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

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 re-examine 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, as well as excitation energies for broken-axisymmetry state. We show that the broken-axisymmetry state can be prepared at three different regimes of applied magnetic field. We also present the magnetic state diagrams for each regime of realizing the broken-axisymmetry state.Comment: 14 pages, 2 figures, 4 table

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

In the context of quantum gases, we obtain a many-body Hamiltonian for spin-3/2 atoms with general multipole (spin, quadrupole, and octupole) exchange interaction by employing the apparatus of irreducible spherical tensor operators. This Hamiltonian implies the finite-range interaction, whereas, for zero-range (contact) potentials parameterized by the $s$-wave scattering length, the multipole exchange interaction becomes irrelevant. Following the reduced description method for quantum systems, we derive the quantum kinetic equation for spin-3/2 atoms in a magnetic field and apply it to examine the high-frequency oscillations known as zero sound.Comment: 21 pages, 2 figure

Second quantization method in the presence of bound states of particles

We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of compound particles). In this approximation the compound and elementary particles are considered on an equal basis. This means that creation and annihilation operators of compound particles can be introduced. The Hamiltonians, which specify the interactions between compound and elementary particles and between compound particles themselves are found in terms of the interaction amplitudes for elementary particles. The nonrelativistic quantum electrodynamics is developed for systems containing both elementary and compound particles. Some applications of this theory are considered.Comment: 35 page