Concept of contact spectrum and its applications in atomic quantum Hall states

Abstract

A unique feature of ultracold atoms is the separation of length scales, $r_0\ll k_F^{-1}$, where $k_F$ and $r_0$ are the Fermi momentum characterizing the average particle distance and the range of interaction between atoms respectively. For $s$-wave scattering, Shina Tan discovered that such diluteness leads to universal relations, all of which are governed by contact, among a wide range of thermodynamic quantities. Here, we show that the concept of contact can be generalized to an arbitrary partial-wave scattering. Contact of all partial-wave scatterings form a contact spectrum, which establishes universal thermodynamic relations with notable differences from those in the presence of $s$-wave scattering alone. Moreover, such a contact spectrum has an interesting connection with a special bipartite entanglement spectrum of atomic quantum Hall states, and enables an intrinsic probe of these highly correlated states using two-body short-ranged correlations.

8 pages, 1 figures

References in corpus (16)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Thermodynamics of the BCS-BEC crossover
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Verification of universal relations in a strongly interacting Fermi gas
• Universal Properties of the Ultra-Cold Fermi Gas
• Viscosity and scale invariance in the unitary Fermi gas
• Two-dimensional dynamics of expansion of a degenerate Bose gas
• Measurement of the Homogeneous Contact of a Unitary Fermi gas
• Pressure, compressibility, and contact of the two-dimensional attractive Fermi gas
• Momentum Distribution and Contact of the Unitary Fermi gas
• 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
• Universal contact of strongly interacting fermions at finite temperatures
• Temperature and coupling dependence of the universal contact intensity for an ultracold Fermi gas
• Critical behaviours of contact near phase transitions

Cited by in corpus (56)

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• High-momentum distribution with subleading $k^{-3}$ tail in the odd-wave interacting one-dimensional Fermi gases
• Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions
• Contact matrix in dilute quantum systems
• P-Wave Contact Tensor -- Universal Properties of Axisymmetry-Broken P-Wave Fermi Gases
• Probing open- and closed-channel p-wave resonances
• Effective theory and universal relations for Fermi gases near a $d$-wave interaction resonance
• Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction
• Universal relations and normal phase of an ultracold Fermi gas with coexisting $s$- and $p$-wave interactions
• Sigature of the universal super Efimov Effect: three-body contact in two dimensional Fermi gases
• Contact theory for spin-orbit-coupled Fermi gases
• Fermion superfluid with hybridized $s$- and $p$-wave pairings
• A strongly interacting high partial wave Bose gas
• Normal State Properties of a resonantly interacting p-wave Fermi Gas
• Unitary $p$-wave Fermi gas in one dimension
• The Role of the Effective Range in Resonantly Interacting Fermi Gases: How Breaking Scale Symmetry Affects the Bulk Viscosity
• Two-dimensional Fermi gases near a p-wave resonance: effect of quantum fluctuations
• $s$-wave Contacts of Quantum Gases in Quasi-one and Quasi-two Dimensions
• Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries
• Universal Feature in Optical Control of a p-wave Feshbach Resonance
• High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance
• Contact formalism for coupled channels
• Strong-Coupling and Finite Temperature Effects on $p$-wave Contacts
• P-wave contacts of quantum gases in quasi-one-dimensional and quasi-two-dimensional traps
• Universal relations for spin-orbit coupled Fermi gas near an s-wave resonance
• Universal Relations of Ultracold Fermi Gases with Arbitrary Spin-Orbit Coupling
• Universal relations for a spin-polarized Fermi gas in two dimensions
• Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules
• Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions
• Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions
• Multichannel Molecular State and Rectified Short-range Boundary Condition for Spin-orbit Coupled Ultracold Fermions Near p-wave Resonances
• Universal relations for hybridized $s$- and $p$-wave interactions from spin-orbital coupling
• Quantum fluctuations of a resonantly interacting $p$-wave Fermi superfluid in two dimensions
• Dynamical excitation processes and correlations of three-body two-dimensional mixtures
• Studies of Single Component Fermi Gas near a $P$-wave Resonance with Lowest Order Constrained Variational Method
• Resonantly interacting $p$-wave Fermi superfluid in two dimensions: Tan's contact and breathing mode
• Emergent $s$-wave interactions in orbitally active quasi-two-dimensional Fermi gases
• Large-momentun tail of one-dimensional Fermi gases with spin-orbit coupling
• Three-body contact for fermions. I. General relations
• Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter
• Dynamic virial theorem at nonequilibrium and applications
• Toward precision Fermi liquid theory in two dimensions
• Temperature dependence of $p$-wave contacts in a harmonically trapped Fermi gas
• Universal scattering phase shift in the presence of spin-orbit coupling
• Exact Thermodynamics For Weakly Interacting Normal-Phase Quantum Gases: Equations of State For All Partial Waves
• Measurement of $p$-wave contacts in an ultracold Fermi gas of ${}^6$Li atoms
• Local manipulation of quantum magnetism in 1D ultracold Fermi gases across narrow resonances
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Universal Bound States in Long-range Spin Chains with an Impurity
• Single Particle Spectroscopies of $p$-wave and $d$-wave Interacting Bose Gases in Normal Phase
• Resonance-facilitated three-channel p-wave scattering
• Quench Dynamics of Thermal Bose Gases Across Wide and Narrow Feshbach
• Universal Relations in Long-range Quantum Spin Chains