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arXiv:cond-mat/0312237 · Physical Review Letters

Superfluid Transitions in Bosonic Atom-Molecule Mixtures near a Feshbach Resonance

Leo Radzihovsky, Jae Park, Peter B. Weichman

Published Apr 20, 2004• 127 citations
arXivHTMLPDF

Abstract

We study bosonic atoms near a Feshbach resonance and predict that, in addition to standard normal and atomic superfluid phases, this system generically exhibits a distinct phase of matter: a molecular superfluid, where molecules are superfluid while atoms are not. We explore zero- and finite-temperature properties of the molecular superfluid (a bosonic, strong-coupling analog of a BCS superconductor), and study quantum and classical phase transitions between the normal, molecular superfluid, and atomic superfluid states.

DOI
10.1103/physrevlett.92.160402

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We study bosonic atoms near a Feshbach resonance and predict that, in addition to standard normal and atomic superfluid phases, this system generically exhibits a distinct phase of matter: a molecular superfluid, where molecules are superfluid while atoms are not. We explore zero- and finite-temperature properties of the molecular superfluid (a bosonic, strong-coupling analog of a BCS superconductor), and study quantum and classical phase transitions between the normal, molecular superfluid, and atomic superfluid states.
We study a degenerate two-species gas of bosonic atoms interacting through a ppp-wave Feshbach resonance as, for example, realized in a 85{}^{85}85Rb-87{}^{87}87Rb mixture. We show that, in addition to a conventional atomic and a ppp-wave molecular spinor-1 superfluidity at large positive and negative detunings, respectively, the system generically exhibits a finite-momentum atomic-molecular superfluidity at intermediate detuning around the unitary point. We analyze the detailed nature of the corresponding phases and the associated quantum and thermal phase transitions.
We examine theoretically a continuity between atomic and molecular Fermi superfluids in a Bose-Fermi mixture near the Feshbach resonance. Considering a two-channel model with Fermi atoms fff, Bose atoms bbb, and the closed-channel molecules FFF, we construct a mean-field framework based on the perturbative expansion of the $b\text{\ensuremath{-}}f\text{\ensuremath{-}}F$ Feshbach coupling. The resulting effective Hamiltonian not only exhibits the continuity between atom-atom to molecule-molecule Cooper pairings but also becomes equivalent to the two-band-superconductor model with Suhl-Matthias-Walker--type pair-exchange coupling. We demonstrate how these atomic and molecular Fermi superfluids coexist within the two-band-like superfluid theory. The pair-exchange coupling $ff\ensuremath{\leftrightarrow}FF$ and resulting superfluid gaps $\ensuremath{\langle}ff\ensuremath{\rangle}$ and $\ensuremath{\langle}FF\ensuremath{\rangle}$ are found to be strongly enhanced near the Feshbach resonance due to the interplay between the infrared singularity of Bogoliubov phonons and their Landau damping arising from the coupling with fermions. The pair-exchange coupling can be probed via the observation of the intrinsic Josephson effect between atomic and molecular superfluids.
We consider a mixture of two-species atomic Bose-Einstein condensates coupled to a bound molecular state at zero temperature via an interspecies Feshbach resonance. The interspecies Feshbach coupling precludes the possibility of doubly mixed phases while enables not only the pure molecular superfluid but also the pure atomic superfluids to exist as distinct phases. We show that this system is able to support a rich set of phase separations, including that between two distinct mixed atom-molecule phases. We pay particular attention to the effects of the Feschbach coupling and the particle collisions on the miscibility of this multicomponent condensate system.
This doctoral dissertation is concerned with the physics of strongly interacting cold alkali atoms at low temperatures near a Feshbach resonance. In Chapter 1, we establish a connection between superfluid 4He and the BCS theory of superconductivity, and cold alkali atoms. We give the history of cold atoms, describing the significant achievements, pitfalls and challenges. In Chapter 2, we explore the thermodynamics of strongly interacting Bosonic atoms. We explore the stability of atomic Bosonic condensates near a Feshbach resonance. We show that the experimentally attained atomic condensate is a saddle point of the free energy, but the kinetics of its decay is slow. We also show that there is a second, higher density condensate branch which has an Ising-like phase transition to a molecular (paired) condensate when ramped across the Feshbach resonance. We argue that due to the high density, inelastic 3-body processes possibly render this transition unobservable. In Chapter 3, we explore the thermodynamics of Fermionic atoms near a Feshbach resonance. We determine the zero-temperature (T less than/less than T sub(F) ) pair propagator for a spinimbalanced mixture of up and down spin Fermions, and use it to show that such a mixture becomes completely polarized at mu sub(down arrow)= -0.9 mu sub(up arrow) . We also determine the Thouless criterion for superfluidity in a spin-imbalanced Fermi mixture, and construct a phase diagram of such a system at zero temperature. We then compare our results with experiments performed by two different groups. We find that interaction modifications to the minority spin self-energy inferred from our analysis is roughly double those observed in experiments. This discrepancy is consistent with the expected accuracy of the theory. In Chapter 4, we extend our analysis of the preceding chapter to calculate the surface tension of an interface between spin-polarized Fermions in the normal and superfluid phases. We show that, as expected, this surface tension decreases with increasing temperature and vanishes at a tricritical temperature, above which the transition becomes continuous. We also calculate the thickness of the interface; at T = 0, this is a few interparticle spacings, but diverges at the tricritical temperature. To compare with a set of relevant experiments, we also develop a phenomenological model for surface tension, and conclude that experimental surface tensions are an order of magnitude higher than what our microscopic calculation yields. We hypothesize possible mechanisms. In Chapter 5, we calculate the finite temperature phase diagram of a Bose-Fermi mixture produced from a spin-imbalanced two-component Fermi gas deep in the BEC phase. We show that there is a discontinuous transition between the superfluid and normal phase, with an entropy of mixing sufficient to cool the system down. We detail the construction of such a cooling scheme to cool a Fermi system below what is possible evaporatively, and find that the cooling efficiency is comparable to typical evaporative schemes. In Chapter 6, we shift our focus from thermodynamics to dynamics. We calculate shifts in the energy spectrum of a spin-balanced Fermionic superfluid of Cooper pairs due to the presence of energetically close states coupled by a Feshbach resonance. These shifts manifest themselves as clock-shifts in the radio-frequency spectrum of the superfluid. In addition to a broad asymmetric peak coming from the break-up of Cooper pairs, we find (for certain parameter ranges) a sharp, symmetric "bound-bound" spectral line coming from the conversion of Cooper pairs in one channel to pairs or molecules in another channel. Our theory shows remarkable quantitative agreement with experiments performed by an experimental group.
Fermionic superfluidity in atomic Fermi gases across a Feshbach resonance is normally described by the atom-molecule theory, which treats the closed channel as a noninteracting point boson. In this work we present a theoretical description of the resonant superfluidity in analogy to the two-band superconductors. We employ the underlying two-channel scattering model of Feshbach resonance where the closed channel is treated as a composite boson with binding energy ${\ensuremath{\varepsilon}}_{0}$ and the resonance is triggered by the microscopic interchannel coupling U12{U}_{12}U12​. The binding energy ${\ensuremath{\varepsilon}}_{0}$ naturally serves as an energy scale of the system, which has been sent to infinity in the atom-molecule theory. We show that the atom-molecule theory can be viewed as a leading-order low-energy effective theory of the underlying fermionic theory in the limit ${\ensuremath{\varepsilon}}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$ and ${U}_{12}\ensuremath{\rightarrow}0$, while keeping the phenomenological atom-molecule coupling finite. The resulting two-band description of the superfluid state is in analogy to the BCS theory of two-band superconductors. In the dilute limit ${\ensuremath{\varepsilon}}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$, the two-band description recovers precisely the atom-molecule theory. The two-band theory provides a natural approach to study the corrections because of a finite binding energy ${\ensuremath{\varepsilon}}_{0}$ in realistic experimental systems. For broad and moderate resonances, the correction is not important for current experimental densities. However, for extremely narrow resonance, we find that the correction becomes significant. The finite binding energy correction could be important for the stability of homogeneous polarized superfluid against phase separation in imbalanced Fermi gases across a narrow Feshbach resonance.
We study the superfluid state of atomic Fermi gases using a BCS-Bose-Einstein-condensation crossover theory. Our approach emphasizes noncondensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above Tc{T}_{c}Tc​ and non-BCS characteristics below. We discuss how these effects influence the experimental signatures of superfluidity.