The artificial magnetic fields engineered for ultracold gases depend on the internal structure of the neutral atoms. Therefore the components of a mixture composed of two atomic gases can exhibit a different response to an artificial magnetic field. Such a mixture can be interpreted as a mixture of two atomic gases, carrying different synthetic charges. We consider such mixtures of two superfluids with unequal synthetic charges in a ring trap subject to a uniform artificial magnetic field. The charge imbalance in such a mixture changes the distribution of excited particles over angular momentum states compared to that of an equally charged mixture. This microscopic difference exhibits macroscopic consequences, such as the occurrence of an angular momentum transfer between two unequally charged components. Due to the interfluid atomic interactions in a ring, the angular momentum transfer can create a counterflowing persistent current in the weakly charged superfluid. Even in the limiting case of a charged and an uncharged superfluid mixture, a persistent current can be induced in the uncharged superfluid, despite the fact that it is not directly coupled to the magnetic field. The stability analysis shows that the induction depends on the interplay between the interfluid interaction and the applied magnetic field. We obtain instability boundaries of the system and construct phase diagrams as a function of the interfluid interaction and the magnetic field. We investigate these properties employing the Bogoliubov approximation.
The artificial magnetic fields engineered for ultracold gases depend on the internal structure of the neutral atoms. Therefore the components of a mixture composed of two atomic gases can exhibit a different response to an artificial magnetic field. Such a mixture can be interpreted as a mixture of two atomic gases, carrying different synthetic charges. We consider such mixtures of two superfluids with unequal synthetic charges in a ring trap subject to a uniform artificial magnetic field. The charge imbalance in such a mixture changes the distribution of excited particles over angular momentum states compared to that of an equally charged mixture. This microscopic difference exhibits macroscopic consequences, such as the occurrence of an angular momentum transfer between two unequally charged components. Due to the interfluid atomic interactions in a ring, the angular momentum transfer can create a counterflowing persistent current in the weakly charged superfluid. Even in the limiting case of a charged and an uncharged superfluid mixture, a persistent current can be induced in the uncharged superfluid, despite the fact that it is not directly coupled to the magnetic field. The stability analysis shows that the induction depends on the interplay between the interfluid interaction and the applied magnetic field. We obtain instability boundaries of the system and construct phase diagrams as a function of the interfluid interaction and the magnetic field. We investigate these properties employing the Bogoliubov approximation.
Atoms with different internal states can exhibit different responses to an artificial magnetic field. An atomic gas mixture of two different components can therefore be interpreted as a mixture of two atomic gases carrying different synthetic charges. We consider the superfluid state of such unequally charged Fermi gases coupled to a magnetic field via the orbital effect and trapped in a torus geometry. The orbital coupling to the magnetic field favors an inhomogeneous superfluid state with optimum finite-center-of-mass-momentum pairing. The resulting population-balanced orbital Fulde-Ferrell (FF) state is robust against the magnetic field and does not undergo pair breaking, unlike the conventional BCS and Fulde-Ferrell-Larkin-Ovchinnikov-type pairing states under the Zeeman effect. We contrast the homogeneous and inhomogeneous cases, emphasizing the advantages of the unequally charged systems, and present their momentum distributions. We conclude that an unequally charged atomic Fermi gas system orbitally coupled to an artificial magnetic field provides an ideal candidate for experimental realization of the FF state.
Artificial magnetic fields (AMFs) created for ultracold systems depend sensitively on the internal structure of the atoms. In a mixture, each component experiences a different AMF depending on its internal state. This enables the study of Bardeen-Cooper-Schrieffer pairing of fermions with unequal effective charges. In this Letter, we investigate the superconducting (SC) transition of a system formed by such pairs as a function of field strength. We consider a homogeneous two-component Fermi gas of unequal effective charges but equal densities with attractive interactions. We find that the phase diagram is altered drastically compared to the usual balanced charge case. First, for some AMFs there is no SC transition and isolated SC phases are formed, reflecting the discrete Landau level (LL) structure. SC phases become reentrant both in AMF and temperature. For extremely high fields where both components are confined to their lowest LLs, the effect of the charge imbalance is suppressed. Charge asymmetry reduces the critical temperature even in the low-field semiclassical regime. We discuss a pair breaking mechanism due to the unequal Lorentz forces acting on the components of the Cooper pairs to identify the underlying physics.
Artificial magnetic fields (AMFs) created for ultracold systems depend sensitively on the internal structure of the atoms. In a mixture, each component experiences a different AMF depending on its internal state. This enables the study of Bardeen-Cooper-Schrieffer pairing of fermions with unequal effective charges. In this Letter, we investigate the superconducting (SC) transition of a system formed by such pairs as a function of field strength. We consider a homogeneous two-component Fermi gas of unequal effective charges but equal densities with attractive interactions. We find that the phase diagram is altered drastically compared to the usual balanced charge case. First, for some AMFs there is no SC transition and isolated SC phases are formed, reflecting the discrete Landau level (LL) structure. SC phases become reentrant both in AMF and temperature. For extremely high fields where both components are confined to their lowest LLs, the effect of the charge imbalance is suppressed. Charge asymmetry reduces the critical temperature even in the low-field semiclassical regime. We discuss a pair breaking mechanism due to the unequal Lorentz forces acting on the components of the Cooper pairs to identify the underlying physics.
We consider ultracold imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mixtures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species. In both cases, the number of atoms for each component is allowed to be different, leading to a spin imbalance or a polarization. In the second case, the two different species also give rise to a mass imbalance for the particles. Imbalanced Fermi mixtures play a fundamental role in condensed-matter, nuclear and astroparticle physics. Experimentally, the atomic mixtures are made strongly interacting with the use of two-channel Feshbach resonances. We start out by treating these in more detail. We review the relevant scattering theory, and apply it to the well-studied case of resonant s-wave collisions with zero angular momentum. Furthermore, we discuss the less-studied case of p-wave collisions with nonzero angular momentum, and the inhomogeneous case due to a trapping potential. Having discussed the two-body physics, we turn to the many-body physics. The pioneering experimental studies of Cooper pairing in lithium-6 mixtures with a spin imbalance were performed by Zwierlein et al. [Science 311, 492 (2006)] and Partridge et al. [Science 311, 503 (2006)]. We study the mean-field theory for the polarized Fermi mixture to obtain a qualitative understanding of these experiments. In the unitarity limit, where the scattering length of the interatomic interaction diverges, the theory gives rise to two exotic superfluid phases that are absent in the balanced mixture. These are the gapless superfluid Sarma phase and the phase-separated phase. By using renormalization group techniques to account for the effects of strong interactions, we obtain also quantitative agreement with Monte-Carlo calculations and experiments. We then generalize our knowledge of the solely spin-imbalanced mixture to the mass-imbalanced case, where in particular the mixture consisting of lithium-6 and potassium-40 is experimentally promising. We study the mean-field phase diagram for this mixture in the unitarity limit, where we not only find phase separation and Sarma superfluidity, but also a Lifshitz point. The latter signals an instability towards a supersolid phase. We also include the effects of fluctuations, which do not alter the topology of the phase diagram. However, fluctuation effects lower the critical temperatures with an experimentally relevant factor of three. Finally, we study superfluidity in a fully polarized gas of potassium-40 atoms near a p-wave Feshbach resonance. In particular, we consider coherent Josephson oscillations between the superfluid components in the two channels of the resonance, whose frequencies contain a clear signature of the quantum phase transition that occurs as a function of applied magnetic field.
In this thesis we first review the theory of the normal state of the unitary Fermi gas at T = 0 and the main properties of the normal-to-superfluid transition. Then we study the trapped gas under adiabatic rotation, i.e., avoiding the formation of vortices. We show that for polarized systems the rotation enhances the Chandrasekhar-Clogston limit due to pair breaking at the border between the superfluid and the normal phase, while it leaves the global critical polarization Pc of the trapped system unaffected. In the case of an unpolarized unitary superfluid the rotation causes a phase separation between a superfluid core and an unpolarized normal shell, in which the densities of the spin-up and spin-down atom numbers is equal. For both the polarized and the unpolarized systems we calculate experimental observables such as the density profiles and the angular momenta. From the study of Bose-Einstein condensates it is well known that an adiabatic rotation induces a quadrupole deformation of the trapped atomic cloud when the rotation exceeds a certain angular velocity. In Fermi gases the situation is different due to the phase separation discussed above, and the quadrupole instabilities are found to set on at smaller angular velocity than in the BEC case. This phenomenon together with a more general discussion concerning not only the energetic but also the dynamic instabilities of the phase separated system is presented. We use the present knowledge of the equation of state of Fermi mixtures with unequal masses to give quantitative predictions for the phase separation between the normal and superfluid components. The analysis is based on the study of the zero temperature μ-h phase diagram of the uniform two component gas. The phase diagram at unitarity is determined thanks to the knowledge of the equation of state available from diagrammatic techniques applied to highly polarized configurations and from Monte Carlo simulations. The phase diagram is then used, in the local density approximation, to calculate the density profiles of the two Fermi components in the presence of harmonic trapping. Eventually we investigate the polarization produced by the relative displacement of the potentials trapping two spin species of a unitary Fermi gas with population imbalance. We investigate the dipole polarizability of a polarized system both in the two-fluid and the three-fluid model at zero temperature and point out the major differences between the two treatments.
Ultracold gases are remarkably versatile and controllable systems with untapped potential to emulate a variety of quantum phenomena [1]. Atoms are, however, electrically neutral and therefore it is highly desirable to make them behave as charged particles. This capability has recently been demonstrated in a series of recent experiments [2–4]. Although many challenges remain ahead, atoms exposed to synthetic gauge field offer great opportunities for the realization of new classes of quantum materials with custom-designed properties, and with unforeseen applications. The first implementation of an effective magnetic field was accomplished by rotating an atomic cloud [5]. In the rotating frame of reference, an atom experiences the Coriolis force that emulates the Lorentz force experienced by a charged particle in a uniform magnetic field. Large vortex lattices have been created in this way, however, so far the strength of the effective magnetic field achieved by rotation is too weak to lead to new physics. An alternative approach invokes the vector potential, A, that induces a geometric phase as a charged particle moves around a closed loop. This notion of geometric phase can be adapted to a neutral atom that slowly moves in the presence of laser fields. If the lasers are chosen to ‘dress’ the internal atomic levels, so that the dressed eigenstates become position dependent, the center of mass adiabatically evolves according the operator p-A, instead of just p = −iℏ∇. The atom thus effectively moves as a charged particle in a magnetic field B = ∇ × A (see Fig. 1a). Exploiting this idea series of experiments have implemented artificial magnetic and electric fields [2–4]. The idea has also been implemented in the presence of a superimposed periodic optical lattice potential (see Fig. 1b). In this case, the length scale imposed by the lattice competes with the one associated with the magnetic field and can lead to frustration, manifested as an energy spectrum with fractal characteristics [2,3]. Light induced synthetic gauge fields: (a) A gas of neural atoms (green oval) can behave as a gas of charged particles when it is illuminated by a pair of laser beams (red arrows) that imparts momentum to the atoms and couples their internal (.|↑.〉, .|↓.〉) and motional degrees of freedom. The Raman beams that induce transitions between internal states also transfer two units of their linear momentum 2kL. This leads to the formation of dressed states (superpositions of states with different internal levels and center of mass momenta) which experience a modified kinetic energy, with an effective vector potential. If the effective vector potential has nonzero curl, the atoms move as charged particles in a magnetic field. (b) In the presence of an optical lattice potential, Raman beams can also induce an effective vector potential. In this case, the lattice is engineered so that along one direction atoms can tunnel between adjacent lattice sites (Jlight) only by absorbing and emitting photons from the beams. The imparted momentum from the lasers produces path-dependent phases that resemble the magnetic flux accumulated by a charged particle as it moves in a closed loop. The flux accumulated by the atoms when they move around a single unit cell, ϕ, can be significant (equivalent to the one generated by a real magnetic field of thousands tesla in an electronic system) and induce a fractal energy spectrum. Generalizations to emulate non-Abelian gauge potentials, associated in many cases to spin-orbit coupling can emerge when the geometric phase is replaced by a matrix acting on the internal Hilbert space [2–5]. This happens if there is a manifold of degenerate dressed states, such that even for arbitrarily slow motion, after traveling around a contour the particle ends up in a different internal state. Although various proposals for generating non-Abelian potentials exist, they remain to be implemented. On the other hand, Abelian spin-orbit coupling, arising from the momentum kicks imparted on the atom by the laser photons that drive internal transitions, has been realized in several laboratories using different laser configurations in alkali-metal (one outer electron) and alkaline-earth (two outer electrons) atoms [2–5]. There is a great vista ahead. For example, the inclusion of collisions or dipolar interactions will open a window to engineer fractional Hall liquids, unconventional superfluids and interacting topological phases. The creation of dynamical gauge fields important in many areas of physics such as quantum chromodynamics is also an open direction. The time is just ripe for investigating rich and unexplored physics with synthetic gauge fields for ultracold matter.