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arXiv:1303.4599 · Physical Review A

Matter-wave interference versus spontaneous pattern formation in spinor Bose-Einstein condensates

Marcin Witkowski, R. Gartman, Bartłomiej Nagórny, Marcin Piotrowski, Marcin Płodzień, Krzysztof Sacha, J. Szczepkowski, Jerzy Zachorowski, M. Zawada, Wojciech Gawlik

Published Aug 29, 2013• 3 citations
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Abstract

We describe effects of matter-wave interference of spinor states in the ${}^{87}$Rb Bose-Einstein condensate. The components of the $F=2$ 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 ${m}_{F}$ 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.

DOI
10.1103/physreva.88.025602

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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.
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.
Wave mechanics and interference have always been at the heart of quantum mechanics. Many ofthe most striking quantum effects, at their heart, arise from the wave nature that quantum particles exhibit. In this thesis, I describe two experiments which showcase two different interference effects using a rubidium Bose-Einstein condensate. The first experiment examines the ways geometric phases enter into two-dimensional spin systems by studying their effect on an atomic Ramsey interferometer. The addition of an off-resonantly coupled level causes the location of interference minima to shift on frequency scales comparable to relevant Rabi frequencies of the system, as well as potentially creating locations with increased or decreased sensitivity to magnetic noise. The second experiment is a weak Stern-Gerlach experiment, showing how the components of a superposition state, with different magnetic moments, can interfere to show a greatly increased shift due to a magnetic gradient. The effect is observed using the second-order magnetic sensitivity of the clock states of 87Rb, with a greater than fivefold amplification of the momentum shift created by the magnetic gradient.
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 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.
We study several problems in Bose-Einstein condensates with internal degrees of freedom, and we find that this kind of condensates, which are usually referred to as spinor condensates, exhibit several phenomena that are qualitatively different from scalar (i.e. spinless) condensates. We analyze the ground state of a condensate with the constraint of maintaining a constant value of the total spin, and we find a number of different structures depending on the value of the total spin and the applied external magnetic field. We also study a certain type of measurement on spinor condensates in an attempt to distinguish between the so-called coherent and singlet states. We find that this kind of measurement cannot distinguish between the two states in question. We then consider a different experiment based on the interference between spinor condensate. It turns out that interference experiments cannot be used to distinguish between coherent and singlet states either. One of the interesting results regarding interference between two spinor condensates is that both the offset and visibility of the interference fringes vary from shot to shot, even if the initial conditions are identical in all the runs of the experiment. We then turn to the problem of condensing a gas of effectively spin 1/2 atoms. We argue that if spin relaxation mechanisms are slow enough, the condensate displays the phenomenon of fragmentation. The main difference of the fragmented state that we study and other fragmented states discussed in the literature is that this one is not caused by interatomic interactions, but rather by the constraint on the total spin of the system. We investigate the consequences of performing the experiment in a toroidal trap, and we find that, under certain conditions, the system spontaneously builds up a macroscopic value of orbital angular momentum. We finally discuss several problems related to the external Josephson effect. We derive simple equations of motion for the case of a two-component condensate that are identical to the extensively analyzed Bloch equations. We also find equilibrium points of the motion that are unstable in the spinless case.