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Physical Review A

Spin-mixing dynamics of a spinor Bose-Einstein condensate

Han Pu, C. K. Law, S. Raghavan, Joseph H. Eberly, N. P. Bigelow

Published Aug 1, 1999• 231 citations
Publisher

Abstract

We study the spin-mixing dynamics of an $f=1$ spinor condensate. We show that the dynamics is sensitive to the relative phase and particle number distribution among the individual components of the condensate, and find that complex structures can develop in the density profiles during the time evolution. We investigate the different time scales of the spin-mixing process and their dependence on the total particle number.

DOI
10.1103/physreva.60.1463

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We study the spin-mixing dynamics of an f=1f=1f=1 spinor condensate. We show that the dynamics is sensitive to the relative phase and particle number distribution among the individual components of the condensate, and find that complex structures can develop in the density profiles during the time evolution. We investigate the different time scales of the spin-mixing process and their dependence on the total particle number.
We discuss the quantum phases and their diffusion dynamics in a spinor-1 atomic Bose-Einstein condensate. For ferromagnetic interactions, we obtain the exact ground-state distribution of the phases associated with the total atom number (N),(N),(N), the total magnetization (M),(\mathcal{M}),(M), and the alignment (or hypercharge) (Y) of the system. The mean-field ground state is stable against fluctuations of atom numbers in each of the spin components, and the phases associated with the order parameter for each spin components diffuse while dynamically recovering the two broken continuous symmetries [U(1) and SO(2)] when N and M\mathcal{M}M are conserved, as in current experiments. We discuss the implications to the quantum dynamics due to an external (homogeneous) magnetic field. We also comment on the case of a spinor-1 condensate with antiferromagnetic interactions.
We investigate dynamical behavior of fragmentation of a spinor Bose-Einstein condensate in both the semiclassical and quantum regimes. We show that an unfragmented condensate can become fragmented at later times due to the inherent interactions of elastic atomic collisions, when a certain phase relationship exists among the state amplitudes in different components initially. A close relationship between the fragmentation and population dynamics of atomic distributions within different spin components is found for certain initial states with zero magnetization. The type of fragmentation regime is characterized via atom-number fluctuations. We also address complications of our study when the condensate spatial mode function is different for each spin component.
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.
Spin mixing induced dynamics of spinor solitons in F=1F=1F=1 Bose Einstein condensates
We explore soliton interactions in a homogeneous spinor F=1F=1F=1 Bose Einstein Condensate (BEC) in the presence of a magnetic field, focusing on dark bright dark and bright dark bright configurations. We investigate how these interactions depend on the phase differences among bright solitons and their influence during the dynamics. Our findings align with prior non spinor results, i.e., repulsion among in phase bright solitons and attraction among out of phase pairs in self repulsive atomic BECs. The potential bright soliton attraction, added to the short range repulsion of dark dark soliton interactions, can lead to bound states. However, we find that these bound states break in the presence of spinor interactions due to the particle exchange dynamics between the hyperfine states of the components. Additonally, we develop an effective classical model to describe the soliton dynamics, using a Lagrangian approach. The accuracy of the model is tested by comparing it against numerical simulations. Our results suggest that the proposed model captures the essential features of soliton behavior in the presence of spin interactions, and provides congruent soliton trajectories and interspecies particle exchange dynamics in most of the cases.
Hydrodynamics of the spin-1 Bose-Einstein condensate is investigated without restriction of its allowed manifold to either the ferromagnetic or the antiferromagnetic phase. Mixing of the two manifolds is found to be a generic feature in the temporal evolution of the condensate, regardless of the sign and strength of the spin-dependent interaction. Hydrodynamic theory is developed based on a new representation of the spin-1 condensate wave function as a linear combination of the well-known wave functions specific to antiferromagnetic and ferromagnetic manifolds only. Dynamical constraints unique to each submanifold are derived for the first time, demonstrating that efforts to write down hydrodynamic theory in one specific manifold are generally invalid. Certain exceptions, such as a uniform spiral state in the antiferromagnetic manifold, are shown to sustain dynamical evolution within the same manifold over time.