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

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

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

Recent experiments of strong dipolar BEC

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

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

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

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

Nature 530, 194 (2016)

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

166Er Collapse is suppressed

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

Gross-Pitaevskii equation with DDI Numerical simulation Collapse always occurs for collapse of 52Cr BEC Lahaye et al., PRL 101, 080401 (2008) However, collapse does not occur in these experiments. Why?

Quantum many-body effect on droplet stabilization

Quantum many-body effect F. Wachtler and L. Santos, PRA 93, 061603R (2016) Lee-Huang-Yang correction Lee-Huang-Yang corrected GP equation

Stable droplets by GP eq. with LHY F. Wachtler and L. Santos, PRA 93, 061603R (2016) experiment

Direct many-body simulation Path-integral Monte Carlo method Probability of configuration Numbef of atoms = 1024 Numbef of slices = 256 - 2048

Non-interacting part Hard-sphere part DDI part

Ground and metastable states H. Saito, J. Phys. Soc. Jpn. 85, 053001 (2016) Mean-field theory is well reproduced DDI is correctly included in PIMC

Stable droplet state H. Saito, J. Phys. Soc. Jpn. 85, 053001 (2016) diverges at r = 0 and cutoff at Rcutoff. M Collapse is suppressed by quantum many-body effect.

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, 205301 (2016)

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

Another possibility: 3-body repulsion

If 3-body repulsion exists… Dipole interaction 3-body interaction Collapse can be stopped K. -T. Xi and HS, PRA 93, 011604(R) (2016) R. N. Bisset and P. B. Blakie, PRA 92, 061603(R) (2015)

GP eq. with 3-body interaction K. -T. Xi and HS, PRA 93, 011604(R) (2016) y z x x

Cigar-shaped stable droplets K. -T. Xi and HS, PRA 93, 011604(R) (2016) R. N. Bisset and P. B. Blakie, PRA 92, 061603(R) (2015)

Triangular lattice of droplets experiment K. -T. Xi and HS, PRA 93, 011604(R) (2016)

N-dependence of droplet number Our result Experiment

Long-time behavior Our result Experiment

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

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, 053001 (2016) Another possibility may be 3-body repulsion. K. -T. Xi and HS, PRA 93, 011604(R) (2016)

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

Hysteresis