Motivated by the famous physicist Richard Feynman, we are eager to create a universal quantum simulator with ultracold atoms. Because of it's versatile controllability and clean environment, ultracold atomic system serves as a versatile plateform for imitating quantum systems with energy scale, time scale and length scale which is many orders of magnitude different. Oftentimes, it's very difficult to conduct direct experiment on the system to be simulated. Through the universality of the physics law, one could reproduce the same physical phenomena in another system which could be tested in a more convenience energy scale, time scale and length scale. In this thesis, we demonstrate three different examples of quantum simulation. With the help of optical lattices, we measure the equation of states of two-dimensional Bose gases, create effective ferromagnetic domains, and also create roton quasi-particle in the atomic superfluid. The last two items rely on the technique of lattice shaking, and we are able to engineer atomic dispersion and create a double-well structure in the momentum space by dynamically modulating the lattice potential. We take advantage of the high resolution imaging system to study the effective ferromagnetism and many-body excitation in this system. The essential techniques we use include \textit{in situ} imaging, optical projection, Feshbach resonance, and optical lattice. An 1-$\mu$m imaging resolution is achieved by implementing an aberration-compensated objective which also allows projecting optical potentials crafted with a digital micromirror device. The Feshbach resonance and optical lattice, on the other hand, allows us tuning the interaction strength to a strongly interacting regime while keeping the gas stable. We first characterize the performance of static optical lattices by using it to enhance atomic interaction strength. From the weakly interacting regime to the strongly interacting regime, we study the critical behavior of two-dimensional Bose gas in the Berezinskii-Kosterlitz-Thouless transition and vacuum-to-superfluid transition. We compared the measurements of the critical points with different theoretical predictions. The scaling of the critical point deviates from the mean-field prediction but is still captured by the classical field theory in the strongly interacting regime. Through dynamically modulating the phase of the optical lattice, we create an effective ferromagnetic system where the quasi-momentum of the atoms represents the pseudo-spin in the corresponding effective ferromagnetism. Using a shallow optical lattice and tuning the atomic scattering length to a small value help the system remain stable. The lifetime of the system is long enough for us to measure the susceptibility and observe formation of domains. We present the analysis of spin correlation function. From the spin correlation function, we find domain walls tend to align along the short axis of the cloud. We further investigate the many-body excitation spectrum with projection Bragg spectroscopy. The measurement reveals the existence of roton and maxon signatures in the dispersion. The roton and maxon energies scale with the chemical potential linearly which is an indication of many-body effect. The existence of roton leads to suppression of critical velocity of the system and is proved by a moving speckle experiment.
Motivated by the famous physicist Richard Feynman, we are eager to create a universal quantum simulator with ultracold atoms. Because of it's versatile controllability and clean environment, ultracold atomic system serves as a versatile plateform for imitating quantum systems with energy scale, time scale and length scale which is many orders of magnitude different. Oftentimes, it's very difficult to conduct direct experiment on the system to be simulated. Through the universality of the physics law, one could reproduce the same physical phenomena in another system which could be tested in a more convenience energy scale, time scale and length scale. In this thesis, we demonstrate three different examples of quantum simulation. With the help of optical lattices, we measure the equation of states of two-dimensional Bose gases, create effective ferromagnetic domains, and also create roton quasi-particle in the atomic superfluid. The last two items rely on the technique of lattice shaking, and we are able to engineer atomic dispersion and create a double-well structure in the momentum space by dynamically modulating the lattice potential. We take advantage of the high resolution imaging system to study the effective ferromagnetism and many-body excitation in this system. The essential techniques we use include \textit{in situ} imaging, optical projection, Feshbach resonance, and optical lattice. An 1-μm imaging resolution is achieved by implementing an aberration-compensated objective which also allows projecting optical potentials crafted with a digital micromirror device. The Feshbach resonance and optical lattice, on the other hand, allows us tuning the interaction strength to a strongly interacting regime while keeping the gas stable. We first characterize the performance of static optical lattices by using it to enhance atomic interaction strength. From the weakly interacting regime to the strongly interacting regime, we study the critical behavior of two-dimensional Bose gas in the Berezinskii-Kosterlitz-Thouless transition and vacuum-to-superfluid transition. We compared the measurements of the critical points with different theoretical predictions. The scaling of the critical point deviates from the mean-field prediction but is still captured by the classical field theory in the strongly interacting regime. Through dynamically modulating the phase of the optical lattice, we create an effective ferromagnetic system where the quasi-momentum of the atoms represents the pseudo-spin in the corresponding effective ferromagnetism. Using a shallow optical lattice and tuning the atomic scattering length to a small value help the system remain stable. The lifetime of the system is long enough for us to measure the susceptibility and observe formation of domains. We present the analysis of spin correlation function. From the spin correlation function, we find domain walls tend to align along the short axis of the cloud. We further investigate the many-body excitation spectrum with projection Bragg spectroscopy. The measurement reveals the existence of roton and maxon signatures in the dispersion. The roton and maxon energies scale with the chemical potential linearly which is an indication of many-body effect. The existence of roton leads to suppression of critical velocity of the system and is proved by a moving speckle experiment.
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 understanding of quantum many-body physics is the key to develop new quantum technologies including novel quantum materials, high-precision sensors, and quantum computers. However, understanding the general quantum many-body physics is extremely difficult, particularly when such systems are driven far from an equilibrium state. Ultracold atoms, a clean, fully controllable, and coherent quantum many-body systems can provide useful insights into the fundamental properties of quantum matter. This thesis discusses experiments on studying nonequilibrium dynamics in driven ultracold bosonic atoms with fantastic static and dynamical controls of the inter-particle interactions through Feshbach resonances and external trapping potentials using optical lattices and digital micromirror device (DMD). With this versatile apparatus, we first study the critical dynamics across a quantum phase transition in shaken optical lattices. Across a ferromagnetic transition where the Z2 inversion symmetry is broken, we are interested in how the system evolves toward the new ground states generally with a different symmetry. Utilizing the phase imprinting technique with DMD, we show that the macroscopic coherence is maintained across the phase transition, the system undergoes a coherent population transfer of particles toward lower energy states and quantum fluctuations determine the domain structure but do not destroy the macroscopic coherence. We then present the complex correlations rising from the matter-wave version of a high-harmonic generation with oscillating interaction. This high-harmonic generation of matterwave is a result of stimulated secondary collisions. The stimulated primary collisions, two condensate atoms collide absorbing one energy quantum from the oscillating field, give rise to the first observation of Bose fireworks. The scattered atoms from the primary collisions can further collide with each other or the ground-state atoms from the condensate and such secondary collisions promote atoms to higher momentum modes. Moreover, we show the density-wave dynamics prior to the jets emission within the condensate with oscillating interactions and explain the asymmetry in the jets emission pattern based on near-field interference. Besides, we further demonstrate the spatial and temporal phase coherence of the emitted jets using matter-wave interference and connect our matter-wave jets emission to the famous Unruh radiation in relativistic physics.
In this thesis I report on experiments that enter a new regime in the many body physics of ultracold atomic gases. A Bose-Einstein condensate is loaded into a three-dimensional optical lattice potential formed by a standing wave laser light field. In this novel quantum system we have been able to both realize a quantum phase transition from a superfluid to a Mott insulator, and to observe the collapse and revival of a macroscopic matter wave field. Quantum phase transitions are driven by quantum fluctuations and occur, even at zero temperature, as the relative strength of two competing energy terms in the underlying Hamiltonian is varied across a critical value. In the first part of this work I report on the observation of such a quantum phase transition in a Bose-Einstein condensate with repulsive interactions, held in a three-dimensional optical lattice potential. In the superfluid ground state, each atom is spread-out over the entire lattice, whereas in the Mott insulating state, exact numbers of atoms are localized at individual lattice sites. We observed the reversible transition between those states and detected the gap in the excitation spectrum of the Mott insulator. A Bose-Einstein condensate is usually described by a macroscopic matter wave field. However, a quantized field underlies such a "classical" matter wave field of a Bose-Einstein condensate. The striking behavior of ultracold matter due to the field quantization and the nonlinear interactions between the atoms is the focus of the second part of this work. The matter wave field of a Bose-Einstein condensate is observed to undergo a series of collapses and revivals as time evolves. Furthermore, we show that the collisions between individual pairs of atoms lead to a fully coherent collisional phase shift in the corresponding many-particle state, which is a crucial cornerstone of proposed novel quantum computation schemes with neutral atoms. With these experiments we enter a new field of physics with ultracold quantum gases. In this strongly correlated regime, interactions between atoms dominate the behavior of the many-body system such that it can no longer be described by the usual theories for weakly interacting Bose gases. This novel quantum system offers the unique possibility to experimentally address fundamental questions of modern solid state physics, atomic physics, quantum optics, and quantum information.
Ultracold atoms in optical lattices can be used to model condensed matter systems. They provide a clean, tuneable system which can be engineered to reach parameter regimes that are not accessible in condensed matter systems. Furthermore, they provide different techniques for probing the properties of these systems.This thesis presents an experimental and theoretical study of ultracold atoms in optical lattices for quantum simulation of two-dimensional systems.The first part of this thesis describes an experiment with a Bose-Einstein condensate of 87Rb loaded into a two-dimensional optical lattice. The beams that generate the optical lattice are controlled by acousto-optic deflection to provide a flexible optical lattice potential. The use of a dynamic ‘accordion’ lattice with ultracold atoms, where the spacing of the lattice is increased in both directions from 2.2 to 5.5 μm, is described. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice. The optical lattice can also be rotated, generating an artificial magnetic field. Previous experiments with the rotating optical lattice are summarised, and steps to reaching the strongly correlated regime are discussed.The second part of this thesis details numerical techniques that can be used to describe strongly correlated two-dimensional systems. These systems are challenging to simulate numerically, as the exponential growth in the size of the Hilbert space with the number of particles means that they can only be solved exactly for very small systems. Recently proposed correlator product states [Phys. Rev. B 80, 245116 (2009)] provide a numerically efficient description which can be used to simulate large two-dimensional systems. In this thesis we apply this method to the two-dimensional quantum Ising model, and the Bose-Hubbard model subject to an artificial magnetic field in the regime where fractional quantum Hall states are predicted to occur.
Recent advances in using microscopes in ultracold atom experiment have allowed experimenters for the first time to directly observe and manipulate individual atoms in individual lattice sites. This technique enhances our capability to simulate strongly correlated systems such as Mott insulator and high temperature superconductivity. Currently, all ultracold atom experiments with high resolution imaging capability use bosonic atoms. In this thesis, I present our progress towards creating the fermionic version of the microscope experiment which is more suitable for simulating real condensed matter systems. Lithium is ideal due to the existence of both fermionic and bosonic isotopes, its light mass, which means faster experiment time scales that suppresses many sources of technical noise, and also due to the existence of a broad Feshbach resonance, which can be used to tune the inter-particle interaction strength over a wide range from attractive, non-interacting, and repulsive interactions. A high numerical aperture objective will be used to image and manipulate the atoms with single lattice site resolution. This setup should allow us to implement the Hubbard hamiltonian which could describe interesting quantum phases such as antiferromagnetism, d-wave superfluidity, and high temperature superconductivity. I will also discuss the feasibility of the Raman sideband cooling method for cooling the atoms during the imaging process. We have also developed a new electronic control system to control the sequence of the experiment. This electronic system is very scalable in order to keep up with the increasing complexity of atomic physics experiments. Furthermore, the system is also designed to be more precise in order to keep up with the faster time scale of lithium experiment.
The three experiments described in this thesis investigate fundamental properties of ultracold atoms. Using laser cooling and evaporative cooling, a dilute gas of sodium atoms is cooled to ~100 nK. Under these circumstances a Bose-Einstein condensate (BEC) forms, where millions of atoms collapse into the lowest energy state of the system and share a macroscopic wavefunction. The experiments are done in an ultrahigh vacuum and the atoms are manipulated remotely using laser beams, magnetic fields, and RF-fields. Using ultracold atoms allows unprecedented control over the internal and external degrees of freedom of the system, making it very suitable for precision measurements. Ultracold atoms also serve as a model system for more complicated or remote fields such as solid-state physics and cosmology. In the first experiment the refractive index of an ultracold bosonic gas is studied. The atomic clouds are analyzed for temperature and number of particles using nearly non-destructive phase-contrast imaging. After each pulse of probe light a small fraction of the atoms is lost, while the cloud is simultaneously slightly heated. This makes it possible to study the scattering rate as a function of temperature using only a single sample. It is observed that the scattering rate increases below the critical temperature for BEC by more than a factor of 3 compared to the classical value. This enhancement is in good agreement with the predictions by theoretical work that takes two-body correlation and the Lorentz-Lorenz correction into account. The method is also used to perform calorimetry on the Bose gas and directly measure the heat capacity of the BEC. The second chapter deals with magnetism in ultracold gases. When cooling an ultracold gas containing different spin components below the critical temperature for BEC, stable magnetic domains form. The appearance of these domains and the dynamics of the domain walls are studied. The spin mixture is prepared by performing an RF-sweep on ground state atoms in the presence of a magnetic field. Spin dynamics are induced by applying magnetic gradients. Spin drag, which is the transport coefficient responsible for damping spin currents, was measured in a two-component system. Furthermore a new method for spin resolved phase contrast imaging is presented, which is used to study time evolution in situ non-destructively. The last experiment focuses on spontaneous symmetry breaking. When passing a continuous phase transition, spontaneous symmetry breaking causes the development of domains with an independently chosen order parameter. The domains are separated by boundary defects. In this experiment the spontaneous creation of solitons was observed, which are boundary defects in the phase of the condensate, as well as magnetic domain walls, which are the boundary defects in the magnetization. Through the Kibble-Zurek mechanism it is possible to determine the critical exponents that characterize the phase transition. The critical exponents are predicted to be universal, i.e. do not depend on the microphysics of the system, so the results from our ultracold atoms lab can help answer universal questions for example from cosmology and from the early universe.