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arXiv:2201.05909 · Science Advances

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

Alexander Aeppli, Anjun Chu, Tobias Bothwell, Colin J. Kennedy, Dhruv Kedar, Peiru He, Ana María Rey, Jun Ye

Published Oct 12, 2022• 53 citations
arXivHTMLPDF

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.

DOI
10.1126/sciadv.adc9242

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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.
Scaling up the performance of atomic clocks requires understanding complex many-body Hamiltonians to ensure meaningful gains for metrological applications. Here we use a degenerate Fermi gas loaded into a three-dimensional optical lattice to study the effect of a tunable Fermi-Hubbard Hamiltonian. The clock laser introduces a spin-orbit coupling spiral phase and breaks the isotropy of superexchange interactions, leading to XXZ-type spin anisotropy. By tuning the lattice confinement and applying imaging spectroscopy, we map out favorable atomic coherence regimes. We transition through various interaction regimes and observe coherent superexchange, tunable through on-site interaction and site-to-site energy shift, affecting the Ramsey fringe contrast over timescales >1 second. This study lays the groundwork for using a three-dimensional optical lattice clock to probe quantum magnetism and spin entanglement.
We propose the use of optical lattice clocks operated with fermionic alkaline-earth atoms to study spin-orbit coupling (SOC) in interacting many-body systems. The SOC emerges naturally during the clock interrogation, when atoms are allowed to tunnel and accumulate a phase set by the ratio of the "magic" lattice wavelength to the clock transition wavelength. We demonstrate how standard protocols such as Rabi and Ramsey spectroscopy that take advantage of the sub-Hertz resolution of state-of-the-art clock lasers can perform momentum-resolved band tomography and determine SOC-induced s-wave collisions in nuclear-spin-polarized fermions. With the use of a second counterpropagating clock beam, we propose a method for engineering controlled atomic transport and study how it is modified by p- and s-wave interactions. The proposed spectroscopic probes provide clean and well-resolved signatures at current clock operating temperatures.
Quantum metrology with ultrahigh precision usually requires atoms prepared in an ultrastable environment with well-defined quantum states. Thus, in optical lattice clock systems deep lattice potentials are used to trap ultracold atoms. However, decoherence, induced by Raman scattering and higher order light shifts, can significantly be reduced if atomic clocks are realized in shallow optical lattices. On the other hand, in such lattices, tunneling among different sites can cause additional dephasing and strongly broadening of the Rabi spectrum. Here, in our experiment, we periodically drive a shallow ^{87}Sr optical lattice clock. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4 Hz linewidth. With careful comparison between the theory and experiment, we demonstrate that the Rabi frequency and the Bloch bands can be tuned, simultaneously and independently. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phases of matter by engineering exotic spin orbit couplings.
The quantum metrology with ultra-high precision usually requires the atoms prepared in an ultra-stable environment with well-defined quantum states. Thus, the optical lattice clock system chooses deep lattice potential to trap the ultra-cold atoms. However, building atomic clock in shallow optical lattice can greatly reduce decoherence rate induced by Raman scattering as well as higher order light shift, but tunneling among the lattice sites will cause additional dephasing and strongly broadening of the Rabi spectrum. Here, we periodically drive the shallow 87^{87}87Sr optical lattice clock in the experiment. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4Hz line-width. With careful comparison between the theory and experiment, we demonstrate the Rabi frequency and Bloch bands can be simultaneously and independently tuned by adjusting the driving frequency and amplitude. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phase of matter, such as engineering exotic spin orbit coupling Hamiltonian.
Motivated by a recent experiment [L. F. Livi et al., Phys. Rev. Lett. 117, 220401 (2016)], we study the ground-state properties of interacting fermions in a one-dimensional optical lattice clock with spin-orbit coupling. As the electronic and the hyperfine-spin states in the clock-state manifolds can be treated as effective sites along distinct synthetic dimensions, the system can be considered as multiple two-leg ladders with uniform magnetic flux penetrating the plaquettes of each ladder. As the interorbital spin-exchange interactions in the clock-state manifolds couple individual ladders together, we show that exotic interaction-induced vortex states emerge in the coupled-ladder system, which compete with existing phases of decoupled ladders and lead to a rich phase diagram. Adopting the density matrix renormalization group approach, we map out the phase diagram, and investigate in detail the currents and the density-density correlations of the various phases. Our results reveal the impact of interactions on spin-orbit coupled systems, and are particularly relevant to the ongoing exploration of spin-orbit coupled optical lattice clocks.
A Wannier-Stark optical lattice clock has demonstrated unprecedented measurement precision for optical atomic clocks. We present a systematic evaluation of the lattice light shift, a necessary next step for establishing this system as an accurate atomic clock. With precise control of the atomic motional states in the lattice, we report accurate measurements of the multipolar and the hyperpolar contributions and the operational lattice light shift with a fractional frequency uncertainty of 3.5×10^{-19}.