Quasi-long-range order in trapped two-dimensional Bose gases

Abstract

We study the fate of algebraic decay of correlations in a harmonically trapped two-dimensional degenerate Bose gas. The analysis is inspired by recent experiments on ultracold atoms where power-law correlations have been observed despite the presence of the external potential. We generalize the spin wave description of phase fluctuations to the trapped case and obtain an analytical expression for the one-body density matrix within this approximation. We show that algebraic decay of the central correlation function persists to lengths of about 20% of the Thomas--Fermi radius. We establish that the trap-averaged correlation function decays algebraically with a strictly larger exponent weakly changing with trap size and find indications that the recently observed enhanced scaling exponents receive significant contributions from the normal component of the gas. We discuss radial and angular correlations and propose a local correlation approximation which captures the correlations very well. Our analysis goes beyond the usual local density approximation and the developed summation techniques constitute a powerful tool to investigate correlations in inhomogeneous systems.

6 pages + supplemental material

References in corpus (12)

• Superfluid behaviour of a two-dimensional Bose gas
• Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas
• Observation of pair condensation in the quasi-2D BEC-BCS crossover
• Equation of State of Ultracold Fermions in the 2D BEC-BCS Crossover Region
• Non-equilibrium Berezinskii-Kosterlitz-Thouless Transition in a Driven Open Quantum System
• Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas
• Connecting Berezinskii-Kosterlitz-Thouless and BEC phase transitions by tuning interactions in a trapped gas
• Matter wave Fourier optics with a strongly interacting two-dimensional Fermi gas
• Semiclassical theory of the quasi two-dimensional trapped Bose gas
• Probing superfluidity in a quasi two-dimensional Bose gas through its local dynamics
• Quasi-condensation in two-dimensional Fermi gases
• Noise correlations of two-dimensional Bose gases

Cited by in corpus (9)

• Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
• Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
• Observation of the BKT Transition in a 2D Bose Gas via Matter-Wave Interferometry
• Fermi-to-Bose crossover in a trapped quasi-2D gas of fermionic atoms
• Universal Scaling of the Dynamic BKT Transition in Quenched 2D Bose Gases
• Josephson junction dynamics in a two-dimensional ultracold Bose gas
• Observation of Algebraic Time Order for Two-Dimensional Dipolar Excitons
• Quantitative Studies on the Quantum Critical Regime near Superfluid to Mott Insulator Transition
• A phase microscope for quantum gases