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arXiv:2310.01639 · Physical Review A

Stability and dynamics of atom-molecule superfluids near a narrow Feshbach resonance

Zhiqiang Wang, Ke Wang, Zhendong Zhang, Shu Nagata, Cheng Chin, Kathryn Levin

Published Jul 11, 2024• 5 citations
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Abstract

The recent observations of a stable molecular condensate emerging from a condensate of bosonic atoms and related ``super-chemical'' dynamics have raised an intriguing set of questions. Here we provide a microscopic understanding of this unexpected stability and dynamics in atom-molecule superfluids; we show one essential element behind these phenomena is an extremely narrow Feshbach resonance in $^{133}\mathrm{Cs}$ at 19.849G. Comparing theory and experiment, we demonstrate how this narrow resonance enables the dynamical creation of a large closed-channel molecular fraction superfluid, appearing in the vicinity of unitarity. Theoretically, the observed superchemistry (i.e., Bose-enhanced reactions of atoms and molecules) is found to be assisted by the formation of Cooper-like pairs of bosonic atoms that have opposite momenta. Importantly, this narrow resonance opens the possibility to explore the quantum critical point of a molecular Bose superfluid and related phenomena which would not be possible near a more typically broad Feshbach resonance.

DOI
10.1103/physreva.110.013306

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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.

•Oct 14, 2009•0 citations
The recent observations of a stable molecular condensate emerging from a condensate of bosonic atoms and related ``super-chemical'' dynamics have raised an intriguing set of questions. Here we provide a microscopic understanding of this unexpected stability and dynamics in atom-molecule superfluids; we show one essential element behind these phenomena is an extremely narrow Feshbach resonance in 133Cs^{133}\mathrm{Cs}133Cs at 19.849G. Comparing theory and experiment, we demonstrate how this narrow resonance enables the dynamical creation of a large closed-channel molecular fraction superfluid, appearing in the vicinity of unitarity. Theoretically, the observed superchemistry (i.e., Bose-enhanced reactions of atoms and molecules) is found to be assisted by the formation of Cooper-like pairs of bosonic atoms that have opposite momenta. Importantly, this narrow resonance opens the possibility to explore the quantum critical point of a molecular Bose superfluid and related phenomena which would not be possible near a more typically broad Feshbach resonance.
Quench experiments on a unitary Bose gas around a broad Feshbach resonance have led to the discovery of universal dynamics. This universality manifests in the measured atomic momentum distributions, where, asymptotically, a quasiequilibrated metastable state is found in which both the momentum distribution and the timescales are determined by the particle density. In this Letter we present counterpart studies for the case of a very narrow Feshbach resonance of Cs 133 atoms with a width of 8.3 mG. In dramatic contrast to the behavior reported earlier, a rapid quench of an atomic condensate to unitarity is observed to ultimately lead to coherent oscillations involving dynamically produced condensed and noncondensed molecules and atoms. The same characteristic frequency, determined by the Feshbach coupling, is observed in all types of particles. To understand these quench dynamics and how these different particle species are created, we develop a beyond Hartree-Fock-Bogoliubov dynamical framework including a type of cross-correlation between atoms and molecules. This leads to quantitative consistency with the measured frequency. Our results, which can be applied to the general class of bosonic superfluids associated with narrow Feshbach resonances, establish a alternate paradigm for universal dynamics dominated by quantum many-body interactions.
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 extend our previous investigations of fermionic condensation in broad Feshbach resonances by using the two-channel model developed for narrow Feshbach resonances. We investigate two crossovers: the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover by changing the sss-wave scattering length and the crossover from a narrow to a broad resonance by changing the atom-molecule coupling. At zero temperature we analyze, as a function of both atom-molecule coupling and sss-wave scattering length, the chemical potential, the energy gap, and the condensate fraction of atoms. In particular, we predict the contribution of Cooper pairs and preformed molecules to the total condensate density along the two crossovers.
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.
Understanding and controlling interactions of ultracold molecules is a cornerstone of quantum chemistry. While the laboratory creation of degenerate molecular gases comprised of bosonic atoms has unlocked powerful platforms for quantum simulation, progress is limited by the absence of a robust theoretical framework for characterizing intermolecular interactions. This is in stark contrast to the situation for Fermi gases. In this Letter, we present such a framework providing universal expressions for these molecular scattering lengths as functions of experimentally measurable quantities. Our discoveries are crucial for understanding molecular condensate formation. Calculations of the compressibility reveal that a sign change in such molecular scattering lengths is directly correlated with the instability of these condensates. These results offer fresh insight with broad applications for atomic, molecular, and condensed matter physics, as well as quantum chemistry.
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.