How to Observe Dipolar Effects in Spinor Bose-Einstein Condensates

Abstract

We propose an experiment which proves the possibility of spinning gaseous media via dipolar interactions in the spirit of the famous Einstein-de Haas effect for ferromagnets. The main idea is to utilize resonances we find in spinor condensates of alkali atoms while these systems are placed in an oscillating magnetic field. A significant transfer of angular momentum from spin to motional degrees of freedom observed on resonance is a spectacular manifestation of dipolar effects in spinor condensates.Historically, first attempts at proving the relationship between magnetism and angular momentum (i.e., the Ampère's hypothesis on "molecular currents") were already performed in the 19th century [1]. They were all unsuccessful because of difficulties in measuring the tiny forces involved in the process. The efforts continued in the beginning of 20th century resulted in the emergence of a new class of effects named as magnetomechanical. The most known is certainly the Einstein-de Haas effect [2] in which a magnetized ferromagnetic rod is forced to rotate when its magnetization is reversed. In the experiment the magnetomechanical ratio is measured and its value can be directly related to the motion of electrons in the rod. It tells us how large a portion of magnetization comes from the spin of electrons and how large from the orbital motion of electrons.Experiments with neutral "molecular currents" would be of particular interest in proving the direct and sole relation between the spin and the magnetization of the system. The recent realization of chromium condensates [3] has launched huge interest in ultracold dipolar systems [4,5] which would be an ideal candidate for such studies. Although spectacular features due to dipolar forces related to expansion [6] and collapse [7] were already observed, the Einstein-de Haas effect so far remains elusive. A route towards observing the Einstein-de Haas effect in chromium condensates via controlling the magnetic field was recently suggested [8,9] and first experiments demonstrated the possibility to control the dipolar relaxation rate in this way [10].It is tempting to test these concepts also in alkali systems which represent the majority of experiments. It is certainly less obvious that alkali atoms (whose magnetic dipole moment is an order of magnitude lower than that of chromium atoms) might be a good candidate to observe how spin is transmitted into orbital motion. However, some authors suggested that the magnetic dipolar interactions could already lead to observable effects in condensates of alkali atoms [9,[11][12][13][14][15][16][17]. Also a first experiment showed that a spin-1 87 Rb spinor condensate can exhibit dipolar properties [18].In this Letter we demonstrate that controlling the dipolar interactions by using an oscillating magnetic field is a perfect way to observe the Eintein-de Haas effect in alkali condensates provided it is done under a resonance condition. In the following we explain our reasoning in detail.The equation of motion for a spinor condensate in t...

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