OSCAR Reports

an SFB/TR 185 magazine

Second Funding Period, Issue 5

Author: Prof. Dr. Stefan Linden

**Nonequilibrium Floquet Steady States of Time-Periodic Driven Luttinger Liquids**

Serena Fazzini, Piotr Chudzinski, Christoph Dauer, Imke Schneider, and Sebastian Eggert

Phys. Rev. Lett. **126**, 243401 (2021)

Floquet engineering, i.e., the time-periodic perturbation of an otherwise static system by an external drive, is a powerful method to create and study novel quantum states inaccessible in equilibrium. Examples include Floquet topological insulators, induced quantum phase transitions, and artificial gauge fields. In combination with strong interactions, the dynamics of periodically driven systems can become quiet complex and full solutions for such many-body systems are in general not known.

In their work, S. Fazzini and coworkers theoretically analyze a one-dimensional quantum gas, modeled by a Luttinger liquid, with periodically changing interactions. For this purpose, they developed a novel Floquet-Bogoliubov ansatz that allows to solve the Floquet eigenvalue problem for this model in one single step by mapping it to a static problem in the original Hilbert space. The authors find that the periodic driving results in the excitation of density waves in the steady state. For large driving frequencies, the time average of the number of density excitations approaches the static limit. Interestingly, a resonance phenomenon occurs when integer multiples of the driving frequency approximately match twice the dispersion energy. In this case, the formation of intrinsic instabilities, which result in stable standing density waves throughout the system, is expected.

The authors do not only provide a novel approach to exactly solve time-periodically driven model with Bogoliubov-type interactions, they also propose an experiment with realistic parameters that might allow observing the predicted standing density waves.

*Fig 1. Scheme of standing density waves in independent 1D quantum gases with time-periodic interactions.*

**Experimental realization of a 3D random hopping model**

Carsten Lippe, Tanita Klas, Jana Bender, Patrick Mischke, Thomas Niederprüm, and Herwig Ott

Nature Communications **12**, Article number: 6976 (2021)

Disorder plays a key role in many transport phenomena. For instance, the Ohmic resistance of a metal wire can be attributed to the scattering of electrons by irregularities of the crystal lattice. While the influence of random variations of the potential has already been intensively studied, considerably less attention has been payed to systems with disordered hoppings. The latter type of disorder is relevant for systems in which the coupling is due to dipole-dipole interactions.

In their work, C. Lippe and coworkers report on the experimental realization of a 3D random hopping model. For this purpose, they used a pump-probe excitation scheme to prepare a dipole–dipole coupled many-body Rydberg system. The Hamiltonian of this system can be mapped onto the XY model with random couplings. When increasing the pump power, they observe in the spectroscopic measurements a broadening of the spectral line as well as a suppression of the signal on resonance for short delay times between pump and probe pulse (interacting case). Monte Carlo simulations of spectra in the framework of the random XY model show the same effects. Interestingly, the random XY model predicts a crossover from a regime with predominantly delocalized states to pair-localized states, depending on the energy of the state. The excellent agreement between the measured and the simulated spectra is a strong indication for the occurrence of a localization–delocalization crossover also in the many-body Rydberg system. This interpretation is further supported by lifetime measurements on the Rydberg-states as a function of the laser detuning.

The reported findings show that interacting Rydberg gases can serve as a model system to study the interplay between long-range interactions, random hopping and localization.

*Fig 2 a Dipole-dipole interaction between two Rydberg atoms. b Spatial distribution of Rydberg excitations corresponding to localized and delocalized states. The figure is taken from the publication.*

**Observation of bound states in the continuum embedded in symmetry bandgaps**

Alexander Cerjan, Christina Jörg, Sachin Vaidya, Shyam Augustine, Wladimir A. Benalcazar, Chia Wei Hsu, Georg von Freymann, and Mikael C. Rechtsman

Sci. Adv. **7**, eabk1117 (2021)

A bound state in the continuum (BIC) is a localized eigenstate of an open system whose resonance frequency falls within the continuum of radiating modes but nevertheless does not couple to the continuum, e.g., for symmetry reasons. As a result, its lifetime is only limited by non-radiative processes, which makes BICs attractive for applications that require a high-Q resonance. In particular in nanophotonics, BICs have attracted considerable interest as a new approach to cavity design and to tailor light–matter interactions.

A C2-symmetric photonic crystal slab embedded in a homogeneous medium supports symmetry protected BICs at the Γ-point (zero in-plane momentum) for frequencies below the Bragg diffraction limit. However, away from the Γ-point, BICs cannot exist in this structure. In their work, A. Cerjan and coworkers report on a new approach that allows to get around this limitation. Their key idea is to sandwich a slab between two woodpile photonic crystals in order to tailor the radiative environment surrounding the slab. Along the boundary of the first Brillouin zone of the in-plane projected photonic band structure, the radiative modes of the woodpile are even modes with respect to mirror reflection about the high symmetry planes of the structure. An odd mode of the slab cannot couple to these radiating modes in the woodpile and hence is a symmetry-protected BIC. To test their ideas, A. Cerjan and coworkers fabricated the photonic crystal samples by 3D direct laser writing and confirmed the existence of the BICs by angle-resolved transmission spectroscopy.

The authors have demonstrated that tailoring the photonic environment opens new opportunities to design BIC-based devices. This approach might be relevant, e.g., for optical sensor applications.

*Fig 3 Left: Scanning electron micrograph of the fabricated structure. Middle: Projected band structure of the woodpile environment. Right: Measured and calculated transmission of the BIC structure. The images are taken from the publication.*