This thesis contains a study of ultracold paramagnetic atoms or polar molecules characterized by a long-range anisotropic dipolar interaction. We particularly focus on two aspects of ultracold dipolar gases. In the first problem the ground state properties of dipolar Bose-Einstein condensates (BEC) are investigated. This problem has gained importance due to recent experimental advances in achieving a condensate of Chromium atoms and ongoing research to produce quantum degenerate polar molecules. In the second problem, we consider possible applications of ultracold polar molecules to rotation sensing and interferometry. First, we concentrate on the interplay between the trapping geometry and dipole-dipole interaction for a polarized dipolar bosonic condensate. As the dipole-dipole interaction is attractive along the polarized direction, the lowest energy state of the BEC is always a collapsed state. However by applying a trapping potential along the polarization direction it is possible to achieve a metastable dipolar BEC. By numerically solving the Gross-Pitaevskii equation, we show that below a critical interaction strength, a metastable state exists depending on the trapping geometry. We also show that a novel feature of dipolar BEC is the appearance of different structural metastable ground states for certain combinations of trapping geometry and particle number. Next, by mixing in single component fermions we show that dipolar BEC can be stabilized against collapse in pancake shaped or cylindrical traps. We also show that the excitation spectrum of the BEC may have a minimum for non-zero momentum, termed a “roton minimum”. This minimum leads to a transition to stable or metastable density-wave states depending on the density of the bosons and boson-fermion interaction strength. In the second problem, we study a proposal for a large-angle coherent beam splitter for polar molecules. By taking into account the effect of a quasi-static external electric field on the rotational levels of the polarized molecules we show that it is possible to coherently split a stationary cloud of molecules into two counter-propagating components. We then investigate the effect of longitudinal acceleration on the transverse motion of the particles, assuming that the longitudinal motion of the molecules can be approximated classically by a wave packet with some mean velocity while the transverse motion is governed by quantum mechanics. We propose a particular time-dependent shape of acceleration to minimize the excitations in the transverse motion. Our theory is also applicable to the general case of particles moving along a circular guide with time-dependent longitudinal velocity. In addition, we include the effects of velocity fluctuations due to noise in the accelerating field.
This thesis contains a study of ultracold paramagnetic atoms or polar molecules characterized by a long-range anisotropic dipolar interaction. We particularly focus on two aspects of ultracold dipolar gases. In the first problem the ground state properties of dipolar Bose-Einstein condensates (BEC) are investigated. This problem has gained importance due to recent experimental advances in achieving a condensate of Chromium atoms and ongoing research to produce quantum degenerate polar molecules. In the second problem, we consider possible applications of ultracold polar molecules to rotation sensing and interferometry. First, we concentrate on the interplay between the trapping geometry and dipole-dipole interaction for a polarized dipolar bosonic condensate. As the dipole-dipole interaction is attractive along the polarized direction, the lowest energy state of the BEC is always a collapsed state. However by applying a trapping potential along the polarization direction it is possible to achieve a metastable dipolar BEC. By numerically solving the Gross-Pitaevskii equation, we show that below a critical interaction strength, a metastable state exists depending on the trapping geometry. We also show that a novel feature of dipolar BEC is the appearance of different structural metastable ground states for certain combinations of trapping geometry and particle number. Next, by mixing in single component fermions we show that dipolar BEC can be stabilized against collapse in pancake shaped or cylindrical traps. We also show that the excitation spectrum of the BEC may have a minimum for non-zero momentum, termed a “roton minimum”. This minimum leads to a transition to stable or metastable density-wave states depending on the density of the bosons and boson-fermion interaction strength. In the second problem, we study a proposal for a large-angle coherent beam splitter for polar molecules. By taking into account the effect of a quasi-static external electric field on the rotational levels of the polarized molecules we show that it is possible to coherently split a stationary cloud of molecules into two counter-propagating components. We then investigate the effect of longitudinal acceleration on the transverse motion of the particles, assuming that the longitudinal motion of the molecules can be approximated classically by a wave packet with some mean velocity while the transverse motion is governed by quantum mechanics. We propose a particular time-dependent shape of acceleration to minimize the excitations in the transverse motion. Our theory is also applicable to the general case of particles moving along a circular guide with time-dependent longitudinal velocity. In addition, we include the effects of velocity fluctuations due to noise in the accelerating field.
In this thesis we study the effects of the dipole-dipole interaction on the physics of ultracold quantum gases, both bosonic and fermionic, within the theoretical framework provided by the mean-field regime. This kind of interaction takes place in ultracold atomic gases (for instance 52Cr or 164Dy) due to their atomic magnetic dipole moment, and in ultracold molecular gases due to the magnetic or electric dipole moment. \n \nIn the case of quantum gases of bosonic atoms, or Bose-Einstein condensates, the dipole-dipole interaction can be studied within mean-field approximation using the Gross-Pitaevskii equation, which now contains a new non-linear term due to the dipole-dipole interaction. We investigate, on the one hand dipolar condensates confined in harmonic traps, and on the other dipolar condensates confined in toroidal traps. In the harmonic geometry, our focus is on the study of the ground state and the quantized vortex state, where the density profile is characterized as well as some properties leading to the process of vortex formation, such as the critical frequency and the energy barrier that has to be overcome to bring the vortex from the surface to the centre of the gas. We finish the study of dipolar condensates in harmonic traps by dynamically simulating the precession frequency of an off-center vortex in a non-rotating condensate. \n \nIn the toroidal geometry the dipolar effects are strongly magnified when the polarization axis of the dipoles is perpendicular to the trap symmetry axis. In this case, the anisotropic structure of the density can be understood as the response of the system to the double-well effective potential along the ring. We have studied the dynamics of this system when the initial number of atoms in the left and right wells is imbalanced, predicting Josephson and self-trapping oscillations depending on the initial condition. This has led us to name this new system as Self-induced Josephson Junction. We have studied in detail the self-trapping regime and we have seen that the particle flux inversion is closely related to the crossing of vortices across the Josephson junctions. This result opens the door to establishing a more direct connection between the phase-slip regime, widely addressed in superfluid helium, and the self-trapping regime of condensates. \n \nIn the case of quantum gases of fermionic dipolar particles, we have studied how the radial quadrupole mode allows one to distinguish between hydrodynamic and collisionless regimes. We have analytically calculated the frequency of this mode in the mean-field approximation, generalizing the results from the Thomas-Fermi approximation for trapped ideal Fermi gases. On the one hand, we observe that the frequency in the hydrodynamic regime is smaller than in non-dipolar Fermi gases, while in the collisionless regime the frequency is larger or smaller than that corresponding to the non-interacting system depending on the geometry of the harmonic trap. On the other hand, we predict that reducing the trap deformation (aspect ratio) an observable jump in the frequency of the radial quadrupole mode would take place, which would correspond to the transition between the collisionless and hydrodynamic regimes, for instance when the gas undergoes the transition to the superfluid state.
Today, sixteen years after the realization of the first Bose-Einstein condensate (BEC), the field of ultracold many-body physics is booming. In particular, much excitement has been generated by the prospect of creating a degenerate quantum gas of dipolar atoms or molecules. Already, some experimental groups have succeeded in Bose-condensing atomic 52Cr and 164Dy, while other groups have made significant progress towards achieving degeneracy of heteronuclear molecules, such as fermionic 40K87Rb and bosonic 87Rb133Cs, where the strength of the dipolar interaction promises to be much greater than that of the already rich 52Cr condensate. Just as the creation of BEC launched a whole new field of research, dipolar BECs are likely to do the same. However, such systems present a theoretical challenge due to the long-range, anisotropic nature of the dipolar interaction. In this thesis, I present a theoretical investigation of ultracold Bose gases with dipolar interactions.\nThe first part of this thesis is dedicated to the field theoretical treatment of a quantum Bose fluid with dipolar interactions in the ultracold, dilute regime, where the system is well-described by a classical condensate field with quasiparticle excitations. The set of nonlinear integrodifferential equations that describe these objects are derived and novel methods for solving them are presented that, in general, require intricate numerical treatment. Of particular importance is the emergence of a roton mode, reminiscent of that in superfluid 4He. In the second part of this thesis, I show how the roton plays a critical role in the ground state structure and dynamics of a dipolar BEC. Full numerical simulations show that the roton can, for example, be seen in the radial density profile of a quantized vortex state or in the angular collapse and explosion of a dipolar BEC. Additionally, I show the crucial role that this roton plays in determining the transition to superfluidity in these systems. Thus, a set of novel phenomena in ultracold dipolar Bose gases is explained by the presence of the roton, and experimental signatures of these phenomena are made clear.
Ultracold dilute atomic gases are highly controllable systems whose properties are fundamentally determined by the interatomic interactions.In typical experiments on ultra cold gases particles interact dominantly via a short-range isotropic potential.However, during the last years a new generation of experiments is starting to explore systems, where an additional interaction, the long-range and anisotropic dipole-dipole interaction plays a significant or possibly dominant role.The effects induced by the anisotropy of the dipole-dipole interaction are crucially enhanced if the dipolar gas is confined in a deep optical lattice.In this thesis we study novel phenomena in such systems of dipolar gases in deep optical lattices.The nonlocal nonlinearity introduced by the dipole-dipole interaction plays a crucial role in the physics of dipolar Bose-Einstein condensates.In particular, it may distort significantly the stability of straight vortex lines.Remarkably, in the presence of a periodic potential along the vortex line, the spectrum of transverse modes shows a roton-like minimum, which eventually destabilizes the straight vortex when the BEC as a whole is still stable, opening the possibility for new scenarios for vortex line configurations in dipolar gases.We have analyzed this instability, and showed that it leads to a second-order-like phase transition from a straight vortex line into novel helical or snake-like configurations, depending on the dipole orientation.Strong 1D lattices usually lead to unconnected two-dimensional gases.The long-range character of the dipole-dipole interactions leads to a novel scenario where non-overlapping gases at different sites may interact significantly.We show that the excitations of non-overlapping condensates in 1D optical lattices acquire a band-like character, being collectively shared by different sites.In particular, the hybridization of the modes significantly enhances the rotonization of the excitations, and may induce roton-instability.We discuss the observability of this effect in on-going experiments.Fermionic polar molecules in deep 1D optical lattices may form selfassembled filaments when the electric dipoles are oriented along the lattice axis.These composites are bosons or fermions depending on the number of molecules per chain, leading to a peculiar and complex Bose-Fermi mixture, vi which we discuss in detail for the simplest case of a three-well potential.We show that the interplay between filament binding energy, transverse filament modes, and trimer Fermi energy leads to a rich variety of possible scenarios ranging from a degenerate Fermi gas of trimers to a binary mixture of two different types of bosonic dimers.We study the intriguing zero temperature and finite temperature physics of these composites for the particular case of an ideal filament gas loaded in 1D sites, and discuss possible methods to probe these chain mixtures.
The work of this thesis concerns the properties of a Bose gas of polarised dipoles that have long-range and anisotropic interactions. Our work is divided into two parts. First, the stability of a dipolar Bose gas at finite temperature (both above and below the critical Bose-Einstein condensation (BEC) temperature Tc). Second, the fluctuations of a dipolar BEC at zero and small finite temperature (T ≪ Tc) in a regime where rotonic excitations emerge. \n \nPart I: Stability of a Trapped Finite Temperature Dipolar Bose Gas: Above Tc we implement a semiclassical Hartree-Fock theory and characterise the dependence of the stability boundary on temperature, trap geometry and the strength of the dipole-dipole interaction and contact interaction. We find that stability is greatly enhanced above Tc and that trap geometry continues to play a key role. Furthermore, we find that for oblate traps a novel double instability feature emerges. \nTo extend our stability analysis to the low temperature regime, T < Tc, we develop a beyond semiclassical Hartree theory. We use this to characterise the stability boundary as a function of geometry. Interestingly, we find large beyond semiclassical effects above Tc for prolate trapping geometries. We characterise thermal effects on biconcave condensate states. \n \nPart II: Rotons and Fluctuations in a Trapped Dipolar Condensate: To study density fluctuations we implement a numerical scheme to solve the Gross-Pitaevskii equation and the Bogoliubov de Gennes equations. We find that the phonon and roton gases spatially separate and we characterise the role of the anomalous density on the density fluctuations of the thermally activated rotons. We develop a numerical scheme that calculates number fluctuations within cells of various shapes and sizes, and find a strong peak in the fluctuations when the cell size is around half the roton wavelength, which should be detectable by current experiments. By tailoring the cell shape we predict that experiments should be able to detect the effects of individual roton modes. \nFor the study of zero temperature fluctuations we deploy the Gross-Pitaevskii and Bogoliubov de Gennes equations to calculate the dynamic and static structure factors for a highly oblate BEC. We find a clear signature of the roton gas dispersion relation within the structure factors. This signature should be detectible in current experiments using Bragg spectroscopy.
Physics of ultra cold atoms and molecules is one of the most rapidly developing areas of the modern atomic, molecular, optical physics and quantum optics.This area covers several sub-areas of diverse importance, but definitely two trends can be easily identifies: i) fundamental research on properties of ultra cold atoms and molecules, and in particular atomic and molecular condensates trapped and lattice gases; here the fundamental questions of nature and form of phase transitions in degenerate systems are being posed and studied; ii) more applications oriented research on ultracold atoms and molecules, involving in particular applications in precision measurements, atomic clocks, frequency standards, atom and molecule interferometry, quantum information, quantum engineering, "super" chemistry etc.This thesis concerns both of these major trends.The applications, or more specifically quantum engineering aspect are discussed in the first four chapters of the thesis, which deal with optical manipulations of ultra cold gases, in particular optical generation of vortices in Bose condensates, quasi-solitons in Fermi gases, and retarded dipole-dipole interactions in Bose, or Fermi gases.This thesis consists of four main chapters.Chapter 2, "Optical generation of vortices in Bose Einstein Condensates".In this chapter we study theoretically the generation of vortices by phase imprinting in trapped Bose-Einstein condensates.Phase imprinting is achieved by passing a short off-resonance laser pulse through an appropriately designed absorption plate, and impinging it on a condensate.We answer the fundamental question of how the circulation and the vortex are introduced into the system, and discuss the creation of vortex arrays.We discuss vortex dynamics and interactions in such configurations.Various methods of vortex detection based on interference combined with Bragg scattering are also analyzed.In Chapter 3, "Fermionic 'Solitons'" we investigate in detail the concept of low energy excitations of ultra cold Fermi gases.This excitations are generated using the same idea of phase imprinting as that employed in the generation of vortices in BEC.We address in this chapter some questions concerning the generation (via phase imprinting) of soliton-like solutions in a single-component Fermi gas of neutral atoms at zero and finite temperatures.By using both numerical and analytical calculations, we find the conditions under which it is possible to find in non-interacting Fermi gases, quasisolitons which resemble the properties of solitons in non-linear integrable equations.We present the results for both spatially homogeneous and trapped cases, and emphasize the importance of Fermi statistics and the absence of interactions for the existence of such solutions.In Chapter 4, "Generating Dipole Condensate" we keep studying the possibilities of optical manipulations of ultracold gases.In particular, we study two different ways to laser-induce dipole-dipole interactions in trapped Bose-Einstein condensates.The first one employs the fact that those atoms in high Rydberg states posses a large dipolar moment.We first analyze the idea of imposing the dipole moment as a time average over short stroboscopic pulses.These pulses are coherently transporting the atoms from the ground atomic state to some high Rydberg state and back.The second idea is based on the observation that in strong static or oscillatory electric fields, atoms polarize and acquire dipole moment.We analyze the possibilities and limitations of inducing such a high electric field using lasers of low frequency.In Chapter 5, "Dipolar BCS", we continue our study of trapped fermionic gases, with the analysis of the BCS transition in trapped dipolar fermionic gases.We find that the critical strength of the dipole-dipole interaction to achieve BCS pairing, depends on the trap geometry.We find the particular form of this dependence, and present the solutions for the order parameter.This first chapter is meant as a general introduction to the thesis.This introduction is by no means exhaustive, and should be rather treated as a collection of basic facts concerning ultra cold gases, without rigorous derivations.The last subsection of the introductory chapter, discusses very briefly the most important achievements and trends in the field and the current state of the art.
Interactions between particles play an important role in quantum degenerate gases.\nIn fact, the system’s behavior is usually largely determined by the strength, range, and\nsymmetry of the interactions, even if very weak. For more than two decades after the\nfirst experimental realization of a Bose-Einstein condensate (BEC) in 1995, investigations of ultracold atomic gases have mainly considered contact-type interactions, which\nmodel the short-range van der Waals interactions between the atoms in terms of a single\nparameter, the s-wave scattering length. However, some atomic or molecules species\npossess a magnetic or electric dipole moment and additionally interact among each\nother via the dipole-dipole interaction (DDI), which is long-ranged and anisotropic.\nSignatures of the DDI have been first observed in a BEC of chromium atoms in 2005.\nIn the last several years, a new class of atoms from the lanthanide series, e.g., dysprosium and erbium, with stronger dipolar properties, have come into play. This permits\na more full-fledged study of dipolar effects in BECs. Furthermore, ultracold molecules\nand highly excited Rydberg atoms are other promising examples for futures studies of\nsystems where dipolar interaction will be even more dominant, but they still need experimental efforts to achieve the desired quantum regime. Whereas the weak DDI in a\nchromium BEC is well described with the Gross-Pitaevskii equation, stronger dipolar\ninteractions certainly necessitate a beyond-mean-field description within a Bogoliubov\ntheory.\nIn parallel to research on bosons, cold fermions also trigger great interest because\nthey are actually often found in nature, e.g., within the electron gas of metals, as\nneutrons of heavy stars, or as quarks in plasmas as constituent elements of composite particles. Contrary to Bose systems, quantum degeneracy in experiments is much\nmore difficult to achieve in Fermi systems, since s-wave scattering is absent between\nidentical fermions, due to the Pauli exclusion principle. It was first achieved in 1999\nfor alkali atoms using a technique based on the sympathetic cooling with a second spin\nstate, another species, or a different isotope. For highly magnetic atoms, quantum degeneracy was achieved for dysprosium in 2012 using the standard sympathetic cooling\ntechnique, while in 2014 erbium was cooled deep into the degenerate regime using a\ndirect evaporative cooling mediated by dipolar collisions. This direct cooling scheme\nivallows producing very dense Fermi gas down to 10% of the Fermi temperature.\nFurthermore, a novel kind of strongly dipolar quantum gases became available in\nthe last several years. These are weakly bound polar molecules produced from atoms\nwith large magnetic dipole moments, such as erbium. Only very recently a quantum\ndegenerate dipolar Fermi gas of potassium-rubidium molecules has been experimentally realized. Unlike previously considered magnetic systems, heteronuclear molecules\nsuch as potassium-rubidium possess large electric dipole moments. The next natural\nstep is to polarize this system in a preferential direction by an external electric field,\nsuch that the DDI dominates the behavior of the system, which would open up the\nrealm for experimental investigation of strong dipolar Fermi gases...