Quantum disordered spin models/bose condensation

M A Brackstone, J M F Gunn

The authors consider a random magnetic model which is related to Bose condensation in the presence of a random potential. It is an XY model with a random z field. The classical model always has an ordered ground state. The nature of the ground state is unusual: the main contribution to the spontaneous magnetisation comes from a dilute set of weakly interacting pairs of spins. Within each pair the spins are strongly coupled, so for low-energy dynamics only the motion of the total spin of the pair is relevant. This allows the construction of an effective Hamiltonian only involving the pairs' total spins. When this is semi-classically quantised via a 1/S expansion, they find that the zero-point spin wave motion destroys the magnetised ground state if either the number of spin states is sufficiently small (for fixed strength of disorder), or for sufficiently large disorder (for fixed number of spin states). Finally they discuss the relation of the model to the problem of Bose condensation in a random potential, where the interaction strength is related to the number of spin states in the spin model.

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

Thomas Jaeck, Joseph V. Pulé, Valentin Anatol'evich Zagrebnov

Maciej Lewenstein, Anna Sanpera, V. Ahufinger

This chapter starts with an introduction to disordered systems, with an emphasis on disorder in condensed matter, and discusses such phenomena as the Anderson localization, and quantum phases such as with Bose glass. It then turns to various experimental realizations of disorder in ultracold atomic gases. The chapter focuses on disordered Bose-Einstein condensates and the phenomenon of Anderson localization in speckle or quasi-periodic, quasi-random potential. It moves on to disordered ultracold fermionic systems, and disordered ultracold Bose–Fermi (B–F) and Bose–Bose (B–B) mixtures. Finally, the chapter examines spin glasses (providing a brief presentation of the mean field theory of Parisi, and the droplet model) and disorder induced order.

Huan Zhang, Sheng Liu, Yong-Sheng Zhang

We present numerical results of a one-dimensional spin–orbit coupled Bose–Einstein condensate expanding in a speckle disorder potential by employing the Gross–Pitaevskii equation. Localization properties of a spin–orbit coupled Bose–Einstein condensate in zero-momentum phase, magnetic phase and stripe phase are studied. It is found that the localizing behavior in the zero-momentum phase is similar to the normal Bose–Einstein condensate. Moreover, in both magnetic phase and stripe phase, the localization length changes non-monotonically as the fitting interval increases. In magnetic phases, the Bose–Einstein condensate will experience spin relaxation in disorder potential.