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1 BREAKDOWN OF VORTEX-FREE STATE IN BEC BY VORTEX-ANTIVORTEX PAIRS W. V. Pogosov and K. Machida Department of Physics, Okayama University, Japan

2 1. Introduction 2. Stability of the nonvortex state 3. Penetration of topological defects 4. Summary Outlook

3 Introduction London model in Thomas-Fermi regime Disadvantages: -in reality, there is no TF boundary. How vortices nucleate? -strong gradients of the order parameter Linear analysis; surface modes Disadvantage: -No vortices, only stability of axially-symmetric nonvortex state Numerical simulations Disadvantages: -Transition can be very sharp -Artificial boundary for the system

4 The aim of the present work: Where and how vortices nucleate? What is the role of surface modes and Landau instability in vortex nucleation?

5 The energy in dimensionless form: Gas parameter:

6 Method Nonvortex state: Stability of the nonvortex state

8 Normalization condition:

9 Linear analysis around a local minimum The energy: F is diagonal for the vortex-free phase Stability criteria:

10 Landau criterion:

12 Penetration of topological defects In the vicinity of the instability point, the order parameter can be represented as

14 -The same mechanism for vortex penetration is realized for the range of p corresponding to the generation of excitations with l inst = 5

15 Mechanism of vortex nucleation at even l inst (l inst = 4, 6) -Nonvortex axially-symmetric state becomes unstable with respect to the generation of excitations with l inst -With increasing of the rotation frequency, the number of particles condensed in the state with l inst increases. -Just before the formation of l inst vortices, other harmonics of ψ appear: l = 3 for l inst = 6; l = 2 for l inst = 4 at p > 1.5; l = 1 and 2 for l inst = 4 at p < 1.5; -Final state contains l inst /2 or l inst /4 vortices in the inner part of the cloud

16 The case of finite-size cloud Boundary condition -When R b > 2-3 R TF, vortex-antivortex pairs nucleate. With increasing of the rotation frequency, antivortices leave the system. -When R b ~ R TF, vortices penetrate from the edge. No antivortices.

17 3D case -Prediction: vortex loops nucleate instead of vortex-antivortex pairs -Bending of vortices in 3D case was observed in numerical simulations

18 - Topological defects in BEC nucleate via creation of vortex-antivortex pairs (2D) or vortex loops (3D). Vortices move to the inner part of the cloud and antivortices – in the opposite direction. - Vortices penetrate just above the Landau instability. This supports Anglins scenario (PRL 2001) - Vortex state in infinite BEC always consists of vortices and antivortices. Total topological charge is zero. Summary

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