Trapped one-dimensional ideal Fermi gas with a single impurity

Abstract

Properties of a single impurity in a one-dimensional Fermi gas are investigated in homogeneous and trapped geometries. In a homogeneous system we use McGuire's expression [J. B. McGuire, J. Math. Phys. 6, 432 (1965)] to obtain interaction and kinetic energies, as well as the local pair correlation function. The energy of a trapped system is obtained (i) by generalizing McGuire expression (ii) within local density approximation (iii) using perturbative approach in the case of a weakly interacting impurity and (iv) diffusion Monte Carlo method. We demonstrate that a closed formula based on the exact solution of the homogeneous case provides a precise estimation for the energy of a trapped system for arbitrary coupling constant of the impurity even for a small number of fermions. We analyze energy contributions from kinetic, interaction and potential components, as well as spatial properties such as the system size. Finally, we calculate the frequency of the breathing mode. Our analysis is directly connected and applicable to the recent experiments in microtraps.

5 pages, 4 figures

References in corpus (11)

• Theory of ultracold Fermi gases
• Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• Metastability and Coherence of Repulsive Polarons in a Strongly Interacting Fermi Mixture
• Fermionization of two distinguishable fermions
• Ultra-cold Polarized Fermi Gases
• Trimers, molecules and polarons in imbalanced atomic Fermi gases
• Highly polarized Fermi gases in two dimensions
• Ground state of a tightly bound composite dimer immersed in a Fermi Sea
• Polarons and Molecules in a Two-Dimensional Fermi Gas
• Highly polarized Fermi gases: One-dimensional case

Cited by in corpus (39)

• Polarons, Dressed Molecules, and Itinerant Ferromagnetism in ultracold Fermi gases
• From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
• Strongly interacting confined quantum systems in one dimension
• Universal many-body response of heavy impurities coupled to a Fermi sea
• Recent development of complex scaling method for many-body resonances and continua in light nuclei
• One-dimensional mixtures of several ultracold atoms: a review
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
• Effective approach to impurity dynamics in one-dimensional trapped Bose gases
• Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
• Polaron Interactions and Bipolarons in One-Dimensional Bose Gases in the Strong Coupling Regime
• Ionic polaron in a Bose-Einstein condensate
• Magnetism in strongly interacting one-dimensional quantum mixtures
• Crossover between few and many fermions in a harmonic trap
• Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment
• One-dimensional Fermi gas with a single impurity in a harmonic trap: Perturbative description of the upper branch
• Reentrant behavior of the breathing-mode-oscillation frequency in a one-dimensional Bose gas
• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Exploring the few- to many-body crossover using cold atoms in one dimension
• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Universality of the unitary Fermi gas: A few-body perspective
• Coherent Oscillations in Small Fermi Polaron Systems
• Strongly interacting Bose-Fermi mixtures in one dimension
• Magnetic impurity in a one-dimensional few-fermion system
• Strongly Interacting One-Dimensional Systems with Small Mass Imbalance
• One-dimensional Fermi polaron in a combined harmonic and periodic potential
• Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas
• Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity
• Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity
• Trace of broken integrability in stationary correlation properties
• Impurities in systems of noninteracting trapped fermions
• Quench dynamics of dipolar fermions in a one-dimensional harmonic trap
• Mobile Spin Impurity in an Optical Lattice
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
• Emergence of a Bose polaron in a small ring threaded by the Aharonov-Bohm flux
• Integrability and weak diffraction in a two-particle Bose-Hubbard model
• Dynamical resistivity of a few interacting fermions to the time-dependent potential barrier
• Effective theory for strongly attractive one-dimensional fermions
• Several fermions strongly interacting with a heavy mobile impurity in a one-dimensional harmonic trap
• Momentum Evolution Numerics of an Impurity in a Quantum Quench