Bose-Einstein Condensation of Particles with Half-Integer Spin

Kamel Ourabah

This chapter will focus on the application of kinetic and hydrodynamic approaches to Bose–Einstein condensates. A Bose–Einstein condensate is a state of matter, formed of identical bosons (usually atoms behaving like bosons), so that at a sufficiently low temperature, many of the particles making up the system occupy the lowest energy state (ground state). This is only possible for bosons (particles with an integer spin) unlike fermions (particles with a half-integer spin) due to the Pauli exclusion principle.

Александр Сергеевич Пелетминский, S. V. Peletminsky, Yu. V. Slyusarenko

Harley D. Scammell, Oleg P. Sushkov

We consider the Bose condensation of bosonic particles with spin 1/2. The condensation is driven by an external magnetic field. Our work is motivated by ideas of quantum critical deconfinement and bosonic spinons in spin liquid states. We show that both the nature of the novel Bose condensate and the excitation spectrum are fundamentally different from that in the usual integer spin case. We predict two massive ("Higgs") excitations and two massless Goldstone excitations. One of the Goldstone excitations has a linear excitation spectrum and another has a quadratic spectrum. This implies that the Bose condensate does not support superfluidity, the Landau criterion is essentially violated. We formulate a "smoking gun" criterion for searches of the novel Bose condensation.

Andrei I. Pavlov, V. S. Babichenko, Ilya Polishchuk

Richard M. Friedberg, T. D. Lee, H. C. Ren

Barbara Goss Levi

Experimenters have been romping in the BEC playground ever since a gaseous Bose–Einstein condensate was first produced four years ago. It was almost inevitable, then, that researchers would also want to explore its fermionic cousin—the quantum degenerate state one expects to get by cooling a gas of atoms with half-integer spins. Whereas the integer-spin atoms (bosons) in a Bose–Einstein condensate all pile into the lowest energy state, the half-integer spin atoms (fermions) are prevented from doing so by the Pauli exclusion principle, which prohibits two identical fermions from occupying the same quantum state. Instead, the atoms fill all the lowest energy levels up to the Fermi energy, just as electrons do in a solid. The crossover into this quantum degenerate state is gradual, compared to the abrupt phase transition into a Bose condensate. But that crossover has now been convincingly detected by Deborah Jin, a physicist at the National Institute of Standards and Technology, and Brian DeMarco, a physics graduate student at the University of Colorado at Boulder, both working at JILA.