Synthetic Dimensions and Spin-Orbit Coupling with an Optical Clock Transition
Lorenzo Francesco Livi, Giacomo Cappellini, M. Diem, Lorenzo Franchi, Cecilia Clivati, Matteo Frittelli, Filippo Levi, Davide Calonico, Jacopo Catani, M. Inguscio, L. Fallani
We demonstrate a novel way of synthesizing spin-orbit interactions in ultracold quantum gases, based on a single-photon optical clock transition coupling two long-lived electronic states of two-electron ^{173}Yb atoms. By mapping the electronic states onto effective sites along a synthetic "electronic" dimension, we have engineered fermionic ladders with synthetic magnetic flux in an experimental configuration that has allowed us to achieve uniform fluxes on a lattice with minimal requirements and unprecedented tunability. We have detected the spin-orbit coupling with fiber-link-enhanced clock spectroscopy and directly measured the emergence of chiral edge currents, probing them as a function of the flux. These results open new directions for the investigation of topological states of matter with ultracold atomic gases.
We demonstrate a novel way of synthesizing spin-orbit interactions in ultracold quantum gases, based on a single-photon optical clock transition coupling two long-lived electronic states of two-electron ^{173}Yb atoms. By mapping the electronic states onto effective sites along a synthetic "electronic" dimension, we have engineered fermionic ladders with synthetic magnetic flux in an experimental configuration that has allowed us to achieve uniform fluxes on a lattice with minimal requirements and unprecedented tunability. We have detected the spin-orbit coupling with fiber-link-enhanced clock spectroscopy and directly measured the emergence of chiral edge currents, probing them as a function of the flux. These results open new directions for the investigation of topological states of matter with ultracold atomic gases.
The recent experimental realization of clock-laser-induced synthetic gauge fields and one-dimensional spin-orbit coupling in ultracold alkaline-earth(-like) atoms provides a new way to explore topological quantum states with suppressed heating effects. Here, we propose a scheme for realizing a synthetic quantum Hall tube and ribbon in an optical lattice clock system with multiple optical clock transition couplings. The legs of the synthetic Hall system are composed of the atomic ground and metastable orbital states, and the couplings between the legs are generated by clock lasers, resulting in a synthetic gauge flux. We investigate the band structure and topological phase diagram under various conditions and demonstrate the phase transition. The momentum-resolved quench dynamics of the synthetic Hall system is analyzed to demonstrate the presence of gauge flux on plaquettes and reveal the critical point of the phase transition. The hyperfine spin can serve as an additional synthetic dimension, allowing a two-component Hall system to be realized in synthetic dimensions. A size-enlarged Hall system could be realized by coupling the magnetic sublevels and orbital states simultaneously. Our scheme is within reach of existing optical lattice clocks and thus provides a realistic method to achieve topological quantum Hall systems with ultracold alkaline-earth(-like) atoms. This study paves the way for realizing quantum spin Hall states with hyperfine spins and has the potential to explore more interesting topological phases.
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time-reversal) topological insulators and two-dimensional quantum Hall insulators. We reveal three instances of their promising potential: (i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, (ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and (iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of quantum Hall insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.
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.
Realizing the topological bands of helical states poses a challenge in studying ultracold atomic gases. Motivated by the recent experimental success in realizing chiral optical ladders, here we present a scheme for synthesizing topological quantum matter, especially the quantum spin Hall phase, in the chiral optical ladders. More precisely, we first establish the synthetic pseudo-spin-orbit coupling and Zeeman splitting in the chiral ladders. After analyzing the band structure of the ladders exposed to the bichromatic optical potentials, we report the existence of quantum spin Hall phase. We further identify a rich phase diagram of the bichromatic chiral ladders, illustrating that our proposal features a large space of system parameters exhibiting quantum phase transitions. Our scheme is within reach of the existing ladder optical lattices and hence provides a new method to engineer the elaborate topological bands for cold atomic gases.
Ultra-cold quantum gases subjected to light-induced synthetic gauge potentials have become an emergent field of theoretical and experimental studies. Because of the novel application of two-photon Raman transitions, ultra-cold neutral atoms behave like charged particles in magnetic field. The Raman coupling naturally gives rise to an effective spin-orbit interaction which couples the atom’s center-of-mass motion to its selected pseudo-spin degrees of freedom. Combined with unprecedented controllability of interactions, geometry, disorder strength, spectroscopy, and high resolution measurement of momentum distribution, etc., we are truly in an exciting era of ful- filling and going beyond Richard Feynman’s vision of realizing quantum simulators to better understand the quantum mechanical nature of the universe, manifested immensely in the ultra-cold regimes. In this dissertation, we present a collection of theoretical progresses made by the doctoral candidate and his colleagues and collaborators. From the past few years of work, we mainly address three aspects of the synthetic spin-orbit and light field induced coupling in ultracold quantum gases: a) The ground-state physics of single- particle system, two-body bound states, and many-body systems, all of which are subjected to spin-orbit coupling originated from synthetic gauge potentials; b) The symmetry breaking, topological phase transition and quench dynamics, which are conveniently offered by the realized experimental setup; c) The proposal and impli- cations of light field induced dynamical spin-orbit coupling for atoms inside optical cavity. Our work represents an important advancement of theoretical understanding to the active research frontier of ultra-cold atom physics with spin-orbit coupling.
Artificial synthetic gauge field and spin-orbit coupling has been extensively studied following their experimental realization in ultracold atomic systems. Thanks for the versatile controllability, such systems not only provide possibilities to simulate and study important models in multidisciplinary fields of physics, but also work as an excellent platform to engineer novel states of matter and quantum phenomena. This paper reviews some recent progresses on the study of ultracold atomic systems with spin-orbit coupling, focusing on the effects induced by dissipation, novel interaction forms, large symmetry of spins, and long-range interactions. The investigation in these aspects is closely related to the characteristics of ultracold atomic systems, hence can bring new inspirations and perspectives on the understanding of spin-orbit coupling. In this review, we firstly investigate the appearance of a topological superradiant state in a quasi-one-dimensional Fermi gas with cavity-assisted Raman process. A cavity-assisted spin-orbit coupling and a bulk gap opening at half filling will be induced by the superradiant light generated in the transversely driven cavity mode. The topological superradiant state and the corresponding topological phase transition in the system can be driven by this mechanism. Then, symmetry-protected topological states of interacting fermions will be introduced in a quasi-one-dimensional cold gas of alkaline-earth-like atoms. Raman-assisted spin-orbit couplings in the clock states, together with the spin-exchange interactions in the clock-state manifolds will give rise to symmetry-protected topological states for interacting fermions, by taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these alkaline-earth-like atoms. Furthermore, we show that an exotic topological defect, double-quantum spin vortices, which are characterized by doubly quantized circulating spin currents and unmagnetized filled cores, can exist in the ground states of SU(3) spin-orbit-coupled Bose-Einstein condensates. It is found that the combined effects of SU(3) spin-orbit coupling and spin-exchange interaction determine the ground-state phase diagram. Finally, we demonstrate that spin-orbit coupling and soft-core long-range interaction can induce an exotic supersolid phase of Bose gas, with the emergence of spontaneous circulating particle current. This implies that a finite angular momentum can be generated with neither external rotation nor synthetic magnetic field, and the direction of the angular momentum can be altered by adjusting the strength of spin-orbit coupling or interatomic interaction.