The non-Abelian gauge fields play a key role in achieving novel quantum phenomena in condensed-matter and high-energy physics. Recently, the synthetic non-Abelian gauge fields have been created in the neutral degenerate Fermi gases, and moreover, generate many exotic effects. All the previous predictions can be well understood by the microscopic Bardeen-Cooper-Schrieffer theory. In this work, we establish an SU(2) Ginzburg-Landau theory for degenerate Fermi gases with the synthetic non-Abelian gauge fields. We firstly address a fundamental problem how the non-Abelian gauge fields, imposing originally on the Fermi atoms, affect the pairing field with no extra electric charge by a local gauge-field theory,and then obtain the first and second SU(2) Ginzburg-Landau equations. Based on these obtained SU(2) Ginzburg-Landau equations, we find that the superfluid critical temperature of the intra- (inter-) band pairing increases (decreases) linearly, when increasing the strength of the synthetic non-Abelian gauge fields. More importantly, we predict a novel SU(2) non-Abelian Josephson effect, which can be used to design a new atomic superconducting quantum interference device.
The non-Abelian gauge fields play a key role in achieving novel quantum phenomena in condensed-matter and high-energy physics. Recently, the synthetic non-Abelian gauge fields have been created in the neutral degenerate Fermi gases, and moreover, generate many exotic effects. All the previous predictions can be well understood by the microscopic Bardeen-Cooper-Schrieffer theory. In this work, we establish an SU(2) Ginzburg-Landau theory for degenerate Fermi gases with the synthetic non-Abelian gauge fields. We firstly address a fundamental problem how the non-Abelian gauge fields, imposing originally on the Fermi atoms, affect the pairing field with no extra electric charge by a local gauge-field theory,and then obtain the first and second SU(2) Ginzburg-Landau equations. Based on these obtained SU(2) Ginzburg-Landau equations, we find that the superfluid critical temperature of the intra- (inter-) band pairing increases (decreases) linearly, when increasing the strength of the synthetic non-Abelian gauge fields. More importantly, we predict a novel SU(2) non-Abelian Josephson effect, which can be used to design a new atomic superconducting quantum interference device.
Quantum emulation property of the cold atoms has generated a lot of interest in studying systems with synthetic gauge fields. In this article, we describe the physics of two component Fermi gas in the presence of synthetic non-Abelian SU(2) gauge fields. Even for the non-interacting system with the gauge fields, there is an interesting change in the topology of the Fermi surface by tuning only the gauge field strength. When a trapping potential is used in conjunction with the gauge fields, the non-interacting system has the ability to produce novel Hamiltonians and show characteristic change in the density profile of the cloud. Without trap, the gauge fields act as an attractive interaction amplifier and for special kinds of gauge field configurations, there are two-body bound states for any attraction even in three dimensions. For a many body system, the gauge fields can induce a crossover from a weak superfluid to a strong superfluid with transition temperature as high as the Fermi temperature. The superfluid state obtained for a very large gauge field strength is a superfluid of new kind of bosons, called ``rashbons'', the properties of which are independent of its constituent two component fermions and are solely determined by the gauge field strength. We also discuss the collective excitations over the superfluid ground states and the experimental relevance of the physics.
Generation and study of synthetic gauge fields has enhanced the possibility of using cold atom systems as quantum emulators of condensed matter Hamiltonians. In this article we describe the physics of interacting spin -1/2 fermions in synthetic non-Abelian gauge fields which induce a Rashba spin-orbit interaction on the motion of the fermions. We show that the fermion system can evolve to a Bose-Einstein condensate of a novel boson which we call rashbon. The rashbon-rashbon interaction is shown to be independent of the interaction between the constituent fermions. We also show that spin-orbit coupling can help enhancing superfluid transition temperature of weak superfluids to the order of Fermi temperature. A non-Abelian gauge field, when used in conjunction with another potential, can generate interesting Hamiltonians such as that of a magnetic monopole.
Recent advances in the generation of synthetic gauge fields in cold atomic systems have stimulated interest in the physics of interacting bosons and fermions in them. In this paper, we discuss interacting two-component fermionic systems in uniform non-Abelian gauge fields that produce a spin-orbit interaction and uniform spin potentials. Two classes of gauge fields discussed include those that produce a Rashba spin-orbit interaction and the type of gauge fields (SM gauge fields) obtained in experiments by the Shanxi and MIT groups. For high symmetry Rashba gauge fields, a two-particle bound state exists even for a vanishingly small attractive interaction described by a scattering length. Upon increasing the strength of a Rashba gauge field, a finite density of weakly interacting fermions undergoes a crossover from a BCS like ground state to a BEC state of a new kind of boson called the rashbon whose properties are determined solely by the gauge field and not by the interaction between the fermions. The rashbon Bose-Einstein condensate (RBEC) is a quite intriguing state with the rashbon-rashbon interactions being independent of the fermion-fermion interactions (scattering length). Furthermore, we show that the RBEC has a transition temperature of the order of the Fermi temperature, suggesting routes to enhance the transition temperatures of weakly interacting superfluids by tuning the spin-orbit coupling. For the SM gauge fields, we show that in a regime of parameters, a pair of particles with finite centre-of-mass momentum is the most strongly bound. In other regimes of centre-of-mass momenta, there is no two-body bound state, but a resonance like feature appears in the scattering continuum. In the many-body setting, this results in flow enhanced pairing. Also, strongly interacting normal states utilizing the scattering resonance can be created opening the possibility of studying properties of helical Fermi liquids. This paper contains a general discussion of the physics of Feshbach resonance in a non-Abelian gauge field, where several novel features such as centre-of-mass-momentum-dependent effective interactions are shown. It is also shown that a uniform non-Abelian gauge field in conjunction with a spatial potential can be used to generate novel Hamiltonians; we discuss an explicit example of the generation of a monopole Hamiltonian.
Chiral superfluidity in ultracold Fermi gases represents a fascinating frontier in condensed matter physics, offering a pristine platform for exploring exotic quantum phases with topological properties. This paper provides a comprehensive review of the theoretical underpinnings and potential experimental realizations of chiral superfluids when ultracold Fermi gases are subjected to artificial gauge fields. We begin by introducing the concept of artificial gauge fields, detailing how they can be engineered using laser-atom interactions to impart synthetic spin-orbit coupling and break time-reversal symmetry, thereby creating conditions conducive to chiral order. We then delve into the microscopic theory of chiral pairing, particularly focusing on p-wave and p+ip superfluid states, which are intrinsically chiral and support topologically protected edge modes, such as Majorana fermions. The methodology section outlines the theoretical tools employed, including mean-field BCS theory and Bogoliubov-de Gennes equations, to predict the phase diagrams and spectroscopic signatures of these exotic states. We discuss the effects of varying interaction strengths, gauge field parameters, and trapping potentials on the emergence and stability of chiral phases. The potential for experimental detection through rf spectroscopy, noise correlations, and direct imaging of vortex cores is also addressed. Our findings underscore the significant potential of ultracold atomic systems as quantum simulators for unraveling the mysteries of topological phases, with profound implications for fundamental physics and quantum information science.
Since the realization of Bose-Einstein condensation in 1995, experimentalists in ultracold atomic gas community have developed a set of entirely new methods to study quantum gases. In ultracold atomic gases, implementation of synthetic gauge fields, the spin-orbit coupling, optical lattices and Feshbach resonances, provides a clean and highly controllable platform to tune the parameters of the system, which are typically fixed for real materials. Motivated by the rapid developments of experimental progresses, I investigate the ultracold atomic gases with synthetic gauge fields. \n \nIn this thesis, a bosonic gas in optical lattices in the presence of an effective staggered magnetic flux will be studied, using a generalized Bose-Hubbard model. Phase transition from the Mott insulating phase to the superfluid phase will be discussed. Novel superfluid phases including the stripe phase and the plane wave phase will be discussed. Furthermore, the existence of a tricritical point in the phase diagram is predicted. \n \nTo study Fermi systems with synthetic gauge fields, a spin-1=2 Fermi gas with Rashba spin-orbit coupling is investigated by studying the structure of vortex line through the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCSBEC) crossover. Due to the spin-orbit coupling, the s-wave interacting Fermi gas behaves like an effective p-wave paired system. A discussion about the vortex line structure will be provided by calculating the spatial distribution of the gap function, the density, the particle current, and also the elementary excitations. It has been found that the most robust superfluid occurs around the unitary point, indicated by the smallest healing length and the largest critical current. \n \nFinally, motivated by the recent progress of p-wave resonantly Fermi gas in experiment, an extension of Nozières-Schmitt-Rink method to the p-wave case will be given. An investigation of the normal state properties will be given by calculating the equation of state and the p-wave contacts, which have been measured by the experiment. Furthermore, the superfluid transition temperature with realistic parameters appropriate for experiment is calculated and is found to be within experimental reach.
On increasing the coupling strength ($\ensuremath{\lambda}$) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density $\ensuremath{\rho}\ensuremath{\sim}{k}_{F}^{3}$ undergoes a change at a critical value, ${\ensuremath{\lambda}}_{T}\ensuremath{\approx}{k}_{F}$ [Phys. Rev. B 84, 014512 (2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-21 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing $\ensuremath{\lambda}$. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling $\ensuremath{\lambda}$. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.