Emergence of classical rotation in superfluid Bose-Einstein condensates

Abstract

Phase transitions can modify quantum behaviour on mesoscopic scales and give access to new and unusual quantum dynamics. Here we investigate the superfluid properties of a rotating twocomponent Bose-Einstein condensate as a function of changes in the interaction energy and in particular through the phase transition from miscibility to immiscibility. We show that the breaking of one of the hallmarks of superfluid flow, namely the quantisation condition on circulation, is continuous throughout an azimuthal phase separation process and displays intriguing density dynamics. We find that the resulting currents are stable for long times and possess a phase boundary that exhibits classical solid body rotation, despite the quantum nature of superfluid flow. To support this co-existence of classical and quantum behaviour the system develops a unique velocity flow profile, which includes unusual radial flow in regions near the phase boundary.Phase transitions in quantum systems can have a dramatic impact on the quantum mechanical behaviour on mesoscopic scales. Superfluidity in Bose-condensed gases is a mesoscopic manifestation of quantum mechanical effects and one of its hallmarks is the existence of quantised flow around phase singularities as a response to external rotation [1][2][3][4]. However, as the quantisation condition arises from the requirement of the single-valuedness of the wavefunction, an interesting, and less well investigated, generalization appears in superfluids composed of several components. In these systems, due to the interplay of intra-and inter-component interactions, the spinor order parameter can undergo a phase transition that modifies the global symmetry of the system. As the quantisation condition applies to each component independently, the path along which circulation is determined consequently depends on the presence of the other component. This has proven to be particularly striking in toroidally trapped binary mixtures of BECs, where immiscibility can drive a transition to azimuthal phase separation, breaking the requirement of quantised circulation around the toroid [5]. Below we show that this transition is continuous and leads to a phase boundary, which rotates as a classical solid body. While this might seem at first to be incompatible with the quantum nature of superfluid flow, this co-existence can be explained through the presence of a radial flow.In superfluids the circulation around a closed path p is quantised according to p v · dr = n2π /m . Here n is an integer winding number, m the atomic mass, the reduced Planck constant, and the superfluid velocity field, v = ∇θ/m, is completely determined by the gradient of the condensate phase, θ. This implies the velocity field of a vortex has a tangential 1/r velocity profile, in contrast to classical rigid-body rotation, where v = Ω × r. The creation of vortices is a response to external rotation and depends, in particular, on the confining geometry. While in simply connected trapping potentials vortices with higher winding numbers a...

Immiscible and miscible states in binary condensates in the ring geometry

“…The boundary between them, analytically predicted by equation (18), also exactly coincides with the numerically found counterpart, shown by the black curve in figure 2(b). The single-peak demixed modes are completely stable in their existence domain, which is consistent with earlier findings [69].…”

“…Focusing on the phase-separation scenarios, we identify two different types of 2D demixed modes, namely, those which may be defined as demixed in the radial direction (see [67]), and azimuthally demixed ones, see [63,67,68]. In previous works, similar scenarios of the phase separation were also reported for other binary systems, which include rotation [63,69] and spin-orbit coupling [71].…”

“…The 2D setting supports, as well, stable modes which are phase-separated in the azimuthal direction (with zero vorticity) [69,71], an example of such modes can be seen in figure 10 . These modes are related to their 1D counterparts displayed above in the insets of figures 2(b)-(d), and unstable 2D radially-demixed modes transform into them (in an excited oscillating state), see figure 7 .…”

“…These configurations are interesting as they lead to closed geometries with controlled flows, that are also of potential use to the emerging field of atomtronics [58,61]. In this context, mixtures of atomic condensates in toroidal traps and the possibility of sustaining stable persistent currents in them have been previously considered in [62][63][64][65][66][67][68][69][70][71], and the corresponding experimental observation [72] has helped to clarify some issues, also raising new questions, such as expansion of the stability area for such states. The aim of the present work is to perform a full classification of accessible stable mixture states in such a geometry, including examination of their stability and decay channels of their unstable counterparts, both in the where m 1,2 are scaled atomic masses, g 1,2 are coefficients of self-interaction in species f and ψ, and g 0 12 > is the cross-interaction coefficient.…”

Quench induced vortex-bright-soliton formation in binary Bose-Einstein condensates

“…Moreover, both species acquire a non integer angular momentum per particle. We remark here that the merging of the two segments in species B actually changes the rotational properties of the system by leading it to acquire vortices in the periphery of the cloud and thus to rotate in a nearly rigid-body rotation as a result [123,124]. It is also important to stress that the above-described angular momentum transfer among the different species depends on the initially imprinted relative phase difference between the segments of species B.…”