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Phase diffusion in a Bose-Einstein condensate of magnons

H.A.Q. Enneking

Published Feb 11, 2015• 0 citations
OpenAlex

Abstract

Research on the phase transition and phase diffusion between the Mott-insulator and superfluid phase has not yet been done extensively for the case of magnons. In this thesis we start from a model Hamiltonian for an easy-plane magnetic insulator and construct the phase diagram describing the transition between the Mott insulator and superfluid phase. Finally, we consider phase diffusion of the Bose-Einstein condensate in the superfluid phase and find that phase diffusion indeed occurs in a finite-sized system.

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Research on the phase transition and phase diffusion between the Mott-insulator and superfluid phase has not yet been done extensively for the case of magnons. In this thesis we start from a model Hamiltonian for an easy-plane magnetic insulator and construct the phase diagram describing the transition between the Mott insulator and superfluid phase. Finally, we consider phase diffusion of the Bose-Einstein condensate in the superfluid phase and find that phase diffusion indeed occurs in a finite-sized system.
In this thesis we will construct a phase diagram showing the transitions to the superfluid and Mott insulating states of magnons in an easy-plane ferromagnetic insulator with an external magnetic field applied. First we transform the Hamiltonian describing this system in several ways, to explore the basic behaviour and to obtain a boundary for the superfluid phase of these magnons. We then use a mean-field approach with the Bose-Hubbard Hamiltonian, done by van Oosten et al., "Quantum Phases in an Optical Lattice", Physical Review A 63, 053601 (2001), to find the Mott insulating regions. Finally, we scrutinize the validity of using this Hamiltonian for our system, by showing some of the different results it yields as compared to the original spin-Hamiltonian. We conclude that the obtained phase diagram is inaccurate for low spins (S=2 or lower) but significantly more reliable for high spins (S=6 and higher).
We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.
87Rb Bose Einstein Condensate in 3D optical lattice was studied in the regime of weak interaction(the superfluid phase) and strong interaction(the Mott insulating phase). The stability of superfluid currents was studied using a moving optical lattice. The critical momentum for stable superfluid current varies from 0.5 recoil momentum (shallow lattice) to 0 (the Mott insulator) as the system reaches the Mott insulator transition. The phase diagram for the disappearance of superfluidity was studied as a function of momentum and lattice depth. Our phase diagram boundary ex-trapolates to the critical lattice depth for the superfluid-to-MI transition. When a one-dimensional gas was loaded into a moving optical lattice a sudden broadening of the transition between stable and unstable phases was observed. A new auxiliary vacuum chamber, which is called the science chamber, was de-signed and installed to improve optical lattice experimental performance and imaging resolution power. Atoms are transported from the main chamber to the science cham-ber. By further evaporation cooling, BECs with N- 2-3 x 104 atoms are produced
An equation for the dynamics of a Bose-Einstein condensate of magnons in a ferromagnetic film is presented, derived from quantum-mechanical theory. The main interactions affecting the evolution of the condensed state are considered. The transition from the equation for the annihilation operator of condensed magnons to an autonomous system of first-order differential equations describing their amplitude and phase is made. Phase trajectories of such a system were studied by constructing phase portraits and determining the stability of stationary points.
We present a general lattice model for a multicomponent atomic Bose-Einstein system in an optical lattice. Using the model, we analytically study the quantum phase transition between the Mott insulator and a superfluid. A mean-field theory is developed from the Mott-insulator ground state. When the interspecies interactions are strong enough, the Mott insulator demonstrates the phase separation behavior. For weak interspecies interactions, the multispecies system is miscible. Finally, the phase diagram is discussed with emphasis on the role of interspecies interactions. The tip and the shape of the Mott insulator lobes do not depend on the interspecies interactions, but the latter indeed modify the position of the phase boundaries.