Bose-Einstein Condensation of Photons in a Four-Site Quantum Ring.

Thermalization of radiation by contact to matter is a well-known concept, but the application of thermodynamic methods to complex quantum states of light remains a challenge. Here, we observe Bose-Einstein condensation of photons into the hybridized ground state of a coupled four-site ring potential. In our experiment, the periodically closed ring lattice superimposed by a weak harmonic trap for photons is realized inside a spatially structured dye-filled microcavity.

Observation of nonlinear response and Onsager regression in a photon Bose-Einstein condensate.

The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the single-time averages. This provides a powerful framework for the investigation of the intrinsic microscopic behaviour of physical systems by studying their macroscopic response to a controlled external perturbation. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath.

Observation of a Topological Edge State Stabilized by Dissipation.

Robust states emerging at the boundary of a system constitute a hallmark for topological band structures. Other than in closed systems, topologically protected states can occur even in systems with a trivial band structure, if exposed to suitably modulated losses. Here, we study the dissipation-induced emergence of a topological band structure in a non-Hermitian one-dimensional lattice system, realized by arrays of plasmonic waveguides with tailored loss.

Fluctuation-Dissipation Relation for a Bose-Einstein Condensate of Photons.

For equilibrium systems, the magnitude of thermal fluctuations is closely linked to the dissipative response to external perturbations. This fluctuation-dissipation relation has been described for material particles in a wide range of fields. Here, we experimentally probe the relation between the number fluctuations and the response function for a Bose-Einstein condensate of photons coupled to a dye reservoir, demonstrating the fluctuation-dissipation relation for a quantum gas of light.

Emergence of Isotropy and Dynamic Scaling in 2D Wave Turbulence in a Homogeneous Bose Gas.

We realize a turbulent cascade of wave excitations in a homogeneous 2D Bose gas and probe on all relevant time and length scales how it builds up from small to large momenta, until the system reaches a steady state with matching energy injection and dissipation. This all-scales view directly reveals the two theoretically expected cornerstones of turbulence formation-the emergence of statistical momentum-space isotropy under anisotropic forcing and the spatiotemporal scaling of the momentum distribution at times before any energy is dissipated.

Compressibility and the equation of state of an optical quantum gas in a box.

The compressibility of a medium, quantifying its response to mechanical perturbations, is a fundamental property determined by the equation of state. For gases of material particles, studies of the mechanical response are well established, in fields from classical thermodynamics to cold atomic quantum gases. We demonstrate a measurement of the compressibility of a two-dimensional quantum gas of light in a box potential and obtain the equation of state for the optical medium.

Observation of first and second sound in a BKT superfluid.

Superfluidity in its various forms has been of interest since the observation of frictionless flow in liquid helium II. In three spatial dimensions it is conceptually associated with the emergence of long-range order at a critical temperature. One of the hallmarks of superfluidity, as predicted by the two-fluid model and observed in both liquid helium and in ultracold atomic gases, is the existence of two kinds of sound excitation-the first and second sound.

Observation of a non-Hermitian phase transition in an optical quantum gas.

Quantum gases of light, such as photon or polariton condensates in optical microcavities, are collective quantum systems enabling a tailoring of dissipation from, for example, cavity loss. This characteristic makes them a tool to study dissipative phases, an emerging subject in quantum many-body physics. We experimentally demonstrate a non-Hermitian phase transition of a photon Bose-Einstein condensate to a dissipative phase characterized by a biexponential decay of the condensate's second-order coherence.

[A case management questionnaire for family caregivers of geriatric patients].

Background: To ease the burden for family caregivers healthcare concepts are urgently needed. The healthcare concept continuous care in a regional network (RubiN) offers a care and case management in physician networks for geriatric patients and aims to relieve family caregivers. The aim of the study was to develop and to test the psychometric properties of a questionnaire that evaluates the satisfaction and acceptance of the healthcare provided by case management (CM) from the perspective of family caregivers.

First-order spatial coherence measurements in a thermalized two-dimensional photonic quantum gas.

Phase transitions between different states of matter can profoundly modify the order in physical systems, with the emergence of ferromagnetic or topological order constituting important examples. Correlations allow the quantification of the degree of order and the classification of different phases. Here we report measurements of first-order spatial correlations in a harmonically trapped two-dimensional photon gas below, at and above the critical particle number for Bose-Einstein condensation, using interferometric measurements of the emission of a dye-filled optical microcavity.

Calorimetry of a Bose-Einstein-condensed photon gas.

Phase transitions, as the condensation of a gas to a liquid, are often revealed by a discontinuous behaviour of thermodynamic quantities. For liquid helium, for example, a divergence of the specific heat signals the transition from the normal fluid to the superfluid state. Apart from liquid helium, determining the specific heat of a Bose gas has proven to be a challenging task, for example, for ultracold atomic Bose gases.

Spontaneous Symmetry Breaking and Phase Coherence of a Photon Bose-Einstein Condensate Coupled to a Reservoir.

We examine the phase evolution of a Bose-Einstein condensate of photons generated in a dye microcavity by temporal interference with a phase reference. The photoexcitable dye molecules constitute a reservoir of variable size for the condensate particles, allowing for grand canonical statistics with photon bunching, as in a lamp-type source. We directly observe phase jumps of the condensate associated with the large statistical number fluctuations and find a separation of correlation time scales.

Outcome and prognostic factors of multimodal therapy for pulmonary large-cell neuroendocrine carcinomas.

Background: There is controversy whether patients diagnosed with large-cell neuroendocrine carcinoma (LCNEC) should be treated according to protocols for non-small cell lung cancers (NSCLC) or small cell lung cancers (SCLC), especially with regard to the administration of prophylactic cranial irradiation (PCI). This study was set up to determine the incidence of brain metastases and to investigate the outcome following multimodal treatment in 70 patients with LCNEC.

Methods: Seventy patients with histologically confirmed LCNEC were treated at the University Hospital of Heidelberg between 2001 and 2014.

Observation of grand-canonical number statistics in a photon Bose-Einstein condensate.

We report measurements of particle number correlations and fluctuations of a photon Bose-Einstein condensate in a dye microcavity using a Hanbury Brown-Twiss experiment. The photon gas is coupled to a reservoir of molecular excitations, which serve as both heat bath and particle reservoir to realize grand-canonical conditions. For large reservoirs, we observe strong number fluctuations of the order of the total particle number extending deep into the condensed phase.

Statistical physics of Bose-Einstein-condensed light in a dye microcavity.

We theoretically analyze the temperature behavior of paraxial light in thermal equilibrium with a dye-filled optical microcavity. At low temperatures the photon gas undergoes Bose-Einstein condensation, and the photon number in the cavity ground state becomes macroscopic with respect to the total photon number. Owing to a grand-canonical excitation exchange between the photon gas and the dye molecule reservoir, a regime with unusually large fluctuations of the condensate number is predicted for this system that is not observed in present atomic physics Bose-Einstein condensation experiments.

Bose-Einstein condensation of photons in an optical microcavity.

Bose-Einstein condensation (BEC)-the macroscopic ground-state accumulation of particles with integer spin (bosons) at low temperature and high density-has been observed in several physical systems, including cold atomic gases and solid-state quasiparticles. However, the most omnipresent Bose gas, blackbody radiation (radiation in thermal equilibrium with the cavity walls) does not show this phase transition. In such systems photons have a vanishing chemical potential, meaning that their number is not conserved when the temperature of the photon gas is varied; at low temperatures, photons disappear in the cavity walls instead of occupying the cavity ground state.