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arXiv:0710.5481 · Journal of Physics A Mathematical and Theoretical

Bose–Einstein condensates of atoms with arbitrary spin

P. Van Isacker, Stefan G. Heinze

Published Nov 21, 2007• 22 citations
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Abstract

We show that the ground state of a Bose-Einstein condensate of atoms with hyperfine spin f = 2 can be either spin aligned, condensed into pairs of atoms coupled to F = 0, or condensed into triplets of atoms coupled to F = 0. The complete phase diagram is constructed for f = 2 and the generic properties of the phase diagram are obtained for f > 2.

DOI
10.1088/1751-8113/40/49/014

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We show that the ground state of a Bose-Einstein condensate of atoms with hyperfine spin f = 2 can be either spin aligned, condensed into pairs of atoms coupled to F = 0, or condensed into triplets of atoms coupled to F = 0. The complete phase diagram is constructed for f = 2 and the generic properties of the phase diagram are obtained for f > 2.
Three hyperfine states of Bose-condensed sodium atoms, recently optically trapped, can be described as a spin-1 Bose gas. We study the behavior of this system in a magnetic field, and construct the phase diagram, where the temperature of the Bose condensation TBEC{T}_{\mathrm{BEC}}TBEC​ increases with magnetic field. In particular the system is ferromagnetic below TBEC{T}_{\mathrm{BEC}}TBEC​ and the magnetization is proportional to the condensate fraction in a vanishing magnetic field. Second derivatives of the magnetization with regard to temperature or magnetic field are discontinuous along the phase boundary.
We demonstrate a possibility to create a new state of ultracold atoms which we call a Bose-Einstein-Young condensate. Atoms are supposed to be in different hyperfine state of the same isotope. The wave function of such a state, although totally symmetric with respect to simultaneous permutation of co-ordinates and spins of any pair of atoms, has more complicated structure than a simple product of totally symmetric co-ordinate and spin parts. Its properties with respect to permutations of only co-ordinates or only spins are characterized by a particular Young diagram, a symbol denoting an irreducible representation of the permutation group.
We study the ground state and classify its phase diagram for a mixture of two spin-1 condensates in the absence of an external magnetic (B)(B)(B) field according to atomic parameters for intra- and interspecies spin-exchange coupling and singlet-pairing interaction. Ignoring the interspecies singlet-pairing interaction, the ground-state phases are found analytically. A numerical approach of simulated annealing is adopted when the singlet-pairing interaction is present. Our results on the phase diagram and the boundaries between phases allow for easy identifications of quantum phase transitions, which can be induced through the tuning of optical traps and atom numbers. They provide insight and guidance for several ongoing experiments on mixtures of spinor condensates.
Abstract We obtain and justify a many-body Hamiltonian of pairwise interacting spin-1 atoms, which includes eight generators of the SU(3) group associated with spin and quadrupole degrees of freedom. It is shown that this Hamiltonian is valid for non-local interaction potential, whereas for local interaction specified by s -wave scattering length, the Hamiltonian should be bilinear in spin operators only (of the Heisenberg type). We apply the obtained Hamiltonian to study the ground-state properties and single-particle excitations of a weakly interacting gas of spin-1 atoms with Bose–Einstein condensate (BEC) taking into account the quadrupole degrees of freedom. It is shown that the system under consideration can be in ferromagnetic, quadrupole, and paramagnetic phases. The corresponding phase diagram is constructed and discussed. The main characteristics such as the density of the grand thermodynamic potential, condensate density, and single-particle excitation spectra modified by quadrupole degrees of freedom are determined in different phases.
Since the first experimental realization of Bose-Einstein condensates in a spin-orbit-coupled Zeeman lattice, a wide range of applications have been found in these systems. Here, we systematically study the ground-state phase diagram of the systems. The spin-orbit-coupled Zeeman lattice generates multiple energy minima in the lowest Bloch band. These minima may locate at Brillouin-zone edges and center, or inside the Brillouin zone. Interacting atoms condensing into these minima constitute ground-state quantum phases. Among these phases, the band-edge condensation states have no analog in either spin-orbit-coupled homogeneous systems or lattice systems without the spin-orbit coupling. They exist in a very broad parameter regime of the spin-orbit-coupled Zeeman lattice system. We address superfluidity of the band-edge states by analyzing their elementary excitations and superfluid fraction.