Session U09: Gauge Fields and Spin-Orbit Coupling

Orbital order and chiral currents of interacting bosons with π-flux

Higher Bloch bands provide a remarkable setting for realizing many-body states that spontaneously break time-reversal symmetry, offering a promising path towards the realization of interacting topological phases. Here, we propose a different approach by which chiral orbital order effectively emerges in the low-energy physics of interacting bosons moving on a square plaquette pierced by a π-flux. We analyze the low-energy excitations of the condensate in terms of two orbital degrees of freedom and identify a gapped collective mode corresponding to the out-of-phase oscillations of the relative density and phase of the two orbitals. We further highlight the chiral nature of the ground state by revealing the cyclotron-like dynamics of the density upon quenching an impurity potential on a single site. Our single-plaquette results can be used as building blocks for extended dimerized lattices, as we exemplify using the BBH model of higher-order topological insulators. Our results provide a distinct direction to realize interacting orbital-like models with broken time-reversal symmetry, without resorting to higher bands nor to external drives, with direct implications for cold gases and nonlinear photonics.   

Crystallization of bosonic quantum Hall states

The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high-strength magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here we study the purely interaction-driven dynamics of a Landau gauge Bose–Einstein condensate in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons, excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin–Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.   

Engineering a Fractional Quantum Hall State of Bosons in an Optical Lattice

Realization of strongly interacting particles under the presence of a magnetic field can lead to novel phases of matter with topological order. Here, we demonstrate adiabatic preparation of the ground state of a two-particle Harper-Hofstadter system under different fluxes with ultracold bosonic ⁸⁷Rb atoms in an optical lattice. A superimposed running lattice of two Raman beams and a magnetic field gradient are utilized to apply a tunable synthetic gauge field on the atoms. With the single-site resolution provided by our quantum gas microscope, we explore the ground-state fidelity of our protocol over the space of multiple parameters. There are more observables being studied to exhibit phase transition into the fractional quantum Hall state. Our study presents characterization of passage towards topological states in optical-lattice experiments.   

Geometric squeezing of a degenerate Fermi gas

We report on the realization of a geometrically squeezed state of a rapidly rotating atomic Fermi gas and the measurement of its Hall response. A rotating, elliptical harmonic trap realizes the squeezing Hamiltonian for guiding center motion. The Fermi gas thus shrinks down in one direction to a size limited, via Pauli exclusion, to the width of the highest occupied cyclotron mode. In the orthogonal direction it expands exponentially, at a local speed given by the local Hall drift velocity, analogous to the $\vec{E} \times \vec{B}$ drift of charged particles in crossed electric and magnetic fields. Our work paves the way towards studying quantum Hall physics with atomic Fermi gases.   

Measurement of Excitations in the Stripe Phase of a Spin-Orbit Coupled Bose-Einstein Condensate

Recent experimental progress with quantum gases is providing new avenues for the study of exotic stripe phases and supersolid-like properties from a variety of different perspectives. In our lab, we generate a superfluid stripe phase by combining Raman induced spin-orbit coupling with an additional weak optical lattice. We study the excitation spectrum by applying Raman detuning quenches and observing the resulting spin polarization. We characterize the zero-momentum bandgap as a function of the optical lattice coupling strength and find good agreement between the experimental observations and numerical simulations. This work provides a direct experimental confirmation of the gapped pseudo-Goldstone spectrum and opens the door for further investigations into the excitation dynamics of a superfluid stripe phase.   

Interacting spin-orbit coupled fermions in a Wannier-Stark optical lattice clock

We theoretically analyze the interactions between driven spin-orbit coupled fermions in an optical lattice clock based on the partially delocalized Wannier-Stark states in a gravity-tilted shallow lattice. We derive a many-body spin model and consider the following two cases: In carrier transition, we show that the relative strength of the on-site p-wave interactions and off-site s-wave interactions can be easily tuned by lattice intensity, which allows us to precisely cancel the density shift at a "magic" lattice depth; In off-site Wannier-Stark transitions, the s-wave interaction can be significantly enhanced, providing an ideal platform for realizing a ferromagnetic to paramagnetic dynamical phase transition. Our predictions have been demonstrated by recent experimental observations in an optical lattice clock with record clock precision.   

Engineering many-body interactions in a spin-orbit-coupled Wannier-Stark optical lattice clock

We present recent experimental work towards understanding and harnessing atomic interactions within a strontium optical lattice clock [1]. Our vertically oriented, shallow, 1D optical lattice realizes partially delocalized Wannier-Stark eigenstates with superior quantum coherence [2]. On a single site, fermionic Sr atoms interact via weak p-wave interactions. Due to incommensurate lattice and clock wavelengths, spin-orbit coupling allows atoms in neighboring sites to interact via the s-wave channel. Balancing these collisional shifts, we can operate our optical lattice clock with a far higher on-site density while realizing a negligible density shift. Interactions are enhanced by addressing a site-changing Wannier-Stark transition. With the s-wave channel effectively opened to on-site interactions, the collisional shift is far greater in magnitude. We utilize this technique along with in situ imaging to observe a dynamical phase transition between dynamical ferromagnetic and paramagnetic states. 

[1] A Aeppli, A Chu, et al. "Hamiltonian engineering of spin-orbit coupled fermions in a Wannier-Stark optical lattice clock." arXiv preprint arXiv:2201.05909 (2022).

[2] Bothwell, Tobias, et al. "Resolving the gravitational redshift within a millimeter atomic sample." arXiv preprint arXiv:2109.12238 (2021);  Nature, in press (2022).    

Self-Spinning Crystallized Rotating Bose-Einstein Condensates

The dynamics of interacting Bose-Einstein Condensates (BEC) coupled to artificial gauge fields remains a crucial question for understanding exotic quantum phenomenon like the quantum Hall effect and type-II superconductivity. Under extreme rotation and weak interactions, a Landau gauge BEC will spontaneously crystallize into a persistent array of droplets, due to the balance between effective magnetic forces and interactions¹. Here we study the long-time dynamics of these condensed droplets. We find that in the rotating frame the droplets are spinning at a constant frequency. In Lowest Landau Level (LLL), the rate of rotation continously increases from zero upon turning on interaction. While in Thomas-Fermi regime, when multiple Landau levels are occupied, the rotation speed saturates to a particular fraction of cyclotron frequency. Our results provide a novel realization of time crystals and flat-band localization.

¹Mukherjee, B., Shaffer, A., Patel, P.B. et al. Crystallization of bosonic quantum Hall states in a rotating quantum gas. Nature 601, 58–62 (2022).   

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Supersolids are an exotic phase of matter combining the contrasting characteristics of rigidity in crystalline solids and frictionless flow in superfluids. In spin-orbit coupled Bose-Einstein condensates, the double minimum structure of the dispersion at small coupling enables the existence of a supersolid-like stripe phase. The stability of the stripe phase is limited by the miscibility of the components of the spin-orbit coupled system. We present a scheme to exploit highly tunable interactions in potassium-39 to enter a highly stable stripe phase with attractive interstate interactions. The characteristic density modulation can be imaged directly using matterwave optics. Furthermore, we investigate the effect of highly imbalanced intrastate interactions on the phase diagram and the excitation spectrum of the system.   

Collective excitations of Bose-Einstein condensate in a synthetic magnetic field

The realization of synthetic magnetic field offers a new opportunity for the study of topological phenomena with ultracold neutral atoms. Synthetic magnetic field can also strongly modify the superfluid properties of a Bose-Einstein condensate by generating a rotational velocity field and creating vortices. We explore the collective excitations in a spin-orbit-coupled Bose-Einstein condensate in the presence of a position-dependent detuning or Raman coupling. We find that various collective modes such as the scissors mode, the quadrupole mode, and the dipole mode can be coupled together due to the rotational velocity field. We have developed a hydrodynamic theory for the description of the collective excitations in both the single-minimum phase and the plane-wave phase. Our theoretical results are also compared to the numerical simulation of the Gross-Pitaevskii equation.