Hamiltonian engineering of spin-orbit–coupled fermions in a Wannier-Stark optical lattice clock

Abstract

Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice supports superior quantum coherence and adjustable interactions via spin-orbit coupling, thus presenting a powerful spin model realization. The relative strength of the on-site and off-site interactions can be tuned to achieve a zero density shift at a “magic” lattice depth. This mechanism, together with a large number of atoms, enables the demonstration of the most stable atomic clock while minimizing a key systematic uncertainty related to atomic density. Interactions can also be maximized by driving off-site Wannier-Stark transitions, realizing a ferromagnetic to paramagnetic dynamical phase transition.

Evaluation of lattice light shift at mid 10$^{-19}$ uncertainty for a shallow lattice Sr optical clock

“…Important ingredients for such significant progress in clock precision include cooling a large yet dilute sample of fermionic 87 Sr atoms to below 100 nK, well-characterized motional states, microscopic imaging spectroscopy, long coherence time (> 30 s), and the precise control of atomic interaction effects. Further, at low lattice depths atom-atom interactions are modified, nearly eliminating density dependent frequency shifts [14]. Thus, a shallow, partially delocalized, WS optical lattice clock contains ideal characteristics for next generation timekeeping.…”

“…is the detuning from E1 magic frequency (ν E1 ). The reference condition is chosen to be at the magic lattice depth to minimize any potential systematic error from collisional shifts [14]. Uncertainty from the hyperpolarizability is reduced to well below 1 × 10 −19 at this depth.…”

“…Clock in tilted, shallow lattice. Our 1D 87 Sr optical lattice clock is detailed in previous publications [1,14]. We prepare stretched states (m F = ±9/2) spinpolarized ensembles in a single motional ground state axially and T r ∼700 nK radially at U = 300E r .…”

“…The camera readout provides a high-resolution spatial distribution of the density and excitation fraction. With this information, we correct the density shift shot-byshot [14], providing a robust rejection of systematics related to the atomic density fluctuation.…”

“…As a result, we have a single anchor point (u ref , δ ref L ) = (10, −15 MHz). By choosing the anchor point near the magic lattice depth where the atomic density effect is suppressed [1,14], we establish a reference frequency with minimal potential systematic effects. We use model (1) to fit data with or without fixing αqm and the results are summarized in Table I (see also [18] for the extended table ).…”