Broken-axisymmetry state and magnetic state diagram of spin-1 condensate through the prism of quadrupole degrees of freedom

Abstract

We theoretically study a weakly interacting gas of spin-1 atoms with Bose-Einstein condensate in external magnetic field within the Bogoliubov approach. To this end, in contrast to previous studies, we employ the general Hamiltonian, which includes both spin and quadrupole exchange interactions as well as the couplings of the spin and quadrupole moment with the external magnetic field (the linear and quadratic Zeeman terms). The latter is responsible for the emergence of the broken-axisymmetry state. We also reexamine ferromagnetic, quadrupolar, and paramagnetic states employing the proposed Hamiltonian. For all magnetic states, we find the relevant thermodynamic characteristics such as magnetization, quadrupole moment, thermodynamic potential. We also obtain three-branch excitation spectrum of the broken-axisymmetry state. We show that this state can be prepared at three different regimes of applied magnetic field. Finally, we present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.

Zero sound in a quantum gas of spin-3/2 atoms with multipole exchange interaction

“…[45] for F = 3/2) or operators that provide a representation of the SU(2F + 1) group (e.g. Gell-Mann matrices for F = 1; see [21][22][23]).…”

“…However, if the finite range of interaction is essential in systems with total atomic spin F > 1/2, then we are faced with the necessity to consider the multipole degrees of freedom. In particular, the quadrupole degrees of freedom should be included into the interaction Hamiltonian while studying the foregoing spin-1 condensate beyond the scattering-length approximation [21][22][23]. Therefore, the experimental observation of physical effects associated with multipole degrees of freedom must indicate the non-contact character of interatomic interaction in quantum gases.…”

“…Therefore, the experimental observation of physical effects associated with multipole degrees of freedom must indicate the non-contact character of interatomic interaction in quantum gases. Moreover, since the quadrupole exchange is related to the long-range dipole-dipole interaction [24], for atoms with a sufficiently large dipole moment (like erbium [25,26] and dysprosium [27,28]), the strengths of short-range and long-range interactions can be of the same order of magnitude [3,23].…”