Observation of Critical Scaling Confirms. Universality Class in a Two-dimensional Bose Gas

The behaviour of gases undergoing phase transitions, such as becoming more or less dense, reveals fundamental properties that categorise physical systems, but identifying these properties has proven challenging for ideal Bose gases. Leon Kleebank, Frank Vewinger, and colleagues from Universität Bonn, alongside Arturo Camacho-Guardian, Victor Romero-Rochín, Rosario Paredes, and others from Universidad Nacional Autónoma de México, now present compelling evidence for a unique universality class in these gases. The team observed critical scaling in a two-dimensional gas of photons, which behave like Bose particles and thermalise within a specially designed microcavity, allowing them to measure spatial correlations near the point of condensation. These measurements determine a critical exponent, confirming long-standing theoretical predictions and representing the first experimental validation of the predicted scaling behaviour for the Bose gas universality class, a significant step forward in understanding the fundamental properties of matter.

Pöschl-Teller Potential and 2D Bose Gas

This work details the theoretical foundation for an experiment investigating the Bose-Einstein condensation (BEC) of photons within a two-dimensional system. Researchers utilize a carefully designed potential, known as the Pöschl-Teller potential, to confine the photons and create a 2D gas, allowing them to study the transition into a BEC as temperature decreases. The density of states, crucial for understanding the gas’s thermodynamic properties, is precisely calculated using this potential, approximating a harmonic trap at low energies and a rigid box at high energies. A critical phase-space density is required for BEC to occur, and this document explores the critical temperature below which BEC occurs, and the correlation length, which describes the spatial extent of coherence in the system.

As the system approaches the critical point, the correlation length diverges, indicating that particles become correlated over macroscopic distances. The critical exponent describes how the correlation length changes near this critical point. The document systematically addresses different aspects of the theoretical framework, detailing the derivation of the density of states within the Pöschl-Teller potential. Researchers compare the density of states in this potential to those found in simpler harmonic traps or rigid boxes, demonstrating that it is linear at low energies and constant at high energies.

An equation of state relating pressure, volume, and temperature is derived, and the critical phase-space density needed for BEC is determined. Analysis reveals that the correlation length diverges with a critical exponent of 0. 5, consistent with established theory.

Uniform Photon Gas in Dye Microcavity

This study pioneered a method for observing critical behavior in a two-dimensional photon gas, achieving a nearly uniform density essential for studying phase transitions. Scientists engineered a system where photons are trapped and thermalized within a dye-filled microcavity, formed by a plane mirror and a nanostructured mirror creating a box-shaped potential. This configuration allows for the realization of a uniform 2D Bose gas, described by a Pöschl-Teller potential, and facilitates the observation of critical phenomena even with minimal photon interactions. The experimental setup involved trapping photons and inducing thermalization through radiative contact with a molecular reservoir contained within the microcavity, minimizing inter-photon interactions.

Researchers meticulously characterized the confining potential created by the nanostructured mirror, demonstrating a depth of 1. 4times the thermal energy and a softened edge profile well-described by the Pöschl-Teller potential with a parameter of 1. 5. This precise control over the potential is crucial for achieving a uniform density and enabling systematic studies of the correlation length. Measurements focused on the spatial correlations within the photon gas near the condensation transition, allowing scientists to determine the critical exponent for the correlation length.

The team measured the far-field angular intensity distribution, which corresponds to the photon momentum distribution, and related it to the first-order correlations through a Fourier transform. Analysis of these correlations revealed an algebraic divergence of the correlation length, with a determined critical exponent of 0. 5. The surface density of the quantum degenerate photon gas reached a specific value, and the box size was 80 micrometers. This result constitutes a direct experimental demonstration of critical scaling in the 2D Bose gas universality class, confirming theoretical predictions for this system.

Photonic Gas Exhibits Universal Critical Scaling

This work reports a groundbreaking observation of critical scaling in a two-dimensional gas of photons, providing the first experimental test of predictions for the Bose gas universality class. Researchers investigated a gas of essentially non-interacting photons trapped within a microcavity, where photons thermalize by radiative contact with molecules. The experiment utilized a carefully designed box trap to create a nearly uniform density, enabling systematic studies of critical phenomena. By measuring the spatial correlations near the condensation transition, the team determined the critical exponent for the correlation length to be 0.

52(3). This precise measurement confirms a long-standing theoretical prediction for the Bose gas universality class, differing from the behavior observed in interacting quantum systems. The experiment demonstrates an algebraic divergence of the correlation length as the critical point is approached, providing strong evidence for critical scaling in this unique system. The team achieved this by analyzing the far-field angular intensity distribution of the photons, which is directly related to the spatial correlations within the gas. The carefully engineered trap potential, created using a nanostructured mirror, closely approximates a Pöschl-Teller potential with a parameter of 1.

5, ensuring a nearly uniform density and facilitating the observation of true two-dimensional behavior. The observed critical exponent of 0. 52(3) represents a significant achievement, validating theoretical models and opening new avenues for exploring fundamental physics in non-interacting quantum gases. This research establishes a novel platform for studying critical phenomena and provides crucial insights into the behavior of matter at the quantum level.

Photon Gas Exhibits Bose-Einstein Condensation

This research successfully demonstrates critical scaling in a two-dimensional gas of photons, providing the first experimental verification of theoretical predictions for the Bose gas universality class. Researchers meticulously measured spatial correlations near the condensation transition, determining the critical exponent for the correlation length to be consistent with theoretical predictions. This experiment demonstrates critical scaling in a unique system, analyzing the far-field angular intensity distribution of the photons to reveal spatial correlations within the gas.