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arXiv:2306.02736

Mass-imbalanced Fermi mixtures with resonant interactions

Matteo Zaccanti

Published Jun 5, 2023• 0 citations
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Abstract

In these notes I provide an overview of ongoing theoretical and experimental research on ultracold atomic mixtures composed by two different fermionic species. First, I describe a general and simple framework that should allow also a non-expert reader to understand the rich few-body phenomena connected with such systems, and their possible impact at the many-body level. I then move to discuss the specific combination of fermionic lithium ($^6$Li) and chromium ($^{53}$Cr) atoms, currently investigated in our lab, highlighting its peculiar properties with respect to other Fermi mixtures nowadays available. Finally, I summarize recent experimental progress achieved in producing and characterizing this novel system, providing an outlook for future studies based on ultracold $^6$Li-$^{53}$Cr Fermi mixtures.

DOI
10.48550/arxiv.2306.02736

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In these notes I provide an overview of ongoing theoretical and experimental research on ultracold atomic mixtures composed by two different fermionic species. First, I describe a general and simple framework that should allow also a non-expert reader to understand the rich few-body phenomena connected with such systems, and their possible impact at the many-body level. I then move to discuss the specific combination of fermionic lithium (6^66Li) and chromium (53^{53}53Cr) atoms, currently investigated in our lab, highlighting its peculiar properties with respect to other Fermi mixtures nowadays available. Finally, I summarize recent experimental progress achieved in producing and characterizing this novel system, providing an outlook for future studies based on ultracold 6^66Li-53^{53}53Cr Fermi mixtures.
The thesis reports on the design and implementation of a novel experimental apparatus for the realization and investigation of ultracold Fermi-Fermi mixtures of Cr-53 and Li-6 atoms. After a brief introduction to the physics of ultracold Fermi gases with tunable interactions, the manuscript also reports on the exceptional peculiarities and unprecedented potentiality of the Cr-Li mixture. The thesis describes the first realization and investigation of magneto-optically trapped cold clouds of Cr and Li atoms worldwide. Furthermore, the thesis also reports on the study of normal and superfluid fermionic currents of Li-6 atoms through a thin Josephson junction across the BEC-BCS crossover. The study led to the extraction of the critical values of particle imbalance across the junction beyond which dissipative dynamics is established.
We investigate ultracold collisions in a novel mixture of ^{6}Li and ^{53}Cr fermionic atoms, discovering more than 50 interspecies Feshbach resonances via loss spectroscopy. Building a full coupled-channel model, we unambiguously characterize the ^{6}Li-^{53}Cr scattering properties and yield predictions for other isotopic pairs. In particular, we identify various Feshbach resonances that enable the controlled tuning of elastic s- and p-wave ^{6}Li-^{53}Cr interactions. Our studies thus make lithium-chromium mixtures emerge as optimally suited platforms for the experimental search of elusive few- and many-body regimes of highly correlated fermionic matter, and for the realization of a new class of ultracold polar molecules possessing both electric and magnetic dipole moments.
The topic of the present lecture notes are two-species quantum mixtures composed of a deeply degenerate Fermi gas and a second component, the latter being fermionic or bosonic. A key ingredient is the possibility to tune the sss-wave interaction between the different species by means of magnetically controlled Feshbach resonances, which allow us to investigate regimes of strong interactions. In two case studies, we review our experiments on mixtures of 6^66Li fermions with fermionic 40^{40}40K or bosonic 41^{41}41K atoms and on mixtures of fermionic 161^{161}161Dy with 40^{40}40K atoms. We cover various topics of fermionic quantum many-body physics, ranging from impurity physics and quasiparticles over phase separation to the formation of ultracold molecules and progress towards novel superfluids.
We consider ultracold imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mixtures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species. In both cases, the number of atoms for each component is allowed to be different, leading to a spin imbalance or a polarization. In the second case, the two different species also give rise to a mass imbalance for the particles. Imbalanced Fermi mixtures play a fundamental role in condensed-matter, nuclear and astroparticle physics. Experimentally, the atomic mixtures are made strongly interacting with the use of two-channel Feshbach resonances. We start out by treating these in more detail. We review the relevant scattering theory, and apply it to the well-studied case of resonant s-wave collisions with zero angular momentum. Furthermore, we discuss the less-studied case of p-wave collisions with nonzero angular momentum, and the inhomogeneous case due to a trapping potential. Having discussed the two-body physics, we turn to the many-body physics. The pioneering experimental studies of Cooper pairing in lithium-6 mixtures with a spin imbalance were performed by Zwierlein et al. [Science 311, 492 (2006)] and Partridge et al. [Science 311, 503 (2006)]. We study the mean-field theory for the polarized Fermi mixture to obtain a qualitative understanding of these experiments. In the unitarity limit, where the scattering length of the interatomic interaction diverges, the theory gives rise to two exotic superfluid phases that are absent in the balanced mixture. These are the gapless superfluid Sarma phase and the phase-separated phase. By using renormalization group techniques to account for the effects of strong interactions, we obtain also quantitative agreement with Monte-Carlo calculations and experiments. We then generalize our knowledge of the solely spin-imbalanced mixture to the mass-imbalanced case, where in particular the mixture consisting of lithium-6 and potassium-40 is experimentally promising. We study the mean-field phase diagram for this mixture in the unitarity limit, where we not only find phase separation and Sarma superfluidity, but also a Lifshitz point. The latter signals an instability towards a supersolid phase. We also include the effects of fluctuations, which do not alter the topology of the phase diagram. However, fluctuation effects lower the critical temperatures with an experimentally relevant factor of three. Finally, we study superfluidity in a fully polarized gas of potassium-40 atoms near a p-wave Feshbach resonance. In particular, we consider coherent Josephson oscillations between the superfluid components in the two channels of the resonance, whose frequencies contain a clear signature of the quantum phase transition that occurs as a function of applied magnetic field.
We report on the realization of a degenerate mixture of ultracold fermionic lithium and chromium atoms. Based on an all-optical approach, with an overall duty cycle of about 13 s, we produce large and degenerate samples of more than $2\ifmmode\times\else\texttimes\fi{}{10}^{5}{\phantom{\rule{4pt}{0ex}}}^{6}\mathrm{Li}$ atoms and ${10}^{5}^{53}\mathrm{Cr}$ atoms, with both species exhibiting normalized temperatures of about T/TF=0.25T/{T}_{F}=0.25T/TF​=0.25. Additionally, through the exploitation of a crossed bichromatic optical dipole trap, we can controllably vary the density and degree of degeneracy of the two components almost independently and widely tune the lithium-to-chromium density ratio. Our $^{6}\mathrm{Li}\text{\ensuremath{-}}^{53}\mathrm{Cr}$ Fermi mixture opens the way to the investigation of a variety of exotic few- and many-body regimes of quantum matter and it appears as an optimally suited system to realize ultracold paramagnetic polar molecules, characterized by both electric and magnetic dipole moments. Ultimately, our strategy also provides an efficient pathway to produce dipolar Fermi gases, or spin mixtures, of ultracold 53Cr^{53}\mathrm{Cr}53Cr atoms.
Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two- and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higher-spin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification.