Permutation symmetry in spinor quantum gases: selection rules, conservation laws, and correlations

Abstract

Many-body systems of identical arbitrary-spin particles, with separable spin and spatial degrees of freedom, are considered. Their eigenstates can be classified by Young diagrams, corresponding to non-trivial permutation symmetries (beyond the conventional paradigm of symmetric--antisymmetric states). The present work obtains (a) selection rules for additional non-separable (dependent on spins and coordinates) $k$-body interactions: the Young diagrams, associated with the initial and the final states of a transition, can differ by relocation of no more than $k$ boxes between their rows; and (b) correlation rules: eigenstate-averaged local correlations of $k$ particles vanish if $k$ exceeds the number of columns (for bosons) or rows (for fermions) in the associated Young diagram. It also elucidates the physical meaning of the quantities conserved due to permutation symmetry --- in 1929, Dirac identified those with characters of the symmetric group --- relating them to experimentally observable correlations of several particles. The results provide a way to control the formation of entangled states belonging to multidimensional non-Abelian representations of the symmetric group. These states can find applications in quantum computation and metrology.

A citation added

References in corpus (11)

• Many-Body Physics with Ultracold Gases
• Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• Degenerate Fermi Gases of Ytterbium
• Ultracold fermions and the SU(N) Hubbard model
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Cold Bosons in Optical Lattices
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Optical atomic coherence at the one-second time scale
• Double-degenerate Bose-Fermi mixture of strontium
• Spectroscopy for a Few Atoms Harmonically-Trapped in One Dimension

Cited by in corpus (13)

• One-dimensional mixtures of several ultracold atoms: a review
• Non-Equilibrium Thermodynamics of Harmonically Trapped Bosons
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: II. $N$ Particles
• Entanglement of an Impurity in a Few-Body One-Dimensional Ideal Bose System
• Molecular spectra in collective Dicke states
• Entanglement production by statistical operators
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: spin-independent interactions and spin-dependent external fields
• Long-lived states with well-defined spins in spin-$1/2$ homogeneous Bose gases
• Phase transitions in definite total spin states of two-component Fermi gases
• Sum rules for spin-$1/2$ quantum gases in states with well-defined spins: II. Spin-dependent two-body interactions
• Symmetry oscillations sensitivity to SU(2)-symmetry breaking in quantum mixtures