Session X04: Topology in Cold Gases

Experimental realization of a fermionic spin-momentum lattice

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 ultra-narrow Chern bands that support robust fractional quantum Hall states.   

Topological pumping in the strongly correlated regime

A topological pump can be regarded as the one-dimensional counterpart to the quantum Hall effect, in which time plays the role of a second dimension. Quantisation of charge transport is achieved by slowly encircling a topological transition point in Hamiltonian parameter space. Previously, topological pumps have been realised with non-interacting and mean-field states in synthetic quantum systems, such as ultracold atoms and photonics. However, the fate of quantised pumping in the strongly correlated regime has remained out of reach to date. Here, we present recent experimental progress towards investigating the effects of Hubbard interactions on topological charge transport of ultracold fermions. Our measurements suggest significant deviations from the quantised value for attractive and repulsive interactions. We compare our results to recent theoretical studies that predict a breakdown of pumping in the Mott regime.   

Quantized transport of solitons in nonlinear Thouless pumps: From Wannier drags to ultracold topological mixtures

Recent progress in synthetic lattice systems has opened the door to novel explorations of topological matter. In particular, photonic devices and ultracold matter waves offer the unique possibility of studying the rich interplay between topological band structures and tunable nonlinearities. In this emerging field of nonlinear topological physics, a recent experiment revealed the quantized motion of localized nonlinear excitations (solitons) upon driving a Thouless pump sequence; the reported observations suggest that the quantized displacement of solitons is dictated by the Chern number of the band from which they emanate. In this work, we elucidate the origin of this intriguing nonlinear topological effect, by showing that the motion of solitons is established by the quantized displacement of Wannier functions. Our general theoretical approach, which fully clarifies the central role of the Chern number in solitonic pumps, provides a rigorous framework for describing the topological transport of nonlinear excitations in a broad class of physical systems. Exploiting this interdisciplinarity, we introduce an interaction-induced topological pump for ultracold atomic mixtures, where solitons of impurity atoms experience a quantized drift resulting from genuine interaction processes with their environment.   

Wavepacket dynamics in topological Floquet bands

Floquet engineering, i.e., the periodic modulation of a system’s parameters, has proven as a powerful tool for the realization of quantum systems with exotic properties, which are otherwise not accessible in static realizations. We have engineered such systems on our experimental platform, which consists of bosonic atoms in a periodically driven optical honeycomb lattice. Depending on the driving parameters several topological phases can be realized, including genuine out-of-equilibrium topological phases without any static analogue [1].

As the bulk-boundary correspondence relates the properties of the bulk of a topological system to the number of topologically protected edge modes at the boundaries, we study the behavior in both regions. To this end, we investigate the real-space evolution of an initially-localized wavepacket after release from a tightly-focused optical tweezer in the vicinity of a hard-wall potential as well as in the bulk of this system.

[1] Wintersperger et al. Realization of an anomalous Floquet topological system with ultracold atoms. Nat. Phys. 16, 1058–1063 (2020).

    

Realization of a non-Hermitian optical Raman lattice for ultracold fermions

The recent advances in non-Hermitian physics open new possibilities for exploring unprecedented quantum states in an open atomic system. In our previous study[1], we have realized non-Hermitian spin-orbit coupled bands for ultracold fermions in bulk, and demonstrated the topological nature of non-Hermitian energy band near the band closing point when the Parity-Time symmetry breaking transition occurs. In this talk, we report our progress on the experimental development of the non-Hermitian optical Raman lattice, which generalizes non-Hermitian spin-orbit coupling into the lattice system. Focusing on the time evolution of spin texture in Bloch bands, we explore the distinct features induced by a highly controllable spin-dependent dissipation and spin-orbit coupling. It is expected that this non-Hermitian platform would allow us to further expand the possibilities of studying the non-Hermitian topological phases in lattices.    

Two-dimensional momentum state lattices

Cold atoms offer a clean, precise, and highly controllable platform for quantum simulation. The technique of momentum state lattices (MSLs) in one dimension allows the spectroscopic engineering of synthetic lattices with single site precision, offering independent control over all tunneling terms and site energies. In this talk, I present the extension of 1-D MSLs to engineer 2-D synthetic lattices of laser coupled atomic states. The platform of 2-D MSLs offer the potential to explore topological, disordered, and kinetically frustrated lattice models in two dimensions. Due to our experimental switch from Rb-87 to K-39, our system offers tunable interactions via magnetic Feshbach resonance. The ability to augment the aforementioned two-dimensional models with tunable interactions promises an exploration of a broad range of nonlinear lattice phenomena.   

Interaction induced topology in a Bose-Hubbard chain under non-Hermitian Drive

Exotic topological phases with no analogue in traditional static Hermitian systems have been observed in Floquet and non-Hermitian systems. We propose a model that combines non-Hermiticity and Floquet engineering to realize topological energy spectrum in a 1D bosonic system. Our Hamiltonian is a 1D Bose gas with an asymmetric density dependent non-Hermitian gauge field. The single particle spectrum is topologically trivial while the spectrum with multiple particles has a non-trivial winding number, suggesting the topology arises from interactions. We calculate a non-trivial winding number of 2 under periodic boundary conditions if there are two particles in the system. Equivalently, we observe a skin effect in the open boundary geometry, only if there are multiple particles in the system. We further find that the spectrum can be separated into two sectors: one where the particles cluster and one where the particles avoid each other. We derive an effective theory that accurately describes the properties of the clustering sector as a non-Hermitian SSH model. Finally, we propose that our model can be realized in bosons trapped in optical lattices or in coupled optical waveguide arrays.   

Topological charge pumping in a Fermi gas with Hubbard interactions

We consider charge pumping in one-dimensional interacting systems of spinful fermions, where each species is described by a (possibly shifted) Rice-Mele model.The ionic Hubbard model [1-3] is visited twice during a pump cycle. It hosts three phases: The Mott-Insulating (MI) phase is separated from the band-insulating (BI) phase via a spontaneously dimerized (SDI) phase. A dimerized hopping connects the BI and MI phases without closing the charge gap. We show via the many-body polarization and time-dependent calculations of the integrated current that a closed loop around one charge critical point of the ionic Hubbard model leads to the pumping of a single unit of charge per pump cycle in the adiabatic limit, as opposed to two charges for a usual Rice-Mele pump. Pumping through the SDI phase does not change the quantization of pumped charge, contrary to what was recently reported in [4].

[1] Torio, Aligia, and Cecatto, Phys. Rev. B 64, 121105 (2001).

[2] Torio et al., Phys. Rev. B 73, 115109 (2006).

[3] Manmana et al., Phys. Rev. B 70, 155115 (2004).

[4] Nakagawa et al., Phys. Rev. B 98, 115147 (2018).   

Non-Abelian Euler topology in ultracold atoms

Topological insulators (TIs) are gapped quantum phases that have a topological nature by virtue of protecting symmetries. Following time reversal symmetry (TRS) protected TIs, past years have seen remarkable progress in characterizing topological materials taking into account crystal symmetries. These pursuits also revealed fragile invariants that can be trivialized by gap closings with trivial bands, rather than involving those having opposite topological charge. An archetypal novel invariant emerging from such studies, which goes beyond symmetry eigenvalue indicated phases and relates to refined partitioning schemes is Euler class. It acts as the fragile crystalline-protected analogue of Chern number in systems having C₂T [product of two-fold rotations and TRS] or PT [product of parity P and TRS] symmetry. Moreover, band nodes in Euler class models have charges that have non-Abelian braiding properties, enabling the study of non-Abelian physics essentially in a single particle setting and making their experimental realization highly desirable. On another front, ultracold atomic gases have proven versatile platforms for exploring topological phenomena with particular advances in periodic driving and artificial gauge fields, calling for expansion of these notions to out of equilibrium and bringing new classification schemes. In light of recent experiments calibrated to explore Euler topology, we here investigate the dynamics of Euler class in optical lattices. We study non-Abelian Euler properties in different out-of-equilibrium settings and identify unique observable signatures.   

Non-Hermitian Many-Body Localization of Coupled Hatano-Nelson Chains

The physics of non-Hermitian systems has attracted significant interests in recent years. The phenomena of non-Hermiticity originate from an exchange of energy or particles with environment and leads to several rich properties such as parity-time symmetry breaking, exceptional points unique to non-Hermitian topology etc. Recently, it has been shown that a non-Hermitian system with random disorder or quasiperiodic potential possessing time-reversal symmetry exhibit complex-real transition. In this work, we explore the eigenspectrum and localization properties of the interacting coupled Hatano-Nelson chains in the presence of random disorder potential. In contrast to the previous studies of the spinless fermionic system, the two-chain system shows a complex-real transition which does not coincide to the localization transition. Moreover, the critical coupling strength of the transition decreases as the ratio of respective non-reciprocal hoppings varied. We further investigate the spectral statistics and dynamical properties of the system. Our study opens up a direction towards an exploration of the critical effects of disordered non-Hermitian many-body systems in cold-atom experiments.