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Register a new userCompetition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms
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Robustness against perturbations lies at the heart of topological phenomena. If, however, a perturbation such as disorder becomes dominant, it may cause a topological phase transition between topologically non-trivial and trivial phases. Here we experimentally reveal the competition and interplay between topology and quasi-periodic disorder in a Thouless pump realized with ultracold atoms in an optical lattice, by creating a quasi-periodic potential from weak to strong regimes in a controllable manner. We demonstrate a disorder-induced pumping in which the presence of quasi-periodic disorder can induce a non-trivial pump for a specific pumping sequence, while no pump is observed in the clean limit. Our highly controllable system, which can also straightforwardly incorporate interatomic interaction, could be a unique platform for studying various disorder-related novel effects in a wide range of topological quantum phenomena.
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We investigate the spin-polarized chain of ultracold fermionic atoms with spin-3/2 described by the fermionic Hubbard model with SU(4) symmetric attractive interaction. The competition of bound pairs, trions, quartets and unbound atoms is studied analytically and by density matrix renormalization group simulations. We find several distinct states where bound particles coexist with the ferromagnetic state of unpaired fermions. In particular, an exotic inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-type superfluid of quartets in a magnetic background of uncorrelated atoms is found for weaker interactions. We show that the system can be driven from this quartet-FFLO state to a molecular state of localized quartets which is also reflected in the static structure factor. For strong enough coupling, spatial segregation between molecular crystals and ferromagnetic liquids emerges due to the large effective mass of the composite particles.
We propose a two-dimensional (2D) version of Thouless pumping that can be realized by using ultracold atoms in optical lattices. To be specific, we consider a 2D square lattice tight-binding model with an obliquely introduced superlattice. It is demonstrated that quantized particle transport occurs in this system, and that the transport is expressed as a solution of a Diophantine equation. This topological nature can be understood by mapping the Hamiltonian to a three-dimensional (3D) cubic lattice model with a homogeneous magnetic field. We also propose a continuum model with obliquely introduced superlattice and obtain the amount of pumping by calculating the Berry curvature. For this model, the same Diophantine equation can be derived from the plane-wave approximation. Furthermore, we investigate the effect of a harmonic trap by solving the time-dependent Schrodinger equation. Under a harmonic trap potential, as often used in cold atom experiments, we show, by numerical simulations, that nearly quantized pumping occurs when the phase of the superlattice potential is driven at a moderate speed. Also, we find that two regions appear, the Hofstadter region and the rectifying region, depending on the modulation amplitude of the superlattice potential. In the rectifying region with larger modulation amplitudes, we uncover that the pumping direction is restricted to exactly the $x$-axis or the $y$-axis direction. This difference in these two regions causes a crossover behavior, characterizing the effect of the harmonic trap.
More than 30 years ago, Thouless introduced the concept of a topological charge pump that would enable the robust transport of charge through an adiabatic cyclic evolution of the underlying Hamiltonian. In contrast to classical transport, the transported charge was shown to be quantized and purely determined by the topology of the pump cycle, making it robust to perturbations. On a fundamental level, the quantized charge transport can be connected to a topological invariant, the Chern number, first introduced in the context of the integer quantum Hall effect. A Thouless quantum pump may therefore be regarded as a dynamical version of the integer quantum Hall effect. Here, we report on the realization of such a topological charge pump using ultracold bosonic atoms that form a Mott insulator in a dynamically controlled optical superlattice potential. By taking in-situ images of the atom cloud, we observe a quantized deflection per pump cycle. We reveal the genuine quantum nature of the pump by showing that, in contrast to ground state particles, a counterintuitive reversed deflection occurs when particles are prepared in the first excited band. Furthermore, we were able to directly demonstrate that the system undergoes a controlled topological phase transition in higher bands when tuning the superlattice parameters.
We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic 2D Chern insulator subjected to a circular time-periodic perturbation: due to the systems chiral nature, the depletion rate is shown to depend on the orientation of the circular shake. Most importantly, taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number of the populated band ($ u$): this differential integrated rate is directly related to the strength of the driving field through the quantized coefficient $eta_0!=! u /hbar^2$. Contrary to the integer quantum Hall effect, this quantized response is found to be non-linear with respect to the strength of the driving field and it explicitly involves inter-band transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the non-linear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion-rate measurements as a universal probe for topological order in quantum matter.
The study of topological effects in physics is a hot area, and only recently researchers were able to address the important issues of topological properties of interacting quantum systems. But it is still a great challenge to describe multi-particle and interaction effects. Here, we introduce multi-particle Wannier states for interacting systems with co-translational symmetry. We reveal how the shift of multi-particle Wannier state relates to the multi-particle Chern number, and study the two-boson Thouless pumping in an interacting Rice-Mele model. In addition to the bound-state Thouless pumping in which two bosons move unidirectionally as a whole, we find topologically resonant tunneling in which two bosons move unidirectionally, one by the other, provided the neighboring-well potential bias matches the interaction energy. Our work creates a new paradigm for multi-particle topological effects and lays a cornerstone for detecting interacting topological states.
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