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arXiv:1011.4642 · Physical Review A

Spatial Landau-Zener-Stückelberg interference in spinor Bose-Einstein condensates

Jun-Song Zhang, C. P. Sun, S. Yi, Franco Nori

Published Mar 16, 2011• 24 citations
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Abstract

We investigate the St\"uckelberg oscillations of a spin-1 Bose-Einstein condensate subject to a spatially inhomogeneous transverse magnetic field and a periodic longitudinal field. We show that the time-domain St\"uckelberg oscillations result in modulations in the density profiles of all spin components due to the spatial inhomogeneity of the transverse field. This phenomenon represents the Landau-Zener-St\"uckelberg interference in the space domain. Since the magnetic dipole-dipole interaction between spin-1 atoms induces an inhomogeneous effective magnetic field, interference fringes also appear if a dipolar spinor condensate is driven periodically. We also point out some potential applications of this spatial Landau-Zener-St\"ukelberg interference.

DOI
10.1103/physreva.83.033614

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We investigate the St"uckelberg oscillations of a spin-1 Bose-Einstein condensate subject to a spatially inhomogeneous transverse magnetic field and a periodic longitudinal field. We show that the time-domain St"uckelberg oscillations result in modulations in the density profiles of all spin components due to the spatial inhomogeneity of the transverse field. This phenomenon represents the Landau-Zener-St"uckelberg interference in the space domain. Since the magnetic dipole-dipole interaction between spin-1 atoms induces an inhomogeneous effective magnetic field, interference fringes also appear if a dipolar spinor condensate is driven periodically. We also point out some potential applications of this spatial Landau-Zener-St"ukelberg interference.
In BECs, collisions between condensate atoms give rise to a nonlinear contribution to the dynamics which is typically included as a mean-field term in the Schrodinger equation. This nonlinearity leads to a modification of well-known effects associated with matter waves in periodic potentials and adds a number of phenomena that are absent in the linear problem. We focused on the dynamics of a BEC in an accelerated optical lattice. In the linear case, this gives rise to Bloch oscillations and, above a critical acceleration, to Landau-Zener tunneling. In the nonlinear case, the probability for Landau-Zener tunneling is modified depending on the direction in which it occurs between two bands. By varying the acceleration of the optical lattice and measuring the time-dependence of the interference contrast, we were able to identify the instability regime and the characteristic time in which the dynamical instability destroys the interference pattern. Furthermore, we observed an increase in the condensate dimensions perpendicular to the lattice direction when the unstable region was reached. This indicates a mechanism whereby the longitudinal instability leads to an increase in the transverse release energy
We report the formation of spin texture resulting from the magnetic dipole-dipole interaction in a spin-2 87Rb Bose-Einstein condensate. The spinor condensate is prepared in the transversely polarized spin state and the time evolution is observed under a magnetic field of 90 mG with a gradient of 3 mG/cm using Stern-Gerlach imaging. The experimental results are compared with numerical simulations of the Gross-Pitaevskii equation, which reveals that the observed spatial modulation of the longitudinal magnetization is due to the spin precession in an effective magnetic field produced by the dipole-dipole interaction. These results show that the dipole-dipole interaction has considerable effects even on spinor condensates of alkali metal atoms.
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.
The interference between a sequence of Landau-Zener (LZ) transitions can produce Rabi oscillations (LZROs). This phenomenon is a kind of time-domain Landau-Zener-St\"uckelberg-Majorana (LZSM) interference. However, experimental demonstrations of this LZSM interference induced Rabi oscillation are extremely hard due to the short coherence time of the driven quantum system. Here, we study theoretically the time-domain LZSM interference between the clock transition in a one-dimensional 87Sr^{87}\mathrm{Sr}87Sr optical lattice clock (OLC) system. With the help of both the adiabatic-impulse model and Floquet numerical simulation method, the LZROs with special steplike structure are clearly found both in the fast- and slow-passage limit in the real experiment parameter regions. In addition, the dephasing effect caused by the system temperature can be suppressed with destructive interference in the slow-passage limit. Finally, we discuss the possible Bloch-Siegert shift while the pulse time is away from the half-integer and integer periods. Our work provides a clear road map to observe the LZROs on the OLC platform.
With current magnetic-field shielding and high-precision detection in dipolar spinor Bose-Einstein condensates, it is possible to experimentally detect the low- or zero-field nonsecular dipolar dynamics. Here we analytically investigate the zero-field nonsecular magnetic dipolar interaction effect, with an emphasis on magnetization dynamics in a spin-1 Bose-Einstein condensate under the single spatial mode approximation within the mean-field theory. Due to the biaxial nature of the dipolar interaction, a novel resonance occurs in the condensate magnetization oscillation, in contrast to the previous assumption of a conserved magnetization in strong magnetic fields. Furthermore, we propose a dynamical-decoupling detection method for such a resonance, which cancels the stray magnetic fields in experiment but restores the magnetization dynamics. Our results shed light on the dipolar systems and may find potential applications beyond cold atoms.