Systems of ultracold atoms in optical potentials have taken a place at the forefront of research into many-body atomic systems because of the clean experimental environment they exist in and the tunability of the system parameters. In this thesis we study how light scattered from these ultracold atomic gases reveals information about the state of the atomic gas and also leads to changes in that state.We begin by investigating the angular dependence of light scattered from atoms in optical lattices at finite temperature. We demonstrate how correlations in the superfluid and Mott insulator states affect the scattering pattern, and we show that temperature affects the number of photons scattered. This effect could be used to measure the temperature of the gas, however, we show that when the lattice band structure is taken into account the efficiency of this temperature measurement is reduced.We then investigate light scattering from small optical lattices where the Bose-Hubbard Hamiltonian can be solved exactly. For small lattices, scattering a photon from the atomic system significantly perturbs the atomic system. We develop a model of the evolution of the many-body state that results from the consecutive scattering and detection of photons. This model shows that light scattering pushes the system towards eigenstates of the light scattering measurement process, in some cases leading to a superposition of atomic states.In the second half of this thesis we study light scattering that depends on the internal hyperfine spin state of the atoms, in which case the scattered light can form images of the spatial atomic spin distribution. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. We also show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution.We then apply this theory of spin-dependent light scattering to the detection of different spin states of ultracold gases in synthetic magnetic fields. We show that it is possible to distinguish between ground states in the quantum Hall regime using light scattering. Moreover, we show how noise correlation analysis of the spin state images can be used to identify the correlations between atoms and how a variant on phase-contrast imaging can reveal the relationship between the atomic spins.
Systems of ultracold atoms in optical potentials have taken a place at the forefront of research into many-body atomic systems because of the clean experimental environment they exist in and the tunability of the system parameters. In this thesis we study how light scattered from these ultracold atomic gases reveals information about the state of the atomic gas and also leads to changes in that state.We begin by investigating the angular dependence of light scattered from atoms in optical lattices at finite temperature. We demonstrate how correlations in the superfluid and Mott insulator states affect the scattering pattern, and we show that temperature affects the number of photons scattered. This effect could be used to measure the temperature of the gas, however, we show that when the lattice band structure is taken into account the efficiency of this temperature measurement is reduced.We then investigate light scattering from small optical lattices where the Bose-Hubbard Hamiltonian can be solved exactly. For small lattices, scattering a photon from the atomic system significantly perturbs the atomic system. We develop a model of the evolution of the many-body state that results from the consecutive scattering and detection of photons. This model shows that light scattering pushes the system towards eigenstates of the light scattering measurement process, in some cases leading to a superposition of atomic states.In the second half of this thesis we study light scattering that depends on the internal hyperfine spin state of the atoms, in which case the scattered light can form images of the spatial atomic spin distribution. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. We also show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution.We then apply this theory of spin-dependent light scattering to the detection of different spin states of ultracold gases in synthetic magnetic fields. We show that it is possible to distinguish between ground states in the quantum Hall regime using light scattering. Moreover, we show how noise correlation analysis of the spin state images can be used to identify the correlations between atoms and how a variant on phase-contrast imaging can reveal the relationship between the atomic spins.
In the present thesis we study several schemes where the detection of the emitted light from an atomic ensemble gives information about the state of the atoms. In chapter 1 we review the basic theory for the light matter interaction in second quantized form. In chapter 2 we show how conservative potentials for the atoms, such as dispersive optical lattices, can be realized experimentally due to the dispersive interaction with a far detuned laser We then review some basic properties of the physics of a particle in a periodic potential. We show that the ground state and the lowest lying excitations of a Bose-Einstein condensate in a dispersive optical lattice can be described by the Bose-Hubbard Hamiltonian. In chapter 3 we study the photonic bandstructure of a chain of fixed pointlike atoms in a biperiodic configuration. We calculate the photonic spectra and the probe transmission if the atoms are in free space and inside a standing wave optical resonator. In chapter 4 we consider light scattering from ultracold atoms in an optical lattice where we calculate the photonic scattering cross section as a function of energy and direction of emission along the Mott-insulator-superfluid phase transition. We take into account the finite tunneling rate for the atoms, when evaluating the scattering cross section of the photons and the effect of photon recoil onto the atoms. In chapter 5 we consider a gas of ultracold atoms trapped at two spatially separated regions in space. Using a two Raman lasers to couple atoms out of the systems we show that it is possible to measure the mean value of the atomic field operator of the two systems by measuring the scattered light intensity of one of the Raman lasers. We show how this setup might be used to measure the temperature of a Bose-Einstein condensate and to monitor the superfluid to Mott-insulator phase transition for a gas of ultracold atoms in an optical lattice.
We study the scattering of a weak and far-detuned light from a system of ultracold bosons in one-dimensional and three-dimensional optical lattices. We show the connection between angular distributions of the scattered light and statistical properties of a Bose gas in a periodic potential. The angular patterns are determined by the Fourier transform of the second-order correlation function, and thus they can be used to retrieve information on particle number fluctuations and correlations. We consider superfluid and Mott-insulator phases of the Bose gas in a lattice and we analyze in detail how the scattering depends on the system dimensionality, temperature, and atom-atom interactions.
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.
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].
Quantum trapping potentials for ultracold gases change the landscape of classical properties of scattered light and matter. The atoms in a quantum many-body correlated phase of matter change the properties of light and vice versa. The properties of both light and matter can be tuned by design and depend on the interplay between long-range (nonlocal) interactions mediated by an optical cavity and short-range processes of the atoms. Moreover, the quantum properties of light get significantly altered by this interplay, leading the light to have nonclassical features. Further, these nonclassical features can be designed and optimised. Introduction and background. Under some of the most extreme experimental conditions of temperature and vacuum, atoms can be controlled by lasers in optical lattices. Beyond controlling the spatial distribution of atoms by light, one can selectively pump at a particular wavelength optimising the interaction with light by several orders of magnitude with additional mirrors. As this occurs, the light in the cavity mediates a true quantum potential that couples all the atoms along the optical lattice, leading to the formation of a quantum optical lattice. The structural arrangement of the atoms can be modified by the light, as photons interact with atoms and vice versa. Main results. In this paper, we concentrate on understanding and showing how the light scattered by the atoms acquires features that are inherently quantum mechanical and originated due to the atomic condensation into a many-body state. The atoms have strong correlations among them as they locally interact and move in the optical lattice in addition to the cavity mediated long-range interaction. We show how one can design and optimise the quantum properties of the scattered light by the atoms, and how it contains information regarding the correlated phases of matter that emerge. Wider Implications. Our results will allow to consider the design of quantum properties of light and the interplay between different energy scales in the system towards the implementation of new quantum simulators, the possibility to optimise these properties for technological applications and ultimately innovate towards possible implementations of quantum system engineering of states.
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.