Universal Vortex Statistics and Stochastic Geometry of Bose-Einstein Condensation

Abstract

The cooling of a Bose gas in finite time results in the formation of a Bose-Einstein condensate that is spontaneously proliferated with vortices. We propose that the vortex spatial statistics is described by a homogeneous Poisson point process (PPP) with a density dictated by the Kibble-Zurek mechanism (KZM). We validate this model using numerical simulations of the two-dimensional stochastic Gross-Pitaevskii equation (SGPE) for both a homogeneous and a hard-wall trapped condensate. The KZM scaling of the average vortex number with the cooling rate is established along with the universal character of the vortex number distribution. The spatial statistics between vortices is characterized by analyzing the two-point defect-defect correlation function, the corresponding spacing distributions, and the random tessellation of the vortex pattern using the Voronoi cell area statistics. Combining the PPP description with the KZM, we derive universal theoretical predictions for each of these quantities and find them in agreement with the SGPE simulations. Our results establish the universal character of the spatial statistics of point-like topological defects generated during a continuous phase transition and the associated stochastic geometry.

16 pages, 16 figures

References in corpus (18)

• Quantum fluids of light
• Spontaneous vortices in the formation of Bose-Einstein condensates
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Critical Dynamics of Spontaneous Symmetry Breaking in a Homogeneous Bose gas
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Emergence of a Turbulent Cascade in a Quantum Gas
• Homogeneous Atomic Fermi Gases
• XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations
• Critical Behavior of a Trapped Interacting Bose Gas
• Topological defects as relics of emergent continuous symmetry and Higgs condensation of disorder in ferroelectrics
• Structural defects in ion crystals by quenching the external potential: the inhomogeneous Kibble-Zurek mechanism
• Defect formation beyond Kibble-Zurek mechanism and holography
• Universal far-from-equilibrium Dynamics of a Holographic Superconductor
• In situ imaging of vortices in Bose-Einstein condensates
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition
• Vortex detection in atomic Bose-Einstein condensates using neural networks trained on synthetic images
• The Kibble-Zurek Scenario and Coarsening Across Nonequilibrium Phase Transitions in Driven Vortices and Skyrmions

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