynamical quantum phase transitions in discrete time crystals and for the
demonstration of various non-trivial condensed matter phenomena in the time
domain. We show that Anderson localization effects, which are typically
associated with spatial disorder and exponential localization of eigenstates of
a particle in configuration space, can be observed in the time domain when
ultra-cold atoms are bouncing on a randomly moving mirror.Comment: 15 pages, 7 figures, version accepted for publication in Phys. Rev.
Anderson Molecules
Atoms can form molecules if they attract each other. Here, we show that atoms
are also able to form bound states not due to the attractive interaction but
because of destructive interference. If the interaction potential changes in a
disordered way with a change of the distance between two atoms, Anderson
localization can lead to the formation of exponentially localized bound states.
While disordered interaction potentials do not exist in nature, we show that
they can be created by means of random modulation in time of the strength of
the original interaction potential between atoms and objects that we dub
Anderson molecules can be realized in the laboratory.Comment: 13 pages, 5 figures, references added and minor correction
Discrete Time Quasi-Crystals
Between space crystals and amorphous materials there exists a third class of
aperiodic structures which lack translational symmetry but reveal long-range
order. They are dubbed quasi-crystals and their formation, similarly as the
formation of space crystals, is related to spontaneous breaking of
translational symmetry of underlying Hamiltonians. Here, we investigate
spontaneous emergence of quasi-crystals in periodically driven systems. We
consider a quantum many-body system which is driven by a harmonically
oscillating force and show that interactions between particles result in
spontaneous self-reorganization of the motion of a quantum many-body system and
in the formation of a quasi-crystal structure in time.Comment: Version accepted for publication in Phys. Rev. B as a Rapid
Communicatio
Discrete Time Crystals with Absolute Stability
We show that interacting bosons on a ring which are driven periodically by a
rotating potential can support discrete time crystals whose absolute stability
can be proven. The absolute stability is demonstrated by an exact mapping of
discrete time crystal states to low-lying eigenstates of a time-independent
model that reveals spontaneous breaking of space translation symmetry. The
mapping ensures that there are no residual time-dependent terms that could lead
to heating of the system and destruction of discrete time crystals. We also
analyze periodically kicked bosons where the mapping is approximate only and
cannot guarantee the absolute stability of discrete time crystals. Besides
illustrating potential sources of instability, the kicked bosons model
demonstrates a rich field for investigating the interplay between different
time and space symmetry breaking, as well as the stability of time crystal
behavior in contact with a thermal reservoir.Comment: Version accepted for publication in Physical Review B as a Lette
Bose-Hubbard realization of fracton defects
Bose-Hubbard models are simple paradigmatic lattice models used to study
dynamics and phases of quantum bosonic matter. We combine the extended
Bose-Hubbard model in the hard-core regime with ring-exchange hoppings. By
investigating the symmetries and low-energy properties of the Hamiltonian we
argue that the model hosts fractonic defect excitations. We back up our claims
with exact numerical simulations of defect dynamics exhibiting mobility
constraints. Moreover, we confirm the robustness of our results against fracton
symmetry breaking perturbations. Finally we argue that this model can be
experimentally realized in recently proposed quantum simulator platforms with
big time crystals, thus paving a way for the controlled study of many-body
dynamics with mobility constraints.Comment: 12 pages, 7 figure
Topological time crystals
By analogy with the formation of space crystals, crystalline structures can also appear in the time domain. While in the case of space crystals we often ask about periodic arrangements of atoms in space at a moment of a detection, in time crystals the role of space and time is exchanged. That is, we fix a space point and ask if the probability density for detection of a system at this point behaves periodically in time. Here, we show that in periodically driven systems it is possible to realize topological insulators, which can be observed in time. The bulk-edge correspondence is related to the edge in time, where edge states localize. We focus on two examples: Su-Schrieffer-Heeger model in time and Bose Haldane insulator which emerges in the dynamics of a periodically driven many-body system