We investigate the possibilities for the generation of solitons and vortices in a degenerate gas of neutral fermionic atoms. In analogy with the already experimentally demonstrated technique applied to a gaseous Bose-Einstein condensate we propose the phase engineering of a Fermi gas as a practical route to excited states with solitons and vortices. We stress that solitons and vortices appear even in a non-interacting fermionic gas. For solitons, in a system with a sufficiently large number of fermions and appropriate trap configuration, the Pauli blocking acts as the interaction between particles.
We investigate the possibilities for the generation of solitons and vortices in a degenerate gas of neutral fermionic atoms. In analogy with the already experimentally demonstrated technique applied to a gaseous Bose-Einstein condensate we propose the phase engineering of a Fermi gas as a practical route to excited states with solitons and vortices. We stress that solitons and vortices appear even in a non-interacting fermionic gas. For solitons, in a system with a sufficiently large number of fermions and appropriate trap configuration, the Pauli blocking acts as the interaction between particles.
We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic bright solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a quasi-one-dimensional cigar-shaped geometry. Due to a strong Pauli-blocking repulsion among spin-polarized fermions at short distances there cannot be bright fermionic solitons in the case of repulsive boson-fermion interactions. However, we demonstrate that stable bright fermionic solitons can be formed for a sufficiently attractive boson-fermion interaction in a boson-fermion mixture. We also consider the formation of fermionic solitons in the presence of a periodic axial optical-lattice potential. These solitons can be formed and studied in the laboratory with present technology.
We theoretically consider the formation of bright solitons in a mixture of Bose and Fermi degenerate gases. While we assume the forces between atoms in a pure Bose component to be effectively repulsive, their character can be changed from repulsive to attractive in the presence of fermions provided the Bose and Fermi gases attract each other strongly enough. In such a regime the Bose component becomes a gas of effectively attractive atoms. Hence, generating bright solitons in the bosonic gas is possible. Indeed, after a sudden increase of the strength of attraction between bosons and fermions (realized by using a Feshbach resonance technique or by firm radial squeezing of both samples) soliton trains appear in the Bose-Fermi mixture.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the s-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
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.
In 1995 two different research groups observed for the first time the Bose-Einstein condensation (BEC) in ultracold gases. When the confining magnetic trap was turned off the gas was left free to expand, and the velocity of the particles showed a clear peak: most of the particles were occupying the same single particle state, the one of lowest energy. The Bose-Einstein condensation had been predicted in 1925 by Einstein, written by inspiration of a work on the statistic of the photons by Bose (1924). In this work Bose described the behavior of an ensemble of photons, treating them as massless particles, with no number conservation associated. Einstein extended this approach to particles with a mass and with fixed number, creating what is now called the Bose-Einstein distribution. The particles that follow such a description are called ``bosons'', as opposed to the ``fermions'' of the Fermi-Dirac statistics. Einstein predicted that in a gas of bosons - under a critical temperature - a finite fraction of the total number of particles would have been in the ground state, and act as a single entity. This amusing theoretical discovery found its utility a few years later. In the late thirties, new techniques allowed to cool Helium-4 at few Kelvins above the absolute zero. The properties of the resulting liquid were a puzzlement to the scientific community: among others, it could flow without experiencing friction. The liquid was called a ``superfluid''. A first explanation was given by London in 1938, which linked the superfluid behavior to the presence of a BEC among the bosonic Helium particles. The fermions cannot condense by themselves. On the other hand, they can form bound pairs and act as bosons, as it happens in a metal at low temperature. Using this approach, in 1957 Bardeen, Cooper and Schrieffer created a successful model of superconductivity by describing a superconductor as a superfluid in a charged system. During the course of these years we explored the superfluid properties of Bosons and Fermions in different settings. The original contributions of the thesis are described starting from the third chapter, where we speak about the generation and stability of solitons in a periodic optical lattices, both fixed or in motion. In the fourth chapter we study the generation of giant vortices in cold fermions, by using a generalized hydrodynamical approach. In chapter 5 we study the effect of a quasiperiodic lattice and the glassy phase it produces on a gas of bosons. Finally, we study the interaction of normal matter and superfluids with gravitational waves. While this interaction is seen to be extremely small, we believe that the resulting formalism is interesting by itself.