Dynamical Instability of a Doubly Quantized Vortex in a Bose-Einstein Condensate

Abstract

Doubly quantized vortices were topologically imprinted in |F = 1 23 Na condensates, and their time evolution was observed using a tomographic imaging technique. The decay into two singly quantized vortices was characterized and attributed to dynamical instability. The time scale of the splitting process was found to be longer at higher atom density.PACS numbers: 03.75. Kk, 03.75.Lm, 67.90.+z Quantum fluids, like superfluid He, electrons in a superconductor or a Bose-Einstein condensate of atoms, are described by a macroscopic wavefunction. This requires the flow field to be irrotational, and gives rise to superfluidity and quantized circulation [1]. Atoms in a BoseEinstein condensate, for example, can only circulate with angular momentum equal to integer multiple ofh, in the form of a quantized vortex [2].Vortices are excited states of motion and therefore energetically unstable towards relaxation into the motional ground state, where the condensate is at rest. However, quantization constrains the decay: a vortex in BoseEinstein condensates cannot simply fade away or disappear, it is only allowed to move out of the condensate or annihilate with another vortex of opposite circulation. Vortex decay and metastability, due to inhibition of decay, have been a central issue in the study of superfluidity [3,4,5,6,7,8]. In almost pure Bose-Einstein condensates, vortices with lifetimes up to tens of seconds have been observed [9,10,11].Giving a Bose-Einstein condensate angular momentum per particle larger thanh can result in one multiplyquantized vortex with large circulation or, alternatively, in many singly-quantized vortices each with angular momentumh. The kinetic energy of atoms circulating around the vortex is proportional to the square of the angular momentum; therefore the kinetic energy associated with the presence of a multiply-quantized vortex is larger than the kinetic energy of a collection of singlyquantized vortices carrying the same angular momentum. A multiply-quantized vortex can decay coherently by splitting into singly-quantized vortices and transferring the kinetic energy to coherent excitation modes, a phenomenon called dynamical instability which is driven by atomic interactions [5,12,13,14], and not caused by dissipation in an external bath. Observations of arrays of singly-quantized vortices in rapidly rotating condensates [10,11] indirectly suggests that the dynamical instability leads to fast decay of multiply-quantized vortices. However, the existence of stable multiply-quantized vortices in trapped Bose-Einstein condensates has been predicted with a localized pinning potential [12] or in a quartic potential [15]. Stable doubly-quantized vortices were observed in superconductors in presence of pinning forces [16] and in superfluid 3 He-A which has a multicomponent order parameter [17]. Recently, formation of a multiply-quantized vortex in a Bose-Einstein condensate has been demonstrated using topological phases [18,19], and surprisingly long lifetime of a "giant" vortex core has been report...

Vortices in Polariton OPO Superfluids

“…In particular, it has been established that the nature of the splitting is the dynamical instability. Nevertheless, m = 2 vortices have been predicted to be stable for specific ranges of density and interaction strength [92,93], though, so far, they have not been observed experimentally [94]. As for single vortices, multiply quantised vortices can be however stabilised in multiply connected geometry.…”

Is a Doubly Quantized Vortex Dynamically Unstable in Uniform Superfluids?

“…The realization of MQV in the BECs of ultra-cold gases sheds light on this problem, and vortex splitting has been observed. [7][8][9] The MQV in trapped systems can be dynamically unstable, and split into vortices with smaller winding numbers according to the Bogoliubovde Gennes (BdG) analysis at zero temperature. [10][11][12][13][14][15][16][17] Dynamic instability may occur when the excitation modes have complex frequencies as a result of coupling or "mixing" between two modes with positive and negative excitation energies.…”

Stabilization and Pumping of Giant Vortices in Dilute Bose–Einstein Condensates

“…(5)]. In the case of a multiquantum vortex, dynamical instability typically signifies that the vortex is unstable against splitting into singly quantized vortices [24][25][26][27][28][29][30][31].…”

“…Although this result is generally true only in an infinite homogeneous system, it still holds in finite-sized BECs for a majority of trap geometries and particle numbers. Being able to create vortices with large winding numbers would provide access to novel vortex-splitting patterns beyond the typical linear chain that prevails in the decay of two-and four-quantum vortices [25,28]. Because of the distinct nature of the different splitting patterns predicted for highly quantized vortices [30], observing the decay of such states would enable a lucid comparison between theory and experiment.…”

“…However, a serious challenge is posed by the dynamical instability of the giant vortices that becomes more pronounced as the vorticity increases [20,23]. Dynamical instabilities can lead to dissociation of the vortex even in the absence of dissipation [24][25][26][27][28][29][30][31], and therefore their effect cannot be disposed of by reducing temperature.…”