Effective multi-body SU(N)-symmetric interactions of ultracold fermionic atoms on a 3D lattice

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 87 Sr atoms in a three-dimensional optical lattice, we develop a low-energy effective theory of fermionic AEAs which exhibits emergent multibody 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. 1 0 and P 3 0 states, AEAs exhibit decoupled orbital and OPEN ACCESS RECEIVED

Engineering infinite-range SU($n$) interactions with spin-orbit-coupled fermions in an optical lattice

“…As a result, AMO experiments can directly probe the role of SU(n) interactions * mika.perlin@gmail.com in controllable settings. Recent progress includes studies of the thermodynamic properties of SU(n) fermionic gases [20][21][22][23][24][25][26][27], SU(n) Hubbard phases and phase transitions [28][29][30], single- [31] and two-orbital [32][33][34][35] SU(n) magnetism, and multi-body SU(n)-symmetric interactions [36,37].…”

Quantum Entropic Self-Localization with Ultracold Fermions

“…9/2, 7/2, 5/2), and subsequently remove these excited atoms from the lattice. Note that in order for these excitations to be nuclear-spin selective on multiply-occupied lattice sites, the magnetic shifts to the electronic transitions must be large compared to on-site interaction energies (that are on the scale of kHz [61,63]). The presence of interaction energy shifts will also require several excite-remove cycles in order to address lattice sites with different numbers of atoms.…”

“…excites an atom with nuclear spin 7/2 and moves it to the left by one lattice site. Note that interaction energies, coming from both two-and three-body interactions [61,63], need to be taken into account when tuning laser frequencies to resonance on a desired transition. Once one atom has been moved to each of the lattice sites on either side of the central (initially triply-occupied) lattice site, the excited atoms on the sides can be brought down to their electronic ground state and all atoms can be pumped into a single nuclear spin state, thereby preparing a 3-tuplet.…”

“…Once we have removed all but three nuclear spin states on the lattice, we wish to vacate all singly-and doubly-occupied lattice sites. Here, we can make use of the inter-atomic interaction energy shifts to electronic excitation energies [61,63] by selectively exciting, and subsequently removing, only atoms on doubly-and singly-occupied lattice sites. At this point, the lattice should be mostly vacant, with roughly one in 10 3 = 120 lattice sites containing three atoms that occupy the previously chosen nuclear spin states.…”

Degenerate Rabi spectroscopy of the Floquet engineered optical lattice clock

“…Meanwhile, owing to the strong decoupling between the nuclear spin I and electronic angular momentum J = 0 of the two lowest electronic states 1 S 0 and 3 P 0 (clock states), AEAs exhibit that the nuclear spin is independent of both interatomic collision and trapping potential. Hence, it directly leads to the SU(N ≤ 2I + 1) symmetry emerging in the AEAs [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. AEAs possessing high-dimensional symmetries with large N (e.g.…”