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arXiv:2111.04301 · Nature Physics

Transition from a polaronic condensate to a degenerate Fermi gas of heteronuclear molecules

Marcel Duda, Xing-Yan Chen, Andreas Schindewolf, Roman Bause, Jonas von Milczewski, Richard Schmidt, Immanuel Bloch, Xinyu Luo

Published Feb 13, 2023• 81 citations
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Abstract

Abstract The interplay of quantum statistics and interactions in atomic Bose–Fermi mixtures leads to a phase diagram markedly different from pure fermionic or bosonic systems. However, investigating this phase diagram remains challenging when bosons condense due to the resulting fast interspecies loss. Here we report observations consistent with a phase transition from a polaronic to a molecular phase in a density-matched degenerate Bose–Fermi mixture. The condensate fraction, representing the order parameter of the transition, is depleted by interactions, and the build-up of strong correlations results in the emergence of a molecular Fermi gas. The features of the underlying quantum phase transition represent a new phenomenon complementary to the paradigmatic Bose–Einstein condensate/Bardeen–Cooper–Schrieffer crossover observed in Fermi systems. By driving the system through the transition, we produce a sample of sodium–potassium molecules exhibiting a large molecule-frame dipole moment in the quantum-degenerate regime.

DOI
10.1038/s41567-023-01948-1

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Abstract The interplay of quantum statistics and interactions in atomic Bose–Fermi mixtures leads to a phase diagram markedly different from pure fermionic or bosonic systems. However, investigating this phase diagram remains challenging when bosons condense due to the resulting fast interspecies loss. Here we report observations consistent with a phase transition from a polaronic to a molecular phase in a density-matched degenerate Bose–Fermi mixture. The condensate fraction, representing the order parameter of the transition, is depleted by interactions, and the build-up of strong correlations results in the emergence of a molecular Fermi gas. The features of the underlying quantum phase transition represent a new phenomenon complementary to the paradigmatic Bose–Einstein condensate/Bardeen–Cooper–Schrieffer crossover observed in Fermi systems. By driving the system through the transition, we produce a sample of sodium–potassium molecules exhibiting a large molecule-frame dipole moment in the quantum-degenerate regime.
Preparation of molecular quantum gas promises novel applications including quantum control of chemical reactions, precision measurements, quantum simulation and quantum information processing. Experimental preparation of colder and denser molecular samples, however, is frequently hindered by fast inelastic collisions that heat and deplete the population. Here we report the formation of two-dimensional Bose-Einstein condensates (BECs) of spinning g−g-g−wave molecules by inducing pairing interactions in an atomic condensate. The trap geometry and the low temperature of the molecules help reducing inelastic loss to ensure thermal equilibrium. We determine the molecular scattering length to be +220(30)+220(30)+220(30)~Bohr and investigate the unpairing dynamics in the strong coupling regime. Our work confirms the long-sought transition between atomic and molecular condensates, the bosonic analog of the BEC-BCS (Bardeen-Cooper-Schieffer superfluid) crossover in a Fermi gas.
We study resonantly-paired s-wave superfluidity in a degenerate gas of two species (hyperfine states labeled by ↑, ↓) of fermionic atoms when the numbers N↑ and N↓ of the two species are unequal, i.e., the system is "polarized." We find that the continuous crossover from the Bose-Einstein condensate (BEC) limit of tightly-bound diatomic molecules to the Bardeen-Cooper-Schrieffer (BCS) limit of weakly correlated Cooper pairs, studied extensively at equal populations, is interrupted by a variety of distinct phenomena under an imposed population difference ΔN ≡ N↑ - N↓. Our findings are summarized by a "polarization" (ΔN) versus Feshbach-resonance detuning (δ) zero-temperature phase diagram, which exhibits regions of phase separation, a periodic FFLO superfluid, a polarized normal Fermi gas and a polarized molecular superfluid consisting of a molecular condensate and a fully polarized Fermi gas. We describe numerous experimental signatures of such phases and the transitions between them, in particular focusing on their spatial structure in the inhomogeneous environment of an atomic trap. © 2006 Elsevier Inc. All rights reserved.
We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. This is related to the phenomenon of superconductivity described by the seminal Bardeen-Cooper-Schrieffer (BCS) theory. In superconductivity, the phase transition is caused by a coupling between pairs of electrons within the medium. This coupling is perturbative and leads to a critical temperature Tc which is small compared to the Fermi temperature TF. Even high-Tc superconductors typically have a critical temperature which is two orders of magnitude below TF. Here we describe a resonance pairing mechanism in a quantum degenerate gas of potassium (40K) atoms which leads to superfluidity in a novel regime--a regime that promises the unique opportunity to experimentally study the crossover from the BCS phase of weakly-coupled fermions to the Bose Einstein condensate of strongly-bound composite bosons. We find that the transition to a superfluid phase is possible at the high critical temperature of about 0.5TF. It should be straightforward to verify this prediction, since these temperatures can already be achieved experimentally.
We calculate the phase diagrams for a harmonically trapped ideal gas mixture of fermionic atoms and bosonic molecules in chemical and thermal equilibrium, where the internal energy of the molecules can be adjusted relative to that of the atoms by use of a tunable Feshbach resonance. We plot the molecule fraction and the fraction of Bose-condensed molecules as functions of the temperature and internal molecular energy. We show the paths traversed in the phase diagrams when the molecular energy is varied either suddenly or adiabatically. Our model calculation helps to interpret the adiabatic phase diagrams obtained in recent experiments on the Bose–Einstein condensation to Bardeen–Cooper–Schrieffer crossover, in which the condensate fraction is plotted as a function of the initial temperature of the Fermi gas measured before a sweep of the magnetic field through the resonance region.
We describe the properties of a mixture of fermionic and bosonic atoms, as they are tuned across a Feshbach resonance associated with a fermionic molecular state. Provided the number of fermionic atoms exceeds the number of bosonic atoms, we argue that there is a critical detuning at which the Bose-Einstein condensate (BEC) is completely depleted. The phases on either side of this quantum phase transition can also be distinguished by the distinct Luttinger constraints on their Fermi surfaces. In both phases, the total volume enclosed by all Fermi surfaces is constrained by the total number of fermions. However, in the phase without the BEC, which has two Fermi surfaces, there is a second Luttinger constraint: the volume enclosed by one of the Fermi surfaces is constrained by the total number of bosons, so that the volumes enclosed by the two Fermi surfaces are separately conserved. The phase with the BEC may have one or two Fermi surfaces, but only their total volume is conserved. We obtain the phase diagram as a function of atomic parameters and temperature, and describe critical fluctuations in the vicinity of all transitions. We make quantitative predictions valid for the case of a narrow Feshbach resonance, but we expect the qualitative features we describe to be more generally applicable. As an aside, we point out intriguing connections between the BEC depletion transition and the transition to the fractionalized Fermi liquid in Kondo lattice models.