All-Perovskite Multicomponent Nanocrystal Superlattices

Nanocrystal superlattices (NC SLs) have long been sought as promising metamaterials, with nanoscale-engineered properties arising from collective and synergistic effects among the constituent building blocks. Lead halide perovskite (LHP) NCs come across as outstanding candidates for SL design, as they demonstrate collective light emission, known as superfluorescence, in single- and multicomponent SLs. Thus far, LHP NCs have only been assembled in single-component SLs or coassembled with dielectric NC building blocks acting solely as spacers between luminescent NCs. Here, we report the formation of multicomponent LHP NC-only SLs, i.e., using only CsPbBr3 NCs of different sizes as building blocks. The structural diversity of the obtained SLs encompasses the ABO6, ABO3, and NaCl structure types, all of which contain orientationally and positionally locked NCs. For the selected model system, the ABO6-type SL, we observed efficient NC coupling and Förster-like energy transfer from strongly confined 5.3 nm CsPbBr3 NCs to weakly confined 17.6 nm CsPbBr3 NCs, along with characteristic superfluorescence features at cryogenic temperatures. Spatiotemporal exciton dynamics measurements reveal that binary SLs exhibit enhanced exciton diffusivity compared to single-component NC assemblies across the entire temperature range (from 5 to 298 K). The observed coherent and incoherent NC coupling and controllable excitonic transport within the solid NC SLs hold promise for applications in quantum optoelectronic devices.

Single-photon superradiance in individual caesium lead halide quantum dots

The brightness of an emitter is ultimately described by Fermi's golden rule, with a radiative rate proportional to its oscillator strength times the local density of photonic states. As the oscillator strength is an intrinsic material property, the quest for ever brighter emission has relied on the local density of photonic states engineering, using dielectric or plasmonic resonators1,2. By contrast, a much less explored avenue is to boost the oscillator strength, and hence the emission rate, using a collective behaviour termed superradiance. Recently, it was proposed3 that the latter can be realized using the giant oscillator-strength transitions of a weakly confined exciton in a quantum well when its coherent motion extends over many unit cells. Here we demonstrate single-photon superradiance in perovskite quantum dots with a sub-100 picosecond radiative decay time, almost as short as the reported exciton coherence time4. The characteristic dependence of radiative rates on the size, composition and temperature of the quantum dot suggests the formation of giant transition dipoles, as confirmed by effective-mass calculations. The results aid in the development of ultrabright, coherent quantum light sources and attest that quantum effects, for example, single-photon emission, persist in nanoparticles ten times larger than the exciton Bohr radius.

Modulated Rashba-Dresselhaus Spin-Orbit Coupling for Topology Control and Analog Simulations

We show theoretically that Rashba-Dresselhaus spin-orbit coupling (RDSOC) in lattices acts as a synthetic gauge field. This allows us to control both the phase and the magnitude of tunneling coefficients between sites, which is the key ingredient to implement topological Hamitonians and spin lattices useful for simulation perpectives. We use liquid crystal based microcavities in which RDSOC can be switched on and off as a model platform. We propose a realistic scheme for implementation of a Su-Schrieffer-Heeger chain in which the edge states existence can be tuned, and a Harper-Hofstadter model with a tunable contrasted flux for each (pseudo)spin component. We further show that a transverse-field Ising model and classical XY Hamiltonian with tunable parameters can be implemented, opening up prospects for analog physics, simulations, and optimization.

Structural Diversity in Multicomponent Nanocrystal Superlattices Comprising Lead Halide Perovskite Nanocubes

Nanocrystal (NC) self-assembly is a versatile platform for materials engineering at the mesoscale. The NC shape anisotropy leads to structures not observed with spherical NCs. This work presents a broad structural diversity in multicomponent, long-range ordered superlattices (SLs) comprising highly luminescent cubic CsPbBr₃ NCs (and FAPbBr₃ NCs) coassembled with the spherical, truncated cuboid, and disk-shaped NC building blocks. CsPbBr₃ nanocubes combined with Fe₃O₄ or NaGdF₄ spheres and truncated cuboid PbS NCs form binary SLs of six structure types with high packing density; namely, AB₂, quasi-ternary ABO₃, and ABO₆ types as well as previously known NaCl, AlB₂, and CuAu types. In these structures, nanocubes preserve orientational coherence. Combining nanocubes with large and thick NaGdF₄ nanodisks results in the orthorhombic SL resembling CaC₂ structure with pairs of CsPbBr₃ NCs on one lattice site. Also, we implement two substrate-free methods of SL formation. Oil-in-oil templated assembly results in the formation of binary supraparticles. Self-assembly at the liquid-air interface from the drying solution cast over the glyceryl triacetate as subphase yields extended thin films of SLs. Collective electronic states arise at low temperatures from the dense, periodic packing of NCs, observed as sharp red-shifted bands at 6 K in the photoluminescence and absorption spectra and persisting up to 200 K.

Shape-Directed Co-Assembly of Lead Halide Perovskite Nanocubes with Dielectric Nanodisks into Binary Nanocrystal Superlattices

Self-assembly of colloidal nanocrystals (NCs) holds great promise in the multiscale engineering of solid-state materials, whereby atomically engineered NC building blocks are arranged into long-range ordered structures-superlattices (SLs)-with synergistic physical and chemical properties. Thus far, the reports have by far focused on single-component and binary systems of spherical NCs, yielding SLs isostructural with the known atomic lattices. Far greater structural space, beyond the realm of known lattices, is anticipated from combining NCs of various shapes. Here, we report on the co-assembly of steric-stabilized CsPbBr₃ nanocubes (5.3 nm) with disk-shaped LaF₃ NCs (9.2-28.4 nm in diameter, 1.6 nm in thickness) into binary SLs, yielding six columnar structures with AB, AB₂, AB₄, and AB₆ stoichiometry, not observed before and in our reference experiments with NC systems comprising spheres and disks. This striking effect of the cubic shape is rationalized herein using packing-density calculations. Furthermore, in the systems with comparable dimensions of nanocubes (8.6 nm) and nanodisks (6.5 nm, 9.0 nm, 12.5 nm), other, noncolumnar structures are observed, such as ReO₃-type SL, featuring intimate intermixing and face-to-face alignment of disks and cubes, face-centered cubic or simple cubic sublattice of nanocubes, and two or three disks per one lattice site. Lamellar and ReO₃-type SLs, employing large 8.6 nm CsPbBr₃ NCs, exhibit characteristic features of the collective ultrafast light emission-superfluorescence-originating from the coherent coupling of emission dipoles in the excited state.

Enhanced Room-Temperature Photoluminescence Quantum Yield in Morphology Controlled J-Aggregates

Supramolecular assemblies from organic dyes forming J-aggregates are known to exhibit narrowband photoluminescence with full-width at half maximum of ≈9 nm (260 cm-1). Applications of these high color purity emitters, however, are hampered by the rather low photoluminescence quantum yields reported for cyanine J-aggregates, even when formed in solution. Here, it is demonstrated that cyanine J-aggregates can reach an order of magnitude higher photoluminescence quantum yield (increase from 5% to 60%) in blend solutions of water and alkylamines at room temperature. By means of time-resolved photoluminescence studies, an increase in the exciton lifetime as a result of the suppression of non-radiative processes is shown. Small-angle neutron scattering studies suggest a necessary condition for the formation of such highly emissive J-aggregates: the presence of a sharp water/amine interface for J-aggregate assembly and the coexistence of nanoscale-sized water and amine domains to restrict the J-aggregate size and solubilize monomers, respectively.

Monodisperse Long-Chain Sulfobetaine-Capped CsPbBr3 Nanocrystals and Their Superfluorescent Assemblies

Ligand-capped nanocrystals (NCs) of lead halide perovskites, foremost fully inorganic CsPbX₃ NCs, are the latest generation of colloidal semiconductor quantum dots. They offer a set of compelling characteristics-large absorption cross section, as well as narrow, fast, and efficient photoluminescence with long exciton coherence times-rendering them attractive for applications in light-emitting devices and quantum optics. Monodisperse and shape-uniform, broadly size-tunable, scalable, and robust NC samples are paramount for unveiling their basic photophysics, as well as for putting them into use. Thus far, no synthesis method fulfilling all these requirements has been reported. For instance, long-chain zwitterionic ligands impart the most durable surface coating, but at the expense of reduced size uniformity of the as-synthesized colloid. In this work, we demonstrate that size-selective precipitation of CsPbBr₃ NCs coated with a long-chain sulfobetaine ligand, namely, 3-(N,N-dimethyloctadecylammonio)-propanesulfonate, yields monodisperse and sizable fractions (>100 mg inorganic mass) with the mean NC size adjustable in the range between 3.5 and 16 nm and emission peak wavelength between 479 and 518 nm. We find that all NCs exhibit an oblate cuboidal shape with the aspect ratio of 1.2 × 1.2 × 1. We present a theoretical model (effective mass/k·p) that accounts for the anisotropic NC shape and describes the size dependence of the first and second excitonic transition in absorption spectra and explains room-temperature exciton lifetimes. We also show that uniform zwitterion-capped NCs readily form long-range ordered superlattices upon solvent evaporation. In comparison to more conventional ligand systems (oleic acid and oleylamine), supercrystals of zwitterion-capped NCs exhibit larger domain sizes and lower mosaicity. Both kinds of supercrystals exhibit superfluorescence at cryogenic temperatures-accelerated collective emission arising from the coherent coupling of the emitting dipoles.

Low-loss optical waveguides made with a high-loss material

For guiding light on a chip, it has been pivotal to use materials and process flows that allow low absorption and scattering. Based on subwavelength gratings, here, we show that it is possible to create broadband, multimode waveguides with very low propagation losses despite using a strongly absorbing material. We perform rigorous coupled-wave analysis and finite-difference time-domain simulations of integrated waveguides that consist of pairs of integrated high-index-contrast gratings. To showcase this concept, we demonstrate guiding of visible light in the wavelength range of 550-650 nm with losses down to 6 dB/cm using silicon gratings that have a material absorption of 13,000 dB/cm at this wavelength and are fabricated with standard silicon photonics technology. This approach allows us to overcome traditional limits of the various established photonics technology platforms with respect to their suitable spectral range and, furthermore, to mitigate situations where absorbing materials, such as highly doped semiconductors, cannot be avoided because of the need for electrical driving, for example, for amplifiers, lasers and modulators.

Unraveling the Origin of the Long Fluorescence Decay Component of Cesium Lead Halide Perovskite Nanocrystals

A common signature of nearly all nanoscale emitters is fluorescence intermittency, which is a rapid switching between "on"-states exhibiting a high photon emission rate and "off"-states with a much lower rate. One consequence of fluorescence intermittency occurring on time scales longer than the exciton decay time is the so-called delayed photon emission, manifested by a long radiative decay component. Besides their dominant fast radiative decay, fully inorganic cesium lead halide perovskite quantum dots exhibit a long fluorescence decay component at cryogenic temperatures that is often attributed to the decay of the dark exciton. Here, we show that its origin is delayed photon emission by investigating temporal variations in fluorescence intensity and concomitant decay times found in single CsPbBr₃ perovskite quantum dots. We attribute the different intensity levels of the intensity trace to a rapid switching between a high-intensity exciton state and an Auger-reduced low-intensity trion state that occurs when the excitation is sufficiently strong. Surprisingly, we observe that the exponent of this power-law-dependent delayed emission is correlated with the emission intensity, which cannot be explained with existing charge carrier trapping models. Our analysis reveals that the long decay component is mainly governed by delayed emission, which is present in both the exciton and trion state. The absence of a fine structure in trions clarifies the vanishing role of the dark exciton state for the long decay component. Our findings are essential for the development of a complete photophysical model that captures all observed features of fluorescence variations in colloidal nanocrystals.

Lasing Supraparticles Self-Assembled from Nanocrystals

One of the most attractive commercial applications of semiconductor nanocrystals (NCs) is their use in lasers. Thanks to their high quantum yield, tunable optical properties, photostability, and wet-chemical processability, NCs have arisen as promising gain materials. Most of these applications, however, rely on incorporation of NCs in lasing cavities separately produced using sophisticated fabrication methods and often difficult to manipulate. Here, we present whispering gallery mode lasing in supraparticles (SPs) of self-assembled NCs. The SPs composed of NCs act as both lasing medium and cavity. Moreover, the synthesis of the SPs, based on an in-flow microfluidic device, allows precise control of the dimensions of the SPs, i.e. the size of the cavity, in the micrometer range with polydispersity as low as several percent. The SPs presented here show whispering gallery mode resonances with quality factors up to 320. Whispering gallery mode lasing is evidenced by a clear threshold behavior, coherent emission, and emission lifetime shortening due to the stimulation process.

Long Exciton Dephasing Time and Coherent Phonon Coupling in CsPbBr2Cl Perovskite Nanocrystals

Fully inorganic cesium lead halide perovskite nanocrystals (NCs) have shown to exhibit outstanding optical properties such as wide spectral tunability, high quantum yield, high oscillator strength as well as blinking-free single photon emission, and low spectral diffusion. Here, we report measurements of the coherent and incoherent exciton dynamics on the 100 fs to 10 ns time scale, determining dephasing and density decay rates in these NCs. The experiments are performed on CsPbBr₂Cl NCs using transient resonant three-pulse four-wave mixing (FWM) in heterodyne detection at temperatures ranging from 5 to 50 K. We found a low-temperature exciton dephasing time of 24.5 ± 1.0 ps, inferred from the decay of the photon-echo amplitude at 5 K, corresponding to a homogeneous line width (fwhm) of 54 ± 5 μeV. Furthermore, oscillations in the photon-echo signal on a picosecond time scale are observed and attributed to coherent coupling of the exciton to a quantized phonon mode with 3.45 meV energy.

Single Cesium Lead Halide Perovskite Nanocrystals at Low Temperature: Fast Single-Photon Emission, Reduced Blinking, and Exciton Fine Structure

Metal-halide semiconductors with perovskite crystal structure are attractive due to their facile solution processability, and have recently been harnessed very successfully for high-efficiency photovoltaics and bright light sources. Here, we show that at low temperature single colloidal cesium lead halide (CsPbX3, where X = Cl/Br) nanocrystals exhibit stable, narrow-band emission with suppressed blinking and small spectral diffusion. Photon antibunching demonstrates unambiguously nonclassical single-photon emission with radiative decay on the order of 250 ps, representing a significant acceleration compared to other common quantum emitters. High-resolution spectroscopy provides insight into the complex nature of the emission process such as the fine structure and charged exciton dynamics.

Room-temperature Bose-Einstein condensation of cavity exciton-polaritons in a polymer

A Bose-Einstein condensate (BEC) is a state of matter in which extensive collective coherence leads to intriguing macroscopic quantum phenomena. In crystalline semiconductor microcavities, bosonic quasiparticles, known as exciton-polaritons, can be created through strong coupling between bound electron-hole pairs and the photon field. Recently, a non-equilibrium BEC (ref. ) and superfluidity have been demonstrated in such structures. With organic crystals grown inside dielectric microcavities, signatures of polariton lasing have been observed. However, owing to the deleterious effects of disorder and material imperfection on the condensed phase, only crystalline materials of the highest quality have been used until now. Here we demonstrate non-equilibrium BEC of exciton-polaritons in a polymer-filled microcavity at room temperature. We observe thermalization of polaritons and, above a critical excitation density, clear evidence of condensation at zero in-plane momentum, namely nonlinear behaviour, blueshifted emission and long-range coherence. The key signatures distinguishing the behaviour from conventional photon lasing are presented. As no crystal growth is involved, our approach radically reduces the complexity of experiments to investigate BEC physics and paves the way for a new generation of opto-electronic devices, taking advantage of the processability and flexibility of polymers.

Slotted photonic crystal nanobeam cavity with an ultrahigh quality factor-to-mode volume ratio

We describe the design, fabrication, and characterization of a 1-dimensional silicon photonic crystal cavity with a quality factor-to-mode volume ratio greater than 10(7), which exceeds the highest previous values by an order of magnitude. The maximum of the electric field is outside the silicon in a void formed by a central slot. An extremely small calculated mode volume of 0.0096 (λvac/n)(3) is achieved through the abrupt change of the electric field in the slot, despite which a high quality factor of 8.2 × 10(5) is predicted by simulation. Quality factors up to 1.4 × 10(5) are measured in actual devices. The observation of pronounced thermo-optic bistability is consistent with the strong confinement of light in these cavities.

A strong electro-optically active lead-free ferroelectric integrated on silicon

The development of silicon photonics could greatly benefit from the linear electro-optical properties, absent in bulk silicon, of ferroelectric oxides, as a novel way to seamlessly connect the electrical and optical domain. Of all oxides, barium titanate exhibits one of the largest linear electro-optical coefficients, which has however not yet been explored for thin films on silicon. Here we report on the electro-optical properties of thin barium titanate films epitaxially grown on silicon substrates. We extract a large effective Pockels coefficient of r(eff) = 148 pm V(-1), which is five times larger than in the current standard material for electro-optical devices, lithium niobate. We also reveal the tensor nature of the electro-optical properties, as necessary for properly designing future devices, and furthermore unambiguously demonstrate the presence of ferroelectricity. The integration of electro-optical active films on silicon could pave the way towards power-efficient, ultra-compact integrated devices, such as modulators, tuning elements and bistable switches.

Exciton dynamics within the band-edge manifold states: the onset of an acoustic phonon bottleneck

Exciton dynamics within the band-edge state manifold of CdSe/ZnS and CdSe/CdS quantum dots (QDs) have been investigated. Low-temperature time-resolved photoluminescence (PL) experiments demonstrate that exciton relaxation is mediated by LO phonons, whereas an acoustic phonon bottleneck is observed for splitting energies lower than the optical phonon energy. This has important implications since the main source affecting exciton dephasing is considered to be a spin-flip process. Our results concur with recent observations of long exciton dephasing times in CdSe/CdS QDs and show a way to engineer nanoparticles with enhanced coherence time, a prerequisite for their use in quantum optical applications.

Controlling the exciton fine structure splitting in CdSe/CdS dot-in-rod nanojunctions

We demonstrate control and tunability of the exciton fine-structure splitting by properly engineering a nanojunction consisting of a CdSe nanocrystal core and an asymmetric rod-like CdS shell. Samples with small core and/or thick rod diameters exhibit a strongly reduced fine-structure splitting resulting from a reduced electron-hole exchange interaction. These results shed light onto the electronic configuration of such nanosystems and, apart from being of fundamental interest, could enable the use of colloidal nanocrystals as a source of entangled photons.

Band-edge exciton fine structure of small, nearly spherical colloidal CdSe/ZnS quantum dots

The exciton fine structure of small (2-3.5 nm) wurtzite (WZ) and zincblende (ZB) CdSe quantum dots (Qdots) has been investigated by means of nanosecond and picosecond time-resolved photoluminescence spectroscopy, at temperatures ranging from 5 K to room temperature. For both crystal structures, we observe a similar dark-bright energy level splitting of 2.4-5 meV, with a larger splitting corresponding to smaller Qdots. In addition, spectrally resolved streak camera images collected at 5 K reveal the presence of a third state, split from the lower dark-bright manifold by 30-70 meV, again independently of the crystal structure of the Qdots. The data thus reveal that small WZ and ZB CdSe Qdots are optically indistinguishable. This contrasts with theoretical calculations within the effective-mass approximation, which, in the limit of spherical Qdots, yield a different fine structure for both. However, experimental and theoretical results converge when taking the Qdot shape into account. With transmission electron microscopy, we determined that our Qdots are prolate, with an aspect ratio of 1.15:1. Incorporating this value into our calculations, we obtain a similar fine structure for both WZ and ZB Qdots. Moreover, the opposite sign of the crystal field and shape anisotropy in CdSe suggests that the lowest energy level in small CdSe Qdots has an angular momentum projection F = 0, in contrast with (perfectly) spherical Qdots, where the lowest level corresponds to the dark ±2 state. From the experimental and theoretical data we conclude that shape anisotropy and exchange interactions dominate over the crystal field anisotropy-induced splitting in this size range.

Probing the wave function delocalization in CdSe/CdS dot-in-rod nanocrystals by time- and temperature-resolved spectroscopy

Colloidal semiconductor quantum structures allow controlling the strong confinement of charge carriers through material composition and geometry. Besides being a unique platform to study fundamental effects, these materials attracted considerable interest due to their potential in opto-electronic and quantum communication applications. Heteronanostructures like CdSe/CdS offer new prospects to tailor their optical properties as they take advantage of a small conduction band offset allowing tunability of the electron delocalization from type-I toward quasi-type-II. Here, we report on a detailed study of the exciton recombination dynamics in CdSe/CdS heterorods. We observed a clear size-dependent radiative lifetime, which can be linked to the different degree of electron wave function (de)localization. Moreover, by increasing the temperature from 70 to 300 K, we observed a considerable increase of the radiative lifetime, clearly demonstrating a reduction of the conduction band offset at higher temperatures. Understanding and controlling electron delocalization in such heterostructures will be pivotal for realizing efficient and low-cost photonic devices.

Plasmonic nanohybrid with ultrasmall Ag nanoparticles and fluorescent dyes

We investigate a hybrid nanocomposite combining fluorescent dyes and ultrasmall (<3 nm) silver nanocrystals in a block copolymer micelle. Although the metal nanoparticles are significantly smaller than the electromagnetic skin depth, we observe a modification of the exciton lifetime and the nonradiative energy transfer among the dyes. This behavior is absent in a control experiment with dyes whose energetic levels are far from the plasmonic resonance, establishing the plasmonic nature of the interaction.

Ultrafast all-optical modulator with femtojoule absorbed switching energy in silicon-on-insulator

We demonstrate an all-optical switch based on a waveguide-embedded 1D photonic crystal cavity fabricated in silicon-on-insulator technology. Light at the telecom wavelength is modulated at high-speed by control pulses in the near infrared, harnessing the plasma dispersion effect. The actual absorbed switching power required for a 3 dB modulation depth is measured to be as low as 6 fJ. While the switch-on time is on the order of a few picoseconds, the relaxation time is almost 500 ps and limited by the lifetime of the charge carriers.

Ultracompact silicon/polymer laser with an absorption-insensitive nanophotonic resonator

A planar nanophotonic Fabry-Perot-like resonator that can defy strong absorption of about 20 000 cm(-1) in the cavity material is demonstrated. Visible laser emission is observed from two silicon subwavelength-sized high index contrast gratings with embedded polymer gain material. The size of the laser is reduced by an order of magnitude compared to established designs based on photonic bandgap structures. As silicon constitutes the most common carrier for electronics, the cost-efficient integration of compact laser sources for visible wavelengths comes within reach.

Ultra-high quality-factor resonators with perfect azimuthal modal-symmetry

We study circular grating resonators (CGRs) which are formed by a central defect surrounded by concentric rings composing a grating and which display perfect azimuthal modal-symmetry. Because of their radial symmetry they exhibit a complete band gap for a minimal index contrast. However, as is the case for all 2D resonators their quality factors are limited by vertical losses. To reduce the vertical losses we introduce a chirp of the grating period by reducing it towards the central defect. The chirped CGRs exhibit drastically improved quality factors of up to tens of millions with a modal volume of a few cubic wavelengths.

Circular grating resonators as small mode-volume microcavities for switching

We demonstrate the suitability of microcavities based on circular grating resonators (CGRs) as fast switches. This type of optical resonator is characterized by a high quality factor and very small mode volume. The waveguide-coupled CGRs are fabricated with silicon-on-insulator technology compatible with standard complementary metal-oxide semiconductor (CMOS) processing. The linear optical properties of the CGRs are investigated by transmission spectroscopy. From 3D finite-difference time-domain simulations of isolated CGRs, we identify the measured resonances. We probe the spatial distribution and the parasitic losses of a resonant optical mode with scanning near-field optical microscopy. We observe fast all-optical switching within a few picoseconds by optically generating free charge carriers within the cavity.

Energy transfer in hybrid organic/inorganic nanocomposites

Chemically synthesized colloidal quantum dots can easily be incorporated into conjugated polymer host systems allowing for novel organic/inorganic hybrid materials combining the natural advantages from both organic as well as inorganic components into one system. In order to obtain tailored optoelectronic properties, a profound knowledge of the fundamental electronic energy transfer processes between the inorganic and organic parts is necessary. Previous studies have attributed the observed efficient energy transfer to a dipole-dipole coupling with Förster radii of about 50-70 A. Here, we report on resonant energy transfer of nonequilibrium excitons in an amorphous polyfluorene donor CdSe/ZnS core-shell nanocrystal acceptor system. By time-resolved photoluminescence (PL) spectroscopy, we have investigated the PL decay behavior of the primarily excited polyfluorene as a function of temperature. We show that the transfer efficiency drops from about 30% at room temperature to around 5% at low temperature. These results shed light on the importance of temperature-activated exciton diffusion in the energy transfer process. As a consequence the exciton has to migrate very close to the surface of the quantum dot in order to couple to the quantum dot. Hence, the coupling strength is much weaker than that anticipated in previous work and requires treatment beyond Förster theory.

Bose-fermi mixtures in a three-dimensional optical lattice

We have studied mixtures of fermionic (40)K and bosonic (87)Rb quantum gases in a three-dimensional optical lattice. We observe that an increasing admixture of the fermionic species diminishes the phase coherence of the bosonic atoms as measured by studying both the visibility of the matter wave interference pattern and the coherence length of the bosons. Moreover, we find that the attractive interactions between bosons and fermions lead to an increase of the boson density in the lattice which we measure by studying three-body recombination in the lattice. In our data, we do not observe three-body loss of the fermionic atoms. An analysis of the thermodynamics of a noninteracting Bose-Fermi mixture in the lattice suggests a mechanism for sympathetic cooling of the fermions in the lattice.

Molecules of fermionic atoms in an optical lattice

We create molecules from fermionic atoms in a three-dimensional optical lattice using a Feshbach resonance. In the limit of low tunneling, the individual wells can be regarded as independent three-dimensional harmonic oscillators. The measured binding energies for varying scattering length agree excellently with the theoretical prediction for two interacting atoms in a harmonic oscillator. We demonstrate that the formation of molecules can be used to measure the occupancy of the lattice and perform thermometry.

p-Wave interactions in low-dimensional fermionic gases

We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of /m/ = 1 (or m = 0) can be inhibited. In two and three dimensions, we observe the doublet structure of the p-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.

Confinement induced molecules in a 1D Fermi gas

We have observed two-particle bound states of atoms confined in a one-dimensional matter waveguide. These bound states exist irrespective of the sign of the scattering length, contrary to the situation in free space. Using radio-frequency spectroscopy we have measured the binding energy of these dimers as a function of the scattering length and confinement and find good agreement with theory. The strongly interacting one-dimensional Fermi gas which we create in an optical lattice represents a realization of a tunable Luttinger liquid.

Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions

We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.

Excitations of a superfluid in a three-dimensional optical lattice

We prepare a Bose-Einstein condensed gas in a three-dimensional optical lattice and study the excitation spectrum of the superfluid phase for different interaction strengths. We probe the response of the system by modulating the depth of the optical lattice along one axis. The interactions can be controlled independently by varying the tunnel coupling along the other two lattice axes. In the weakly interacting regime we observe a small susceptibility of the superfluid to excitations, while for stronger interactions an unexpected resonance appears in the excitation spectrum. In addition we measure the coherent fraction of the atomic gas, which determines the depletion of the condensate.

Transition from a strongly interacting 1d superfluid to a Mott insulator

We study 1D trapped Bose gases in the strongly interacting regime. The systems are created in an optical lattice and are subject to a longitudinal periodic potential. Bragg spectroscopy enables us to investigate the excitation spectrum in different regimes. In the superfluid phase a broad continuum of excitations is observed which calls for an interpretation beyond the Bogoliubov spectrum taking into account the effect of strong interactions. In the Mott insulating phase a discrete spectrum is measured. Both phases are compared to the 3D situation and to the crossover regime from 1D to 3D. The coherence length and coherent fraction of the gas are measured in all configurations. We observe signatures for increased fluctuations characteristic for 1D systems. Moreover, the collective oscillations cease near the transition to the Mott insulator phase.

Exciting collective oscillations in a trapped 1D gas

We report on the realization of a trapped one-dimensional Bose gas and its characterization by means of measuring its lowest lying collective excitations. The quantum degenerate Bose gas is prepared in a 2D optical lattice, and we find the ratio of the frequencies of the lowest compressional (breathing) mode and the dipole mode to be (omega(B)/omega(D))(2) approximately 3.1, in accordance with the Lieb-Liniger and mean-field theory. For a thermal gas we measure (omega(B)/omega(D))(2) approximately 4. By heating the quantum degenerate gas, we have studied the transition between the two regimes. For the lowest number of particles attainable in the experiment the kinetic energy of the system is similar to the interaction energy, and we enter the strongly interacting regime.

Quantum states of neutrons in the Earth's gravitational field

The discrete quantum properties of matter are manifest in a variety of phenomena. Any particle that is trapped in a sufficiently deep and wide potential well is settled in quantum bound states. For example, the existence of quantum states of electrons in an electromagnetic field is responsible for the structure of atoms, and quantum states of nucleons in a strong nuclear field give rise to the structure of atomic nuclei. In an analogous way, the gravitational field should lead to the formation of quantum states. But the gravitational force is extremely weak compared to the electromagnetic and nuclear force, so the observation of quantum states of matter in a gravitational field is extremely challenging. Because of their charge neutrality and long lifetime, neutrons are promising candidates with which to observe such an effect. Here we report experimental evidence for gravitational quantum bound states of neutrons. The particles are allowed to fall towards a horizontal mirror which, together with the Earth's gravitational field, provides the necessary confining potential well. Under such conditions, the falling neutrons do not move continuously along the vertical direction, but rather jump from one height to another, as predicted by quantum theory.