In this thesis we discuss several aspects of ultracold atomic systems and their applications to quantum simulation. These topics cover a degenerate gas near a Feshbach resonance, superfluids in an optical lattice, trapped-ion quantum computation and simulation. We study a degenerate Fermi gas when the interaction is tuned from the Bose-Einstein Condensation (BEC) side to the Bardeen-Cooper-Schrieffer (BCS) side, investigating effects due to population and mass imbalance. We identify various phases and find that an superfluid shell can be observed within a trap because of the mass mismatch. We study a Fermi gas in a quasi-two-dimensional geometry formed by optical lattices. A two-channel model is proposed to describe the BEC-BCS crossover physics. We find that the higher band excitations are significant and contribute to the closed channel as effective Feshbach ``dressed molecules''. This model predicts a decrease in the cloud size as the interaction is tuned from the BCS side to the BEC side. To investigate superfluidity of bosons in an optical lattice, we calculate the momentum distribution related to the time-of-flight (TOF) interference patterns at finite temperature. We find that a distinct bimodal distribution of the TOF image is presented as long as superfluids emerge, and hence can be used as a reliable signature indicating onset of superfluidity. We propose a large-scale quantum computer architecture by stabilizing a one-dimensional ion chain in a simple linear trap geometry. By arranging ions uniformly through optimizing the anharmonic trap potential, we show that high-fidelity quantum gates can be realized in large ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motional modes with simple shaped laser pulses. Finally, we demonstrate the trapped ion quantum simulation of the Ising model. Through control of the laser detuning, various coupling networks can be realized. We give a detailed discussion of the frustrated nature in three-ion cases and show achievable phases for larger systems. A comparison of our calculation and experimental data is presented.
In this thesis we discuss several aspects of ultracold atomic systems and their applications to quantum simulation. These topics cover a degenerate gas near a Feshbach resonance, superfluids in an optical lattice, trapped-ion quantum computation and simulation. We study a degenerate Fermi gas when the interaction is tuned from the Bose-Einstein Condensation (BEC) side to the Bardeen-Cooper-Schrieffer (BCS) side, investigating effects due to population and mass imbalance. We identify various phases and find that an superfluid shell can be observed within a trap because of the mass mismatch. We study a Fermi gas in a quasi-two-dimensional geometry formed by optical lattices. A two-channel model is proposed to describe the BEC-BCS crossover physics. We find that the higher band excitations are significant and contribute to the closed channel as effective Feshbach ``dressed molecules''. This model predicts a decrease in the cloud size as the interaction is tuned from the BCS side to the BEC side. To investigate superfluidity of bosons in an optical lattice, we calculate the momentum distribution related to the time-of-flight (TOF) interference patterns at finite temperature. We find that a distinct bimodal distribution of the TOF image is presented as long as superfluids emerge, and hence can be used as a reliable signature indicating onset of superfluidity. We propose a large-scale quantum computer architecture by stabilizing a one-dimensional ion chain in a simple linear trap geometry. By arranging ions uniformly through optimizing the anharmonic trap potential, we show that high-fidelity quantum gates can be realized in large ion crystals under the Doppler temperature based on coupling to a near-continuum of transverse motional modes with simple shaped laser pulses. Finally, we demonstrate the trapped ion quantum simulation of the Ising model. Through control of the laser detuning, various coupling networks can be realized. We give a detailed discussion of the frustrated nature in three-ion cases and show achievable phases for larger systems. A comparison of our calculation and experimental data is presented.
This thesis summarizes our study on the properties of ultracold Fermions near a Feshbach resonance. The Feshbach resonance allows for a continuous tuning of the interaction strength between the atoms. With this tunability, many properties predicted for the BCS-BEC crossover region in solids can be shown to exist in this ultracold Fermi gas. With the highly controllable parameters and the clean environment in the experiments, the study of the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein Condensation (BEC) crossover in ultracold Fermions provides valuable insights to the strongly interacting crossover region, which has never been achieved before in solids. We first examine the properties of 6 Li and 40 K gases. We find that in the unitary region the properties of the system do not depend on the atom species: outside the unitary region, the properties of the system do depend on the scattering properties of the different atom species. We study the dynamics of the ultracold Fermions in the crossover region in response to the variations in the external magnetic field. We find that the response depends on the time scale and the amplitude of the variations; which is in qualitative agreement with the experimental observations. We derive a set of dynamic mean-field equations for a Fermi gas in an arbitrary potential trap near a wide Feshbach resonance. The equations are more general than the local density approximation (LDA), and less demanding computationally as the Bogoliubov-de-Gennes (BdG) equation. We then analyze the solubility of the equations, as well as solve a simplified version of the equations for illustration and for self-consistency check on the assumptions made during the derivation. We systematically study the possible phases for a trapped Fermi gas with population imbalance near a Feshbach resonance. Our results agree qualitatively well with the recent experimental results, and predict the existence of two exotic non-BCS superfluid phases for the strongly interacting gas with population unbalance: the Breached Pair (BP) phase and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Finally, to guide the experimental efforts in the search of new quantum phases, we propose a detection scheme for the possible exotic phases.
In this habilitation-thesis a collection of 14 experiments is presented. In these experiments we have developed and used novel techniques to control ultracold gases on the quantum level. In brief, Bose-Einstein condensates (BEC) and degenerate Fermi gases of laser-cooled alkali atoms are subjected to specially designed optical and magnetic fields. The fields influence in a coherent way the behavior, properties and dynamics of the gases. On this basis we developed tools to prepare, coherently manipulate, and analyze pre-defined quantum states. With this high level of control, it was possible to investigate interesting physics phenomena, and we were able to achieve several breakthroughs in the field of ultracold atoms. Highlights of our experimental results include the demonstration of phase engineering of a BEC wavefunction where we created solitons in a BEC and studied their propagation. In another experiment we constructed a spatially resolved matter wave interferometer with which we mapped out the phase distribution on a condensate. Illuminating the BEC with a periodic pattern, i.e. an optical lattice, allowed us to study solid states physics phenomena. In a second set of experiments we demonstrated optically tuning of the interaction between atoms with optical Feshbach resonances. Employing either magnetically tunable Feshbach resonances or laser radiation, we were able to produce ground state molecules in well defined quantum states. This led to the production of the first molecular BEC. By tuning the coupling of atom pairs in a Fermi gas of atoms, we could for the first time investigate the so-called BEC-BCS crossover which describes the continuous change from a BEC superfluid to a Bardeen-Cooper Schrieffer (BCS) superfluid. Due to the excellent control on the quantum level, the developed cold atom techniques open up intriguing prospects for future applications and experiments. They represent a general tool box to investigate fundamental physical phenomena in a pure and undisturbed environment. In the future, cold atoms might serve as a testing ground for fundamental theories or as quantum simulators for complex systems.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
We study ultracold gases of alkali-metal atoms in the quantum degenerate regime. The interatomic interactions in these type of systems can be tuned using resonances induced by magnetic or electric fields. The tunability of the interactions, together with the possibility of confining the atoms with several kinds of external potentials, allows for a completely novel approach to study basic problems in many-body physics, and moreover, allows to enter regimes which have never been accessible in condensed matter or nuclear physics. For example, this has led to the experimental demonstration of an intimate relation between two types of superfluidity: the crossover from Bose-Einstein condensation of tightly bound molecules to the superfluid behavior related to weakly bound BCS-like pairs. Another experimental landmark was reached when the existence of universal Efimov three-body bound states was proven in experiments with ultracold bosonic cesium atoms. In this thesis, we study several aspects of these strongly interacting and ultracold atomic gases. We develop an analytical model that encapsulates all of the relevant scattering physics in atomic systems where open-channel shape resonances and closedchannel Feshbach resonances give rise to complicated and non-trivial scattering properties. This model provides lots of physical insight and is shown to describe important quantities, such as the molecular energies and scattering phase shifts, with a high level of accuracy. The model is compared to full numerical coupled-channel calculations in two atomic systems: rubidium and lithium. We study the BCS-BEC crossover using a many-body description of the ultracold gas that includes the non-trivial energy dependence of the scattering model. We show that it gives rise to superfluid behavior associated with the formation of BCS-like pairs while the low-energy interactions are repulsive in character. The energy dependence of the interactions is crucial, as it gives rise to attractive interactions at the Fermi energy, necessary for the formation of Cooper pairs. We demonstrate new ways of controlling the interatomic interactions using a combination of magnetic and electric fields. This leads to experimental control of, for instance, the three-body parameter in the context of Efimov physics and of non-universal behavior in the BCS-BEC crossover in fermionic gases. Using a four-body method based on first principles, we solve the molecule-molecule scattering problem to calculate several important properties of bosonic and fermionic Summary 145 molecules that consist of light and heavy atoms. These type of molecules are of current experimental interest, and we predict several exciting relations between three- and four-body observables in these type of systems.
Ultracold atoms in optical lattices provide an extremely clean and controllable setting to explore quantum many-body phases of matter. Here we give a brief review of the strong-correlation physics that has been realized using such ultracold atoms in optical lattices ranging from the realization of Hubbard models to studies of quantum magnetism and the detection of single atoms with lattice site resolution. All this has opened up fundamentally new opportunities for the investigation of quantum many-body systems. Introduction Over the past years, ultracold atoms in optical lattices have emerged as versatile new systems to explore the physics of quantum many-body systems. On the one hand, they can be helpful in gaining a better understanding of known phases of matter and their dynamical behavior; on the other hand, they allow one to realize completely novel quantum systems that have not been studied before in nature [1, 2, 3]. Commonly, the approach of exploring quantum many-body systems in such a way is referred to as “quantum simulations.” Examples of some of the first strongly interacting many-body phases that have been realized both in lattices and in the continuum include the quantum phase transition from a superfluid to a Mott insulator [4, 5, 6], fermionic Mott insulators [7, 8], the achievement of a Tonks- Girardeau gas [9, 10], and the realization of the Bose-Einsten condensate (BEC)– Bardeen-Cooper-Schrieffer (BCS) crossover (see also Chapter 12) in Fermi gas mixture [11] using Feshbach resonances [12]. In almost all of these experiments, detection was limited to time-of-flight imaging or more refined derived techniques that mainly characterized the momentum distribution of the quantum gas [2]. For several years, researchers in the field have therefore aspired to employ in situ single-particle detection methods for the analysis of ultracold quantum gases. Only recently has it become possible to implement such imaging techniques, marking a milestone for the characterization and manipulation of ultracold quantum gases [13, 14, 15, 16, 17]. In our discussion, we will focus on one of the most successful of these techniques based on high-resolution fluorescence imaging. Despite being a rather new technique, such quantum gas microscopy has already proven to be an enabling technology for probing and manipulating quantum many-body systems. For the first time, controllable and strongly interacting many-body systems, as realized with ultracold atoms, could be observed on a local scale [17, 16].
The main topic of these lectures is the physics of quantum degenerate atomic Fermi gases both under uniform confinement and in harmonic traps. To begin with, a general introduction on ideal Fermi gases is proposed. This "academic" limit is relevant in experiments where ultracold fermionic atoms are all polarized in a single spin state: the low atom momenta together with the fermionic nature of the atoms forbid atomic s-wave scattering and the atoms can be considered as free. Interactions are then introduced for the case of a gas with two spin components. Interactions can be tuned via Feshbach resonances and control the microscopic features of the superfluid phase, ranging from the BCS limit (formation of Cooper pairs) to the BEC limit (Bose-Einstein condensation of dimers). Various theoretical approaches for the description of the BCS-BEC crossover and their predictions in comparison with the experimental results are discussed.