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Register a new userQuantized Floquet topology with temporal noise
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Time-periodic (Floquet) drive is a powerful method to engineer quantum phases of matter, including fundamentally non-equilibrium states that are impossible in static Hamiltonian systems. One characteristic example is the anomalous Floquet insulator, which exhibits topologically quantized chiral edge states similar to a Chern insulator, yet is amenable to bulk localization. We study the response of this topological system to time-dependent noise, which breaks the topologically protecting Floquet symmetry. Surprisingly, we find that the quantized response, given by partially filling the fermionic system and measuring charge pumped per cycle, remains quantized up to finite noise amplitude. We trace this robust topology to an interplay between diffusion and Pauli blocking of edge state decay, which we expect should be robust against interactions. We determine the boundaries of the topological phase for a system with spatial disorder numerically through level statistics, and corroborate our results in the limit of vanishing disorder through an analytical Floquet superoperator approach. This approach suggests an interpretation of the state of the system as a non-Hermitian Floquet topological phase. We comment on quantization of other topological responses in the absence of Floquet symmetry and potential experimental realizations.
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We propose to measure band topology via quantized drift of Bloch oscillations in a two-dimensional Harper-Hofstadter lattice subjected to tilted fields in both directions. When the difference between the two tilted fields is large, Bloch oscillations uniformly sample all momenta, and hence the displacement in each direction tends to be quantized at multiples of the overall period, regardless of any momentum of initial state. The quantized displacement is related to a reduced Chern number defined as a line integral of Berry curvature in each direction, providing an almost perfect measurement of Chern number. Our scheme can apply to detect Chern number and topological phase transitions not only for the energy-separable band, but also for energy-inseparable bands which cannot be achieved by conventional Thouless pumping or integer quantum Hall effect.
We investigate the transition induced by disorder in a periodically-driven one-dimensional model displaying quantized topological transport. We show that, while instantaneous eigenstates are necessarily Anderson localized, the periodic driving plays a fundamental role in delocalizing Floquet states over the whole system, henceforth allowing for a steady state nearly-quantized current. Remarkably, this is linked to a localization/delocalization transition in the Floquet states of a one dimensional driven Anderson insulator, which occurs for periodic driving corresponding to a nontrivial loop in the parameter space. As a consequence, the Floquet spectrum becomes continuous in the delocalized phase, in contrast with a pure-point instantaneous spectrum.
We introduce the concept of a Floquet gauge pump whereby a dynamically engineered Floquet Hamiltonian is employed to reveal the inherent degeneracy of the ground state in interacting systems. We demonstrate this concept in a one-dimensional XY model with periodically driven couplings and transverse field. In the high-frequency limit, we obtain the Floquet Hamiltonian consisting of the static XY and dynamically generated Dzyaloshinsky-Moriya interaction (DMI) terms. The dynamically generated magnetization current depends on the phases of complex coupling terms, with the XY interaction as the real and DMI as the imaginary part. As these phases are cycled, the current reveals the ground-state degeneracies that distinguish the ordered and disordered phases. We discuss experimental requirements needed to realize the Floquet gauge pump in a synthetic quantum spin system of interacting trapped ions.
The concept of Floquet engineering is to subject a quantum system to time-periodic driving in such a way that it acquires interesting novel properties. It has been employed, for instance, for the realization of artificial magnetic fluxes in optical lattices and, typically, it is based on two approximations. First, the driving frequency is assumed to be low enough to suppress resonant excitations to high-lying states above some energy gap separating a low energy subspace from excited states. Second, the driving frequency is still assumed to be large compared to the energy scales of the low-energy subspace, so that also resonant excitations within this space are negligible. Eventually, however, deviations from both approximations will lead to unwanted heating on a time scale $tau$. Using the example of a one-dimensional system of repulsively interacting bosons in a shaken optical lattice, we investigate the optimal frequency (window) that maximizes $tau$. As a main result, we find that, when increasing the lattice depth, $tau$ increases faster than the experimentally relevant time scale given by the tunneling time $hbar/J$, so that Floquet heating becomes suppressed.
The dissipative response of a quantum system upon a time-dependent drive can be exploited as a probe of its geometric and topological properties. In this work, we explore the implications of such phenomena in the context of two-dimensional gases subjected to a uniform magnetic field. It is shown that a filled Landau level exhibits a quantized circular dichroism, which can be traced back to its underlying non-trivial topology. Based on selection rules, we find that this quantized circular dichroism can be suitably described in terms of Rabi oscillations, whose frequencies satisfy simple quantization laws. Moreover, we discuss how these quantized dissipative responses can be probed locally, both in the bulk and at the boundaries of the quantum Hall system. This work suggests alternative forms of topological probes in quantum systems based on circular dichroism.
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