Abstract
Rapid advancements in the experimental capabilities with ultracold alkaline-earth-like atoms (AEAs) bring to a surprisingly near term the prospect of performing quantum simulations of spin models and lattice field theories exhibiting SU(N) symmetry. Motivated in particular by recent experiments preparing high density samples of strongly interacting Sr atoms in a three-dimensional optical lattice, we develop a low-energy effective theory of fermionic AEAs which exhibits emergent multi-body SU(N)-symmetric interactions, where N is the number of atomic nuclear spin levels. Our theory is limited to the experimental regime of (i) a deep lattice, with (ii) at most one atom occupying each nuclear spin state on any lattice site. The latter restriction is a consequence of initial ground-state preparation. We fully characterize the low-lying excitations in our effective theory, and compare predictions of many-body interaction energies with direct measurements of many-body excitation spectra in an optical lattice clock. Our work makes the first step in enabling a controlled, bottom-up experimental investigation of multi-body SU(N) physics.
Highlights
Fermionic alkaline-earth atoms (AEAs), in addition to other atoms such as ytterbium (Yb) sharing similar electronic structure, are currently the building blocks of the most precise atomic clocks in the world [1,2,3]
More recently (2017), a new generation of optical lattice clock (OLC) became operational at JILA, interrogating a Fermi degenerate gas of 87Sr atoms in a 3-D lattice at nanokelvin temperatures [8]
We investigate the first experimental capabilities with ultracold fermionic alkaline-earth-like atoms (AEAs) to prepare high-density samples in a 3-D lattice with multiple occupation of individual lattice sites [34]
Summary
Fermionic alkaline-earth atoms (AEAs), in addition to other atoms such as ytterbium (Yb) sharing similar electronic structure, are currently the building blocks of the most precise atomic clocks in the world [1,2,3]. More recently (2017), a new generation of OLCs became operational at JILA, interrogating a Fermi degenerate gas of 87Sr atoms in a 3-D lattice at nanokelvin temperatures [8] All of these atoms’ degrees of freedom, including the electronic orbital, nuclear spin, and motional states, can be fully controlled with high fidelity in a 3-D lattice [9,10,11,12]. To facilitate this comparison of excitation spectra and to characterize the low-lying excitations in our effective theory, we consider a restriction of our theory to states with at most one orbital excitation per lattice site In this case, we find that the SU(N ) symmetry of atomic collisions allow the effective multi-body interactions to take a remarkably simple form.
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