A scheme is proposed, that allows one for performing homodyne detection of the matter-wave field of ultracold bosonic atoms. It is based on a pump-probe lasers setup, that both illuminates a Bose-Einstein condensate, acting as reference system, and a second ultracold gas, composed by the same atoms but in a quantum phase to determine. Photon scattering outcouples atoms from both systems, which then propagate freely. Under appropriate conditions, when the same photon can either be scattered by the Bose-Einstein condensate or by the other quantum gas, both flux of outcoupled atoms and scattered photons exhibit oscillations, whose amplitude is proportional to the condensate fraction of the quantum gas. This setup allows one, for instance, to perform thermometry of a condensate or to monitor the Mott-insulator/superfluid phase transition in optical lattices, and can be extended in order to measure the first-order correlation function of a quantum gas. The dynamics here discussed make use of the entanglement between atoms and photons, which is established by the scattering process, in order to access detailed information on the quantum state of matter.
A scheme is proposed, that allows one for performing homodyne detection of the matter-wave field of ultracold bosonic atoms. It is based on a pump-probe lasers setup, that both illuminates a Bose-Einstein condensate, acting as reference system, and a second ultracold gas, composed by the same atoms but in a quantum phase to determine. Photon scattering outcouples atoms from both systems, which then propagate freely. Under appropriate conditions, when the same photon can either be scattered by the Bose-Einstein condensate or by the other quantum gas, both flux of outcoupled atoms and scattered photons exhibit oscillations, whose amplitude is proportional to the condensate fraction of the quantum gas. This setup allows one, for instance, to perform thermometry of a condensate or to monitor the Mott-insulator/superfluid phase transition in optical lattices, and can be extended in order to measure the first-order correlation function of a quantum gas. The dynamics here discussed make use of the entanglement between atoms and photons, which is established by the scattering process, in order to access detailed information on the quantum state of matter.
A scheme is discussed that allows for performing homodyne detection of the matter-wave field of ultracold bosonic atoms. It is based on a pump-probe laser setup, which both illuminates a Bose-Einstein condensate, acting as reference system, and a second ultracold gas, composed by the same atoms but in a quantum phase to determine. Photon scattering outcouples atoms from both systems, which then propagate freely. Under appropriate conditions, when the same photon can either be scattered by the Bose-Einstein condensate or by the other quantum gas, both flux of outcoupled atoms and scattered photons exhibit oscillations, the amplitude of which is proportional to the condensate fraction of the quantum gas. The setup can be extended to measure the first-order correlation function of a quantum gas. The dynamics discussed here makes use of the entanglement between atoms and photons, which is established by the scattering process in order to access detailed information on the quantum state of matter.
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.
The first successful experimental realization of a Bose-Einstein condensate (BEC) in 1995 sparked a still growing research activity that in the meantime has led to beautiful and surprising results, such as the interference of matter waves [4], the Mott-superfluid phase transition [49] or the direct observation of Anderson localization of matter waves [10]. The strong interest in BECs arises, among others, from the possibility to investigate known but hard to study quantum systems on a rather macroscopic scale: for example one can load ultra-cold bosons into an optical lattice created by a standing light wave, and thereby simulate a solid state device. When it comes to a measurement on the BEC, however, essentially all measurement techniques result in the destruction of the condensate: for example in the so called “time of flight method” the optical lattice is switched off to observe the expansion of the trapped atoms and thereby directly visualize their momentum distribution, which highlights the condensed component [11]. In this thesis we elaborate on a means to probe a Bose-Einstein condensate from outside, with a scattering particle. The interaction between the probe particle and the bosons allows energy exchange between them, i.e., this setup includes inelastic scattering. After the scattering process, the condensate is still confined in the optical lattice and can therefore be used for further investigations. Of course, this method of probing a BEC is only then a serious alternative if the properties of the BEC can be inferred from the scattering signal. Besides outlining the scattering formalism, the central aim of this work is to show how the properties of the BEC can be deduced from those quantities accessible in a scattering experiment, like for example the transmission or the inelastic cross section. The other, equally strong motivation of this work concerns the signature of the interaction between the bosons in the scattering quantities. The dynamics of an analog classical system depends strongly on the interaction strength, which can induce a complex structure of the underlying phase space like, e.g., the appearance of a separatrix or even the emergence of chaotic dynamics in a globally mixed regular-chaotic phase space. We are interested to which extent such phase-space metamorphosis is reflected in the properties of the scattering particle. Currently light scattering (Bragg spectroscopy) on an optical lattice [78, 77] or rather on an optical lattice embedded into a cavity [62,68,19] is under intense investigation. These efforts predominantly aim at a characterization of the Mott-superfluid transition by specific scattering properties. In the present thesis we focus on condensates loaded in two and three lattice sites, with a large number of bosons. These systems exhibit a diversity of important physical effects (as we will see below) and thus are of paradigmatic relevance for a detailed understanding of multiparticle quantum dynamics in periodic potentials.
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.
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.
We investigate a nondestructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement backaction noise alone.