Spin domains in ground-state Bose–Einstein condensates

Abstract

Bose-Einstein condensates of dilute atomic gases, characterized by a macroscopic population of the quantum mechanical ground state, are a new, weakly interacting quantum fluid [1,2,3]. In most experiments condensates in a single weak field seeking state are magnetically trapped. These condensates can be described by a scalar order parameter similar to the spinless superfluid 4 He. Even though alkali atoms have angular momentum, the spin orientation is not a degree of freedom because spin flips lead to untrapped states and are therefore a loss process. In contrast, the recently realized optical trap for sodium condensates [4] confines atoms independently of their spin orientation. This opens the possibility to study spinor condensates which represent a system with a vector order parameter instead of a scalar. Here we report a study of the equilibrium state of spinor condensates in an optical trap. The freedom of spin orientation leads to the formation of spin domains in an external magnetic field. The structure of these domains are illustrated in spin domain diagrams. Combinations of both miscible and immiscible spin components were realized.A variety of new phenomena is predicted [5,6,7] for spinor condensates, such as spin textures, propagation of spin waves and coupling between superfluid flow and atomic spin. To date such effects could only be studied in superfluid 3 He, which can be described by Bose-Einstein condensation of Cooper pairs of quasi particles having both spin and orbital angular momentum [8]. Compared to the strongly interacting 3 He, the properties of weakly interacting BoseEinstein condensates of alkali gases can be calculated by mean field theories in a much more straightforward and simple way.Other systems which go beyond the description with a single scalar order parameter are condensates of two different hyperfine states of 87 Rb confined in magnetic traps. Recent experimental studies have explored the spatial separation of the two components [9,10] and their relative phase [11]. Several theoretical papers describe their structure [12,13,14,15,16,17,18] and their collective excitations [19,20,21,22].Compared to these two-component condensates, spinor condensates have several new features including the vector character of the order parameter and the changed role of spin relaxation collisions which allow for population exchange among hyperfine states without trap loss. In contrast, for 87 Rb experiments trap loss due to spin relaxation severely limits the lifetime.We consider an F = 1 spinor condensate subject to spin relaxation, in which two m F = 0 atoms can collide and produce an m F = +1 and an m F = −1 atom and vice versa. We investigate the distribution of hyperfine states and the spatial distribution in equilibrium assuming conservation of the total spin. The ground state spinor wave function is found by minimizing the free energy [5]where kinetic energy terms are neglected in the ThomasFermi approximation which is valid as long as the dimension of spin domains (typically 50 µm) is ...

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 .…”

“…The experiment uses spin-1 atomic Bose condensates 6,18,19 with ferromagnetic interactions tightly confined in optical traps such that spin domain formation is energetically suppressed. In this case, the non-trivial dynamical evolution of the system occurs only in the internal spin variables, and the mean-field dynamics of the system can be described by a non-rigid pendulum similar to the two-site Bose-Hubbard model 20,21 .…”

Vortices in a trapped dilute Bose-Einstein condensate

“…In oblate traps with ω z ≫ ω ⊥ , however, the spin-gauge effect can be significant (Ω s could be comparable with ω ⊥ for large enough values of ω z ). Recently, the MIT group has succeeded in trapping a 23 Na Bose condensate by purely optical means [158,159]. In contrast to a magnetic trap, the spins of the alkali atoms in such an optical trap are essentially free, so that the spinor nature of the alkali Bose condensate can be fully realized.…”

Spinor Condensates and Light Scattering from Bose-Einstein Condensates

“…In three different experiments we explored the ground-state spin structure of spinor condensates in external magnetic fields [97], the formation and persistence of metastable spin domain configurations [98], and the transport across spin domain boundaries by quantum tunneling [99]. In this section, we summarize our current understanding of this fluid as derived from our experiments and from a growing number of theoretical works.…”