Lindblad Equation for the Inelastic Loss of Ultracold Atoms

Abstract

The loss of ultracold trapped atoms due to deeply inelastic reactions has previously been taken into account in effective field theories for low-energy atoms by adding local anti-Hermitian terms to the effective Hamiltonian. Here we show that when multi-atom systems are considered, an additional modification is required in the equation governing the density matrix. We define an effective density matrix by tracing over the states containing high-momentum atoms produced by deeply inelastic reactions. We show that it satisfies a Lindblad equation, with local Lindblad operators determined by the local anti-Hermitian terms in the effective Hamiltonian. We use the Lindblad equation to derive the universal relation for the two-atom inelastic loss rate for fermions with two spin states and the universal relation for the three-atom inelastic loss rate for identical bosons.

arXiv comment24 pages, 4 figures

References in corpus (30)

• Universality in Few-body Systems with Large Scattering Length
• Large momentum part of fermions with large scattering length
• Energetics of a strongly correlated Fermi gas
• Renormalization of the Three-Body System with Short-Range Interactions
• Bose-Einstein Condensation of Metastable Helium
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Introduction to Effective Field Theory
• Atomic three-body loss as a dynamical three-body interaction
• Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance
• Geometric scaling of Efimov states in a ${}^6\text{Li}$-${}^{133}\text{Cs}$ mixture
• Viscosity and dissipative hydrodynamics from effective field theory
• 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
• Open EFTs, IR Effects and Late-Time Resummations: Systematic Corrections in Stochastic Inflation
• Universal Relations for Identical Bosons from 3-Body Physics
• Effective Field Theories
• Three-body problem in heteronuclear mixtures with resonant interspecies interaction
• Two-body and Three-body Contacts for Identical Bosons near Unitarity
• Enhanced Dimer Relaxation in an Atomic/Molecular BEC
• Phase Dynamics of Bose-Einstein Condensates: Losses versus Revivals
• The Efimov effect for three interacting bosonic dipoles
• Three-body recombination in heteronuclear mixtures at finite temperature
• The Nature and Properties of a Repulsive Fermi Gas in the "Upper Branch"
• Universal three-body physics for fermionic dipoles
• Open Effective Field Theories from Deeply Inelastic Reactions
• Three body recombination of ultracold dipoles to weakly bound dimers
• Three-body recombination of two-component cold atomic gases into deep dimers in an optical model
• Effective Field Theories
• Universal Relation for the Inelastic Two-Body Loss Rate

Cited by in corpus (20)

• Coherent and dissipative dynamics of entangled few-body systems of Rydberg atoms
• Emission of Photons and Relativistic Axions from Axion Stars
• Lindblad master equation approach to the topological phase transition in the disordered Su-Schrieffer-Heeger model
• Open Effective Field Theories from Deeply Inelastic Reactions
• The fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model
• Complex contact interaction for systems with short-range two-body loss
• Modeling Particle Loss in Open Systems using Keldysh Path Integral and Second Order Cumulant Expansion
• Lindblad and Bloch equations for conversion of a neutron into an antineutron
• Thermalization in the Quantum Ising Model - Approximations, Limits, and Beyond
• Observation of Anomalous Decay of a Polarized Three-Component Fermi Gas
• Medium-induced bosonic clusters in a Bose-Fermi mixture: Towards simulating cluster formations in neutron-rich matter
• Temperature-Dependent Contact of Weakly Interacting Single-Component Fermi Gases and Loss Rate of Degenerate Polar Molecules
• Non-Hermitian Ferromagnetism in an Ultracold Fermi Gas
• Three-body contact for fermions. I. General relations
• Non-Hermitian $p$-wave superfluid and effects of the inelastic three-body loss in a one-dimensional spin-polarized Fermi gas
• The Efimov effect for heteronuclear three-body systems at positive scattering length and finite temperature
• Exact Thermodynamics For Weakly Interacting Normal-Phase Quantum Gases: Equations of State For All Partial Waves
• Fate of thermalization of ultracold fermions with two-body dissipation
• Open quantum systems beyond equilibrium: Lindblad equation and path integral molecular dynamics
• Exact $\mathcal{N}$-point function mapping between pairs of experiments with Markovian open quantum systems