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Bulletin of the American Physical Society

Pairing of Fermions with Unequal Effective Charges in an Artificial Magnetic Field

Nur Unal, Mehmet Özgür Oktel

Published May 26, 2016• 0 citations
OpenAlex

Abstract

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.

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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.
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.
We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of 6Li^{6}\mathrm{Li}6Li atoms trapped in two different hyperfine states.
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.
We study fermionic superfluidity in an ultracold Bose-Fermi mixture loaded into a square optical lattice subjected to a staggered flux. While the bosons form a Bose-Einstein condensate at very low temperature and weak interaction, the interacting fermions experience an additional long-ranged attractive interaction mediated by phonons in the bosonic condensate. This leads us to consider a generalized Hubbard model with on-site and nearest-neighbor attractive interactions, which give rise to two competing pairing channels. We use the Bardeen-Cooper-Schrieffer theory to determine the regimes where distinct fermionic superfluids are stabilized and find that the nonlocal pairing channel favors a superfluid state which breaks both the gauge and the lattice symmetries, similar to unconventional superconductivity occurring in some strongly correlated systems. Furthermore, the particular structure of the single-particle spectrum leads to unexpected consequences, for example, a dome-shaped superfluid region in the temperature versus filing fraction phase diagram, with a normal phase that contains much richer physics than a Fermi liquid. Notably, the relevant temperature regime and coupling strength are readily accessible in state of the art experiments with ultracold trapped atoms.
We analyze the phase diagram of superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of scattering parameter, population imbalance, and mass anisotropy. We identify regions corresponding to normal, or uniform or nonuniform superfluid phases, and discuss topological quantum phase transitions in the BCS, unitarity, and BEC limits. We derive the Ginzburg-Landau equation near the critical temperature, and show that it describes a dilute mixture of paired and unpaired fermions in the BEC limit. We also obtain the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit. Lastly, we discuss the effects of harmonic traps and the resulting density profiles in the BEC regime.