This thesis is concerned with different aspects of many-particle-physics in the context of ultracold quantum gases. The first part deals with the theoretical basis of radio-frequency-spectroscopy of ultracold Fermi gases near Feshbach-resonances. In particular, we calculate spectral functions and the corresponding rf-spectra of strongly interacting Fermi gases at unitarity. Furthermore, we study the polaron-to-molecule transition using variational methods. We calculate the critical value of the interaction strength and compare it to experimental results. The last part deals with non-equilibrium dynamics of Heisenberg-spin-chains, where the unitary time evolution of a Néel-state is analyzed. Quite generally, the antiferromagnetic order parameter relaxes exponentially and the corresponding relaxation time exhibits a minimum at the isotropic Heisenberg point.
This thesis is concerned with different aspects of many-particle-physics in the context of ultracold quantum gases. The first part deals with the theoretical basis of radio-frequency-spectroscopy of ultracold Fermi gases near Feshbach-resonances. In particular, we calculate spectral functions and the corresponding rf-spectra of strongly interacting Fermi gases at unitarity. Furthermore, we study the polaron-to-molecule transition using variational methods. We calculate the critical value of the interaction strength and compare it to experimental results. The last part deals with non-equilibrium dynamics of Heisenberg-spin-chains, where the unitary time evolution of a Néel-state is analyzed. Quite generally, the antiferromagnetic order parameter relaxes exponentially and the corresponding relaxation time exhibits a minimum at the isotropic Heisenberg point.
This thesis presents experiments investigating the
phase diagram of ultracold atomic Fermi gases using radio-frequency
spectroscopy. The tunability of many experimental parameters
including the temperature, the interparticle interaction strength
and the relative population of different Fermions allows to access
very different physical regimes. Radio-frequency spectroscopy has
been developed into an ideal tool to probe correlations between
particles in these different phases. In particular, radio-frequency
spectroscopy of highly population imbalanced atomic Fermi systems
gives access to the impurity problem: A single Fermion, or Boson,
immersed in a sea of Fermions constitutes a polaron, which can be
described by Landau's Fermi liquid theory. A critical interaction
strength can be identified separating the regime of a fermionic
polaron and a bosonic polaron. Radio-frequency spectroscopy of the
polarized superfluid phase allows an accurate measure of the
superfluid gap [Delta] and allows to identify the importance of
Hartree Mean-field energies. Furthermore, it is shown how these
different physical regimes are connected.
Ultracold atomic gases provide an ideal system with which to study fundamental many-body physics.Exhibiting universal interactions in clean and controllable environments, long-used simple models as well as more exotic models can now be realized.The interplay between theory and experiment is therefore very active, and, in this thesis, I will detail several works, both exact analytic results and numerical calculations, which have impacts on current experiments.I begin with an introduction to the field including a brief discussion of experiments, the microscopic model of two species of interacting fermions, the BCS-BEC crossover and an overview of the various phases of atomic Fermi gases.I then describe the various results of my theoretical investigations, which are divided into five chapters.First, I describe radio frequency (RF) spectroscopy experiments and how they probe the single-particle spectral function.This leads to my results on an exact feature of the spectral lineshape, a universal large-momentum structure which exists for all states of interacting Fermi systems and has been verified in recent angle-resolved RF experiments.Second, I focus on gases which have a normal Fermi liquid ground state and show that their lineshape exhibits a characteristic jump discontinuity.I illustrate this Fermi surface singularity and the previously mentioned universal large momentum tail with explicit calculations.Third, I turn to the low energy structure of the single-particle spectral function in the superfluid state.I argue that sharp low energy quasiparticle excitations exist across the BCS-BEC crossover using a general argument that includes the interaction of fermions with the low-energy collective mode.This is illustrated with an explicit calculation within an approximation scheme.Fourth, I address the trap-induced inhomogeneity and use a Bogoliubov-deGennes analysis to test if a simple local density approximation (LDA) can provide an adequate description of a spin imbalanced Fermi system.Finally, I discuss dynamics of atomic gases motivated by a recent experiment in which two spin-polarized clouds are allowed to collide with each other.Despite the underlying attractive interactions, the clouds are seen to bounce off of each other.Using a hydrodynamic description, I argue that the short and intermediate time dynamics reflects a metastable state in which the effective interaction is repulsive.It is my hope that the work presented in this thesis can be used to gain key insights which inspire future endeavors.6.2 Time dependence of the center-of-mass positions zσ of the two spin clouds at unitarity for an initial separation z↑ (t = 0) = R z , z↓ (t = 0) = -R z using the upper branch energy functional and damping γ = 1.Red (upper) and blue (lower) curves denote the different spin species. . . . . . . . . . . . . . . .71 6.3 The upper branch energy functional obtained from lowest order constraint variational method.(a), energy as a function of the polarization P for various values of k F a s as indicated in the figure.(b), energy as a function of the interaction parameter k F a s for various values of polarization P as indicated in the figure.(c), phase diagram of the interacting two-component Fermi gases.The two vertical red dashed lines indicates the separation between three phases.For 1/(k F a s ) > 1.124, the system is in the Fermi liquid (FL) phase.For 1.124 > 1/(k F a s ) > 0.91, the system is in the partially polarized phase (PP) and for 1/(k F a s ) < 0.91, the system is fully polarized. . . . . .74 6.4 (Color online) Time dependence of the center-of-mass positions zσ of the two spin clouds for k F (0)a s = 2. . . . . . . . . . . . . . . . . . . . . . . . . . .75 6.5 (Color online) Time dependence of the center-of-mass positions zσ of the two spin clouds for k F (0)a s = 0.5. . . . . . . . . . . . . . . . . . . . . . . . . .
This thesis studies radio-frequency spectroscopy of superfluid alkali Fermi gases. Radio-frequency and laser fields provide a coherent and well understood tool for manipulating atomic gases. However, new phenomena are expected and have already been seen experimentally when the alkali atoms become strongly interacting. Here we use a simple perturbative treatment of the atom-rf-field coupling for studying the spectroscopy of a strongly interacting gas. At ultracold temperatures fermionic atoms become paired in analogy to electrons in superconductors. The resulting binding energy, or the pairing gap, can be observed as a shift in the radio-frequency spectrum. With strong interactions, the fermions begin pairing already above the critical superfluid transition temperature. The radio-frequency spectroscopy grants a way to study these fluctuation effects quantitatively. The inhomogeneous trapping potential of the atom cloud also adds its own flavour, resulting in distinct mesoscopic effects in the radio-frequency spectra. Our theoretical models are in very good agreement with the experimental results. First order perturbation theory provides qualitatively correct lineshapes, and our generalised perturbative approach gives quantitatively correct magnitudes for the transfer rates. The inhomogeneity plays an important part also in more exotic systems in which the simple BCS-type pairing of atoms is prevented by polarising the gas. Superfluidity and phase separation in such spin-imbalanced gases has been experimentally observed. We have suggested the use of radio-frequency spectroscopy for observing exotic polarised superfluid states, present at the edges of the atom cloud.
The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-Tc superconductivity or the behaviour of neutron stars. Ultracold atomic systems can now be used to simulate model Hamiltonians of condensed matter or nuclear physics, in very well-controlled environnement. In this thesis, we have developed a general method to probe the thermodynamics of homogeneous quantum systems using trapped atomic gases. These measurements are directly compared to the predictions of theories of the quantum many-body problem. We have applied this technique to the spin-1/2 Fermi gas and the Bose with short-range interactions. Using fermionic 6Li, we explored a part of the wide parameter space by changing the interaction strength, the spin-population imbalance or the temperature of the gas. This system exhibits remarkably rich physics, such as normal/superfluid phase transitions (that can be of thermal or quantum character) or a Fermi liquid-type behaviour of the normal phase. We have also used this method to probe a Bose gas of 7Li atoms close to a Feshbach resonance. We have measured the Equation of State of the Bose gas as a function of interactions at very low temperature. For the first time, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground-state energy of the system, first predicted in 1957. We compared the experimental results to Quantum Monte-Carlo calculations. We have extended this study using out-of-equilibrium measurements of the Bose gas in the strongly interacting regime, which gives a first hint on the properties of the hypothetical unitary Bose gas.
We examine pairing and molecule formation in strongly interacting Fermi gases, and we discuss how radio-frequency (rf) spectroscopy can reveal these features. For the balanced case, the emergence of stable molecules in the Bose-Einstein condensation regime results in a two-peak structure in the rf spectrum with clearly visible medium effects on the low-energy part of the molecular wave function. For the highly imbalanced case, we show the existence of a well-defined quasiparticle (a spin polaron) on both sides of the Feshbach resonance, we evaluate its lifetime, and we illustrate how its energy may be measured by rf spectroscopy.
This thesis discusses two important topics in ultracold atomic gases: strong interactions in quantum gases, and quantum Hall physics in neutral atoms.First we give a brief introduction on basic scattering models in atomic physics, and an approach to adjust the interactions between atoms.We also include a list of experimental probes in cold atom physics.After these introductions, in Chapter 3, we report a few interesting problems in strongly interacting quantum gases.We introduce the BCS-BEC crossover model and relevant many-body techniques at the beginning, and discuss the details of several specific systems.We find the Fermi gases across narrow Feshbach resonances are strongly interacting at low temperature even when the magnetic field is several widths away from the resonance.We also discuss an approach to describe the metastable repulsive branch of Bose and Fermi gases across the resonance, and find a stable region of repulsive Bose gas close to unitarity.Some studies in two dimensional Fermi gases with spin imbalance are also included, and they are closely related to a number of recent experiments.In Chapter 4, we discuss quantum Hall physics in the context of neutral atomic gases.After illustrating how the Berry phase experienced by neutral atoms is equivalent to the magnetic field in electrons, we introduce the newly developed synthetic gauge field scheme in which a gauge potential is coupled to the neutral atoms.We give a detail introduction to this Raman coupling scheme developed by NIST group, and derive the theoretical model of the system.Then we make some predictions on the evolution of quantum Hall states when an extra anisotropy is applied from the external trap.Finally, we propose some experiments to verify our predictions.4.9 Phase diagram of the cloud in rotating anisotropic traps: two phases of the BEC and QH are identified. . . . . . . . . . . . . . . . . . . . . . . . . . . .4.10 Distortion and transition in vortex lattices of a rapidly rotating BEC in an anisotropic trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.11 Density profiles at cut x = 0 and y = 0 of the Laughlin wavefunctions at different positions in figure 4.9. . . . . . . . . . . . . . . . . . . . . . . . . .4.12 Distribution of zeros in the relative coordinate of the ground state of two body problem in rotating anisotropic traps. . . . . . . . . . . . . . . . . . .4.13 Variation in the distance of splitting zeros as a function of inverse interaction strength, for fixed anisotropy α = 0.96. . . . . . . . . . . . . . . . . . . . . .4.14 Density profiles after TOF expansion of the gas in a rotating isotropic trap.4.15 Density profiles after TOF expansion of anisotropy α = 0.94. . . . . . . . .4.16 Second order correlation in equation 4.64, in a rotating isotropic (left) and anisotropic (right) trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.17 A sketch of high-resolution in situ imaging technique in neutral atoms. . . .4.18 In situ images of the quantity |ψ(r/2, -r/2)| for an anisotropy α = 0.96. .x