K. Levin

History-dependent phenomena in the transverse Ising ferroglass: The free-energy landscape

A new lattice protein model with a four-helix bundle ground state is analyzed by a parameter-space Monte Carlo histogram technique to evaluate the effects of an extensive variety of model potentials on folding thermodynamics. Cooperative helical formation and contact energies based on a 5-letter alphabet are found to be insufficient to satisfy calorimetric and other experimental criteria for two-state folding. Such proteinlike behaviors are predicted, however, by models with polypeptidelike local conformational restrictions and environment-dependent hydrogen-bondinglike interactions.

Superfluid phase diagrams of trapped Fermi gases with population imbalance.

We present phase diagrams for population-imbalanced, trapped Fermi superfluids near unitarity. In addition to providing quantitative values for the superfluid transition temperature, the pairing onset temperature, and the transition line (separating the Sarma and phase separation regimes), we study experimental signatures of these transitions based on density profiles and density differences at the center. Predictions on the BCS side of resonance show unexpected behavior, which should be searched for experimentally.

Stability conditions and phase diagrams for two-component Fermi gases with population imbalance

Superfluidity in atomic Fermi gases with population imbalance has recently become an exciting research focus. There is considerable disagreement in the literature about the appropriate stability conditions for states in the phase diagram throughout the BCS to Bose-Einstein condensation crossover. Here we discuss these stability conditions for homogeneous polarized superfluid phases, and compare with recent alternative proposals. The requirement of a positive second-order partial derivative of the thermodynamic potential with respect to the fermionic excitation gap

Radio-frequency spectroscopy and the pairing gap in trapped Fermi gases

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Theory of superfluids with population imbalance: Finite-temperature and BCS-BEC crossover effects

(at fixed chemical potentials) is demonstrated to be equivalent to the positive definiteness of the particle number susceptibility matrix. In addition, we show the positivity of the effective pair mass constitutes another nontrivial stability condition. These conditions determine the (local) stability of the system towards phase separation (or other ordered phases). We also study systematically the effects of finite temperature and the related pseudogap on the phase diagrams defined by our stability conditions.

Ground state description of a single vortex in an atomic Fermi gas: From BCS to Bose-Einstein condensation

We present a theoretical interpretation of radio frequency (RF) pairing gap experiments in trapped atomic Fermi gases, over the entire range of the BCS-Bose-Einstein condensation (BEC) crossover, for temperatures above and below T{sub c}. Our calculated RF excitation spectra, as well as the density profiles on which they are based, are in semiquantitative agreement with experiment. We provide a detailed analysis of the physical origin of the two different peak features seen in RF spectra, one associated with nearly free atoms at the edge of the trap, and the other with (quasi-)bound fermion pairs.

The origin of the pseudogap phase: precursor superconductivity versus a competing energy gap scenario

In this paper we present a very general theoretical framework for addressing fermionic superfluids over the entire range of BCS to Bose Einstein condensation (BEC) crossover in the presence of population imbalance or spin polarization. Our emphasis is on providing a theory which reduces to the standard zero temperature mean-field theories in the literature, but necessarily includes pairing fluctuation effects at nonzero temperature within a consistent framework. Physically, these effects are associated with the presence of preformed pairs (or a fermionic pseudogap) in the normal phase, and pair excitations of the condensate, in the superfluid phase. We show how this finite T theory of fermionic pair condensates bears many similarities to the condensation of point bosons. In the process we examine three different types of condensate: the usual breached pair or Sarma phase and both the one- and two-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states. The last of these has been discussed in the literature albeit only within a Landau-Ginzburg formalism, generally valid near T{sub c}. Here we show how to arrive at the two-plane-wave LOFF state in the ground state as well as at general temperature T.

Modified many-body wave function for BCS-BEC crossover in Fermi gases

One of the most exciting developments in atomic and condensed matter physics has been the observation of superfluid ity in trapped fermionic systems [1, 2, 3, 4]. In these system s, the presence of a Feshbach resonance provides a means of tuning the attractive pairing interaction with applied mag netic field. In this way the system undergoes a continuous evolutio n from BCS to Bose-Einstein condensed (BEC) superfluidity. The most conclusive demonstration of the superfluid phase has been the experimental observation of vortices [5]. Particularly interesting from a theoretical viewpoint is the way vortices evolve from BCS to BEC. This evolution is associated, not just with a decrease in vortex size but with a complete rearrangement of the fermionic states which make up the core. As a result, there is a continuous evolution of the particle den sity within a vortex, thereby affecting the visibility of vortic es in the laboratory. In this paper we discuss the behavior of a (si ngle) vortex as the system crosses from BCS to BEC. Our work is based on simplest BCS-like ground state first introduced by Leggett [6] and Eagles [7] to treat BCS-BEC crossover. With this choice of ground state inhomogeneity effects are readily incorporated as in generalized Bogoliubov-de Gennes (BdG) theory. Here we demonstrate analytically that the BdG strong coupling description of the T = 0 vortex state coincides with the usual Gross-Pitaevskii (GP) treatment of vortices in bosonic superfluids. A fermionic theory based on BdG is, thus, very inclusive, and within this approach one expects a smooth evolution of vortices from the BCS to BEC limit as the statistics effectively change from fermionic to bosoni c. Previous studies of vortices in these fermionic superfluids addressed the BCS limit at T = 0 [8] and T ≈ Tc [9]. There is also work [10] on the T = 0 strict unitary case where a BdG approach was used with Hartree-Fock contributions included. In the present work, by contrast, we discuss the entire crossover regime and, importantly, present a detailed analysis of the energy and spatial structure within the core and how it evolves from BCS to BEC. A very different path integral approach was introduced in Ref. [11] to address vortices with BCS-BEC crossover, but here the authors note that density depletion effects appear to be unphysically large in the BCS regime. Our analytical approach builds heavily on previous work [12] which showed a general connection between GP theory and BdG. From this one can conclude that a generalized BCS theory [6] treats the bosonic degrees of freedom at the same level as GP theory. Different ground states can be contemplated, (with incomplete condensation, say) but they will not be compatible with BdG theory. In a similar way, once T 6 0 one has to incorporate noncondensed pairs, and associated pseudogap physics [13] which are not present in a finite temperature BdG theory. For the most part, BdG approaches require detailed numerical solution [8, 14, 15, 16], so it is particularly useful to have analytical tools in the BEC limit. We present this nonnumerical description first. Our general self consistent eq uations [17] are � h − µ �(r) � ∗ (r) −h ∗ + µ �� u n vn � = En � u n vn

Fermionic Superfluidity: From High Tc Superconductors to Ultracold Fermi Gases

Abstract In the last few years evidence has been accumulating that there are a multiplicity of energy scales which characterize superconductivity in the underdoped cuprates. In contrast to the situation in BCS superconductors, the phase coherence temperature T c is different from the energy gap onset temperature T ∗ . In addition, thermodynamic and tunneling spectroscopies have led to the inference that the order parameter Δ sc is to be distinguished from the excitation gap Δ ; in this way, pseudogap effects persist below T c . It has been argued by many in the community that the presence of these distinct energy scales demonstrates that the pseudogap is unrelated to superconductivity. In this paper, we show that this inference is incorrect. We demonstrate that the difference between the order parameter and excitation gap and the contrasting dependences of T ∗ and T c on hole concentration x and magnetic field H follow from a natural generalization of BCS theory. This simple generalized form is based on a BCS-like ground state, but with self-consistently determined chemical potential in the presence of arbitrary attractive coupling g . We have applied this mean field theory with some success to tunneling, transport, thermodynamics, and magnetic field effects. We contrast the present approach with the phase fluctuation scenario and discuss key features which might distinguish our precursor superconductivity picture from that involving a competing order parameter.

A precursor superconductivity approach to magnetic field effects in the pseudogap phase

We present a new many body formalism for BCS-BEC crossover, which represents a modification of the BCS-Leggett ground state to include 4-fermion, and higher correlations. In the BEC regime, we show how our approach contains the \textit{Petrov et al} 4-fermion behavior and associated scattering length