Suppression of Nonequilibrium Quasiparticle Transport in Flat-Band Superconductors.

We study nonequilibrium transport through a superconducting flat-band lattice in a two-terminal setup with the Schwinger-Keldysh method. We find that quasiparticle transport is suppressed and coherent pair transport dominates. For superconducting leads, the ac supercurrent overcomes the dc current, which relies on multiple Andreev reflections. With normal-normal and normal-superconducting leads, the Andreev reflection and normal currents vanish. Flat-band superconductivity is, thus, promising not only for high critical temperatures, but also for suppressing unwanted quasiparticle processes.

Essay: Where Can Quantum Geometry Lead Us?

Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry, including the amplitude distance characterized by the quantum metric, has started to receive attention in the last few years. Various quantum transport and interaction phenomena have been found to be critically influenced by quantum geometry. For example, quantum geometry allows counterintuitive flow of supercurrent in a flat band where single electrons are immobile. In this Essay, I will discuss my view of the important open problems and future applications of this research topic and will try to inspire the reader to come up with further ideas. At its best, quantum geometry can open a new chapter in band theory and lead to breakthroughs as transformative as room-temperature superconductivity. However, first, more experiments directly showing the effect of quantum geometry are needed. We also have to integrate quantum geometry analysis in our most advanced numerical methods. Further, the ramifications of quantum geometry should be studied in a wider range, including electric and electromagnetic responses and interaction phenomena in free- and correlated-electron materials, bosonic systems, optics, and other fields. Part of a series of Essays which concisely present author visions for the future of their field.

Loss-Driven Topological Transitions in Lasing.

We experimentally observe lasing in a hexamer plasmonic lattice and find that, when tuning the scale of the unit cell, the polarization properties of the emission change. By a theoretical analysis, we identify the lasing modes as quasi-bound-states in continuum of topological charges of zero, one, or two. A T-matrix simulation of the structure reveals that the mode quality (Q) factors depend on the scale of the unit cell, with highest-Q modes favored by lasing. The system thus shows a loss-driven transition between lasing in modes of trivial and high-order topological charge.

Quasi-BIC Mode Lasing in a Quadrumer Plasmonic Lattice.

Plasmonic lattices of metal nanoparticles have emerged as an effective platform for strong light-matter coupling, lasing, and Bose-Einstein condensation. However, the full potential of complex unit cell structures has not been exploited. On the other hand, bound states in continuum (BICs) have attracted attention, as they provide topologically protected optical modes with diverging quality factors. Here, we show that quadrumer nanoparticle lattices enable lasing in a quasi-BIC mode with a highly out-of-plane character. By combining theory with polarization-resolved measurements of the emission, we show that the lasing mode has a topological charge. Our analysis reveals that the mode is primarily polarized out-of-plane as a result of the quadrumer structure. The quality factors of the out-of-plane BIC modes of the quadrumer array can be exceedingly high. Our results unveil the power of complex multiparticle unit cells in creating topologically protected high-Q modes in periodic nanostructures.

Quantum Geometry and Flat Band Bose-Einstein Condensation.

We study the properties of a weakly interacting Bose-Einstein condensate (BEC) in a flat band lattice system by using the multiband Bogoliubov theory and discover fundamental connections to the underlying quantum geometry. In a flat band, the speed of sound and the quantum depletion of the condensate are dictated by the quantum geometry, and a finite quantum distance between the condensed and other states guarantees stability of the BEC. Our results reveal that a suitable quantum geometry allows one to reach the strong quantum correlation regime even with weak interactions.

Polarization and Phase Textures in Lattice Plasmon Condensates.

Polarization textures of light may reflect fundamental phenomena, such as topological defects, and can be utilized in engineering light beams. They have been observed, for instance, in photonic crystal lasers and semiconductor polariton condensates. Here we demonstrate domain wall polarization textures in a plasmonic lattice Bose-Einstein condensate. A key ingredient of the textures is found to be a condensate phase that varies spatially in a nontrivial manner. The phase of the Bose-Einstein condensate is reconstructed from the real- and Fourier-space images using a phase retrieval algorithm. We introduce a simple theoretical model that captures the results and can be used for design of the polarization patterns and demonstrate that the textures can be optically switched. The results open new prospects for fundamental studies of non-equilibrium condensation and sources of polarization-structured beams.

Spatial and Temporal Coherence in Strongly Coupled Plasmonic Bose-Einstein Condensates.

We report first-order spatial and temporal correlations in strongly coupled plasmonic Bose-Einstein condensates. The condensate is large, more than 20 times the spatial coherence length of the polaritons in the uncondensed system and 100 times the healing length, making plasmonic lattices an attractive platform for studying long-range spatial correlations in two dimensions. We find that both spatial and temporal coherence display nonexponential decay; the results suggest power-law or stretched exponential behavior with different exponents for spatial and temporal correlation decays.

Multimode Organic Polariton Lasing.

We present a beyond-mean-field approach to predict the nature of organic polariton lasing, accounting for all relevant photon modes in a planar microcavity. Starting from a microscopic picture, we show how lasing can switch between polaritonic states resonant with the maximal gain, and those at the bottom of the polariton dispersion. We show how the population of nonlasing modes can be found, and by using two-time correlations, we show how the photoluminescence spectrum (of both lasing and nonlasing modes) evolves with pumping and coupling strength, confirming recent experimental work on the origin of blueshift for polariton lasing.

Sub-picosecond thermalization dynamics in condensation of strongly coupled lattice plasmons.

Bosonic condensates offer exciting prospects for studies of non-equilibrium quantum dynamics. Understanding the dynamics is particularly challenging in the sub-picosecond timescales typical for room temperature luminous driven-dissipative condensates. Here we combine a lattice of plasmonic nanoparticles with dye molecule solution at the strong coupling regime, and pump the molecules optically. The emitted light reveals three distinct regimes: one-dimensional lasing, incomplete stimulated thermalization, and two-dimensional multimode condensation. The condensate is achieved by matching the thermalization rate with the lattice size and occurs only for pump pulse durations below a critical value. Our results give access to control and monitoring of thermalization processes and condensate formation at sub-picosecond timescale.

Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device.

We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on L×L lattices with L≤32. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal L dependent annealing rate v for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of v and L-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when v is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.

Converting an Organic Light-Emitting Diode from Blue to White with Bragg Modes.

Organic light-emitting diodes (OLEDs) have been established as versatile light sources that allow for easy integration in large-area surfaces and flexible substrates. In addition, the low fabrication cost of OLEDs renders them particularly attractive as general lighting sources. Current methods for the fabrication of white-light OLEDs rely on the combination of multiple organic emitters and/or the incorporation of multiple cavity modes in a thick active medium. These architectures introduce formidable challenges in both device design and performance improvements, namely, the decrease of efficiency with increasing brightness (efficiency roll-off) and short operational lifetime. Here we demonstrate, for the first time, white-light generation in an OLED consisting of a sub-100 nm thick blue single-emissive layer coupled to the photonic Bragg modes of a dielectric distributed Bragg reflector (DBR). We show that the Bragg modes, although primarily located inside the DBR stack, can significantly overlap with the emissive layer, thus efficiently enhancing emission and outcoupling of photons at selected wavelengths across the entire visible light spectrum. Moreover, we show that color temperature can be tuned by the DBR parameters, offering great versatility in the optimization of white-light emission spectra.

Lasing in Ni Nanodisk Arrays.

We report on lasing at visible wavelengths in arrays of ferromagnetic Ni nanodisks overlaid with an organic gain medium. We demonstrate that by placing an organic gain material within the mode volume of the plasmonic nanoparticles both the radiative and, in particular, the high ohmic losses of Ni nanodisk resonances can be compensated. Under increasing pump fluence, the systems exhibit a transition from lattice-modified spontaneous emission to lasing, the latter being characterized by highly directional and sub-nanometer line width emission. By breaking the symmetry of the array, we observe tunable multimode lasing at two wavelengths corresponding to the particle periodicity along the two principal directions of the lattice. Our results are relevant for loss-compensated magnetoplasmonic devices and topological photonics.

Turning the challenge of quantum biology on its head: biological control of quantum optical systems.

When light-harvesting complex II (LHCII), isolated from spinach, is adsorbed onto arrays of gold nanostructures formed by interferometric lithography, a pronounced splitting of the plasmon band is observed that is attributable to strong coupling of the localised surface plasmon resonance to excitons in the pigment-protein complex. The system is modelled as coupled harmonic oscillators, yielding an exciton energy of 2.24 ± 0.02 eV. Analysis of dispersion curves yields a Rabi energy of 0.25 eV. Extinction spectra of the strongly coupled system yield a resonance at 1.43 eV that varies as a function of the density of nanostructures in the array. The enhanced intensity of this feature is attributed to strong plasmon-exciton coupling. Comparison of data for a large number of light-harvesting complexes indicates that by control of the protein structure and/or pigment compliment it is possible to manipulate the strength of plasmon-exciton coupling. In strongly coupled systems, ultra-fast exchange of energy occurs between pigment molecules: coherent coupling between non-local excitons can be manipulated via selection of the protein structure enabling the observation of transitions that are not seen in the weak coupling regime. Synthetic biology thus provides a means to control quantum-optical interactions in the strong coupling regime.

A synthetic biological quantum optical system.

In strong plasmon-exciton coupling, a surface plasmon mode is coupled to an array of localized emitters to yield new hybrid light-matter states (plexcitons), whose properties may in principle be controlled via modification of the arrangement of emitters. We show that plasmon modes are strongly coupled to synthetic light-harvesting maquette proteins, and that the coupling can be controlled via alteration of the protein structure. For maquettes with a single chlorin binding site, the exciton energy (2.06 ± 0.07 eV) is close to the expected energy of the Qy transition. However, for maquettes containing two chlorin binding sites that are collinear in the field direction, an exciton energy of 2.20 ± 0.01 eV is obtained, intermediate between the energies of the Qx and Qy transitions of the chlorin. This observation is attributed to strong coupling of the LSPR to an H-dimer state not observed under weak coupling.

Ultrafast Pulse Generation in an Organic Nanoparticle-Array Laser.

Nanoscale coherent light sources offer potentially ultrafast modulation speeds, which could be utilized for novel sensors and optical switches. Plasmonic periodic structures combined with organic gain materials have emerged as promising candidates for such nanolasers. Their plasmonic component provides high intensity and ultrafast nanoscale-confined electric fields, while organic gain materials offer fabrication flexibility and a low acquisition cost. Despite reports on lasing in plasmonic arrays, lasing dynamics in these structures have not been experimentally studied yet. Here we demonstrate, for the first time, an organic dye nanoparticle-array laser with more than a 100 GHz modulation bandwidth. We show that the lasing modulation speed can be tuned by the array parameters. Accelerated dynamics is observed for plasmonic lasing modes at the blue side of the dye emission.

The Fulde-Ferrell-Larkin-Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review.

We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Bloch's and Luttinger's theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.

Cooperative colloidal self-assembly of metal-protein superlattice wires.

Material properties depend critically on the packing and order of constituent units throughout length scales. Beyond classically explored molecular self-assembly, structure formation in the nanoparticle and colloidal length scales have recently been actively explored for new functions. Structure of colloidal assemblies depends strongly on the assembly process, and higher structural control can be reliably achieved only if the process is deterministic. Here we show that self-assembly of cationic spherical metal nanoparticles and anionic rod-like viruses yields well-defined binary superlattice wires. The superlattice structures are explained by a cooperative assembly pathway that proceeds in a zipper-like manner after nucleation. Curiously, the formed superstructure shows right-handed helical twisting due to the right-handed structure of the virus. This leads to structure-dependent chiral plasmonic function of the material. The work highlights the importance of well-defined colloidal units when pursuing unforeseen and complex assemblies.Colloidal self-assembly is a unique method to produce three-dimensional materials with well-defined hierarchical structures and functionalities. Liljeström et al. show controlled preparation of macroscopic chiral wires with helical plasmonic superlattice structure composed of metal nanoparticles and viruses.

Ultra-strong polarization dependence of surface lattice resonances with out-of-plane plasmon oscillations.

The interplay between localized surface plasmon (LSP) resonances and their collective responses, known as surface lattice resonances (SLRs), in metal nanoparticle arrays can lead to resonances with high Q-factors (∼100). These responses have in the past usually been studied for LSP resonances in the plane of the array of the nanoparticles (assumed to be nonmagnetic), thus restricting efficient coupling to particles separated along a specific direction. In the present study, we demonstrate that LSPs oscillating perpendicular to the plane of the surface can lead to stronger inter-particle coupling, which enhances the SLRs. This stronger coupling occurs because the out-of-plane oscillations can couple in all directions within the plane of the array. We study the resulting SLRs for square and hexagonal lattices using the discrete-dipole approximation, and we predict much larger Q-factors in the wavelength range near 650 nm. This prediction suggests that SLRs could be very useful in enhancing various optical processes, and in many applications such as sensing and nonlinear optical wave mixing.

Strong Coupling of Localized Surface Plasmons to Excitons in Light-Harvesting Complexes.

Gold nanostructure arrays exhibit surface plasmon resonances that split after attaching light harvesting complexes 1 and 2 (LH1 and LH2) from purple bacteria. The splitting is attributed to strong coupling between the localized surface plasmon resonances and excitons in the light-harvesting complexes. Wild-type and mutant LH1 and LH2 from Rhodobacter sphaeroides containing different carotenoids yield different splitting energies, demonstrating that the coupling mechanism is sensitive to the electronic states in the light harvesting complexes. Plasmon-exciton coupling models reveal different coupling strengths depending on the molecular organization and the protein coverage, consistent with strong coupling. Strong coupling was also observed for self-assembling polypeptide maquettes that contain only chlorins. However, it is not observed for monolayers of bacteriochlorophyll, indicating that strong plasmon-exciton coupling is sensitive to the specific presentation of the pigment molecules.