We experimentally realize a spin-momentum lattice with a homogeneously trapped Fermi gas. The lattice is created via cyclically rotated atom-laser couplings between three bare atomic spin states, and are such that they form a triangular lattice in a synthetic spin-momentum space. We demonstrate the lattice and explore its dynamics with spin- and momentum-resolved absorption imaging. This platform will provide new opportunities for synthetic spin systems and the engineering of topological bands. In particular, the use of three spin states in two spatial dimensions would allow the simulation of synthetic magnetic fields of high spatial uniformity, which would lead to ultranarrow Chern bands that support robust fractional quantum Hall states.
We experimentally realize a spin-momentum lattice with a homogeneously trapped Fermi gas. The lattice is created via cyclically rotated atom-laser couplings between three bare atomic spin states, and are such that they form a triangular lattice in a synthetic spin-momentum space. We demonstrate the lattice and explore its dynamics with spin- and momentum-resolved absorption imaging. This platform will provide new opportunities for synthetic spin systems and the engineering of topological bands. In particular, the use of three spin states in two spatial dimensions would allow the simulation of synthetic magnetic fields of high spatial uniformity, which would lead to ultranarrow Chern bands that support robust fractional quantum Hall states.
Quantum gas microscopes have expanded the capabilities of quantum simulation of Hubbard models by enabling the study of spatial spin and density correlations in square lattices.However, quantum gas microscopes have not been realized for fermionic atoms in frustrated geometries.Here, we demonstrate the single-atom resolved imaging of ultracold fermionic 6 Li atoms in a triangular optical lattice with a lattice constant of 1003 nm.The optical lattice is formed by a recycled narrow-linewidth, high-power laser combined with a light sheet to allow for Raman sideband cooling on the D 1 line.We optically resolve single atoms on individual lattice sites using a high-resolution objective to collect scattered photons while cooling them close to the two-dimensional ground vibrational level in each lattice site.By reconstructing the lattice occupation, we measure an imaging fidelity of approximately 98%.Our triangular lattice microscope platform for fermions clears the path for studying spin-spin correlations, entanglement, and dynamics of geometrically frustrated Hubbard systems which are expected to exhibit exotic emergent phenomena including spin liquids and kinetic frustration.
We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [C. L. Kane et al., Phys. Rev. Lett. 88, 036401 (2002)], as well as Meissner phases and vortex phases in double wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e., the Harper-Hofstadter model and the two-leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semicontinuous Harper-Hofstadter model accessible with cold-atom experiments. For the minimal setup of a double wire, we explore how a subwavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in nonplanar geometries such as cylinders, disks, and tori.
We report the experimental realization of a synthetic three-leg Hall tube with ultracold fermionic atoms in a one-dimensional optical lattice. The legs of the synthetic tube are composed of three hyperfine spin states of the atoms, and the cyclic interleg links are generated by two-photon Raman transitions between the spin states, resulting in a uniform gauge flux ϕ penetrating each side plaquette of the tube. Using quench dynamics, we investigate the band structure of the Hall tube system for a commensurate flux ϕ=2π/3. Momentum-resolved analysis of the quench dynamics reveals a critical point of band gap closing as one of the interleg coupling strengths is varied, which is consistent with a topological phase transition predicted for the Hall tube system.
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.
"As the progress of science pushes the frontiers of studying nature to both the extremely large scale and the incredibly small scale, experiments can become increasingly difficult to perform. Therefore, a scale model experiment for these kinds of physics can be useful as long as it is relatively easy to access and control. This is the idea of quantum simulation, where one system exactly mimics another when they are subjected to equivalent physical scenarios. Topological systems, those with a property that is stabilized by their specific configuration, are often quite challenging to experimentally probe. Therefore, test bed systems have been widely and successfully applied to studying topology in an effort to advance the field, which promises enticing applications such as robust quantum technology. Our particular scheme uses a novel type of ""synthetic"" dimension for atoms of a Bose–Einstein condensate, which we call a momentum-space lattice, to emulate one-dimensional lattice models. The idea of a synthetic dimension or synthetic lattices is a useful construct to describe how the particle dynamics can evolve in degrees of freedom that are not directly related to transport in real space. This can relate to population dynamics in an internal degree of freedom, such as spin, or, in our case, in the dynamics of free-particle-like atomic momentum states. We expose a Bose–Einstein condensate to two laser fields that are capable of driving transitions between different momentum states of the condensate atoms through a two-photon Bragg diffraction process. Neighboring states in the free-particle dispersion relation are characterized by a unique momenta and energy spacing such that we can independently control every aspect of their coupling. In this thesis, we report on the design and construction of an apparatus for the production of 87Rb Bose–Einstein condensates as well as the partial construction of an apparatus for the production of 39K Bose–Einstein condensates. We also discuss the experimental realization of, and theoretical background for, our momentum-space lattice. Using the momentum-space lattice, we perform experiments on not only topological systems, but also on driven artificial spins featuring chaotic dynamics, as well as faster-than-adiabatic quantum state control and preparation. Our measurements of topological systems are based in the 1D Su–Schrieffer–Heeger model, where we report on the direct observation of the localized, solitonic edge state created by the topology inherent in the system. Through the addition of exactly tunable tunneling disorder, we observe the destruction of the band topology due to disorder at a random-singlet transition. Furthermore, we drive a trivial system into a topological phase through the addition of disorder, observing a counter-intuitive phenomenon known as the topological Anderson insulator for the first time. We go on to report on our driven, tunable spin experiment, where we probe effective spin ""squeezing"" (in the absence of any entanglement in our noninteracting system), the out-of-time-ordered correlation function, and chaos. And finally, we use our momentum-space lattice to demonstrate a technique which allows a system to be transformed faster than the adiabatic limit with no diabatic transitions in a highly non-trivial regime. Due to the versatility of the momentum-space lattice, the results detailed here have a broad impact. Our observations of topological phenomena in elementary and canonical 1D systems are some of the first experimental verifications of long-standing predictions. Further, our studies of the interplay between classical chaos and quantum systems may help shed light on this complex and rich problem. And from a more ""applied science"" perspective, our demonstrations of generalized counter-diabatic techniques are widely beneficial and applicable to many systems where adiabaticity is challenged."
Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted in dimensions D > 3. We report the realization of an atomic quantum Hall system evolving in four dimensions (4D), with two spatial dimensions and two synthetic ones encoded in the large spin of dysprosium atoms. We measure the nontrivial topological index of the ground band through a full characterization of the nonlinear electromagnetic response and observe the associated anisotropic hyperedge modes. We also excite nonplanar cyclotron motion, in contrast to the planar orbits in D ≤ 3. Our work may enable the investigation of strongly correlated topological liquids in 4D, generalizing fractional quantum Hall states.