Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach

Abstract

Detailed analysis of the system of four interacting ultra-cold fermions confined in a one-dimensional harmonic trap is performed. The analysis is done in the framework of a simple variational ansatz for the many-body ground state and its predictions are confronted with the results of numerically exact diagonalization of the many-body Hamiltonian. Short discussion on the role of the quantum statistics, i.e. Bose-Bose and Bose-Fermi mixtures is also presented. It is concluded that the variational ansatz, although seemed to be oversimplified, gives surprisingly good predictions of many different quantities for mixtures of equal as well as different mass systems. The result may have some experimental importance since it gives quite simple and validated method for describing experimental outputs.

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• A one-dimensional liquid of fermions with tunable spin
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Comparing and contrasting nuclei and cold atomic gases
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
• Quantum magnetism in strongly interacting one-dimensional spinor Bose systems
• Pairing in a system of a few attractive fermions in a harmonic trap

Cited by in corpus (20)

• One-dimensional mixtures of several ultracold atoms: a review
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Effects of coherence on quantum speed limits and shortcuts to adiabaticity in many-particle systems
• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential
• Fast control of interactions in an ultracold two atom system: Managing correlations and irreversibility
• Reduced density matrix approach to ultracold few-fermion systems in one dimension
• Impurity induced quantum chaos for an ultracold bosonic ensemble in a double-well
• Intercomponent correlations in attractive one-dimensional mass-imbalanced few-body mixtures
• Tan's contact scaling behaviour for trapped Lieb-Liniger bosons: from two to many
• Variational approach for interacting ultra-cold atoms in arbitrary one-dimensional confinement
• Variational ansatz for $p$-wave fermions confined in a one-dimensional harmonic trap
• Bunching-antibunching crossover in harmonically trapped few-body Bose-Fermi mixtures
• Spin-orbit coupling in the presence of strong atomic correlations
• Rabi-resonant behavior of periodically-driven correlated fermion systems
• Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential
• Bose-like few-fermion systems
• Quantum correlations in one-dimensional Wigner molecules
• One-Dimensional Quantum Systems - From Few to Many Particles