Exotic superfluid states of ultra-cold Fermi gases

This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.

Techniques for engineering quantum states

In this thesis I theoretically study quantum states of ultracold atoms. The majority of the Chapters focus on engineering specific quantum states of single atoms with high fidelity in experimentally realistic systems. In the sixth Chapter, I investigate the stability and dynamics of new multidimensional solitonic states that can be created in inhomogeneous atomic Bose-Einstein condensates. In Chapter three I present two papers in which I demonstrate how the coherent tunnelling by adiabatic passage (CTAP) process can be implemented in an experimentally realistic atom chip system, to coherently transfer the centre-of-mass of a single atom between two spatially distinct magnetic waveguides. In these works I also utilise GPU (Graphics Processing Unit) computing which offers a significant performance increase in the numerical simulation of the Schrödinger equation. In Chapter four I investigate the CTAP process for a linear arrangement of radio frequency traps where the centre-of-mass of both, single atoms and clouds of interacting atoms, can be coherently controlled. In Chapter five I present a theoretical study of adiabatic radio frequency potentials where I use Floquet theory to more accurately model situations where frequencies are close and/or field amplitudes are large. I also show how one can create highly versatile 2D adiabatic radio frequency potentials using multiple radio frequency fields with arbitrary field orientation and demonstrate their utility by simulating the creation of ring vortex solitons. In the sixth Chapter I discuss the stability and dynamics of a family of multidimensional solitonic states created in harmonically confined Bose-Einstein condensates. I demonstrate that these solitonic states have interesting dynamical instabilities, where a continuous collapse and revival of the initial state occurs. Through Bogoliubov analysis, I determine the modes responsible for the observed instabilities of each solitonic state and also extract information related to the time at which instability can be observed.

Transport, atom blockade and output coupling in a Tonks-Girardeau gas

Recent landmark experiments have demonstrated how quantum mechanical impurities can be created within strongly correlated quantum gases and used to probe the coherence properties of these systems. Here we present a theoretical model to simulate such an output coupler for a Tonks- Girardeau gas that shows excellent agreement with the experimental results for atom transport and output coupling. The solid theoretical basis our model provides allows us to explore non-equilibrium transport phenomena in ultra-cold quantum gases and leads us to predict a regime of atom blockade, where the impurity component becomes localised in the parent cloud despite the presence of gravity. We show that this provides a stable mixed-species quantum gas in the strongly correlated limit.

Measuring work and heat in ultracold quantum gases

We propose a feasible experimental scheme to direct measure heat and work in cold atomic setups. The method is based on a recent proposal which shows that work is a positive operator valued measure (POVM). In the present contribution, we demonstrate that the interaction between the atoms and the light polarization of a probe laser allows us to implement such POVM. In this way the work done on or extracted from the atoms after a given process is encoded in the light quadrature that can be measured with a standard homodyne detection. The protocol allows one to verify fluctuation theorems and study properties of the non-unitary dynamics of a given thermodynamic process.

Nanofiber control of ultracold quantum gases

While a great amount of attention is being given to the development of nanodevices, both through academic research and private industry, the field is still on the verge. Progress hinges upon the development of tools and components that can precisely control the interaction between light and matter, and that can be efficiently integrated into nano-devices. Nanofibers are one of the most promising candidates for such purposes. However, in order to fully exploit their potential, a more intimate knowledge of how nanofibers interact with single neutral atoms must be gained. As we learn more about the properties of nanofiber modes, and the way they interface with atoms, and as the technology develops that allows them to be prepared with more precisely known properties, they become more and more adaptable and effective. The work presented in this thesis touches on many topics, which is testament to the broad range of applications and high degree of promise that nanofibers hold. For immediate use, we need to fully grasp how they can be best implemented as sensors, filters, detectors, and switches in existing nano-technologies. Areas of interest also include how they might be best exploited for probing atom-surface interactions, single-atom detection and single photon generation. Nanofiber research is also motivated by their potential integration into fundamental cold atom quantum experiments, and the role they can play there. Combining nanofibers with existing optical and quantum technologies is a powerful strategy for advancing areas like quantum computation, quantum information processing, and quantum communication. In this thesis I present a variety of theoretical work, which explores a range of the applications listed above. The first work presented concerns the use of the evanescent fields around a nanofiber to manipulate an existing trapping geometry and therefore influence the centre-of-mass dynamics of the atom. The second work presented explores interesting trapping geometries that can be achieved in the vicinity of a fiber in which just four modes are allowed to propagate. In a third study I explore the use of a nanofiber as a detector of small numbers of photons by calculating the rate of emission into the fiber modes when the fiber is moved along next to a regularly separated array of atoms. Also included are some results from a work in progress, where I consider the scattered field that appears along the nanofiber axis when a small number of atoms trapped along that axis are illuminated orthogonally; some interesting preliminary results are outlined. Finally, in contrast with the rest of the thesis, I consider some interesting physics that can be done in one of the trapping geometries that can be created around the fiber, here I explore the ground states of a phase separated two-component superfluid Bose-Einstein condensate trapped in a toroidal potential.

Nonlinear electrostatic excitations of charged dust in degenerate ultra-dense quantum dusty plasmas

The linear and nonlinear properties of low-frequency electrostatic excitations of charged dust particles (or defects) in a dense collisionless, unmagnetized Thomas-Fermi plasma are investigated. A fully ionized three-component model plasma consisting of electrons, ions, and negatively charged massive dust grains is considered. Electrons and ions are assumed to be in a degenerate quantum state, obeying the Thomas-Fermi density distribution, whereas the inertial dust component is described by a set of classical fluid equations. Considering large-amplitude stationary profile travelling-waves in a moving reference frame, the fluid evolution equations are reduced to a pseudo-energy-balance equation, involving a Sagdeev-type potential function. The analysis describes the dynamics of supersonic dust-acoustic solitary waves in Thomas-Fermi plasmas, and provides exact predictions for their dynamical characteristics, whose dependence on relevant parameters (namely, the ion-to-electron Fermi temperature ratio, and the dust concentration) is investigated. An alternative route is also adopted, by assuming weakly varying small-amplitude disturbances off equilibrium, and then adopting a multiscale perturbation technique to derive a Korteweg–de Vries equation for the electrostatic potential, and finally solving in terms for electric potential pulses (electrostatic solitons). A critical comparison between the two methods reveals that they agree exactly in the small-amplitude, weakly superacoustic limit. The dust concentration (Havnes) parameter h = Zd0nd0/ne0 affects the propagation characteristics by modifying the phase speed, as well as the electron/ion Fermi temperatures. Our results aim at elucidating the characteristics of electrostatic excitations in dust-contaminated dense plasmas, e.g., in metallic electronic devices, and also arguably in supernova environments, where charged dust defects may occur in the quantum plasma regime.

Quenching small quantum gases: Genesis of the orthogonality catastrophe

We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two distinct species is suddenly switched on (quenched). We examine the behavior of the densities, the entanglement, the Loschmidt echo, and the spectral function for a large range of interspecies interactions and find that even in such small systems evidence of Anderson's orthogonality catastrophe can be witnessed.

Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases

The time evolution of the out-of-equilibrium Mott insulator is investigated numerically through calculations of space-time-resolved density and entropy profiles resulting from the release of a gas of ultracold fermionic atoms from an optical trap. For adiabatic, moderate and sudden switching-off of the trapping potential, the out-of-equilibrium dynamics of the Mott insulator is found to differ profoundly from that of the band insulator and the metallic phase, displaying a self-induced stability that is robust within a wide range of densities, system sizes and interaction strengths. The connection between the entanglement entropy and changes of phase, known for equilibrium situations, is found to extend to the out-of-equilibrium regime. Finally, the relation between the system`s long time behavior and the thermalization limit is analyzed. Copyright (C) EPLA, 2011

Interactions of Electrons and Rydberg Atoms in Ultra-Cold Plasmas

This thesis discusses an experimental technique for investigating electron temperature control by Rydberg atoms in ultra-cold plasmas. The objective we set ourselves was twofold. Firstly, we sought to gain an insight into the processes whereby the creation of Rydberg atoms within the plasma lengthens the lifetime of the plasma. To this end, we created the plasma using a Littman dye laser and subsequently, at a variable time delay, we excited neutral atoms in the plasma to specific Rydberg states using a narrow bandwidth pulsed dye laser. Secondly, we employed radio-frequency (rf) electric fields to excite electron oscillations within the plasma in order to infer such information as plasma density and electron temperature. Although we found that the introduction of high angular momentum Rydberg states did lengthen the plasma lifetime we were not able to differentiate between the temperature moderation effect due to the Rydberg atoms cooling the plasma, and the binding effect due to an increased positive space charge within the plasma.

Strongly correlated quantum gases in one dimension

In this work, we discuss some theoretical topics related to many-body physics in ultracold atomic and molecular gases. First, we present a comparison between experimental data and theoretical predictions in the context of quantum emulator of quantum field theories, finding good results which supports the efficiency of such simulators. In the second and third parts, we investigate several many-body properties of atomic and molecular gases confined in one dimension.

A scanning electron microscope for ultracold quantum gases

This thesis presents a new imaging technique for ultracold quantum gases. Since the first observation of Bose-Einstein condensation, ultracold atoms have proven to be an interesting system to study fundamental quantum effects in many-body systems. Most of the experiments use optical imaging rnmethods to extract the information from the system and are therefore restricted to the fundamental limitation of this technique: the best achievable spatial resolution that can be achieved is comparable to the wavelength of the employed light field. Since the average atomic distance and the length scale of characteristic spatial structures in Bose-Einstein condensates such as vortices and solitons is between 100 nm and 500 nm, an imaging technique with an adequate spatial resolution is needed. This is achieved in this work by extending the method of scanning electron microscopy to ultracold quantum gases. A focused electron beam is scanned over the atom cloud and locally produces ions which are subsequently detected. The new imaging technique allows for the precise measurement of the density distribution of a trapped Bose-Einstein condensate. Furthermore, the spatial resolution is determined by imaging the atomic distribution in one-dimensional and two-dimensional optical lattices. Finally, the variety of the imaging method is demonstrated by the selective removal of single lattice site. rn

Superfluid and antiferromagnetic phases in ultracold fermionic quantum gases

In this thesis several models are treated, which are relevant for ultracold fermionic quantum gases loaded onto optical lattices. In particular, imbalanced superfluid Fermi mixtures, which are considered as the best way to realize Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states experimentally, and antiferromagnetic states, whose experimental realization is one of the next major goals, are examined analytically and numerically with the use of appropriate versions of the Hubbard model.rnrnThe usual Bardeen-Cooper-Schrieffer (BCS) superconductor is known to break down in a magnetic field with a strength exceeding the size of the superfluid gap. A spatially inhomogeneous spin-imbalanced superconductor with a complex order parameter known as FFLO-state is predicted to occur in translationally invariant systems. Since in ultracold quantum gases the experimental setups have a limited size and a trapping potential, we analyze the realistic situation of a non-translationally invariant finite sized Hubbard model for this purpose. We first argue analytically, why the order parameter should be real in a system with continuous coordinates, and map our statements onto the Hubbard model with discrete coordinates defined on a lattice. The relevant Hubbard model is then treated numerically within mean field theory. We show that the numerical results agree with our analytically derived statements and we simulate various experimentally relevant systems in this thesis.rnrnAnalogous calculations are presented for the situation at repulsive interaction strength where the N'eel state is expected to be realized experimentally in the near future. We map our analytical results obtained for the attractive model onto corresponding results for the repulsive model. We obtain a spatially invariant unit vector defining the direction of the order parameter as a consequence of the trapping potential, which is affirmed by our mean field numerical results for the repulsive case. Furthermore, we observe domain wall formation, antiferromagnetically induced density shifts, and we show the relevant role of spin-imbalance for antiferromagnetic states.rnrnSince the first step for understanding the physics of the examined models was the application of a mean field approximation, we analyze the effect of including the second order terms of the weak coupling perturbation expansion for the repulsive model. We show that our results survive the influence of quantum fluctuations and show that the renormalization factors for order parameters and critical temperatures lead to a weaker influence of the fluctuations on the results in finite sized systems than on the results in the thermodynamical limit. Furthermore, in the context of second order theory we address the question whether results obtained in the dynamical mean field theory (DMFT), which is meanwhile a frequently used method for describing trapped systems, survive the effect of the non-local Feynman diagrams neglected in DMFT.

Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories

Abelian and non-Abelian gauge theories are of central importance in many areas of physics. In condensed matter physics, AbelianU(1) lattice gauge theories arise in the description of certain quantum spin liquids. In quantum information theory, Kitaev’s toric code is a Z(2) lattice gauge theory. In particle physics, Quantum Chromodynamics (QCD), the non-Abelian SU(3) gauge theory of the strong interactions between quarks and gluons, is nonperturbatively regularized on a lattice. Quantum link models extend the concept of lattice gauge theories beyond the Wilson formulation, and are well suited for both digital and analog quantum simulation using ultracold atomic gases in optical lattices. Since quantum simulators do not suffer from the notorious sign problem, they open the door to studies of the real-time evolution of strongly coupled quantum systems, which are impossible with classical simulation methods. A plethora of interesting lattice gauge theories suggests itself for quantum simulation, which should allow us to address very challenging problems, ranging from confinement and deconfinement, or chiral symmetry breaking and its restoration at finite baryon density, to color superconductivity and the real-time evolution of heavy-ion collisions, first in simpler model gauge theories and ultimately in QCD.

Ultra-cold fermions in optical lattices

We summarize recent theoretical results for the signatures of strongly correlated ultra-cold fermions in optical lattices. In particular, we focus on collective mode calculations, where a sharp decrease in collective mode frequency is predicted at the onset of the Mott metal-insulator transition; and correlation functions at finite temperature, where we employ a new exact technique that applies the stochastic gauge technique with a Gaussian operator basis.

Bifurcations in the non-dissipative dynamics of ultra cold atoms

We present the first experimental observation of several bifurcations in a controllable non-linear Hamiltonian system. Dynamics of cold atoms are used to test predictions of non-linear, non-dissipative Hamiltonian dynamics.