Stable Measurement-Induced Floquet Enriched Topological Order.

The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature. The code also possesses a time-crystal order-the e-m transmutation after every cycle, breaking the Floquet symmetry of the measurement schedule. This behavior is distinct from the stationary topological order realized in either random circuits or time-independent Hamiltonian. Therefore, the resultant phase belongs to the overlap between the classes of Floquet enriched topological orders and measurement-induced phases. In this Letter, we construct a continuous path interpolating between the Floquet and toric codes, focusing on the transition between the time-crystal and stationary topological phases. We show that this transition is characterized by a divergent length scale. We also add single-qubit perturbations to the model and obtain a richer two-dimensional parametric phase diagram of the Floquet code, showing the stability of the Floquet enriched topological order.

Dissipative Prethermal Discrete Time Crystal.

An ergodic system subjected to an external periodic drive will be generically heated to infinite temperature. However, if the applied frequency is larger than the typical energy scale of the local Hamiltonian, this heating stops during a prethermal period that extends exponentially with the frequency. During this prethermal period, the system may manifest an emergent symmetry that, if spontaneously broken, will produce subharmonic oscillation of the discrete time crystal (DTC). We study the role of dissipation on the survival time of the prethermal DTC. On one hand, a bath coupling increases the prethermal period by slowing down the accumulation of errors that eventually destroy prethermalization. On the other hand, the spontaneous symmetry breaking is destabilized by interaction with environment. The result of this competition is a nonmonotonic variation, i.e., the survival time of the prethermal DTC first increases and then decreases as the environment coupling gets stronger.

Fermionic Many-Body Localization for Random and Quasiperiodic Systems in the Presence of Short- and Long-Range Interactions.

We study many-body localization (MBL) for interacting one-dimensional lattice fermions in random (Anderson) and quasiperiodic (Aubry-Andre) models, focusing on the role of interaction range. We obtain the MBL quantum phase diagrams by calculating the experimentally relevant inverse participation ratio (IPR) at half-filling using exact diagonalization methods and extrapolating to the infinite system size. For short-range interactions, our results produce in the phase diagram a qualitative symmetry between weak and strong interaction limits. For long-range interactions, no such symmetry exists as the strongly interacting system is always many-body localized, independent of the effective disorder strength, and the system is analogous to a pinned Wigner crystal. We obtain various scaling exponents for the IPR, suggesting conditions for different MBL regimes arising from interaction effects.

Moiré versus Mott: Incommensuration and Interaction in One-Dimensional Bichromatic Lattices.

Inspired by the rich physics of twisted 2D bilayer moiré systems, we study Coulomb interacting systems subjected to two overlapping finite 1D lattice potentials of unequal periods through exact numerical diagonalization. Unmatching underlying lattice periods lead to a 1D bichromatic "moiré" superlattice with a large unit cell and consequently a strongly flattened band, exponentially enhancing the effective dimensionless electron-electron interaction strength and manifesting clear signatures of enhanced Mott gaps at discrete fillings. An important nonperturbative finding is a remarkable fine-tuning effect of the precise lattice commensuration, where slight variations in the relative lattice periods may lead to a suppression of the correlated insulating phase, in qualitative agreement with the observed fragility of the correlated insulating phase in twisted bilayer graphene. Our predictions, which should be directly verifiable in bichromatic optical lattices, establish that the competition between interaction and incommensuration is a key element of the physics of moiré superlattices.

Simplified chirp characterization in single-shot supercontinuum spectral interferometry.

Single-shot supercontinuum spectral interferometry (SSSI) is an optical technique that can measure ultrafast transients in the complex index of refraction. This method uses chirped supercontinuum reference/probe pulses that need to be pre-characterized prior to use. Conventionally, the spectral phase (or chirp) of those pulses can be determined from a series of phase or spectral measurements taken at various time delays with respect to a pump-induced modulation. Here we propose a novel method to simplify this process and characterize reference/probe pulses up to the third order dispersion from a minimum of 2 snapshots taken at different pump-probe delays. Alternatively, without any pre-characterization, our method can retrieve both unperturbed and perturbed reference/probe phases, including the pump-induced modulation, from 2 time-delayed snapshots. From numerical simulations, we show that our retrieval algorithm is robust and can achieve high accuracy even with 2 snapshots. Without any apparatus modification, our method can be easily applied to any experiment that uses SSSI.