1. Matter-wave droplets in a dipolar Bose-Einstein condensate
ADVANCES IN MATHEMATICAL MODELLING AND NUMERICAL SIMULATION OF SUPERFLUIDS
Matter-wave droplets in
a dipolar Bose-Einstein condensate
Univ. of Electro-Communications, Tokyo
Hiroki Saito

2. Collaborator Kui-Tian Xi Supported by Ohio State Univ. (-2015
Beijing National Lab. for
Condensed Matter Physics)
Supported by
・ Grant-in-Aid for Scientific Research (C)
・ Innovation Areas of Fluctuation & Structure

3. Contents Recent experiments of strong dipolar BEC
Quantum many-body effects
Three-body repulsive interaction

4. Recent experiments of
strong dipolar BEC

5. BEC with dipole-dipole interaction (DDI)S N S N S
repulsive
attractive N S
DDI is anisotropic and long-range

6. 164Dy Quench of scattering length Dipolar instability
Nature 530, 194 (2016)
164Dy
Quench of scattering length
Dipolar instability
Droplet formation

7. More droplets for more atoms
Nature 530, 194 (2016)
Stable droplets
More droplets for more atoms
~1000 atoms in each droplet
Triangular lattice of droplets

8. Nature 530, 194 (2016)
number of droplets
∝ number of atoms

9. Nature 530, 194 (2016)

10. Nature 530, 259 (2016)
Self-bound
droplet
3-body loss
“evapolation”
of droplet

11. 166Er
Collapse is suppressed

12. Gross-Pitaevskii equation with DDI
harmonic potential
dipole-dipole interaction
s-wave repulsion

13. Gross-Pitaevskii equation with DDI
Numerical simulation
Collapse always occurs for
collapse of 52Cr BEC
Lahaye et al., PRL 101, (2008)
However, collapse does not occur in these experiments.
Why?

14. Quantum many-body effect on droplet stabilization

15. Quantum many-body effect
F. Wachtler and L. Santos, PRA 93, R (2016)
Lee-Huang-Yang correction
Lee-Huang-Yang corrected GP equation

16. Stable droplets by GP eq. with LHY
F. Wachtler and L. Santos, PRA 93, R (2016)
experiment

17. Direct many-body simulation
Path-integral Monte Carlo method
Probability of configuration
Numbef of atoms = 1024
Numbef of slices =

18. Non-interacting part
Hard-sphere part
DDI part

19. Ground and metastable states
H. Saito, J. Phys. Soc. Jpn. 85, (2016)
Mean-field theory
is well reproduced
DDI is correctly included
in PIMC

20. Stable droplet state
H. Saito, J. Phys. Soc. Jpn. 85, (2016)
diverges at r = 0 and
cutoff at Rcutoff. M
Collapse is suppressed by quantum many-body effect.

21. Droplet lattice by PIMC
Droplet lattice obtained by path integral Monte Carlo method
A. Macia, J. Sánchez-Baena, J. Boronat, and F. Mazzanti, PRL 117, (2016)

22. Recent experiment arXiv:1708.07806 39K Two-component
self-bound droplet

23. Another possibility:
3-body repulsion

24. If 3-body repulsion exists…
Dipole interaction
3-body interaction
Collapse can be stopped
K. -T. Xi and HS, PRA 93, (R) (2016)
R. N. Bisset and P. B. Blakie, PRA 92, (R) (2015)

25. GP eq. with 3-body interaction
K. -T. Xi and HS, PRA 93, (R) (2016) y z x x

26. Cigar-shaped stable droplets
K. -T. Xi and HS, PRA 93, (R) (2016)
R. N. Bisset and P. B. Blakie, PRA 92, (R) (2015)

27. Triangular lattice of droplets
experiment
K. -T. Xi and HS, PRA 93, (R) (2016)

28. N-dependence of droplet number
Our result
Experiment

29. Long-time behavior
Our result
Experiment

30. Measurement of L3? arXiv:1509.06844 85Rb cf. for 164Dy, we used
By comparing oscillation with GP eq…..
85Rb
cf. for 164Dy, we used

31. Summary Stable droplets of strong dipolar BECs
were observed in recent experiments.
However, simple GP eq. with DDI cannot reproduce it.
GP eq. with LHY correction was proposed by Wachtler et al., which can reproduce the experiments.
Direct quantum many-body calculation (PIMC) support this model.
H. Saito, J. Phys. Soc. Jpn. 85, (2016)
Another possibility may be 3-body repulsion.
K. -T. Xi and HS, PRA 93, (R) (2016)

34. Variational analysis In a harmonic trap z A collapse B energy barrier
droplet state

36. Hysteresis