arXiv subjects

Julian Schmitt

Publications and source records attributed to Julian Schmitt.

At least 19 recordsLinked to original sources

arXiv2026

Observation of critical scaling in the Bose gas universality class

Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle interactions fall into the XY model universality class, the ideal Bose gas has been predicted to form a distinct universality class whose signatures have not yet been revealed experimentally. Here, we report the observation of critical scaling in a two-dimensional trapped quantum gas of essentially noninteracting photons, which thermalize by radiative contact to a reservoir of molecules inside a microcavity. By measuring the spatial correlations near the condensation transition, we determine the critical exponent for the correlation length to be $ν= 0.52(4)$. Our results constitute a first experimental test of the long-standing scaling predictions for the Bose gas universality class.

cond-mat.quant-gas↗

arXiv2026

Limit Cycles in a Photonic Dimer with Tuneable Non-Hermitian Interactions

Interactions govern the emergence of collective behaviour in classical and quantum many-body systems. While conservative interactions are well known to generate nonlinear phenomena ranging from self-trapping to pattern formation, it remains largely unexplored whether purely dissipative -- i.e., non-Hermitian -- interactions can give rise to similarly rich dynamics and nontrivial system states. Here, we experimentally realise tuneable non-Hermitian interactions in two coupled condensates of light confined within a dye-filled double-well microcavity. Local coupling to molecular reservoirs generates the effective dissipative photon interactions. We show that the interplay between coherent tunnelling and interactions stabilises limit-cycle oscillations, a hallmark of nonlinear dynamics traditionally associated with Hermitian nonlinearities. By tuning the reservoir coupling, we map out the dynamical phase diagram comprising stable fixed points and limit cycles, thereby demonstrating direct control over the interaction strength. Our experimentally validated model reveals both supercritical and subcritical Hopf bifurcations, giving rise to hysteresis, bistability and excitability. These results validate dissipative interactions as a mechanism for organising collective nonlinear dynamics in driven-dissipative systems and pave the way towards exploring nonequilibrium many-body physics through controlled dissipation.

cond-mat.quant-gas↗

arXiv2026

Fluctuations of a Photon Bose-Einstein Condensate Coupled to a Reservoir: Describing Coherence Properties in a Free-Energy Model

Photons are mutually nearly noninteracting particles, so thermalized photon ensembles are commonly obtained not from direct particle-particle-interactions but rather from contact with matter, which can constitute a reservoir for the photon gas. We develop a theory model for photons in a material-filled (e.g. liquid dye) optical microcavity, with the aim to study the fluctuation properties using a free-energy description for noninteracting photons coupled to a reservoir of material electronic excitations. To begin with, we use a single mode description for the condensate. For a small relative size of the material reservoir, corresponding to the canonical regime, condensate number fluctuations are small, and the derived free energy landscape takes the usual Mexican-hat shaped form such that spontaneous symmetry breaking occurs. In contrast, for a large relative size of the reservoir, corresponding to the grand canonical regime, fluctuations become as large as the average particle number. We show that the resulting free energy landscape acquires a bowl-shaped form, with a single minimum at the origin. Thus, a macroscopic occupation of the ground state (i.e., Bose-Einstein condensation) in the absence of spontaneous symmetry breaking is expected. We also provide a model for the treatment of a photon gas trapped in a box-shaped potential with spatially distributed coupling to a reservoir. The model predicts, for example, a statistically fluctuating pattern of islands with long-range coherence, resembling transient microcondensates.

cond-mat.quant-gas↗

arXiv2026

Universal critical behavior in ideal Bose-Einstein condensation

Ideal Bose-Einstein condensation (BEC) remains a paradigmatic example of a continuous phase transition and a cornerstone for understanding quantum degenerate bosonic matter. We demonstrate that critical behavior of the ideal Bose gas near the BEC phase transition falls into three distinct classes, determined exclusively by the low-energy scaling of the density of states. Depending on its scaling exponent, which is controlled by dimensionality and confinement, the transition displays either the usual algebraic divergences of thermodynamic susceptibilities, divergent behavior with marginal logarithmic corrections, or a more subtle form of criticality, where only the correlation length diverges. Our work provides a unified framework for criticality in noninteracting bosonic systems. This classification applies broadly to atomic, photonic, polaritonic, and magnonic condensates, where dimensionality, confinement, and spectral engineering can strongly reshape the density of states.

cond-mat.quant-gas↗

arXiv2025

Dimensional Crossover in a Quantum Gas of Light

The dimensionality of a system profoundly influences its physical behaviour, leading to the emergence of different states of matter in many-body quantum systems. In lower dimensions, fluctuations increase and lead to the suppression of long-range order. For example, in bosonic gases, Bose-Einstein condensation (BEC) in one dimension requires stronger confinement than in two dimensions. We experimentally study the properties of a harmonically trapped photon gas undergoing Bose-Einstein condensation along the dimensional crossover from one to two dimensions. The photons are trapped in a dye microcavity where polymer nanostructures provide the trapping potential for the photon gas. By varying the aspect ratio of the harmonic trap, we tune from an isotropic two-dimensional confinement to an anisotropic, highly elongated one-dimensional trapping potential. Along this transition we determine the caloric properties of the photon gas and find a softening of the second-order Bose-Einstein condensation phase transition observed in two dimensions to a crossover behaviour in one dimension.

cond-mat.quant-gas↗

arXiv2025

Thermodynamics and State Preparation in a Two-State System of Light

The coupling of two-level quantum systems to the thermal environment is a fundamental problem, with applications ranging from qubit state preparation to spin models. However, for the elementary problem of the thermodynamics of an ensemble of bosons populating a two-level system despite its conceptual simplicity experimental realizations are scarce. Using an optical dye microcavity platform, we thermalize photons in a two-mode system with tunable chemical potential, demonstrating N bosons populating a two-level system coupled to a heat bath. Under pulsed excitation, Josephson oscillations between the two quantum states demonstrate the possibility for coherent manipulation. In contrast, under stationary conditions the thermalization of the two-mode system is observed. As the energetic splitting between eigenstates is two orders of magnitude smaller than thermal energy, at low occupations an almost equal distribution of the modes occupation is observed, as expected from Boltzmann statistics. For larger occupation, we observe efficient population of the ground state and saturation of the upper level at high filling, expected from quantum statistics. Our experiment holds promise for state preparation in quantum technologies as well as for quantum thermodynamics studies.

cond-mat.quant-gas↗

arXiv2025

Time-periodic driving of a bath-coupled open quantum gas of light

We study the frequency-resolved density response of a photon Bose-Einstein condensate coupled to a bath of dye molecules by time-periodic driving. By monitoring the photon number dynamics for different drive frequencies, we obtain the spectral response of the condensate in a phase-sensitive way. We find that as the photon number increases, the response of the coupled condensate-bath system transitions from overdamped to resonant behavior, indicating a transition from closed to open system dynamics. Our spectroscopy method paves the way for studies of collective excitations in complex driven-dissipative systems.

cond-mat.quant-gas↗

arXiv2024

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 four-site ring potential with coherent tunnel couplings. 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. Photons thermalize to room temperature, and above a critical photon number macroscopically occupy the symmetric linear combination of the site eigenstates with zero phase winding, which constitutes the ground state of the system. The mutual phase coherence of photons at different lattice sites is verified by optical interferometry.

cond-mat.quant-gas↗

arXiv2024

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 temporal response of the average values. Such a relation provides a powerful framework for the investigation of physical systems by establishing a formal connection between intrinsic microscopic behaviour and a macroscopic 'effect' due to an external 'cause'. Measuring the response to a controlled perturbation in this way allows to determine, for example, structure factors in condensed matter systems as well as other correlation functions of material systems. 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. This confirms the regression theorem for a quantum gas and, moreover, establishes a test of this relation in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored. For strong perturbations, we observe nonlinear relaxation dynamics which our microscopic theory relates to the equilibrium fluctuations, thereby extending the regression theorem beyond the regime of linear response. The demonstrated nonlinearity of the condensate-bath system paves the way for studies of novel elementary excitations in lattices of driven-dissipative photon condensates.

cond-mat.quant-gas↗

arXiv2023

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. We obtain direct evidence for a topological edge state that resides in the center of the band gap. By tuning dissipation and hopping, the formation and breakdown of an interface state between topologically distinct regions is demonstrated.

quant-ph↗

arXiv2023

A Sunlight-pumped Two-dimensional Thermalized Photon Gas

The Liouville theorem states that the phase-space volume of an ensemble in a closed system remains constant. While gases of material particles can efficiently be cooled by sympathetic or laser cooling techniques, allowing for large phase-space compression, for light both the absence of an internal structure, as well as the usual non-conservation of particle number upon contact to matter imposes fundamental limits e.g. in fluorescence-based light concentrators in three-dimensional systems. A different physical situation can in principle be expected for dye-solution filled microcavities with a mirror spacing in the wavelength range, where low dimensional photon gases with non-vanishing, freely tunable chemical potential have been experimentally realized. Motivated by the goal to observe phase-space compression of sunlight by cooling the captured radiation to room temperature, we in this work theoretically show that in a lossless system the phase space volume scales as $(Δx Δp / T)^d = \mathrm{constant}$, where $Δx$ and $Δp$ denote the rms position and momentum spread and $d$ the dimensionality of the system ($d=1$ or $2$). We also experimentally realize a sunlight pumped dye microcavity, and demonstrate thermalization of scattered sunlight to a two-dimensional room temperature ensemble with non-vanishing chemical potential. Prospects of phase space buildup of light by cooling, as can be feasible in systems with a two- or three-dimensional band gap, can range from quantum state preparation in tailored potentials up to technical applications in diffuse sunlight collection.

physics.optics↗

arXiv2023

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. The observed agreement of the scale factor with the environment temperature both directly confirms the thermal nature of the optical condensate and demonstrates the validity of the fluctuation-dissipation theorem for a Bose-Einstein condensate.

cond-mat.quant-gas↗

arXiv2022

Emergence of isotropy and dynamic scaling in 2D wave turbulence in a homogeneous Bose gas

We realise 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.

cond-mat.quant-gas↗

arXiv2022

Observation of first and second sound in a BKT superfluid

Superfluidity in its various forms has fascinated scientists since the observation of frictionless flow in liquid helium II. In three spatial dimensions (3D), it is conceptually associated with the emergence of long-range order (LRO) at a critical temperature $T_{\text{c}}$. One of its hallmarks, predicted by the highly successful two-fluid model and observed in both liquid helium and ultracold atomic gases, is the existence of two kinds of sound excitations, the first and second sound. In 2D systems, thermal fluctuations preclude LRO, but superfluidity nevertheless emerges at a nonzero $T_{\text{c}}$ via the infinite-order Berezinskii-Kosterlitz-Thouless (BKT) transition, which is associated with a universal jump in the superfluid density $n_{\text{s}}$ without any discontinuities in the fluid's thermodynamic properties. BKT superfluids are also predicted to support two sounds, but the observation of this has remained elusive. Here we observe first and second sound in a homogeneous 2D atomic Bose gas, and from the two temperature-dependent sound speeds extract its superfluid density. Our results agree with BKT theory, including the prediction for the universal superfluid-density jump.

cond-mat.quant-gas↗

arXiv2021

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. Here 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. The experiment is carried out in a nanostructured dye-filled optical microcavity. We observe signatures of Bose-Einstein condensation at high phase-space densities in the finite-size system. Strikingly, upon entering the quantum degenerate regime, the measured density response to an external force sharply increases, hinting at the peculiar prediction of an infinite compressibility of the deeply degenerate Bose gas.

cond-mat.quant-gas↗

arXiv2021

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

Quantum gases of light, as photons or polariton condensates in optical microcavities, are collective quantum systems enabling a tailoring of dissipation from e.g. cavity loss. This makes them a tool to study dissipative phases, an emerging subject in quantum manybody physics. Here we experimentally demonstrate a non-Hermitian phase transition of a photon Bose-Einstein condensate to a new dissipative phase, characterized by a biexponential decay of the condensate's second-order coherence. The phase transition occurs due to the emergence of an exceptional point in the quantum gas. While Bose-Einstein condensation is usually connected to ordinary lasing by a smooth crossover, the observed phase transition separates the novel, biexponential phase from both lasing and an intermediate, oscillatory condensate regime. Our findings pave the way for studies of a wide class of dissipative quantum phases, for instance in topological or lattice systems.

cond-mat.quant-gas↗

arXiv2020

Realizing arbitrary trapping potentials for light via direct laser writing of mirror surface profiles

The versatility of quantum gas experiments greatly benefits from the ability to apply variable potentials. Here we describe a method which allows the preparation of potential structures for microcavity photons via spatially selective deformation of optical resonator geometries with a heat induced mirror surface microstructuring technique. We investigate the thermalization of a two-dimensional photon gas in a dye-filled microcavity composed of the custom surface-structured mirrors at wavelength-scale separation. Specifically, we describe measurements of the spatial redistribution of thermal photons in a coupled double-ridge structure, where photons form a Bose-Einstein condensate in a spatially split ground state, as a function of different pumping geometries.

cond-mat.quant-gas↗

arXiv2019

Fluctuation dynamics of an open photon Bose-Einstein condensate

Bosonic gases coupled to a particle reservoir have proven to support a regime of operation where Bose-Einstein condensation coexists with unusually large particle-number fluctuations. Experimentally, this situation has been realized with two-dimensional photon gases in a dye-filled optical microcavity. Here, we investigate theoretically and experimentally the open-system dynamics of a grand canonical Bose-Einstein condensate of photons. We identify a regime with temporal oscillations of the second-order coherence function $g^{(2)}(τ)$, even though the energy spectrum closely matches the predictions for an equilibrium Bose-Einstein distribution and the system is operated deeply in the regime of weak light-matter coupling. The observed temporal oscillations are attributed to the nonlinear, weakly driven-dissipative nature of the system which leads to time-reversal symmetry breaking.

quant-ph↗