This workshop,
organised by
D.J. Papoular,
A. Honecker,
and Ph. Lecheminant
from
LPTM,
will take place
at
Université de Cergy-Pontoise, site Saint-Martin
(amphithéâtre E1)
from Monday, June 20th, to Friday, June 24th, 2016.
I will present recent experimental results giving a direct
evidence of superfluidity in a quasi two-dimensional Bose gas
by observing the scissors collective excitation. We are able to
identify the superfluid and thermal phases inside the gas and
locate the boundary at which the BKT crossover occurs, through
a novel local correlation analysis relying purely on dynamical
criteria.
It has recently been shown that in a miscible two component
Bose-Einstein condensate close to the Manakov limit, the
polarization dynamics decouple from density excitations, even
at the nonlinear level.We theoretically investigate this
situation, demonstrate the existence of new "trigonometric
solitons", and study the dynamics of dispersive shock waves in
this system.
Classical-field or c-field calculations are a mainstay of
simulations of the dynamics and stationary properties of
quantum
Bose gases at nonzero temperature. They do however omit any
quantum fluctuations and are also rather notorious for giving
results whose details depend on the ultraviolet cutoff. I
will report on two advances we have made which significantly
rectify
these shortcomings.
Firstly, an extended version of the stochastic GPE (SGPE) has
been derived, that preserves quantum fluctuations. Thus, a
very
tractable, nonlinear description of the system has been
obtained in terms of complex-valued fields, that also
includes quantum
fluctuations, depletion, shot noise, antibunching, and
similar effects. In contrast to the known ad-hoc approach of
adding
virtual vacuum noise into the initial conditions, this method
preserves quantum fluctuations even into the long-time
stationary state.
Secondly, we have precisely determined the regime of the 1d
interacting Bose gas for which a classical wave (c-field)
description correctly describes the physics, using a robust
measure of error. It imposes less than 10% discrepancy
simultaneously in the commonly measured observables and
energies. We have found that the classical wave region
extends
significantly beyond the usual quasicondensate, as well as
into quite strongly interacting gases for higher
temperatures.
In our experiment, chromium atoms are loaded in each site of a
3D optical lattice. We study spin dynamics due to long-range
dipole-dipole interactions. This dynamics is inherently
many-body, as each atom is coupled to its many neighbors. We
specifically study in which conditions the spin dynamics can be
seen as classical, and in which conditions quantum correlations
arise.
We present a general method for the high-temperature expansion
of the self-energy of interacting particles. Though the method is
valid for fermions and bosons, we illustrate it for spin one half
fermions interacting via a zero range potential, in the Bose Einstein
Condensate - Bardeen Cooper Schrieffer (BEC-BCS) crossover. The small
parameter of the expansion is the fugacity \(z\). Our results include terms of
order \(z\) and \(z^2\), which take into account respectively of two
and three body correlations. We give results for the high temperature
expansion of Tan's contact at order \(z^3\) in the whole BEC-BCS crossover. We
apply our method to calculate the spectral function at the
unitary limit. We find new structures which were overlooked by previous
approaches, which included only two body correlations.
This shows that including three-body
correlations can play an important role in the structures of the spectral
function. Work done in collaboration with Mingyuan SUN.
We discuss the superfluid properties of a Bose-Einstein condensed gas with
spin-orbit coupling, recently realized in experiments. We find
a finite normal fluid density at zero temperature which turns
out to be a function of the Raman coupling. In particular, the
entire fluid becomes normal at the transition point from the
zero momentum to the plane wave phase, even though the
condensate fraction remains finite. We emphasize the crucial
role played by the breaking of Galilean invariance and by the
gapped branch of the elementary excitations whose contribution
to various sum rules is explicitly discussed. Our predictions
for the superfluid density are compared with the available
experimental results based on the measurement of the sound
velocity. The consequences of spin-orbit coupling on the
rotational properties (moment of inertia, quantization of
circulation) of a trapped gas are also discussed.
Yi-Cai Zhang, Zeng-Qiang Yu, Tai Kai Ng, Shizhong Zhang, Lev
Pitaevskii, Sandro Stringari,
arXiv:1605.02136
The subtle interplay between kinetic energy, interactions, and
dimensionality challenges our comprehension
of strongly correlated physics observed, for example, in the
solid state. In this quest, the Hubbard
model has emerged as a conceptually simple, yet rich model
describing such physics. Here we present an
experimental determination of the equation of state of the
repulsive two-dimensional Hubbard model over a
broad range of interactions \( 0 \lesssim U=t \lesssim 20 \)
and temperatures, down
to \(k_BT/t= 0.63\) using high-resolution
imaging of ultracold fermionic atoms in optical lattices. We
show density profiles, compressibilities,
and double occupancies over the whole doping range, and, hence,
our results constitute
benchmarks for state-of-the-art theoretical approaches.
Topology plays a crucial role in understanding quantum transport
as demonstrated in the context of quantum Hall physics. For 2D
electron gas subject to a transverse magnetic field the
conductance is quantized and given by topological numbers known
as Chern numbers. Quasiperiodic systems are also instrumental in
the context of quantum transport, for instance to study
localization of waves. In this talk I will present a simple
experiment in which we measured the diffraction pattern of a
quasiperiodic grating following the Fibonacci sequence. I will
show that we can directly measure Chern numbers up to very large
values (more than a hundred) and will provide an explanation of
these topological properties.
Entanglement plays a central role in our understanding of quantum
many body physics, and is fundamental in characterising quantum
phases and quantum phase transitions. Developing protocols to
detect and quantify entanglement of many-particle quantum states
is thus a key challenge for present experiments. Here, we show
that the quantum Fisher information, representing a witness for
genuinely multipartite entanglement, becomes measurable for
thermal ensembles via the dynamic susceptibility, i.e., with
resources readily available in present cold atomic gas and
condensed-matter experiments. This moreover establishes a
fundamental connection between multipartite entanglement and
many-body correlations contained in response functions, with
profound implications close to quantum phase transitions. There,
the quantum Fisher information becomes universal, allowing us to
identify strongly entangled phase transitions with a divergent
multipartiteness of entanglement. We illustrate our framework
using paradigmatic quantum Ising models, and point out potential
signatures in optical-lattice experiments.
We consider the unitary Fermi gas (spin 1/2 fermions with
contact interactions in three-dimensional continuous space, a
model which accurately describes cold atomic gases at a
Feshbach resonance and is also relevant to neutron matter) in
the normal phase. Thanks to a diagrammatic Monte Carlo
algorithm, we accurately sample all skeleton diagrams (built on
dressed single-particle and pair propagators) up to order ~8
[1]. The diagrammatic series is divergent and there is no small
parameter so that a resummation method is needed. Previously we
used Abelian resummation methods, which are applicable under
the assumption that the diagrammatic series has a non-zero
radius of convergence; this led to good agreement with cold
atom experimental data for the equation of state [2] and Tan's
contact coefficient [3]. Here we report the large-order
asymptotics of the diagrammatic series, based on a functional
integral representation of the skeleton series [4] and the
saddle-point method. We find that the radius of convergence is
actually zero, and our preliminary numerical results and
analytical arguments suggest that the series is resummable by
an ad hoc generalised conformal-Borel transformation that
incorporates the large-order asymptotics.
[1] K. Van Houcke, F. Werner, N. Prokof'ev, B. Svistunov, "Bold
diagrammatic Monte Carlo for the resonant Fermi gas",
arXiv:1305.3901
[2] K. Van Houcke, F. Werner, E. Kozik, N. Prokof'ev,
B. Svistunov, M. Ku, A. Sommer, L. Cheuk, A. Schirotzek,
M. Zwierlein, "Feynman diagrams versus Fermi-gas Feynman
emulator", Nature Phys. 8, 366 (2012)
[3] K. Van Houcke, F. Werner, E. Kozik, N. Prokof'ev,
B. Svistunov, "Contact and Momentum Distribution of the Unitary
Fermi Gas by Bold Diagrammatic Monte Carlo", arXiv:1303.6245
[4] R. Rossi, F. Werner, N. Prokof'ev, B. Svistunov,
"Shifted-Action Expansion and Applicability of Dressed
Diagrammatic Schemes", Phys. Rev. B 93, 161102 (R) (2016)
Spin-orbit-coupled quantum gases exhibit a rich phase diagram,
with the appearance of novel quantum phases having intriguing
static and dynamic features. In my talk I shall discuss the
effect of a periodic potential generated by a one-dimensional
optical lattice on the magnetic properties of a \(S=1/2\)
spin-orbit-coupled Bose gas. In particular, the occurrence of a
magnetic phase transition between a polarized and an
unpolarized Bloch wave phase, characterized by a significant
enhancement of the contrast of the density fringes, will be
pointed out. If the lattice wave vector is chosen close to the
roton momentum, the transition could take place at very small
lattice intensities, revealing the strong enhancement of the
response of the system to a weak density perturbation. Finally,
I will show the results obtained by solving the
Gross-Pitaevskii equation in the presence of a
three-dimensional trapping potential, which sheds light on the
possibility of observing the phase transition in currently
available experimental conditions.
Weyl massless particles are one of the cornerstones of high
energy physics and were recently observed as low energy
excitation in condensed matter systems. Their linear dispersion
relation and their peculiar topological properties lead to
dramatic phenomena, such as the Klein paradox, allowing them to
tunnel through potential barriers. We show that their dynamics
in a harmonic trap can be mimicked and studied with
non-interacting atoms in a quadrupole trap. Unlike classical
massive particles, an ensemble of Weyl particles dragged away
from the trap center does not abide by Kohn's theorem but
rather relaxes towards a non-Boltzmann steady state with
anisotropic effective temperatures, that we characterize
experimentally, numerically and analytically. This seemingly
simple problem holds several non-intuitive features,
illustrating the wealth of Hamiltonian dynamics.
It is generally assumed that a condensate of paired fermions at
equilibrium is characterized by a macroscopic wavefunction with a
well-defined, immutable phase. In reality, all systems have a
finite size and are prepared at non-zero temperature; the
condensate has then a finite coherence time, even when the system
is isolated. This fundamental effect, crucial for applications
using macroscopic coherence, was scarcely studied. Here, we link
the coherence time to the condensate phase dynamics, and show
using a microscopic theory that the time derivative of the
condensate phase operator \(\hat{\theta}_0\) is proportional to a
chemical potential operator which includes both the fermionic
pair-breaking and the bosonic pair-motion excitation
branches. For a given realization of the number of particle \(N\)
and of the energy \(E\), the phase evolves at long times as
\(-2\mu_{mc}(E,N) t/\hbar\) where \(\mu_{mc}(E,N)\) is the
microcanonical chemical potential; fluctuations of \(N\) and \(E\)
from one realization to the other then lead to a ballistic
spreading of the phase and to a Gaussian decay of the temporal
coherence function with a characteristic time \(\propto N^{1/2}\).
On the contrary, in the absence of energy and number
fluctuations, the decay of the temporal coherence function is
exponential with a characteristic time scaling as \(N\) due to the
diffusive motion of \(\hat{\theta}_0\) in the environnement created
by the excited modes. We give an explict expression of this
characteristic time at low temperature in the case where the
bosonic branch is convex and the phonons undergo
\(2 \leftrightarrow 1\) Beliaev-Landau process.
Finally, we propose methods to measure each contribution to the
coherence time using ultracold atoms.
Synthetic ladders realized with one-dimensional
alkaline-earth(-like) fermionic gases and subject to a gauge
field represent a promising environment for the investigation
of quantum Hall physics with ultracold atoms. We unveil the
existence of a hierarchy of fractional insulating and
conducting states by means of both analytical bosonization
techniques and numerical methods based on the density-matrix
renormalization group algorithm. We show that such states can
be exploited for constructing a topological Thouless pump where
the charge transported after one cycle is quantized to
fractional values and demonstrate this behavior with a full
many-body time-dependent calculation.
1 - S. Barbarino, L. Taddia, D. Rossini, L. Mazza, R. Fazio,
Nat. Commun. 6, 8134 (2015)
2 - S. Barbarino, L. Taddia, D. Rossini, L. Mazza, R. Fazio,
New J. Phys. 18, 035010 (2016)
3 - L. Taddia, E. Cornfeld, D. Rossini, L. Mazza, E. Sela,
R. Fazio, in preparation
We investigate the superfluid-insulator transition of
one-dimensional interacting bosons in
both deep and shallow periodic potentials. We compare a
theoretical analysis based on
quantum Monte Carlo simulations in continuum space and
Luttinger liquid approach with
experiments on ultracold atoms with tunable interactions and
optical lattice depth.
Experiments and theory are in excellent agreement. Our study
provides a quantitative
determination of the critical parameters for the Mott
transition and defines the regimes of
validity of widely used approximate models, namely, the
Bose-Hubbard and sine-Gordon
models.
G. Boéris, L. Gori, M.D. Hoogerland, A. Kumar, E. Lucioni,
L. Tanzi, M. Inguscio, T. Giamarchi, C.
D'Errico, G. Carleo, G. Modugno, and L. Sanchez-Palencia,
Phys. Rev. A 93, 011601(R) (2016).
We address the possibility to realize exotic chiral phases of
bosons through artificial gauge fields. We first discuss the
honeycomb lattice and ladder systems where synthetic gauge
fields allow to realize Haldane and Quantum Hall models. The
response to the synthetic gauge fields can produce exotic
Meissner currents and novel bosonic superfluids which are
analogues of FFLO superconducting states, where bosons condense
at a non-zero wave-vector. We show how to realize such phases
of matter for periodically driven lattices and Floquet theory.
Ladder systems also allow to engineer a plethora of emergent
phases for bosons, through artificial gauge fields : Meissner
phases, spin-Meissner phases, Vortex Phases for example. We
also report the emergence of a bosonic Quantum Hall phase in
2-leg ladder systems. The phases and observables are found
analytically and also confirmed numerically.
Already at the mean field level, Bose mixtures display rich
physics. With repulsive interaction between all constituents, a
miscible-immiscible phase transition is observed. With
attractive interspecies interactions a collapse can
occur. However, liquid-like droplets have recently been
observed in dipolar gases [1] where the collapse is avoided by
quantum fluctuations. It has also been predicted that a
stabilization mechanism should occur and lead to the formation
of liquid droplets in a Bose-Bose mixture with repulsive
intraspecies and attractive interspecies interactions
[2]. These droplets would be remarkable as their very own
existence originates from quantum fluctuations which are
usually a small correction to the mean field description.
I will present a new experimental setup that produces Bose-Bose
mixtures of potassium isotopes with favorable Feshbach
resonances to address these questions. Our apparatus allows
producing large Bose-Einstein condensates (BEC) of 41K by
evaporative cooling in a hybrid trap and dual BECs of 39K and
41K by sympathetic cooling. I will present our characterization
of the Feshbach resonances in the new 39K-41K mixture and of
interspin resonances in 39K using RF association of Feshbach
molecules close to the resonance. These results
are compared with a simple asymptotic bound-state model and a
full coupled channels calculation and are a prerequisite for
the study of the miscible-immiscible phase transition and of
the Bose-Bose liquid droplets.
[1] I. Ferrier-Barbut, H. Kadau, M. Schmitt, M. Wenzel, and
T. Pfau, PRL 116, 215301 (2016)
[2] D. S. Petrov, PRL 115, 155302 (2015)
The absence of energy dissipation leads to an intriguing
out-of-equilibrium dynamics for ultracold polar gases in optical
lattices, characterized by the formation of dynamically-bound
on-site and inter-site clusters of two or more particles, and by
an effective blockade repulsion. These effects combined with the
controlled preparation of initial states available in cold gases
experiments can be employed to create interesting
out-of-equilibrium states. These include quasi-equilibrated
effectively repulsive 1D gases for attractive dipolar
interactions and dynamically-bound crystals. Furthermore,
non-equilibrium polar lattice gases can offer a promising
scenario for the study of many-body localization in the absence
of quenched disorder. This fascinating out-of-equilibrium
dynamics for ultra-cold polar gases in optical lattices may be
accessible in on-going experiments.