1. Production and control of KRb molecules Exploring quantum magnetisms with ultra-cold molecules

2. Strong dipolar interactions: Long range and anisotropic Controllable by electromagnetic fields Why polar molecules?? Polar molecules JILA: Currently only laboratory in the world with a quantum dipolar gas in a lattice Many to come: Innsbruck, JQI, MIT, Columbia, Amsterdam, Kyoto…

3. Atom vs. molecule T = 100 nK N = 10 6 atoms n = 10 13 cm -3 Bose-Einstein Condensation 1995 Molecules (pre-2008): T = 100 mK, n = 10 6 cm -3

4. Molecules are complex! 0.1 K 38 μK 6000 K 10 orders of magnitude 10 10 10 8 10 5 10 2 1 200 nK vibration binding energy rotation hyperfine translation 1 μK trap depth 100 K

5. KRb, LiCs, RbCs, NaK, LiNa, LiRb, RbSr, RbYb and LiYb Two paths to ultra-cold molecules Stark deceleration Buffer-gas cooling Laser cooling? Polarization cooling? Sympathetic cooling? Evaporative cooling? SrF YO BrO CH NO OH CH 3 F

6. KRb molecules (Dipole ~0.5 Debye) K. Ni et al., Science 322, 231 (2008). Nature Phys. 4, 622 (2008) Science 322, 231 (2008) 40 K Fermions 87 Rb Bosons K. Ni et al., Science 322, 231 (2008). KRb molecules Ro-vibrational ground state  T/T F ~ 1  Density ~10 12 /cm 3 (Dipole ~0.5 Debye) 10 5 times colder, 10 6 times more dense than other results for polar molecules! Light provides the answer Photons carry away the energy!

7. Start with ultracold atoms. 40 K 87 Rb K-Rb Feshbach resonance Make large, floppy molecules Convert a pair of atoms into a molecule Control the interactions. Coherent two-photon transfer 11 22 33 11 33 11 Inter-nuclear distance R Energy v = 0, N = 0, J = 0 6000 K

12. Pauli Exclusion principle (2) Angular momentum is quantized: Ultra cold atoms collide via the lowest partial waves (3) Quantum statistics matter Identical fermions  anti- symmetric spatial wave function  p-wave (1) Particles behave like waves (T → 0) s-wave, l=0, Spatially symmetric p-wave, l=1 Spatially anti- symmetric R Centrifugal barrier

13. KRb+ KRb  K 2 +Rb 2 + Ultracold chemistry At low T, the quantum statistics of fermionic molecules suppresses chemical reaction rate! Energy distance between the molecules quantum Ospelkaus et al., Science 327, 853 (2010).

14. Temp. (  K) β (p-wave) ∝ T β (s-wave) 24K

15. -1.5 kV +1.5 kV E = 0 (no induced dipoles)  p-wave suppression Dipolar interaction “turns on” collisions - anisotopic, long range K.-K. Ni et al., Nature 464, 1324 (2010).

16. Rigid Rotor N=0 ~GHz N=1 E=0 Increasing E |1,-1  |1,0  |1,1  |0,0  Electric field mixes rotational states but preserves M N projection |↓|↓ |↑|↑ E induces a dipole moment

17. R E Attract Repel Virtual exchange of photons |1,-1  |1,0  |1,1  |0,0  |1,-1  |1,0  |1,1  |0,0  i j plane

18. Collisions in 3D space average over different channels. m L = +1, -1 m L = 0 p-wave barrier E

19. ~ d 6 (Attractive dipole dipole interaction) miliseconds lifetime

20. Possibility of observing quantum magnetism even at current conditions: PRL 110, 075301 (2013) 3D Trap Lifetime Trapping miliseconds Low density: filling 0.1 PRL 108, 080405 (2012) Pancakes: 2Dseconds Nature Phys. 7, 502 (2011) E 3D lattice Up to 25 s Tubes: 1D seconds

21. PRL.107.115301(2011), PRA 84,033619 (2011)  Use direct dipole-dipole interaction to generate direct strong spin-spin interactions:  Spin temperature, not motional temperature matters: Decoupling between motional and spin degrees of freedom Long range spin-spin interactions even in frozen molecules

22. Project on the two selected rotational levels Two rotational states chosen to encode spin 1/2 ~ GHz N=1 |1,-1  |1,0  |1,1  N=0 |0,0  |↑|↑ |↓|↓ |↑|↑ ~ ~ ~ ~ ~ ~ Reduced by a factor of two!!

23. Non-trivial dependence on the geometry due to the anisotropic dipolar interactions. V 0j Nature 501, 521 (2013). Current experiments are carried out in a 3D lattice with a B field Use rotational state choice to control interaction strength

24. V  : p-wave int U  : s-wave int x y z V  : p-wave int U  : s-wave int Prepare all down and then apply a microwave pulse No dynamics No interactions Interactions introduce correlations?  # of ↑ Measure

25.  Measure # of e particles  e-atoms B=2  L     Detuning Contrast Ramsey spectroscopy: a quench Prepare Evolve T Measure Phase

26. Ramsey fringe: C(T) cos  )T] Contrast Phase   controlled by first pulse Spin precesses with a modified rate which depends on molecule number. No mean field dynamics at  x y z B eff j

27. Nature 501, 521 (2013).

28. Wahuha + echo echo Learn from NMR: By applying the proper pulse sequence it is possible to eliminate dipolar interactions. Pulse scheme for KRb Non-magic trap

29. Need to compare to theory, but looks impossible Strongly interacting and non-equilibrium disordered system Long-range interactions, 3D [ 10 4 particles talking to each other] Mean field prediction: nothing happens! We came up with a way: Improved cluster expansion MACE arXiv: K. Hazzard et al 1402.2354

30. Used before Spins grouped in cluster of max size g. Intra-cluster interactions kept and solved exactly Inter-cluster interactions neglected. g=4 Ours: MACE “Moving Average Cluster Expansion”

31. Contrast Exact solution XX oscillates more

32. Akjdfklsajdlkf; arXiv: K. Hazzad et al 1402.2354 With only one fitting parameter to determine the density we are able to reproduce the experiment Quantum simulation Theory Improves Experiment Improves Theory (MACE) Experiment Contrast 1 0 0.5 1 0 |1,-1  |1,0  |1,-1  |1,0 

33. Hyperfine levels E field + microwaves Other molecules

34. Theory: Jun Ye S. Syzranov, A. Gorshkov, M. Foss-Feig, S. Manmana, M. Lukin, P. Julienne K. Hazzard, M. Wall, A. Koller, B. Zhu, A. Pirovski, S. Li, J. Schachenmayer D. Jin B. Gadway B. Yan J. Covey S. Moses KRb team:

35. Review Material G. Quéméner and P. S. Julienne, Ultracold molecules under control, Chemical Reviews. 112(9), 4949–5011, (2012). M. L. Wall, K. R. A. Hazzard, A. M. Rey Quantum magnetism with ultracold molecules, arXiv:1406.4758. L. D. Carr, D. Demille, R. V. Krems, and J. Ye, Cold and ultracold molecules: Science, technology, and applications, New J. Phys. 11, 055049, (2009).