The recent experimental progress in laser cooling and trapping of neutral atoms brings the atomic samples into the ultracold regime where the bosonic atoms and fermionic atoms are expected to have different dynamic behaviours in the laser fields. In this paper we systematically introduce the theoretical study of interaction of an ultracold atomic ensemble with a light wave in the frame of a vector quantum field theory. The many-body quantum correlation in the ultracold regime of atom optics is studied in terms of vector quantum field theory. A general formalism of nonlinear atom optics for a coherent atomic beam is developed.
The recent experimental progress in laser cooling and trapping of neutral atoms brings the atomic samples into the ultracold regime where the bosonic atoms and fermionic atoms are expected to have different dynamic behaviours in the laser fields. In this paper we systematically introduce the theoretical study of interaction of an ultracold atomic ensemble with a light wave in the frame of a vector quantum field theory. The many-body quantum correlation in the ultracold regime of atom optics is studied in terms of vector quantum field theory. A general formalism of nonlinear atom optics for a coherent atomic beam is developed.
A vector quantum field theory is developed to describe the interaction of an ultracold atomic ensemble with a laser field. The ultracold atomic ensemble is composed of either bosonic atoms or fermionic atoms. The photon exchanges between different ultracold atoms result in a long-range interatom interaction. Under appropriate conditions, such a many-body interaction leads to an effective ``Kerr-type'' nonlinearity of atomic waves. In terms of the nonlinearity, we construct a general formalism of nonlinear atom optics for an ultracold atomic beam. Applying the formalism to the diffraction of an ultracold atomic beam composed of bosonic atoms by a standing-wave laser field, we find that the many-body nonlinearity induces self-phase and cross-phase modulation of diffracted atomic waves. As a result, a standing-wave laser acts as a nonlinear atomic grating which diffracts atoms in the same way as a nonlinear periodic medium diffracts photons.
We have developed the quantum theory of the interaction of ultracold atomic ensemble with the electromagnetic field of vacuum and laser photons. The main attention is paid to the consistent consideration of dynamical dipole-dipole interactions in the case of the second quantized matter. We show that the retardation effects significantly influence the behavior of atomic ensemble in the radiation field. We have derived the general system of equations, which can be used for the investigation of various linear and nonlinear phenomena in atom optics. As an example, we have considered the diffraction of ultracold atomic beam by the standard laser wave. We show that with the increase of the initial density of the intensities of diffractions modes decrease. We also show that the angles of diffraction for different modes depend on the density.
The field of atom optics has progressed rapidly over the past 20 years since the realisation of Bose-Einstein condensation, such that the wave behaviour of atomic gases is now routinely demonstrated. Furthermore, the study of quantum atom optics, which goes beyond a ‘mean-field’ description of quantum systems to consider the behaviour of single particles, has demonstrated both the similarities between photons and massive species, and their differences as a result of the internal structure and external interactions of atoms. An important class of observable quantities which allow such effects to be measured are nth order correlation functions, which can be interpreted as a result of either particle or wave behaviour. These functions provide a statistical description of fluctuations in n-tuples of particles in a source, which rigorously defines concepts such as coherence. The quantum statistics of a Bose-Einstein condensate should be the same as that for an optical laser, while an ideal thermal Bose gas matches the behaviour of incoherent light. However, correlation measurements can also be used to quantify the influence of interactions, dimensionality, confining potentials and waveguides, and the difference in quantum statistics between fermions and bosons, which illustrates the rich range of behaviour exhibited by atomic gases. In this thesis, several aspects of quantum atom optics are explored with experiments using ultracold metastable helium, a species with the unique advantage of facilitating simple single-atom detection with high resolution, while still allowing Bose-Einstein condensates to be formed. The coherence of atomic systems is shown to be maintained when outcoupled as pulsed atom lasers, and the long-range order characteristic of Bose-Einstein condensates is demonstrated to third order for the first time. Conversely, thermal bunching is observed for a variety of atomic systems, including the measurement of correlation functions up to sixth order with near-ideal interference contrast. These results clearly demonstrate the correspondence between the quantum statistics of photons and atoms as was formalised by Glauber, as well as confirming the validity of applying Wick’s theorem to simplify the statistics of atomic gases. Correlation functions are also shown to be an ideal tool to probe the quantum state of an ultracold gas, and were used to observe the phenomenon of transverse condensation in an elongated Bose gas, as well as characterise the mode occupancy of matter waves guided by an optical potential. Ultracold metastable helium is also suitable for exploring other fundamental topics in quantum optics such particle/wave duality. The notion of complementarity stimulated long running philosophical discussions about how apparently mutually exclusive behaviours can coexist, which culminated in Wheeler devising his famous ‘delayed choice’ gedankenexperiment. A proposed experimental method to realise Wheeler’s experiment with ultracold atoms is discussed, and preliminary measurements presented which indicate that the completion of this experiment could be achieved in the near future. Not only is this of interest in its own right, but the implementation of this experiment has also developed techniques which may enable further studies in quantum atom optics such as investigations of the Hong-Ou-Mandel effect and quantum entanglement with massive particles.
Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.
We discuss theoretical foundations of the emerging area of quantum-optical studies of many-body systems: a quantum field theory of atoms interacting with photons. This theory is designed to describe quantum-statistical systems of cooled and trapped atoms undergoing spontaneous and stimulated emission processes. Formulated in the framework of the second quantization, this theory accounts fully for quantum-statistical properties of atoms as bosons or fermions. In particular, it applies to a description of the formation of the Bose-Einstein condensate in bosonic systems, as well as the spectroscopy and other quantum optical properties of the Bose-Einstein condensate. We derive the general second quantized Hamiltonian of this theory and discuss in detail various approximations.
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.