Exact Thermodynamics For Weakly Interacting Normal-Phase Quantum Gases: Equations of State For All Partial Waves

Abstract

While the thermodynamics for bosonic systems with weak $s$-wave interactions has been known for decades, a general and systematic extension to higher partial waves has not yet been reported. We provide closed-form expressions for the equations of state for weakly interacting systems with arbitrary partial waves in the normal phase. Thermodynamics, including contact, loss rate, and compressibility, are derived over the entire temperature regime. Our results offer an improved thermometer for ultracold atoms and molecules with weak high-partial wave interactions.

15 pages, 3 figures

References in corpus (55)

• Theory of Bose-Einstein condensation in trapped gases
• A High Phase-Space-Density Gas of Polar Molecules
• Quantum-State Controlled Chemical Reactions of Ultracold KRb Molecules
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Dipolar collisions of polar molecules in the quantum regime
• Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state
• Ultracold Dipolar Gas of Fermionic ${}^{23}$Na${}^{40}$K Molecules in their Absolute Ground State
• Theory of the Weakly Interacting Bose Gas
• Cold molecules: Progress in Quantum Engineering of Chemistry and Quantum Matter
• Creation of ultracold ${}^{87}$RbCs molecules in the rovibrational ground state
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Creation of an ultracold gas of ground-state ${}^{23}{\mathrm{Na}}^{87}\mathrm{Rb}$ molecules
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• A Fermi Degenerate Gas of Polar Molecules
• Verification of universal relations in a strongly interacting Fermi gas
• Contact Measurements on Atomic BEC
• Trapped Fermi gases
• Laser Cooling of Optically Trapped Molecules
• Universal rate constants for reactive collisions of ultracold molecules
• Universal behavior of pair correlations in a strongly interacting Fermi gas
• Long-Lived Ultracold Molecules with Electric and Magnetic Dipole Moments
• General relations for quantum gases in two and three dimensions. Two-component fermions
• Efimov Physics in Cold Atoms
• Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• General relations for quantum gases in two and three dimensions. II. Bosons and mixtures
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Radio frequency spectroscopy of polarons in ultracold Bose gases
• Precise determination of the structure factor and contact in a unitary Fermi gas
• Sticky collisions of ultracold RbCs molecules
• Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases
• Modeling the adiabatic creation of ultracold, polar ${}^{23}\mathrm{N}{\mathrm{a}}^{40}\mathrm{K}$ molecules
• Evidence for universal relations describing a gas with $p$-wave interactions
• Fermion Superfluids of Non-Zero Orbital Angular Momentum near Resonance
• Strong dependence of ultracold chemical rates on electric dipole moments
• Universal Properties of a Strongly Interacting Fermi Gas at a $p$-wave Resonance
• Universal high-momentum asymptote and thermodynamic relations in a spinless Fermi gas with a resonant $p$-wave interaction
• Concept of contact spectrum and its applications in atomic quantum Hall states
• Three-Body Recombination of Identical Bosons with a Large Positive Scattering Length at Nonzero Temperature
• Observation of "broad" d-wave Feshbach resonances with a triplet structure
• Lindblad Equation for the Inelastic Loss of Ultracold Atoms
• Unified model of ultracold molecular collisions
• Two-body relaxation in a Fermi gas at a p-wave Feshbach resonance
• Observation of unitary p-wave interactions between fermions in an optical lattice
• Evidence for Bosonization in a three-dimensional gas of SU($N$) fermions
• Observation of dipolar splittings in high-resolution atom-loss spectroscopy of ${}^6$Li $p$-wave Feshbach resonances
• Two-body relaxation of spin-polarized fermions in reduced dimensionalities near a p-wave Feshbach resonance
• Quantum defect model of a reactive collision at finite temperature
• Contact matrix in dilute quantum systems
• Universal Relation for the Inelastic Two-Body Loss Rate
• Feshbach spectroscopy of an ultracold ${}^{41}$K-${}^6$Li mixture and ${}^{41}$K atoms
• Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules
• Long-lived fermionic Feshbach molecules with tunable $p$-wave interactions
• Virial coefficients for Bose and Fermi trapped gases beyond the unitary limit: an S-Matrix approach

Cited by in corpus (1)

• Probing $p$-wave effects in spin-density separation of Bose mixtures with the dynamic structure factor