Exact few-body results for strongly correlated quantum gases in two dimensions

Abstract

The study of strongly correlated quantum gases in two dimensions has important ramifications for understanding many intriguing pheomena in solid materials, such as high-$T_c$ superconductivity and the fractional quantum Hall effect. However, theoretical methods are plagued by the existence of significant quantum fluctuations. Here, we present two- and three-body exact solutions for both fermions and bosons trapped in a two-dimensional harmonic potential, with an arbitrary $s$-wave scattering length. These few-particle solutions link in a natural way to the high-temperature properties of many-particle systems via a quantum virial expansion. As a concrete example, using the energy spectrum of few fermions, we calculate the second and third virial coefficients of a strongly interacting Fermi gas in two dimensions, and consequently investigate its high-temperature thermodynamics. Our thermodynamic results may be useful for ongoing experiments on two-dimensional Fermi gases. These exact results also provide an unbiased benchmark for quantum Monte Carlo simulations of two-dimensional Fermi gases at high temperatures.

11 pages, 6 figures

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Theory of ultracold Fermi gases
• Weakly bound dimers of fermionic atoms
• Observation of a two-dimensional Fermi gas of atoms
• Equation of state of a superfluid Fermi gas in the BCS-BEC crossover
• Virial expansion for a strongly correlated Fermi gas
• Quantum phases of a Two-Dimensional Dipolar Fermi Gas
• Pseudo-gap pairing in ultracold Fermi atoms
• Universal Properties of Two-Dimensional Boson Droplets
• Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap
• Berezinskii-Kosterlitz-Thouless transition in trapped quasi-two-dimensional Fermi gas near a Feshbach resonance
• The effect of population imbalance on the Berezinskii-Kosterlitz-Thouless phase transition in a superfluid Fermi gas
• Universal low-energy properties of three two-dimensional particles
• Dynamic response of strongly correlated Fermi gases in the quantum virial expansion

Cited by in corpus (17)

• Universal contact of strongly interacting fermions at finite temperatures
• Two trapped particles interacting by a finite-ranged two-body potential in two spatial dimensions
• Modified Bethe-Peierls boundary condition for ultracold atoms with Spin-Orbit coupling
• High-temperature limit of the resonant Fermi gas
• Virial expansion for a strongly correlated Fermi gas with imbalanced spin populations
• Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap
• Analytic solutions of topologically disjoint systems
• Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures
• Virial expansion coefficients in the harmonic approximation
• Unusual Zeeman-field effects in two-dimensional spin-orbit-coupled Fermi superfluids
• Precision Many-Body Study of the Berezinskii-Kosterlitz-Thouless Transition and Temperature-Dependent Properties in the Two-Dimensional Fermi Gas
• Adiabatic Hyperspherical Representation for the Three-body Problem in Two Dimensions
• Thermodynamics of rotating quantum matter in the virial expansion
• Equation of state and contact of a strongly interacting Bose gas in the normal state
• Dynamical excitation processes and correlations of three-body two-dimensional mixtures
• Many-body theories of density response for a strongly correlated Fermi gas
• Two atoms in a harmonic trap with spin-orbital-angular-momentum coupling