Fit-free determination of scale invariant equations of state: application to the 2D Bose gas across the Berezinksii-Kosterlitz-Thouless transition

Abstract

We present a general "fit-free" method for measuring the equation of state (EoS) of a scale-invariant gas. This method, which is inspired from the procedure introduced by Ku et al. [Science 335, 563 (2012)] for the unitary three-dimensional Fermi gas, provides a general formalism which can be readily applied to any quantum gas in a known trapping potential, in the frame of the local density approximation. We implement this method on a weakly-interacting two-dimensional Bose gas in the vicinity of the Berezinskii-Kosterlitz-Thouless transition, and determine its EoS with unprecedented accuracy in the critical region. Our measurements provide an important experimental benchmark for classical field approaches which are believed to accurately describe quantum systems in the weakly interacting but non-perturbative regime.

5 pages, 5 figures

References in corpus (7)

• Theory of ultracold Fermi gases
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Observation of scale invariance and universality in two-dimensional Bose gases
• Strong saturation absorption imaging of dense clouds of ultracold atoms
• Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas
• Determination of the Equation of State of a Two-Component Fermi Gas at Unitarity
• Universal thermodynamics of a two-dimensional Bose gas

Cited by in corpus (29)

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• Connecting Berezinskii-Kosterlitz-Thouless and BEC phase transitions by tuning interactions in a trapped gas
• Quantum anomaly and 2D-3D crossover in strongly interacting Fermi gases
• Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
• Thermal instability, evaporation and thermodynamics of one-dimensional liquids in weakly-interacting Bose-Bose mixtures
• Observation of scale invariance in two-dimensional matter-wave Townes solitons
• Thermodynamics of dilute Bose gases: Beyond mean-field theory for binary mixtures of Bose-Einstein condensate
• Comparison of strong-coupling theories for a two-dimensional Fermi gas
• Quantized refrigerator for an atomic cloud
• Measurement of the Canonical Equation of State of a Weakly Interacting 3D Bose Gas
• Second sound in 2D Bose gas: from the weakly interacting to the strongly interacting regime
• Measuring pair correlations in Bose and Fermi gases via atom-resolved microscopy
• High-precision multiband spectroscopy of ultracold fermions in a nonseparable optical lattice
• Shell-shaped atomic gases
• Quantum unbinding near a zero temperature liquid-gas transition
• Quantized conductance through the quantum evaporation of bosonic atoms
• Kosterlitz-Thouless signatures in the low-temperature phase of layered three-dimensional systems
• Signatures of a universal jump in the superfluid density in two-dimensional Bose gas with finite number of particles
• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Virial Expansion for a Three-Component Fermi Gas in One Dimension: The Quantum Anomaly Correspondence
• Equation of state of a laser cooled gas
• Observation of Algebraic Time Order for Two-Dimensional Dipolar Excitons
• Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases
• Exploring the Berezinskii-Kosterlitz-Thouless Transition in a Two-dimensional Dipolar Bose Gas
• Bound-state spectrum of an impurity in a quantum vortex
• Non-Analytic Crossover Behavior of SU(${\mathcal{N}}_c$) Fermi Liquid
• Thermodynamics of two-dimensional bosons in the lowest Landau level
• Thermodynamics and renormalized quasi-particles in the vicinity of the dilute Bose gas quantum critical point in two dimensions