Lasing at K Points of a Honeycomb Plasmonic Lattice.

We study lasing at the high-symmetry points of the Brillouin zone in a honeycomb plasmonic lattice. We use symmetry arguments to define singlet and doublet modes at the K points of the reciprocal space. We experimentally demonstrate lasing at the K points that is based on plasmonic lattice modes and two-dimensional feedback. By comparing polarization properties to T-matrix simulations, we identify the lasing mode as one of the singlets with an energy minimum at the K point enabling feedback. Our results offer prospects for studies of topological lasing in radiatively coupled systems.

Coupled dipole approximation across the Γ-point in a finite-sized nanoparticle array.

We study the response of a finite-sized nanoparticle array to an incident field in the vicinity of the Γ-point of the lattice. Using the coupled dipole approximation, we find that the dipole distributions can be strongly inhomogeneous and that strong modulations appear as the energy is above the Γ-point. We highlight how this is reflected in real-space extinction efficiencies as well as in radiation patterns from the finite-sized array.This article is part of the themed issue 'New horizons for nanophotonics'.

Lasing in dark and bright modes of a finite-sized plasmonic lattice.

Lasing at the nanometre scale promises strong light-matter interactions and ultrafast operation. Plasmonic resonances supported by metallic nanoparticles have extremely small mode volumes and high field enhancements, making them an ideal platform for studying nanoscale lasing. At visible frequencies, however, the applicability of plasmon resonances is limited due to strong ohmic and radiative losses. Intriguingly, plasmonic nanoparticle arrays support non-radiative dark modes that offer longer life-times but are inaccessible to far-field radiation. Here, we show lasing both in dark and bright modes of an array of silver nanoparticles combined with optically pumped dye molecules. Linewidths of 0.2 nm at visible wavelengths and room temperature are observed. Access to the dark modes is provided by a coherent out-coupling mechanism based on the finite size of the array. The results open a route to utilize all modes of plasmonic lattices, also the high-Q ones, for studies of strong light-matter interactions, condensation and photon fluids.

Controlling quantum dot emission by plasmonic nanoarrays.

Metallic nanoparticle arrays support localized surface plasmon resonances (LSPRs) and propagating surface lattice resonances (SLRs). We study the control of quantum dot (QD) emission coupled to the optical modes of silver nanoparticle arrays, both experimentally and numerically. With a hybrid lithography-functionalization method, the QDs are deposited in the vicinity of the nanoparticles. Directionality and enhancement of the emission are observed in photoluminescence spectra and fluorescence lifetime measurements, respectively. Similar features are also demonstrated in the numerical simulations. The tunable emission of this type of hybrid structures could lead to potential applications in light sources.

Surface lattice resonances and magneto-optical response in magnetic nanoparticle arrays.

Structuring metallic and magnetic materials on subwavelength scales allows for extreme confinement and a versatile design of electromagnetic field modes. This may be used, for example, to enhance magneto-optical responses, to control plasmonic systems using a magnetic field, or to tailor magneto-optical properties of individual nanostructures. Here we show that periodic rectangular arrays of magnetic nanoparticles display surface plasmon modes in which the two directions of the lattice are coupled by the magnetic field-controllable spin-orbit coupling in the nanoparticles. When breaking the symmetry of the lattice, we find that the optical response shows Fano-type surface lattice resonances whose frequency is determined by the periodicity orthogonal to the polarization of the incident field. In striking contrast, the magneto-optical Kerr response is controlled by the period in the parallel direction. The spectral separation of the response for longitudinal and orthogonal excitations provides versatile tuning of narrow and intense magneto-optical resonances.

Strong coupling between surface plasmon polaritons and emitters: a review.

In this review we look at the concepts and state-of-the-art concerning the strong coupling of surface plasmon-polariton modes to states associated with quantum emitters such as excitons in J-aggregates, dye molecules and quantum dots. We explore the phenomenon of strong coupling with reference to a number of examples involving electromagnetic fields and matter. We then provide a concise description of the relevant background physics of surface plasmon polaritons. An extensive overview of the historical background and a detailed discussion of more recent relevant experimental advances concerning strong coupling between surface plasmon polaritons and quantum emitters is then presented. Three conceptual frameworks are then discussed and compared in depth: classical, semi-classical and fully quantum mechanical; these theoretical frameworks will have relevance to strong coupling beyond that involving surface plasmon polaritons. We conclude our review with a perspective on the future of this rapidly emerging field, one we are sure will grow to encompass more intriguing physics and will develop in scope to be of relevance to other areas of science.

Nonlocal quantum fluctuations and fermionic superfluidity in the imbalanced attractive Hubbard model.

We study fermionic superfluidity in strongly anisotropic optical lattices with attractive interactions utilizing the cluster dynamical mean-field theory method, and focusing in particular on the role of nonlocal quantum fluctuations. We show that nonlocal quantum fluctuations impact the BCS superfluid transition dramatically. Moreover, we show that exotic superfluid states with a delicate order parameter structure, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase driven by spin population imbalance, can emerge even in the presence of such strong fluctuations.

Spatial coherence properties of organic molecules coupled to plasmonic surface lattice resonances in the weak and strong coupling regimes.

We study spatial coherence properties of a system composed of periodic silver nanoparticle arrays covered with a fluorescent organic molecule (DiD) film. The evolution of spatial coherence of this composite structure from the weak to the strong coupling regime is investigated by systematically varying the coupling strength between the localized DiD excitons and the collective, delocalized modes of the nanoparticle array known as surface lattice resonances. A gradual evolution of coherence from the weak to the strong coupling regime is observed, with the strong coupling features clearly visible in interference fringes. A high degree of spatial coherence is demonstrated in the strong coupling regime, even when the mode is very excitonlike (80%), in contrast to the purely localized nature of molecular excitons. We show that coherence appears in proportion to the weight of the plasmonic component of the mode throughout the weak-to-strong coupling crossover, providing evidence for the hybrid nature of the normal modes.

Plasmonic surface lattice resonances at the strong coupling regime.

We show strong coupling involving three different types of resonances in plasmonic nanoarrays: surface lattice resonances (SLRs), localized surface plasmon resonances on single nanoparticles, and excitations of organic dye molecules. The measured transmission spectra show splittings that depend on the molecule concentration. The results are analyzed using finite-difference time-domain simulations, a coupled-dipole approximation, coupled-modes models, and Fano theory. The delocalized nature of the collective SLR modes suggests that in the strong coupling regime molecules near distant nanoparticles are coherently coupled.

Expansion dynamics in the one-dimensional Fermi-Hubbard model.

Expansion dynamics of interacting fermions in a lattice is simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and nonpaired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.

Exotic superfluid states of lattice fermions in elongated traps.

We present real-space dynamical mean-field theory calculations for attractively interacting fermions in three-dimensional lattices with elongated traps. The critical polarization is found to be 0.8, regardless of the trap elongation. Below the critical polarization, we find unconventional superfluid structures where the polarized superfluid and Fulde-Ferrell-Larkin-Ovchinnikov-type states emerge across the entire core region.

Spin-asymmetric Josephson effect.

We propose that with ultracold Fermi gases one can realize a spin-asymmetric Josephson effect in which the two spin components of a Cooper pair are driven asymmetrically--corresponding to driving a Josephson junction of two superconductors with different voltages V(↑) and V(↓) for spin up and down electrons, respectively. We predict that the spin up and down components oscillate at the same frequency but with different amplitudes. Furthermore our results reveal that the standard interpretation of the Josephson supercurrent in terms of coherent bosonic pair tunneling is insufficient. We provide an intuitive interpretation of the Josephson supercurrent as interference in Rabi oscillations of pairs and single particles, the latter causing the asymmetry.

Vacuum Rabi splitting and strong-coupling dynamics for surface-plasmon polaritons and rhodamine 6G molecules.

We report on strong coupling between surface-plasmon polaritons (SPP) and Rhodamine 6G (R6G) molecules, with double vacuum Rabi splitting energies up to 230 and 110 meV. In addition, we demonstrate the emission of all three energy branches of the strongly coupled SPP-exciton hybrid system, revealing features of system dynamics that are not visible in conventional reflectometry. Finally, in analogy to tunable-Q microcavities, we show that the Rabi splitting can be controlled by adjusting the interaction time between waveguided SPPs and R6G deposited on top of the waveguide. The interaction time can be controlled with sub-fs precision by adjusting the length of the R6G area with standard lithography methods.

Induced interactions for ultracold fermi gases in optical lattices.

We investigate the effect of optical lattices on the BCS superfluidity by using the Gorkov-Melik-Barkhudarov (GMB) correction for a two-component Fermi gas. We find that the suppression of the order parameter is strongly enhanced by the lattice effects. The predictions made by the GMB corrections are in qualitative and, for the cases studied, quantitative agreement with previous quantum Monte Carlo results. We discuss how the GMB correction extends the validity of the mean-field theory to a wider range of tunable optical lattice systems in different dimensions.

Fermi condensates for dynamic imaging of electromagnetic fields.

Ultracold gases provide micrometer size samples whose sensitivity to external fields may be exploited in sensor applications. Bose-Einstein condensates of atomic gases have been demonstrated to perform excellently as magnetic field sensors in atom chips. Here we propose that condensates of fermions can be used for noninvasive sensing of time-dependent and static magnetic and electric fields, by utilizing the tunable energy gap in the excitation spectrum as a frequency filter. Perturbations by the field create collective excitations and quasiparticles. The latter requires the frequency of the perturbation to exceed the gap. The frequencies of the field may be selectively monitored from the amount of quasiparticles which is measurable, e.g., by rf spectroscopy. We analyze the method by calculating the density-density susceptibility and discuss its sensitivity and spatial resolution.

Induced interactions and the superfluid transition temperature in a three-component Fermi gas.

We study many-body contributions to the effective interaction between fermions in a three-component Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a 6Li mixture which can deviate strongly from the one in a weakly interacting two-component system.

Spectral signatures of the Fulde-Ferrell-Larkin-Ovchinnikov order parameter in one-dimensional optical lattices.

We address an imbalanced two-component atomic Fermi gas restricted by a one-dimensional (1D) optical lattice and an external harmonic potential, within the mean-field Bogoliubov-de Gennes formalism. We show that characteristic features of the Fulde-Ferrell-Larkin-Ovchinnikov state are visible in the rf spectra and in the momentum-resolved photoemission spectra of the gas. Specially, Andreev states or midgap states can be clearly resolved, which gives a direct experimentally observable signature of the oscillating order parameter.

Finite-temperature phase diagram of a polarized fermi gas in an optical lattice.

We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair, and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.

Strongly interacting Fermi gases with density imbalance.

We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e., unitarity, regime. The Bogoliubov-de Gennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as give rise to both phase separation and Fulde-Ferrel-Larkin-Ovchinnikov-type oscillations in the order parameter. We show how radio-frequency spectroscopy reflects the phase separation, and can provide direct evidence of the FFLO-type oscillations via observing the nodes of the order parameter.

Beyond linear response spectroscopy of ultracold fermi gases.

We study rf spectroscopy of ultracold Fermi gas by going beyond the linear response in the field-matter interaction. Higher order perturbation theory allows virtual processes and energy conservation beyond the single-particle level. We formulate an effective higher order theory, which agrees quantitatively with experiments on the pairing gap and is consistent with the absence of the mean-field shift in the spin-flip experiment.