1. BOSE-EINSTEIN CONDENSATES A REVIEW OF EXPERIMENTAL RESULTS
VORTEX STRUCTURES IN
BOSE-EINSTEIN CONDENSATES
A REVIEW OF EXPERIMENTAL RESULTS
R. Srinivasan
Raman Research Institute, Bangalore

2. CONDENSATE WITH A VORTEX
ORDER PARAMETER OF THE CONDENSATE
F(r,t) = n(r,t) exp(i S(r,t)
V = (h/m) grad S ; V = 0
 V dr = (h/m)   S  dr = k (h/m)
k AN INTEGER  0 IMPLIES A
CONDENSATE WITH A VORTEX

3. GENERATION OF VORTICES
1. Rotating a trap containing a thermal cloud and
simultaneously cooling the cloud below TC
2. By stirring a condensate with an optical spoon.
3. By imprinting a phase on the condensate dynamically
or topologically.

4. DETECTION
1. Vortices are detected by ballistically allowing the
condensate to expand and absorption imaging it.
Core diameter increases one order by expansion.
2. Rotation of the condensate detected by measuring
its aspect ratio in a plane containing the axes of
rotation.

5. 3. The angular momentum of the condensate is
measured By measuring the difference in surface
mode frequencies of l =2, m = +2 and m = -2 modes.
P.C. Haljan et al., (2001), PRL, 87,

6. FIRST EXPERIMENTAL PROOF
OF VORTICES
K.W. Madison et al, (2000), PRL 84, 806

7. RESONANT NUCLEATION OF VORTICES BY SURFACE DEFORMATION.
C. Raman et al. (2001), PRL 87,

8. If the vortex is stirred by a narrow optical spoon then
vortices continuously increase above a critical velocity.
GROWTH AND DECAY OF VORTEX LATTICE
a ms e 1 s
b f 5 s
c g. 10 s
d h 40 s
J.R. Abo-shaeer et al., (2001), Science, 292,476

9. Nc/N
0.78 
0.75
0.71
0.62
J.R. Abo-shaeer et al (2002), PRL, 88,

10. NON-EQUILIBRIUM EFFECTS DUE TO COMPRESSION OF A VORTEX LATTICE
No Surface mode Surface mode l = 2, m = Surface mode l = 2, m = +2
No rotation relative Surface deformation rotates at Surface deformation rotates at
to vortex lattice Hz relative to vortex lattice Hz relative to vortex lattice
Engels et al. (2002), PRL, 89,

11. TKACHENKO OSCILLATIONS IN VORTEX LATTICE
I.Coddington et al.
(2003), PRL,

12. TKACHENKO OSCILLATIONS: TRANSITION FROM T-F TO QUANTUM HALL REGIME
V.Schweikhard etal (2004), PRL
040404

13. GIANT VORTICES AT HIGH SPEEDS OF ROTATION
Laser pulse applied for 2.5 s. Hold time in
trap (a) 0.5 s; (b) 10.5 s; (c) 20.5 s; and (d)
30.5 s
Engels et al. (2003), PRL, 90,
170405
Laser on (b) 14 s; (c) 15 s; (d) 20 s; (e) 22s
(f) 23 s; (g) 40 s and (h) 70 s

14. POSSIBLE FUTURE WORK
1.APPROACH TO QUANTUM HALL AND FRACTIONAL
QUANTUM HALL REGIMES
2. GIANT VORTICES : FORMATION AND STABILITY
3. VORTICES IN SPINOR CONDENSATES:
TEXTURE IN VORTICES: SKYRMIONS