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arXiv:2302.05692 · Nature Physics

Ultracold Feshbach molecules in an orbital optical lattice

Yann Kiefer, Max Hachmann, Andreas Hemmerich

Published Mar 20, 2023• 16 citations
arXivHTMLPDF

Abstract

Abstract Quantum gas systems provide a unique experimental platform to study the crossover between Bose–Einstein condensed molecular pairs and Bardeen–Cooper–Schrieffer superfluidity. The few studies in optical lattices have so far focused on the case when only the lowest Bloch band is populated, thus excluding orbital degrees of freedom. Here we demonstrate the preparation of ultracold Feshbach molecules of fermionic atoms in the second Bloch band of an optical square lattice. We cover a wide range of interaction strengths, including the regime of unitarity in the middle of the crossover. Binding energies and band relaxation dynamics are measured by means of a method resembling mass spectrometry. We find that the longest lifetimes arise for strongly interacting Feshbach molecules at the onset of unitarity. In the case of strong confinement in a deep lattice potential, we observe bound dimers also for negative values of the scattering length, extending previous findings for molecules in the lowest band.

DOI
10.1038/s41567-023-01994-9

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This dissertation discusses the experimental study of strong fermionic interactions in an optical lattice. Ultracold samples of 40^{40}40K are prepared in an intricate experimental platform using the combination of various optical and evaporative cooling techniques. The atoms are adiabatically loaded into an optical lattice to realize isolated pair states. Various tools for the coherent manipulation of spin and orbital degrees of freedom of the atoms in the lattice are developed. The inter-particle interactions between pairs are tuned using magnetic Feshbach resonances. Spectroscopic measurements of resonantly enhanced and controllable s-wave and p-wave interaction energies are reported. The measurements extend to the unitary limit of interactions characterized by diverging scattering lengths and universal observables. These measurements show excellent agreements to an exact solution for two harmonically confined atoms interacting via a pseudopotential and numerical solutions using an \textit{ab initio} interaction potential. For p-wave interactions, exquisite experimental control is demonstrated by measuring Rabi oscillations between non-interacting and strongly interacting atomic pairs, which are used to accurately measure highly sensitive properties such as the two-body wavefunction overlap. With the full suppression of three-body loss processes, the lifetime of p-wave interacting pairs is investigated. The experiments demonstrate that losses of p-wave interacting pairs are limited by the intrinsic lifetime of the free-space molecular dimer, resulting in the observation of lifetimes that are fifty times larger than previous measurements in 40^{40}40K. The observation, control, and comprehensive understanding of strong fermionic interactions demonstrated in this thesis illuminate a path towards the assembly of new many-body states of matter.
We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly bound Cooper pairs to the Bose-Einstein condensate (BEC) of strongly bound molecular dimers in a gas of ultracold atoms loaded on a two-dimensional optical lattice. By using the mean-field BCS equations of the emerging Hubbard model and the concept of off-diagonal long-range order for fermions we calculate analytically and numerically the pair binding energy, the energy gap, and the condensate fraction of Cooper pairs as a function of interaction strength and filling factor of atoms in the lattice at zero temperature.
Abstract This article provides a synopsis of our recent experimental work exploring Bose–Einstein condensation in metastable higher Bloch bands of optical lattices. Bipartite lattice geometries have allowed us to implement appropriate band structures, which meet three basic requirements: the existence of metastable excited states sufficiently protected from collisional band relaxation, a mechanism to excite the atoms initially prepared in the lowest band with moderate entropy increase, and the possibility of cross-dimensional tunneling dynamics, necessary to establish coherence along all lattice axes. A variety of bands can be selectively populated and a subsequent thermalization process leads to the formation of a condensate in the lowest energy state of the chosen band. As examples the 2nd, 4th and 7th bands in a bipartite square lattice are discussed. The geometry of the 2nd and 7th bands can be tuned such that two inequivalent energetically degenerate energy minima arise at the X ± -points at the edge of the 1st Brillouin zone. In this case even a small interaction energy is sufficient to lock the phase between the two condensation points such that a complex-valued chiral superfluid order parameter can emerge, which breaks time reversal symmetry. In the 4th band a condensate can be formed at the Γ-point in the center of the 1st Brillouin zone, which can be used to explore topologically protected band touching points. The new techniques to access orbital degrees of freedom in higher bands greatly extend the class of many-body scenarios that can be explored with bosons in optical lattices.
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We study the thermodynamics of a two-species Feshbach-resonant atomic Fermi gas in a periodic potential, focusing in a deep optical potential where a tight binding model is applicable. We show that for a more than half-filled band the gas exhibits a reentrant crossover with decreased detuning (increased attractive interaction), from a paired BCS superfluid to a Bose-Einstein condensate (BEC) of molecules of holes, back to the BCS superfluid, and finally to a conventional BEC of diatomic molecules. This behavior is associated with the nonmonotonic dependence of the chemical potential on detuning and the concomitant Cooper-pair or molecular size, larger in the BCS and smaller in the BEC regimes. For a single filled band we find a quantum phase transition from a band insulator to a BCS-BEC superfluid, and map out the corresponding phase diagram.
Abstract. We report on the realization of a strongly interacting quantum degenerate gas of fermionic atoms in a three-dimensional optical lattice. We prepare a bandinsulating state for a two-component Fermi gas with one atom per spin state per lattice site. Using a Feshbach resonance, we induce strong interactions between the atoms. When sweeping the magnetic field from the repulsive side towards the attractive side of the Feshbach resonance we induce a coupling between Bloch bands leading to a transfer of atoms from the lowest band into higher bands. Sweeping the magnetic field across the Feshbach resonance from the attractive towards the repulsive side leads to two-particle bound states and ultimately to the formation of molecules. From the fraction of formed molecules we determine the temperature of the atoms in the lattice.