Universal Bose Gases Near Resonance: A Rigorous Solution

Abstract

We obtain a rigorous solution of universal Bose gases near resonance and offer an answer to one of the long-standing challenges of quantum gases at large scattering lengths, where the standard dilute theory breaks down. The solution was obtained by using an $\epsilon$ expansion near four spatial dimension. In dimension $d=4-\epsilon$, the chemical potential of Bose gases near resonances is shown to approach the universal value ${\epsilon }^{(2/(4-\epsilon ))}{\epsilon }_F\sqrt{2/3}(1+0.474\epsilon -i1.217\epsilon +...)$, where ${\epsilon }_F$ is the Fermi energy defined for a Fermi gas of density $n$, and the condensation fraction is equal to $2/3(1+0.0877\epsilon +...)$. We also discuss the implications on ultra-cold gases in physical dimensions.

5 pages, 1 figure

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• Nonequilibrium States of a Quenched Bose Gas
• Incorporating exact two-body propagators for zero-range interactions into $N$-body Monte Carlo simulations
• Conformality Lost in Efimov Physics
• Momentum distribution of a dilute unitary Bose gas with three-body losses
• Quantum Many-Body Conformal Dynamics: Symmetries, Geometry, Conformal Tower States, and Entropy Production
• Few-body Physics in a Many-body World
• Long-lived universal resonant Bose gases
• Non-Perturbative Dynamical Effects in Nearly Scale Invariant Systems: The Action of Breaking Scale Invariance
• Temperature-dependence of small harmonically trapped atom systems with Bose, Fermi and Boltzmann statistics
• Two-dimensional Fermi gases near a p-wave resonance: effect of quantum fluctuations
• Quantum criticality of bosonic systems with the Lifshitz dispersion
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• Equation of state and contact of a strongly interacting Bose gas in the normal state
• Universal coherent atom-molecule oscillations in the dynamics of the unitary Bose gas near a narrow Feshbach resonance
• Structural and quantum properties of van der Waals cluster near the unitary regime
• Stability and Anomalous Compressibility of Bose Gases Near Resonance: The scale-dependent interactions and thermal effects
• Quantum N-Boson States and Quantized Motion of Solitonic Droplets: Universal Scaling Properties in Low Dimensions
• Metastability of Bose and Fermi gases on the upper branch