Observation of Feshbach resonances in an ${}^{167}$Er-${}^6$Li Fermi-Fermi mixture

TL;DR

This study experimentally identified multiple interspecies Feshbach resonances in an ultracold mixture of erbium-167 and lithium-6 atoms, revealing broad resonances suitable for exploring novel quantum states.

Contribution

First experimental observation of Feshbach resonances in an Er-167 and Li-6 mixture, including identification of broad resonances for future quantum state investigations.

Findings

Numerous narrow and six broad Feshbach resonances detected.

Broad resonances (>1 G) identified as promising for future research.

Interspecies inelastic collisional properties characterized up to 800 G.

Abstract

We present our experimental investigation of the interspecies Feshbach spectrum in a mixture of ${}^{167}$Er($F = 19/2, m_F = -19/2$)-${}^6$Li($F = 1/2, m_F = 1/2$) atoms in the microkelvin temperature regime. These temperatures are achieved by means of sympathetic cooling with ${}^{174}$Yb as a third species. Interspecies Feshbach resonances are then identified by investigation of the Er-Li inelastic collisional properties for magnetic fields up to 800 G. Numerous narrow resonances as well as six resonances with widths above 1 G could be identified. It is these broader resonances that hold much promise for interesting future investigations of, for exmample, novel superfluid states and Efimov states in large mass-imbalanced, all-fermionic two-component systems.

Tables

Table 1. Table 1: List of identified 167 Er( m F = − 19 / 2 subscript 𝑚 𝐹 19 2 m_{F}=-19/2 )- 6 Li( m F = 1 / 2 subscript 𝑚 𝐹 1 2 m_{F}=1/2 ) interspecies Feshbach resonances obtained from the data of Fig.  1 . The resonance positions B 0 subscript 𝐵 0 B_{0} and widths Δ ​ B Δ 𝐵 \Delta B are from Lorentzian fits to the data. Note has to be taken of the two different resolution regimes: Up to 100 ​ G 100 G 100\,\mathrm{G} more narrow resonances could be observed due to the higher measurement resolution whereas above that field purposely only broad resonances were detected and listed here. At 72.3 ​ G 72.3 G 72.3\,\mathrm{G} the fit failed to provide a good resonance width estimated due to the finite measurement resolution.

Resolution	$B_0$ ($G$)	$\Delta B$ ($G$)
$0.06G$	$13.1$	$0.1$
	$16.3$	$0.1$
	$17.0$	$0.1$
	$17.5$	$0.1$
	$22.4$	$0.1$
	$33.8$	$0.2$
	$38.1$	$0.2$
	$45.3$	$0.2$
	$69.5$	$0.2$
	$71.2$	$0.2$
	$71.8$	$0.1$
	$72.3$	—
	$72.8$	$0.1$
	$73.4$	$0.1$
	$76.1$	$0.2$
	$77.1$	$0.1$
	$79.9$	$0.1$
	$80.9$	$0.2$
	$86.2$	$0.3$
	$90.6$	$0.2$
	$92.5$	$0.2$
$1.0G$	$110.3$	$1.5$
	$256.7$	$1.0$
	$455.0$	$2.3$
	$700.2$	$1.2$
	$705.3$	$2.6$
	$792.7$	$3.5$

Full text

I Introduction

Ultracold mixtures of quantum gases are a fascinating tool to study in detail the intricate physics of many-body problems Bloch et al. (2008) with both high controllability and high precision. The high degree of control extends to both dimensional control by means of optical lattices Bloch (2005) and interaction control by use of Feshbach resonances Inouye et al. (1998); Chin et al. (2010). Generally speaking, the realm of many-body physics extends far beyond the field of ultracold atomic physics and serves as an interface to interconnect the different research disciplines in physics. Amongst many possible examples the Efimov effect stands out in his broad applicability Naidon and Endo (2017). Originally investigated by Vitaly Efimov in his work on nuclear three-body problems, his famous discovery of three-body bound states is now a prime example of universal many-body physics that can be applied to nearly any field of quantum physics. Physical evidence for the predicted infinite series of three-body bound states, however, remained elusive for more than 30 years until first evidences were found in ultracold quantum gases of Cs Kraemer et al. (2006); Zaccanti et al. (2009). However, due to the large scaling factors involved in the observation of at least three Efimov states it was not until the advent of mass-imbalanced mixture experiments that multiple Efimov states could be observed Pires et al. (2014); Tung et al. (2014). These seminal experiments utilized the large mass-imbalance in the Fermi-boson 6Li-133Cs mixture to reduce the scaling factor from $22.7$ to just $4.9$.

Based on these hallmark experiments, our present work strives to expand the experimental possibilities towards more “exotic” Efimov states involving two heavy Fermions that resonantly couple to a third, light particle. Going beyond the usual Efimov scenario, these novel trimer-states are predicted to only occur for mass ratios beyond a threshold value of $13.6$ where the scaling ratio initially diverges Naidon and Endo (2017). However, with increasing mass imbalance this scaling factor quickly reduces to experimentally feasible values of less than $10$. We here present first steps towards the experimental realization of these states with a Fermi-Fermi 167Er-6Li mixture that with a mass ratio of $27.8$ lies well above the critical value of $13.6$ for the occurrence of these hitherto unobserved Efimov states. In our experiments we demonstrate successful cooling of the mixture to microkelvin temperatures and we probe the system for broad interspecies Feshbach resonances. Such broad Feshbach resonances are required for the necessary fine-tuned control of the interspecies interactions over several orders of magnitude.

In addition, the realized mass-imbalanced Fermi-Fermi mixture of 167Er-6Li is, together with tunable interactions, promising for realizing a novel superfluid state with a spatially varying order parameter, known as a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state Fulde and Ferrell (1964); Larkin and Ovchinnikov (1965); Radzihovsky and Sheehy (2010); Wang et al. (2017), and also other new behaviors like a Lifshitz point Gubbels and Stoof (2013); Gubbels et al. (2009). Quite recently, the theory for a unitary Fermi gas has been extended to large mass-imbalanced systems Endo and Castin (2022). Large mass-imbalanced Fermi-Fermi mixtures can also be useful for quantum simulation of the Fermi-surface effect Kondo (1984a, b, 1986) which manifests itself in quantum diffusion behaviors of heavy particles in solids Storchak and Prokof’ev (1998).

We start with a brief introduction to the experiment and the experimental procedures of relevance to the present research (Sec. II). Next, the results of our Feshbach resonance search for magnetic fields up to $800\,\mathrm{G}$ are introduced (Sec. III). We conclude with a discussion of our findings and some thoughts on possible future works (Sec. IV).

II Experiment

The experiment is based on the setup already used in our earlier works Schäfer et al. (2022). However, while our previous efforts focused on bosonic erbium, some upgrades to the machine have been necessary for our present work with fermionic 167Er. This is because 167Er is known to experience strong losses in optical traps operating at wavelengths around $1064\,\mathrm{nm}$ for reasons that were never completely uncovered Aikawa et al. (2014). An additional far-off resonant trap (FORT) at $1550\,\mathrm{nm}$ is therefore prepared to circumvent this inconvenience. Our modified experimental method is hence as follows: Starting as in Schäfer et al. (2022) a triple-species mixture at roughly $100\,\mu\mathrm{K}$ of 167Er, 6Li and 174Yb is loaded into our horizontally oriented FORT (H-FORT) operating at $1064\,\mathrm{nm}$. It is important to note here the addition of bosonic ytterbium which we will use to sympathetically cool both Er and Li in the evaporation step that is to follow. Since the magneto-optical trap (MOT) light is blue-detuned for the Yb atoms in a FORT at $1550\,\mathrm{nm}$ and thus causes considerable heating and atom loss we are required to first load all atoms from the MOT into the $1064\,\mathrm{nm}$ H-FORT from where, once all MOT lights could be extinguished, they are transferred within $30\,\mathrm{ms}$ into the superimposed $1550\,\mathrm{nm}$ H-FORT. The transfer efficiency for each of the three species is about 50%. Forced evaporation proceeds in a crossed FORT configuration where in addition to the H-FORT beam (waist diameter $50\,\mu\mathrm{m}$) a vertical FORT beam (V-FORT, waist diameter $240\,\mu\mathrm{m}$) at the same wavelength is added for a tighter confinement during the evaporation. As the V-FORT beam is derived from the zeroth-order light of the acousto-optic modulator that prepares the light for the H-FORT, the V-FORT is initially at very low power. However, as the power of the H-FORT is gradually reduced during the evaporation, the V-FORT power can be increased to efficiently support the evaporation efficiency during most important final stages of the evaporation. During evaporation the magnetic fields are carefully chosen for good cooling performance and to maintain the spin polarization of the sample. The magnetic field is initially set to $1.55\,\mathrm{G}$ and after $4\,\mathrm{s}$ reduced to $0.4\,\mathrm{G}$. This procedure ensures that the natural spin-polarization of 167Er in the lowest $F=19/2,m_{F}=-19/2$ magnetic sublevel obtained during the narrow linewidth MOT is maintained. We further found that with this sequence 6Li is also naturally polarized in its lowest magnetic $F=1/2,m_{F}=1/2$ state, alleviating the need for any active optical pumping. After evaporation the remaining 174Yb atoms are removed from the trap by a short pulse of light resonant to the ${}^{1}S_{0}\rightarrow{}^{3}P_{1}$ transition at $556\,\mathrm{nm}$ leaving a pure Er-Li sample for the main part of the experiment.

In our first set of experiments we are interested in a general overview of the 167Er-6Li Feshbach resonance structure in the reasonable magnetic field range of up to about $800\,\mathrm{G}$. For this we choose an evaporation ramp that has a duration of $7\,\mathrm{s}$ and leaves the mixture in a trap with frequencies of about $(\omega_{x},\omega_{y},\omega_{z})=2\pi\times(47,405,400)\,\mathrm{Hz}$ where the $z$-axis is in vertical direction. After evaporation we typically obtain $20(5)\times 10^{3}$ Er atoms at a temperature of $2.4(2)\,\mu\mathrm{K}$ and $7(2)\times 10^{3}$ Li atoms at $3.0(5)\,\mu\mathrm{K}$. Next, the magnetic field is raised in $10\,\mathrm{ms}$ to its desired value and the mixture is allowed to interact for $1000\,\mathrm{ms}$ after which the magnetic field is again lowered and the number of remaining atoms for both species is measured by standard absorption imaging. For each magnetic field setting this experiment is repeated three times. Additionally, at each field control measurements are taken in which either one of the two species is removed from the optical trap by a pulse of resonant $583\,\mathrm{nm}$ (Er) or $671\,\mathrm{nm}$ (Li) light as in Schäfer et al. (2022). These control measurements are repeated two times each. From the ratio of the averaged values we obtain our main observable: the fraction of remaining atoms in the trap for each species. The results are summarized in Fig. 1. The data can be divided into two parts: Up to $100\,\mathrm{G}$ the magnetic field was scanned with a resolution of $0.06\,\mathrm{G}$ to get a better understanding of also the finer Feshbach resonance structure. The remainder of the data has been taken with a step size of $1\,\mathrm{G}$. This greatly speeds up the measurement process and allows us to obtain a good overview of the available broader Feshbach resonances in a reasonable time. It is these resonances that are most important for the physics of interest here.

III Results

Looking at the results in Fig. 1 one immediately recognizes a large number of resonant loss features. Focusing first on the upper two panels that cover the magnetic field range up to $100\,\mathrm{G}$ we identify by eye $21$ resonances. From Lorentzian fits to these resonances we obtain a rough estimate of their positions $B_{0}$ and full-widths at half maximum $\Delta B$. All parameters are listed in the upper part of Tab. 1. Note that due to our selected limited resolution of $0.06\,\mathrm{G}$ we do not expect to have obtained a complete list of resonances. Also all the uncertainties of $B_{0}$ and $\Delta B$ are estimated to be at least $0.1\,\mathrm{G}$. Our primary goal with these first experiment has been to get a good overview of typical resonance densities, on their widths and strengths. In this respect, generally the spectrum is similarly rich as in our earlier results with bosonic Er Schäfer et al. (2022). However, with all resonance widths being well below $0.5\,\mathrm{G}$ it appears unlikely that the observed resonances would be primary candidates to support the search of novel Efimov and superfluid states.

We therefore now turn our attention to the lower two panels of Fig. 1 for the range $100$ to $800\,\mathrm{G}$. In this coarsely scanned magnetic field range several narrow resonances are still visible where a single data point happens to be close enough to such a resonance. We will ignore such single-data-point events and instead focus on the broader resonances of which in total $6$ have been observed. They are listed in the lower part of Tab. 1. Of particular interest seem the resonances at $455$, $705$ and $793\,\mathrm{G}$. Upon closer inspection one notices that only the two resonances at $455$ and $793\,\mathrm{G}$ show nice losses for both species. Of these two remaining resonances we find that the higher one suffers from quite significant background losses also outside of the immediate vicinity of the resonance. For these reasons we will now focus on the resonant loss peak at about $455\,\mathrm{G}$ which additionally is also a magnetic field strengths that is experimentally quite comfortable to work with.

For a more detailed view of this resonance we now work with a slightly modified evaporation sequence: The ramp has been extended by $2\,\mathrm{s}$ to now $9\,\mathrm{s}$ and the final trap frequencies are about $(\omega_{x},\omega_{y},\omega_{z})=2\pi\times(49,285,272)\,\mathrm{Hz}$. After evaporation we then obtain a colder sample with $13(2)\times 10^{3}$ Er atoms at a temperature of $0.9(1)\,\mu\mathrm{K}$ and $5(1)\times 10^{3}$ Li atoms at $1.3(3)\,\mu\mathrm{K}$. The magnetic field range from $450$ to $460\,\mathrm{G}$ is measured in steps of $0.25\,\mathrm{G}$. The interaction time is reduced to $30\,\mathrm{ms}$. The data is otherwise taken and averaged as before and we will this time directly look at the raw atom numbers in Fig. 2. As expected, while in the mixture one observes a nicely synchronized loss of both species close to resonance, there is no magnetic field dependence in the single species data. The lineshapes of both resonances are strongly asymmetric. This is particularly highlighted when trying to describe them by Lorentzian fits (also included in Fig. 2). Still, from the fit minima one can at least deduce the approximate atom loss for both species. The reduction in the number of atoms is $(9.5\pm 1.4)\times 10^{3}$ for Er and $(4.5\pm 0.6)\times 10^{3}$ for Li. This implies that for every Li atom lost about $(2.1\pm 0.4)$ Er atoms are removed from the trap and is consistent with the assumption that the losses are dominated by Er-Er-Li three-body collisions Ye et al. (2022).

In Fig. 3 we take a closer look the typical decay dynamics by studying the number of remaining atoms, $N_{\rm Er}$ and $N_{\rm Li}$, in the trap at a magnetic field of $455.0\,\mathrm{G}$ and for holding times up to $5\,\mathrm{ms}$. In Fig. 3a) the decay is described by a three-body decay model Ye et al. (2022) (solid lines), again assuming Er-Er-Li three-body collisions only, with a three-body collision rate coefficient $K_{3}=2(1)\times 10^{-22}~{}\mathrm{cm}^{3}\,\mathrm{s}^{-1}$. Finally, Fig. 3b further corroborates the applicability of such a model and also our earlier estimation of the relative atom loss by directly showing the relationship between $N_{\rm Er}$ and $N_{\rm Li}$ which is well described by a linear fit of slope $1.9(1)$. This is in good agreement with a complete loss of all particles from the trap in Er-Er-Li three-body collisions which would lead to an expected slope of $2.0$.

IV Summary and Prospects

In the present work three major steps towards establishing ultracold 167Er-6Li mixtures as a new platform for the study of many-body physics in general and Efimov states in particular have been taken: First, we could show that by means of sympathetic cooling with 174Yb this mixture can be brought to microkelvin temperatures and that for the selected spin states no unexpected losses occur at the employed magnetic fields. Second, with these minimum requirements fulfilled we could demonstrate that the mixture indeed supports a wealth of Feshbach resonances that, however, are still sufficiently separated to not interfere with each other. Third, while most of the observed resonances are quite narrow some of them feature widths of at least $2\,\mathrm{G}$. There, it has further to be pointed out that currently we can only estimate the width of the inelastic collisional loss resonance and it is known that the width of the elastic part of the resonance might as well be larger Ye et al. (2022).

We have in particular focused on the broad resonance at about $455\,\mathrm{G}$. There, coordinated losses in both channels have been found and the observed atom number decay dynamics seems to support an Er-Er-Li loss channel for the Feshbach resonance. It is exactly this condition of two heavy Fermions interacting with a light particle that in particular motivated the current work as it brings the study of a new type of Efimov three-body state within reach. Finally, the shape of the observed resonance is highly asymmetric. This might be purely caused by the complicated scattering physics involved Fouché et al. (2019). It might, however, also at least partially be caused by additional losses from Efimov states Pires et al. (2014); Tung et al. (2014). More detailed measurements will be required and are currently planned to clarify this important question in this promising mixture system.

Acknowledgments

This work was supported by the Grant-in-Aid for Scientific Research of JSPS Grants No. JP17H06138, No. 18H05405, and No. 18H05228, JST CREST Grant No. JPMJCR1673 and the Impulsing Paradigm Change through Disruptive Technologies (ImPACT) program by the Cabinet Office, Government of Japan, and MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) Grant No. JPMXS0118069021 and JST Moonshot R&D - MILLENNIA Program (Grant No. JPMJMS2269).