19 research outputs found
Condensation Energy of a Spin-1/2 Strongly Interacting Fermi Gas
We report a measurement of the condensation energy of a two-component Fermi
gas with tunable interactions. From the equation of state of the gas, we infer
the properties of the normal phase in the zero-temperature limit. By comparing
the pressure of the normal phase at T=0 to that of the low-temperature
superfluid phase, we deduce the condensation energy, i.e. the energy gain of
the system in being in the superfluid rather than normal state. We compare our
measurements to a ladder approximation description of the normal phase, and to
a fixed node Monte-Carlo approach, finding excellent agreement. We discuss the
relationship between condensation energy and pairing gap in the BEC-BCS
crossover.Comment: 4 figure
Experimental realization of strong effective magnetic fields in an optical lattice
We use Raman-assisted tunneling in an optical superlattice to generate large
tunable effective magnetic fields for ultracold atoms. When hopping in the
lattice, the accumulated phase shift by an atom is equivalent to the
Aharonov-Bohm phase of a charged particle exposed to a staggered magnetic field
of large magnitude, on the order of one flux quantum per plaquette. We study
the ground state of this system and observe that the frustration induced by the
magnetic field can lead to a degenerate ground state for non-interacting
particles. We provide a measurement of the local phase acquired from
Raman-induced tunneling, demonstrating time-reversal symmetry breaking of the
underlying Hamiltonian. Furthermore, the quantum cyclotron orbit of single
atoms in the lattice exposed to the magnetic field is directly revealed.Comment: 6 pages, 5 figure
Fit-free determination of scale invariant equations of state: application to the 2D Bose gas across the Berezinksii-Kosterlitz-Thouless transition
We present a general "fit-free" method for measuring the equation of state
(EoS) of a scale-invariant gas. This method, which is inspired from the
procedure introduced by Ku et al. [Science 335, 563 (2012)] for the unitary
three-dimensional Fermi gas, provides a general formalism which can be readily
applied to any quantum gas in a known trapping potential, in the frame of the
local density approximation. We implement this method on a weakly-interacting
two-dimensional Bose gas in the vicinity of the Berezinskii-Kosterlitz-Thouless
transition, and determine its EoS with unprecedented accuracy in the critical
region. Our measurements provide an important experimental benchmark for
classical field approaches which are believed to accurately describe quantum
systems in the weakly interacting but non-perturbative regime.Comment: 5 pages, 5 figure
Emergence of coherence in a uniform quasi-two-dimensional Bose gas
Phase transitions are ubiquitous in our three-dimensional world. By contrast
most conventional transitions do not occur in infinite uniform two-dimensional
systems because of the increased role of thermal fluctuations. Here we explore
the dimensional crossover of Bose-Einstein condensation (BEC) for a weakly
interacting atomic gas confined in a novel quasi-two-dimensional geometry, with
a flat in-plane trap bottom. We detect the onset of an extended phase
coherence, using velocity distribution measurements and matter-wave
interferometry. We relate this coherence to the transverse condensation
phenomenon, in which a significant fraction of atoms accumulate in the ground
state of the motion perpendicular to the atom plane. We also investigate the
dynamical aspects of the transition through the detection of topological
defects that are nucleated in a quench cooling of the gas, and we compare our
results to the predictions of the Kibble-Zurek theory for the conventional BEC
second-order phase transition.Comment: main text = 24 pages, 6 figures + supplementary material = 10 pages,
5 figure
Controlling Correlated Tunneling and Superexchange Interactions with AC-Driven Optical Lattices
The dynamical control of tunneling processes of single particles plays a
major role in science ranging from Shapiro steps in Josephson junctions to the
control of chemical reactions via light in molecules. Here we show how such
control can be extended to the regime of strongly interacting particles.
Through a weak modulation of a biased tunnel contact, we have been able to
coherently control single particle and correlated two-particle hopping
processes. We have furthermore been able to extend this control to
superexchange spin interactions in the presence of a magnetic-field gradient.
We show how such photon assisted superexchange processes constitute a novel
approach to realize arbitrary XXZ spin models in ultracold quantum gases, where
transverse and Ising type spin couplings can be fully controlled in magnitude
and sign.Comment: 10 pages, 9 figure
Transmission of near-resonant light through a dense slab of cold atoms
The optical properties of randomly positioned, resonant scatterers is a
fundamentally difficult problem to address across a wide range of densities and
geometries. We investigate it experimentally using a dense cloud of rubidium
atoms probed with near-resonant light. The atoms are confined in a slab
geometry with a sub-wavelength thickness. We probe the optical response of the
cloud as its density and hence the strength of the light-induced dipole-dipole
interactions are increased. We also describe a theoretical study based on a
coupled dipole simulation which is further complemented by a perturbative
approach. This model reproduces qualitatively the experimental observation of a
saturation of the optical depth, a broadening of the transition and a blue
shift of the resonance
Thermodynamique des gaz de fermions ultrafroids
Complex Hamiltonians from condensed matter, such as the Fermi-Hubbard model, can be experimentally studied using ultracold gases. This thesis describes a new method for determining the equation of state of an ultracold gas, making the comparison with many-body theories straightforward. It is based on the measurement of the local pressure inside a trapped gas from the analysis of its in situ image. We first apply this method to the study of a Fermi gas with resonant interactions, a weakly-interacting 7Li gas acting as a thermometer. Surprisingly, none of the existing many-body theories of the unitary gas accounts for the equation of state deduced from our study over its full range. The virial expansion extracted from the high-temperature data agrees with the resolution of the three-body problem. At low temperature, we observe, contrary to some previous studies, that the normal phase behaves as a Fermi liquid. Finally we obtain the critical temperature for superfluidity from a clear signature on the equation of state. We also measure the pressure of the ground state as a function of spin imbalance and interaction strength -- measure directly relevant to describe the crust of neutron stars. Our data validate Monte-Carlo simulations and quantify the Lee-Huang-Yang corrections to mean-field interactions in low-density fermionic or bosonic superfluids. We show that, in most cases, the partially polarized normal phase can be described as a Fermi liquid of polarons. The polaron effective mass extracted from the equation of state is in agreement with a study of collective modes.Les gaz ultrafroids permettent d'étudier sous un angle nouveau des hamiltoniens complexes issus de la matière condensée, tels le modèle de Fermi-Hubbard. Cette thèse présente une nouvelle méthode de mesure de l'équation d'état d'un gaz ultrafroid, autorisant une comparaison directe avec la théorie. Elle repose sur une mesure de la pression à l'intérieur d'un gaz à partir de son image in situ. Nous appliquons cette méthode à l'étude d'un gaz de fermions en interaction résonnante, un gaz de 7Li en interaction faible servant de thermomètre. De manière surprenante, aucune des théories à N corps du gaz unitaire ne rend compte intégralement de l'équation déduite de cette analyse. Le développement du viriel extrait des données à haute température est en accord avec la résolution du problème à trois corps. A basse température nous montrons, contrairement à un certain nombre d'études antérieures, que la phase normale se comporte comme un liquide de Fermi. Enfin, nous obtenons la température critique de superfluidité grâce à une signature claire sur l'équation d'état. Nous avons aussi mesuré la pression de l'état fondamental en fonction du déséquilibre de spin et de la force des interactions - mesure directement utile à la description de la croûte des étoiles à neutrons. Nos données valident les simulations Monte-Carlo et sont en accord avec les corrections Lee-Huang-Yang au champ moyen pour un superfluide fermionique ou bosonique. Nous observons que, dans presque tous les cas, la phase partiellement polarisée peut être décrite comme un liquide de Fermi de polarons. La masse effective du polaron déduite de l'équation d'état est en accord avec une étude de modes collectifs
(a) Spectrum of Bogoliubov excitations (red dots) for a homogeneous system with sharp boundaries, calculated for <em>J<sub>z</sub></em> = δ and <em>J</em> = 2 Δ<sup>(2)</sup>
<p><strong>Figure 4.</strong> (a) Spectrum of Bogoliubov excitations (red dots) for a homogeneous system with sharp boundaries, calculated for <em>J<sub>z</sub></em> = δ and <em>J</em> = 2 Δ<sup>(2)</sup>. It exhibits a bulk gap Δ<sub>bulk</sub> = 0.18 <em>E<sub>r</sub></em> and a pair of zero-energy Majorana states with a residual splitting Δ<sub><em>s</em></sub> ~ 10<sup>−12</sup> <em>E<sub>r</sub></em>. (b) Evolution of the bulk gap amplitude Δ<sub>bulk</sub> as a function of the ratio <em>J<sub>z</sub></em>/δ (red line), for <em>J</em> = Δ<sup>(2)</sup>, with Δ<sup>(2)</sup> given by equation (<a href="http://iopscience.iop.org/0953-4075/46/13/134005/article#jpb448206eqn20" target="_blank">20</a>). The black line represents the prediction of second-order perturbation theory Δ<sub>bulk</sub> = 2 Δ<sup>(2)</sup>. (c) Density distribution along <em>x</em> of a zero-energy Majorana state, in planes <em>A</em> (red line) and <em>B</em> (blue line, offset for clarity). In the strong coupling regime <em>J</em> ~ δ, the population in <em>B</em> is not negligible. (d) Total density distribution along <em>x</em> calculated at zero temperature. Majorana states are not visible in this almost uniform density profile.</p> <p><strong>Abstract</strong></p> <p>We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along the 1D tube and laser-induced atom tunnelling, we obtain a topological superfluid phase. In the regime of weak couplings to the molecular field and for a uniform gas, the atomic system is equivalent to Kitaev's model of a p-wave superfluid. Using a numerical calculation, we show that the topological superfluidity is robust beyond the perturbative limit and in the presence of a harmonic trap. Finally, we describe how to investigate some physical properties of the Majorana fermions located at the topological superfluid boundaries. In particular, we discuss how to prepare and detect a given Majorana edge state.</p
(a) Spectrum of Bogoliubov excitations (red dots) calculated for <em>J<sub>z</sub></em> = 0.2 δ and <em>J</em> = Δ<sup>(2)</sup>, and compared with the prediction of Kitaev's model with <em>J</em> = Δ = Δ<sup>(2)</sup> (black dots)
<p><strong>Figure 3.</strong> (a) Spectrum of Bogoliubov excitations (red dots) calculated for <em>J<sub>z</sub></em> = 0.2 δ and <em>J</em> = Δ<sup>(2)</sup>, and compared with the prediction of Kitaev's model with <em>J</em> = Δ = Δ<sup>(2)</sup> (black dots). (b) Density distribution along <em>x</em> of a zero-energy Majorana state, in planes <em>A</em> (red line) and <em>B</em> (blue line), revealing the non-local character of Majorana states. In the perturbative regime <em>J</em> δ, the population in <em>B</em> remains small.</p> <p><strong>Abstract</strong></p> <p>We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along the 1D tube and laser-induced atom tunnelling, we obtain a topological superfluid phase. In the regime of weak couplings to the molecular field and for a uniform gas, the atomic system is equivalent to Kitaev's model of a p-wave superfluid. Using a numerical calculation, we show that the topological superfluidity is robust beyond the perturbative limit and in the presence of a harmonic trap. Finally, we describe how to investigate some physical properties of the Majorana fermions located at the topological superfluid boundaries. In particular, we discuss how to prepare and detect a given Majorana edge state.</p