Quantum Phase Transition in an Atomic Bose Gas with a Feshbach Resonance

Abstract

We show that in an atomic Bose gas near a Feshbach resonance a quantum phase transition occurs between a phase with only a molecular Bose-Einstein condensate and a phase with both an atomic and a molecular Bose-Einstein condensate. We show that the transition is characterized by an Ising order parameter. We also determine the phase diagram of the gas as a function of magnetic field and temperature: the quantum critical point extends into a line of finite temperature Ising transitions.Introduction. -One of the most important recent developments in the field of ultracold atomic gases is the application of Feshbach resonances. A Feshbach resonance in the scattering amplitude of two atoms occurs when the total energy of the atoms is close to the energy of a molecular state that is weakly coupled to the atomic continuum [1,2]. In the alkali gases of interest, this coupling is provided by the exchange interaction, and consequently the magnetic moments of the two atoms and the molecule differ substantially. As a result the energy difference between the molecule and the threshold of the two-atom continuum, known as the detuning δ, can be experimentally tuned by means of a magnetic field. Moreover, by sweeping the magnetic field from positive to negative detuning through the Feshbach resonance, it is actually possible to form molecules in the atomic gas [3,4,5,6,7].

Superfluidity and phase transitions in a resonant Bose gas

“…As was recently pointed out 27,28 and is the subject of this paper, the phenomenology of resonantly interacting degenerate bosonic atoms contrasts strongly and qualitatively with this picture. 29 For a large positive detuning, molecules are strongly energetically suppressed and unpaired atoms (as in any bosonic system at zero temperature) form an atomic superfluid (ASF), exhibiting atomic off-diagonal long-range order (ODLRO).…”

Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice

“…In that case the symmetry appears due to a conversion term that connects pairs of bosons with a distinct molecular field. This can lead to exotic states in which pairs of bosons are condensed but single bosons are not and in which half vortices are permitted [26,27] Further, due to strong interatomic repulsion, the ground state in 3D (three flavors) breaks a kind of chiral symmetry and displays an additional accidental ground state degeneracy at the mean field level. A similar situation occurs for special parameter values in frustrated XY-models, where parallel zero energy domain walls can be inserted [28].…”

Three-Body Interacting Bosons in Free Space

“…A weakly interacting BEC with two-body attraction (coupling constant g 2 < 0) and three-body repulsion (g 3 > 0) is predicted to be a droplet, the density of which in the absence of external confinement and neglecting the surface tension is flat and equals n = −3g 2 /2g 3 [7][8][9]. For a strong (beyond mean-field) two-body attraction the spinless Bose gas can pass from the atomic to paired superfluid phase via an Ising-type transition with peculiar topological properties [10][11][12]. However, the mechanical stability of the system requires repulsive few-body interactions [13] or other stabilizing mechanisms [14].…”