Stability of Time-Reversal Symmetry Protected Topological Phases.

In a closed system, it is well known that the time-reversal symmetry can lead to Kramers degeneracy and protect nontrivial topological states such as the quantum spin Hall insulator. In this Letter, we address the issue of whether these effects are stable against coupling to the environment, provided that both the environment and the coupling to the environment also respect time-reversal symmetry. By employing a non-Hermitian Hamiltonian with the Langevin noise term and utilizing the non-Hermitian linear response theory, we show that the spectral functions for Kramers degenerate states can be split by dissipation, and the backscattering between counterpropagating edge states can be induced by dissipation. The latter leads to the absence of accurate quantization of conductance in the case of the quantum spin Hall effect. As an example, we demonstrate this concretely with the Kane-Mele model. Our study can also include interacting topological phases protected by time-reversal symmetry.

Tunable Nonreciprocal Quantum Transport through a Dissipative Aharonov-Bohm Ring in Ultracold Atoms.

We report the experimental observation of tunable, nonreciprocal quantum transport of a Bose-Einstein condensate in a momentum lattice. By implementing a dissipative Aharonov-Bohm (AB) ring in momentum space and sending atoms through it, we demonstrate a directional atom flow by measuring the momentum distribution of the condensate at different times. While the dissipative AB ring is characterized by the synthetic magnetic flux through the ring and the laser-induced loss on it, both the propagation direction and transport rate of the atom flow sensitively depend on these highly tunable parameters. We demonstrate that the nonreciprocity originates from the interplay of the synthetic magnetic flux and the laser-induced loss, which simultaneously breaks the inversion and the time-reversal symmetries. Our results open up the avenue for investigating nonreciprocal dynamics in cold atoms, and highlight the dissipative AB ring as a flexible building element for applications in quantum simulation and quantum information.

Topological Quantum Walks in Momentum Space with a Bose-Einstein Condensate.

We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the lattice is effectively governed by a periodically driven Su-Schrieffer-Heeger model, which is equivalent to a discrete-time topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements, which are consistent with our experimental observation of topological phase transitions. We then observe interaction-induced localization in the quantum-walk dynamics, where atoms tend to populate a single momentum-lattice site under interactions that are nonlocal in momentum space. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.

Fixed Points and Dynamic Topological Phenomena in a Parity-Time-Symmetric Quantum Quench.

We identify dynamic topological phenomena such as dynamic Chern numbers and dynamic quantum phase transitions in quantum quenches of the non-Hermitian Su-Schrieffer-Heeger Hamiltonian with parity-time (PT) symmetry. Their occurrences in the non-unitary dynamics are intimately connected with fixed points in the Brillouin zone, where the density matrices do not evolve in time. Based on our theoretical formalism characterizing topological properties of non-unitary dynamics, we prove the existence of fixed points for quenches between distinct static topological phases in the PT-symmetry-preserving regime, thus unveiling the interplay between dynamic topological phenomena and PT symmetry. Interestingly, non-Hermiticity of the driving Hamiltonian gives rise to rich dynamic topological phenomena which are different, either qualitatively or quantitatively, from their counterparts in unitary dynamics. Our work sheds light on dynamic topological phenomena in open systems and is readily accessible in experiments.