Observation of Spinor Dynamics in Optically TrappedRb87Bose-Einstein Condensates

Abstract

We measure spin mixing of F=1 and F=2 spinor condensates of 87 Rb atoms confined in an optical trap. We determine the spin mixing time to be typically less than 600 ms and observe spin population oscillations. The equilibrium spin configuration in the F=1 manifold is measured for different magnetic fields and found to show ferromagnetic behavior for low field gradients. An F=2 condensate is created by microwave excitation from F=1 manifold, and this spin-2 condensate is observed to decay exponentially with time constant 250 ms. Despite the short lifetime in the F=2 manifold, spin mixing of the condensate is observed within 50 ms.PACS numbers: 03.75. Mn, 32.80.Pj, One of the hallmarks of Bose-Einstein condensation (BEC) in dilute atomic gases is the relatively weak and well-characterized inter-atomic interactions that allow quantitative comparison with theory. The vast majority of experimental work has involved single component systems, using magnetic traps confining just one Zeeman sub-level in the ground state hyperfine manifold. An important frontier in BEC research is the extension to multi-component systems, which provides a unique opportunity for exploring coupled, interacting quantum fluids. In particular, atomic BECs with internal spin degrees of freedom offer a new form of coherent matter with complex internal quantum structures. The first twocomponent condensate was produced utilizing two hyperfine states in 87 Rb, and remarkable phenomena such as phase separation were observed [1,2]. Sodium F=1 spinor BECs have been created by transferring spin polarized condensates into a far-off resonant optical trap to liberate the internal spin degrees of freedom. This allowed investigations of the ground state properties of Na spinor condensates, and observations of domain structures, metastability, and quantum spin tunneling [3,4,5].In this letter, we explore the spin dynamics and ground state properties of 87 Rb spinor condensates in an alloptical trap, by starting with well-characterized initial conditions in a known magnetic field. We focus on the F=1 case and confirm the predicted ferromagnetic behavior. We observe population oscillation between different spin states during the spin mixing and observe reduced magnetization fluctuations, pointing the way to future exploration of the underlying spin squeezing and spin entanglement predicted for the system [6]. We also create F=2 spinors using a microwave excitation, measure a decay of the condensate with a time constant of 250 ms. Despite the short lifetime, spin mixing of the spin-2 condensates is observed within 50 ms. Similar results are concurrently reported in Ref [7]; in that work, the emphasis is on the F=2 mixing, while here, we focus mainly on the F=1 manifold.A spinor BEC can be described by a multi-component order parameter which is invariant under gauge transformation and rotation in spin space [8,9,10]. For a spin-1 BEC, the condensate is either ferromagnetic or antiferromagnetic [8], and the corresponding ground state structure and dynamical prope...

Evolution of the average populations of spin components of spin-1 Bose-Einstein condensates beyond mean-field theory

“…The value 1/2 was first obtained numerically by Law, et al [12], and was supported by the recent study by Chang, et al [9]. Now this value is obtained analytically, and is further found not depending on N 0 .…”

“…[6,7,8] Recently, the evolution of spinor condensates has been extensively studied experimentally and theoretically. [9,10,12,13,14] Initially, the condensate was prepared in a Fock-state or a coherent state confined in an optical trap. Then, due to the spin-dependent interaction, the system begin to evolve where a pair of atoms with spin components 1 and -1 can jump to 0 an 0, and vice versa, via scattering.…”

Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate

“…In particular, observation of coherent spin oscillations have confirmed the mean-field pendulum model for small condensates 4,9,10 . Spin evolution has been previously observed from metastable spin states in many experiments 6,8,[13][14][15][16][17] , however, the experiments have not yet demonstrated spin dynamic in agreement with quantum calculations, except in the perturbative, low-depletion limit at very short times (where a Bogoliubov expansion around the mean field can be used) 12,13,17 , or for conditions where the mean-field approach suffices. Here, we are able to observe quantum spin dynamics that agree well with quantum calculations and demonstrate a rich array of non-Gaussian fluctuations.…”

“…The equilibrium states, domain formation and spin dynamics of spinor condensates have been studied in many experiments [6][7][8][9][10][11][12][13][14][15][16][17] . In particular, observation of coherent spin oscillations have confirmed the mean-field pendulum model for small condensates 4,9,10 .…”

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

“…[55]). Spinor condensates with three species have also drawn considerable attention since their experimental creation [66,335]. Such systems give rise to spin domains [290], polarized states [336], spin textures [337], and multicomponent (vectorial) solitons of bright [338][339][340][341], dark [342], gap [343], and brightdark [344] types.…”