PhD offers
The Université de Lille Nord Europe Foundation is funding the following project.
Starting date: before
November 2019 (a research internship during spring 2019 is possible
and encouraged)
Time crystals in the interacting quantum kicked rotor
The
interplay between interactions and disorder is one of the most
challenging problems in physics. On
the one hand, strongly correlated materials cannot be described by
condensed matter paradigmatic models – such as Bogoliubov theory
of superfluid bosons – especially in low dimensions, due to quantum
and thermal fluctuations. On the other hand, disorder, either
inherent in solids or engineered in cold atomic setups, has a strong
effect on the transport and localization properties of quantum
systems. For non-interacting quantum particles, it can induce
Anderson localization, depending on both the energy of the particle
and on the dimension of the system.
Naively,
one would expect that repulsive interactions in presence of disorder
would tend to delocalize the system. However, it has been
demonstrated recently, both on the theoretical and experimental
level, that interactions in addition to disorder give rise to a new
phase of matter, the so-called many-body localized phase, in which
the whole many-body system can be localized, and cannot thermalize if
isolated from a thermal bath.
While
disorder takes place in space, it is also possible to perturb the
system in time. By itself, the dynamics of a quantum interacting
system represents a complicated problem, which gets even more subtle
in presence of disorder. In much the same way as an ensemble of
particles can spontaneously order to form a crystal, and thus breaks
translation invariance, the idea of a time-crystal, which breaks
spontaneously time-translation invariance, has been introduced
recently. Assuming that the system is perturbed periodically with a
period T, a Floquet time-crystal is a system that responds at a
different period (say 2T). The basic ingredients for a time-crystal
are not yet clear, while it seems that long-range interactions and
disorder can help to stabilize this out-of-equilibrium phase. The
recent experimental realizations of both many-body localized systems
and time-crystals have opened an exciting horizon which challenges
our understanding of quantum statistical physics.
A
promising system for the observation of time-crystals and many-body
localization is the interacting quantum kicked rotor, which is a
model of interacting bosons driven periodically, with properties
similar to disordered systems. A cold atom experiment is currently
being built in the laboratory by the Cold Atoms Team to study this
system.
A
better theoretical understanding of this model, and the possible
phases (delocalized/many-body
localized/time-crystal)
is therefore necessary, which is the purpose of the PhD. This
will be done by studying various models, and combining both
analytical and numerical methods.
Please contact me for more information.
Internship offers
Various internship projects on condensed matter theory / cold-atom theory are possible. Please feel free to send me an email.