Spin Dynamics Dominated by Resonant Tunneling into Molecular States

Yoo Kyung Lee, Hanzhen Lin (林翰桢), and Wolfgang Ketterle

Phys. Rev. Lett. 131, 213001 – Published 21 November 2023

Abstract

Optical lattices and Feshbach resonances are two of the most ubiquitously used tools in atomic physics, allowing for the precise control, discrete confinement, and broad tunability of interacting atomic systems. Using a quantum simulator of lithium-7 atoms in an optical lattice, we investigate Heisenberg spin dynamics near a Feshbach resonance. We find novel resonance features in spin-spin interactions that can be explained only by lattice-induced resonances, which have never been observed before. We use these resonances to adiabatically convert atoms into molecules in excited bands. Lattice-induced resonances should be of general importance for studying strongly interacting quantum many-body systems in optical lattices.

Received 11 August 2022
Accepted 29 June 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.213001

Physics Subject Headings (PhySH)

Cold gases in optical lattices Quantum simulation Spin dynamics

Ultracold gases

Atom & ion trapping & guiding Feshbach resonance

Atomic, Molecular & Optical

Authors & Affiliations

Yoo Kyung Lee ^*,†, Hanzhen Lin (林翰桢)^†, and Wolfgang Ketterle

Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA; Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA; and MIT-Harvard Center for Ultracold Atoms, Cambridge, 02139 Massachusetts, USA

^*Corresponding author: eunlee@mit.edu
^†These authors contributed equally to this work.

Observation of Confinement-Induced Resonances in a 3D Lattice

Deborah Capecchi, Camilo Cantillano, Manfred J. Mark, Florian Meinert, Andreas Schindewolf, Manuele Landini, Alejandro Saenz, Fabio Revuelta, and Hanns-Christoph Nägerl

Phys. Rev. Lett. 131, 213002 (2023)

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Vol. 131, Iss. 21 — 24 November 2023

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Images

Figure 1
Resonant tunneling into molecular states. An optical lattice in the Mott insulating regime with one atom per site (a) can host different virtual states, such as two atoms per site with repulsive interaction $U$ (b); two atoms in an excited c.m. mode (c); or a molecule with negative binding energy $U^{'}$ (d). Both states (c) and (d) are typically far detuned from state (a). However, positive c.m. energy (c) can be combined with negative binding energy (d), bringing a molecule in an excited c.m. mode into resonance with the Mott insulator (e). State (a) is connected to (e) via a resonant tunneling process. These are lattice-induced resonances, observed here for a quasi-1D lattice.
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Figure 2
Energy spectrum for two interacting atoms in a harmonic trap. In an isotropic trap (a), only the relative motion (blue curves) is affected by the scattering length $a_{s}$ [34]. A copy of this level structure exists for each unit of c.m. excitation $ℏ ω$ . The lowest three c.m. excitations (magenta, green, and gold curves) for the lowest molecular branch become degenerate with the Mott insulator (black line) near a Feshbach resonance ( $1 / a_{s} = 0$ , dotted line). The square, triangle, and circle correspond to the interactions of Figs. 1, 1, and 1, respectively. Our experimental conditions are more consistent with an anisotropic trap (b) with stronger transverse confinement [35]. In contrast to (a), the first excited branch crosses zero energy at negative finite scattering length. The vertical dashed lines correspond to the observed resonance positions seen in Fig. 3 and agree with the harmonic model. Solid gray curves correspond to the next six accessible c.m. excitations for both panels, while the dashed gray curves are branches with odd transverse excitations that have suppressed coupling to the Mott insulator (see Supplemental Material [36]). Colored numbers refer to $z$ c.m. excitations. The first dashed gray curve corresponds to one excitation in either $x$ or $y$ and zero in $z$ .
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Figure 3
Spin interaction anisotropy at different magnetic fields. We plot the anisotropy $Δ = J_{z} / J_{x y}$ as a function of the magnetic field (a) and enlarged for fields with large $b b$ scattering lengths $| a_{b b} | ≳ 500 a_{0}$ (b). Far from the $b b$ Feshbach resonances (dotted lines), the data (open circles) agree well with perturbative calculations (gray curves). Such theory is not applicable in the regions with large scattering lengths (filled circles). The dispersive features at 845.459, 892.249, 893.182, and 895.537 G (dashed vertical lines) are consistent with lattice-induced resonances corresponding to band excitations of $E_{c . m .} / ℏ ω_{z} = 1$ , 2, and 3 (magenta, green, and gold curves, respectively). Note that the behavior of the spin anisotropy is smooth across the free-space resonances. Some data are inherited from Ref. [52]. Fits are shown in black curves (see Supplemental Material [36]). The statistical errors of the data and fitted resonances are smaller than the symbols and widths of the dashed lines, respectively.
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Figure 4
Creation of molecules with adiabatic sweeps through a lattice-induced resonance. We sweep the magnetic field to different values without crossing the free-space resonance at 894 G (inset, dotted line). In a 3D lattice with shallow axial confinement, molecules are created when sweeping up (filled circles) or down (open squares) past the lattice-induced resonance (dashed line). Statistical errors are given by the shaded area and are larger for the down sweep due to fewer data points. The reduction of molecule fraction beyond 895.7 G can be explained by the finite time of the sweep which was kept constant at 15 ms for all final fields. The small offset of the crossover between the sweeps can be explained by hysteresis of the magnetic field during the ramp.
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