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Chinese Physics B

Coherent spin dynamics in spin-imbalanced ferromagnetic spinor condensates

Haibo Qiu, Liwei Wu

Published Jan 1, 2015• 1 citation
Publisher

Abstract

We study the coherent spin dynamics of a ferromagnetic spinor Bose–Einstein condensate (BEC) in its domain formation process with an arbitrary spin configuration. Through a simplified schematic view of the domain structure, a semiclassical theory that captures the essential dynamics of the system is presented, and the coherent spin mixing dynamics can be understood in terms of oscillation in the phase space diagram. Using the phase diagram analysis method, we identify new phases, including the π phase oscillation and the running phase for the spin-imbalanced ferromagnetic spinor BEC.

DOI
10.1088/1674-1056/24/1/010304

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We study the coherent spin dynamics of a ferromagnetic spinor Bose–Einstein condensate (BEC) in its domain formation process with an arbitrary spin configuration. Through a simplified schematic view of the domain structure, a semiclassical theory that captures the essential dynamics of the system is presented, and the coherent spin mixing dynamics can be understood in terms of oscillation in the phase space diagram. Using the phase diagram analysis method, we identify new phases, including the π phase oscillation and the running phase for the spin-imbalanced ferromagnetic spinor BEC.
Bose-Einstein condensation (BEC) is a phenomenon in which identical bosons occupy the same quantum state below a certain critical temperature. A hallmark of BEC is the coherence between particles every particle shares the same quantum wavefunction and phase. This coherence has been demonstrated for the external (motional) degrees of freedom of the atomic condensates by interfering two condensates. In this thesis, the coherence is shown to extend to the internal spin degrees of freedom of a spin-1 Bose gas evidenced by the observed coherent and reversible spin-changing collisions. The observed coherent dynamics are analogous to Josephson oscillations in weakly connected superconductors and represent a type of matter-wave four-wave mixing. Control of the coherent evolution of the system using magnetic fields is also demonstrated. The studies on spinor condensates begin by creating spinor condensates directly using all-optical approaches that were first developed in our laboratory. All-optical formation of Bose-Einstein condensates (BEC) in 1D optical lattice and single focus trap geometries are developed and presented. These techniques offer considerable flexibility and speed compared to magnetic trap approaches, and the trapping potential can be essentially spin-independent and are ideally suited for studying spinor condensates. Using condensates with well-defined initial non-equilibrium spin configuration, spin mixing of F = 1 and F = 2 spinor condensates of rubidium-87 atoms confined in an optical trap is observed. The equilibrium spin configuration in the F = 1 manifold confirms that 87Rb is ferromagnetic. The coherent spinor dynamics are demonstrated by initiating spin mixing deterministically with a non-stationary spin population configuration. Finally, the interplay between the coherent spin mixing and spatial dynamics in spin-1 condensates with ferromagnetic interactions is investigated.
We consider a ferromagnetic spin-1 Bose-Einstein condensate (BEC) dispersively coupled to a unidirectional ring cavity. We show that the ability of the cavity to modify, in a highly nonlinear fashion, matter-wave phase shifts adds an additional dimension to the study of spinor condensates. In addition to demonstrating strong matter-wave bistability as in our earlier publication [L. Zhou et al., Phys. Rev. Lett. 103, 160403 (2009)], we show that the interplay between atomic and cavity fields can greatly enrich both the physics of critical slowing down in spin-mixing dynamics and the physics of spin-domain formation in spinor condensates.
We present a theory to describe domain formation observed very recently in a quenched 87Rb gas, a typical ferromagnetic spinor Bose system. An overlap factor is introduced to characterize the symmetry breaking of MF=+/-1 components for the F=1 ferromagnetic condensate. We demonstrate that the domain formation is a coeffect of the quantum coherence and the thermal relaxation. A thermally enhanced quantum oscillation is observed during the dynamical process of the domain formation. And the spatial separation of domains leads to significant decay of the MF=0 component fraction in an initial MF=0 condensate.
We discuss the structure of spin-1 Bose-Einstein condensates in the presence of a homogenous magnetic field. We demonstrate that phase separation can occur in the ground state of antiferromagnetic (polar) condensates, while the spin components of ferromagnetic condensates are always miscible, so that no phase separation occurs in them. Our analysis predicts that this phenomenon takes place when the energy of the lowest homogenous state is a concave function of the magnetization. We propose a method for creating spin domains by adiabatic switching-on of a magnetic field. We also discuss the phenomena of dynamical instability and spin domain formation.
Recent experimental studies of 87Rb^{87}\text{R}\text{b}87Rb spinor Bose Einstein condensates have shown the existence of a magnetic field driven quantum phase transition accompanied by structure formation on the ferromagnetic side of the transition. In this theoretical study we examine the dynamics of the unstable modes following the transition within the framework of the semiclassical truncated Wigner approximation. In the process we present a systematic study of the effects of the trap, nonlinearities, finite temperature, and dipole-dipole interactions. Starting from an initial state which includes quantum fluctuations, we attempt to make quantitative comparisons with recent experimental data on this system by combining results presented here with those presented previously [S. Leslie, J. Guzman, M. Vengalattore, J. D. Sau, M. L. Cohen, and D. M. Stamper-Kurn, Phys. Rev. A 79, 043631 (2009)]. In the process we estimate the contribution of quantum zero-point fluctuations to the domain formation with quantitative accuracy and find discrepancies between the calculations and experiments at the quantitative level, despite the qualitative agreement between theory and experiment. We discuss the possible origins of these discrepancies. Finally, using the strong anisotropy of the trap, we propose ways to observe directly the effects of dipole-dipole interactions on the spinor condensate dynamics.
Spinor Bose-Einstein condensates under external magnetic fields exhibit well-characterized spin domains of its ground state due to spin-dependent interactions. At low temperatures, collision-induced spin-mixing instabilities may promote the condensate to dwell into metastable states occurring near the phase boundaries. In this paper, we study theoretically the metastable spin-phase diagram of a spin-1 antiferromagnetic Bose-Einstein condensate at zero and finite temperatures. The approach makes use of Hartree-Fock theory and exploits the symmetry of the Hamiltonian and of the order parameters yielding a closed system of transcendental equations for the free energy, fully avoiding the use of self-consistency methods. Our results are consistent with recent experiments and allow us to explain qualitatively the different types of observed quench dynamics. In addition, we found that similar phenomena should occur in antiferromagnetic spinor condensates with a sudden change in the temperature. It is shown also that the increase in temperature induces a traceable shift of the ferromagnetic-polar transition boundary, behavior previously not noted by self-consistent mean-field calculations.