Seeing zeros of random polynomials: quantized vortices in the ideal Bose gas

Yvan Castin (1) , Zoran Hadzibabic (1) , Sabine Stock (1) , Jean Dalibard (1) , Sandro Stringari (1, 2)

1 LKB (Lhomond) - Laboratoire Kastler Brossel
2 CNR-INFM BEC Center

We propose a physical system allowing one to experimentally observe the distribution of the complex zeros of a random polynomial. We consider a degenerate, rotating, quasi-ideal atomic Bose gas prepared in the lowest Landau level. Thermal fluctuations provide the randomness of the bosonic field and of the locations of the vortex cores. These vortices can be mapped to zeros of random polynomials, and observed in the density profile of the gas.

Mots clés: Bose-Einstein condensates; quantum vortices; lowest Landau level; random polynomials

Domaines: Autre [cond-mat.other]; Dynamique Chaotique [nlin.CD]

Yvan Castin, Zoran Hadzibabic, Sabine Stock, Jean Dalibard, Sandro Stringari. Seeing zeros of random polynomials: quantized vortices in the ideal Bose gas. Physical Review Letters, 2006, 96, pp.040405. ⟨hal-00013658⟩