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arXiv:cond-mat/0202055 · Europhysics Letters (EPL)

Stern-Gerlach entanglement in spinor Bose-Einstein condensates

Sara Cruz-Barrios, Maria Carolina Nemes, A. F. R. de Toledo Piza

Published Jan 1, 2003• 2 citations
arXivHTMLPDF

Abstract

Entanglement of spin and position variables produced by spatially inhomogeneous magnetic fields of Stern-Gerlach type acting on spinor Bose-Einstein condensates may lead to interference effects at the level of one-boson densities. A model is worked out for these effects which is amenable to analytical calculation for gaussian shaped condensates. The resulting interference effects are sensitive to the spin polarization properties of the condensate.

DOI
10.1209/epl/i2003-00200-6

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We describe effects of matter-wave interference of spinor states in the 87{}^{87}87Rb Bose-Einstein condensate. The components of the F=2F=2F=2 manifold are populated by forced Majorana transitions and then fall freely due to gravity in an applied magnetic field. Weak inhomogeneities of the magnetic field, present in the experiment, impose relative velocities onto different mF{m}_{F}mF​ components, which show up as interference patterns upon measurement of atomic density distributions with a Stern-Gerlach imaging method. We show that interference effects may appear in experiments even if gradients of the magnetic field components are eliminated but higher-order inhomogeneity is present and the duration of the interaction is long enough. In particular, we show that the resulting matter-wave interference patterns can mimic spontaneous pattern formation in the quantum gas.
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We present experimental evidence for the spontaneous formation of a macroscopic spin polarization in overlapping regions of two independent Bose-Einstein condensates produced in different hyperfine states of 87Rb. The condensates are independent in the sense that we do not explicitly introduce a relative phase between them. A single "spin-tip" pulse maps the transverse spin polarization into longitudinal spin polarization, and the atomic density distributions are measured with a Stern-Gerlach imaging method. The resulting matter-wave interference patterns are anticorrelated.
We argue that the non-adiabatic evolution of spin states in Stern-Gerlach apparatus can blur the manifestation of path spin entanglement. This fact introduces a contradiction to the usual perception of spin measurement even in a formally ideal situation. Through quantitative calculation, we have pointed out the specific reason behind the breakdown of adiabatic evolution to be the spatial inhomogeneity of applied magnetic field. The angle θθθ between the zzz component of magnetic moment of the particle and applied magnetic field is also a determining factor for the category of evolution of spin states. Adiabaticity always can be restored by choosing a sufficiently small value of θθθ. Considering azimuthal inhomogeneity, we have examined the nature of path spin entanglement in the context of Stern-Gerlach experiment.