Dynamical instability of 3D stationary and traveling planar dark solitons.

Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional (3D) Bose-Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our experimental results. Motivated by numerous experimental efforts, including our own herein, we use fully 3D numerical simulations to explore the existence, stability, and evolution dynamics of planar dark solitons. This also allows us to examine their instability-induced decay products including solitonic vortices and vortex rings. In the trapped case and with no adjustable parameters, our numerical findings are in correspondence with experimentally observed coherent structures. Without a longitudinal trap, we identify numerically exact traveling solutions and quantify how their transverse destabilization threshold changes as a function of the solitary wave speed.

Dynamically Induced Symmetry Breaking and Out-of-Equilibrium Topology in a 1D Quantum System.

Nontrivial topology in lattices is characterized by invariants-such as the Zak phase for one-dimensional (1D) lattices-derived from wave functions covering the Brillouin zone. We realize the 1D bipartite Rice-Mele (RM) lattice using ultracold ^{87}Rb and focus on lattice configurations possessing various combinations of chiral, time-reversal, and particle-hole symmetries. We quench between configurations and use a form of quantum state tomography, enabled by diabatically tuning lattice parameters, to directly follow the time evolution of the Zak phase as well as a chiral winding number. The Zak phase evolves continuously; however, when chiral symmetry transiently appears in the out-of-equilibrium system, the chiral winding number becomes well defined and can take on any integer value. When quenching between two configurations obeying the same three symmetries, the Zak phase is time independent; we confirm the dynamically induced symmetry breaking predicted in [McGinley and Cooper, Phys. Rev. Lett. 121, 090401 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.090401] that chiral symmetry is periodically restored, at which times the winding number changes by ±2, yielding values that are not present in the native RM Hamiltonian.

Floquet Engineering Topological Dirac Bands.

We experimentally realized a time-periodically modulated 1D lattice for ultracold atoms featuring a pair of linear bands, each with a Floquet winding number. These bands are spin-momentum locked and almost perfectly linear everywhere in the Brillouin zone: a near-ideal realization of the 1D Dirac Hamiltonian. We characterized the Floquet winding number using a form of quantum state tomography, covering the Brillouin zone and following the micromotion through one Floquet period. Last, we altered the modulation timing to lift the topological protection, opening a gap at the Dirac point that grew in proportion to the deviation from the topological configuration.

Creating solitons with controllable and near-zero velocity in Bose-Einstein condensates.

Established techniques for deterministically creating dark solitons in repulsively interacting atomic Bose-Einstein condensates (BECs) can only access a narrow range of soliton velocities. Because velocity affects the stability of individual solitons and the properties of soliton-soliton interactions, this technical limitation has hindered experimental progress. Here we create dark solitons in highly anisotropic cigar-shaped BECs with arbitrary position and velocity by simultaneously engineering the amplitude and phase of the condensate wave function, improving upon previous techniques which explicitly manipulated only the condensate phase. The single dark soliton solution present in true one-dimensional (1D) systems corresponds to the kink soliton in anisotropic three-dimensional systems and is joined by a host of additional dark solitons, including vortex ring and solitonic vortex solutions. We readily create dark solitons with speeds from zero to half the sound speed. The observed soliton oscillation frequency suggests that we imprinted solitonic vortices, which for our cigar-shaped system are the only stable solitons expected for these velocities. Our numerical simulations of 1D BECs show this technique to be equally effective for creating kink solitons when they are stable. We demonstrate the utility of this technique by deterministically colliding dark solitons with domain walls in two-component spinor BECs.