towards Ultracold Chromium a dipolar quantum gas Tilman

towards Ultracold Chromium a dipolar quantum gas Tilman Pfau University of Stuttgart

History of BEC Rb 1995 11 Na 1995 3 Li 1997 1 H 1998 1 10 1 3 5 2 1 1 1 2001 1 1 Cs 2002 1 Yb 2003 Cr 2004 1 1 He* 2001 K 3 1 1 1 Stuttgart, 25. Nov 12004 1

Chromium • No HFS • High magnetic moment 6 m. B Yb 70

Why bother?

Contact and Long Range Interaction in Quantum gases Contact interaction • isotropic • short range Dipolar interaction • anisotropic • long range z r nonlinear matter wave optics strong correlations: Bose-Hubbard. . . stability and ground state of BEC magnetism: Heisenberg, Ising, frustrated lattices. . .

Dipolar coupling in fluids Ferrofluids ~ 2 -20 nm Application: rotary seals in disk drives dampers for audio speakers

Dipolar coupling in gases? solid n ~1023/cm 3 Tc~ 1 K (Texc ~ 100 -1000 K) air n ~1019/cm 3 Tc~ 0. 1 m. K ultracold gas n ~1014/cm 3 Tc~ 1 n. K magnetic dipoles n <<1021/cm 3 Weak interaction: electric dipoles n <<109/cm 3

How strong is the dipolar interaction? dipole strength (tunable) compare to contact interaction: scattering length (tunable) atoms m Cr Rb Na edd=0. 15 edd=0. 007 edd=0. 003 magnetic dipoles heteronuclear molecules Rydberg atoms d e. g. : Ca. H, NH 3, Cr. Rb edd~100 e. g. : Rb (n=40) edd~108 electric dipoles

How to tame Chromium 4 stable isotopes: Bosons Fermion 52 Cr 50 Cr 54 Cr 53 Cr 83. 8% 4. 3% 2. 4% 9. 5%

Preparation of an ultracold Cr sample: • Continously loaded Ioffe Pritchard trap (CLIP-trap) J. Stuhler, et al. , Phys. Rev. A 64, 031405 (2001) P. O. Schmidt, et al. , J. Opt. B 5, S 170 (2003) • Compress IP-trap • Doppler cooling in the IP-trap at high offset field P. O. Schmidt, et al. , J. Opt. Soc. Am. B 20, 5 (2003) 2 x 108 atoms in the ground state phase space density r~10 -7 • Temperature is adjusted by evaporation

Evaporation in crossed trap BEC r~0. 5

Cr BEC T>Tc T<Tc tof 0… 13 msec T<Tc

T<Tc time of flight

Phase transition tof = 5 msec Decreasing T

Critical behaviour Condensate fraction ideal gas corr. for finite size and weak interaction exp. Tc~700 n. K nx=581 Hz ny=406 Hz nz=138 Hz

Lifetime and condensate formation t~ 6 sec n 0 i= 2 1014 cm-3 t~400 msec n 0 i= 2 1015 cm-3 Rb F=2, m. F=2 L 3 = 1. 8 10− 29 cm 6 s− 1 J. Söding et al. APB, 69, 257 (1999) Cr S=3, m. S=-3 L 3 < 1 10− 29 cm 6 s− 1

Dipolar interaction as perturbation • isotropic harmonic trap BEC without dipoles perturbation by dipole interaction: • Thomas –Fermi limit parabolic density profile n. TF(r) 2 RTF Fdd(r)

Dipolar interaction and the aspect ratio cf. anisotropic trap + contact interaction no dipoles Isotropic trap: + contact interaction + dipolar interaction in trap time of flight S. Giovanazzi, A. Görlitz, T. P. J. Opt. B 5, 208 (2003) no inversion !

Preliminary data on dipolar expansion 31 measurements aspect ratio ry/rz Theory with no free parameters S. Giovanazzi L. Santos P. Pedri y z nx=942 Hz ny=712 Hz nz=128 Hz time of flight [ms]

equations

Tuning the dipolar interaction spinning polarization z r [-1/2, 1]

Magic angle spinning in solid state NMR Random example: Solid sample Broadening by dipolar coupling

Stability diagram e. DD = 4 cigar trap shape pancake S. Giovanazzi, A. Görlitz, T. P. Phys. Rev. Lett. 89, 130401 (2002) magic angle 54. 7° K. Góral, K. Rzazewski, T. P. ; PRA, 61, 051601 (R) (2000) L. Santos, et al. ; PRL 85, 1791(2000)

How to tune a closed channel coupling open channel

Feshbach resonances I Quantum numbers - notation atomic electrons s, l molecular electrons S, L closed channel coupling molecular nuclei open channel

Feshbach resonances II Ab initio potentials S=2 S=4 model potentials S=6 Cr 2 from: Z. Pavlovic, B. O. Roos, R. Côté, and H. R. Sadeghpour Phys. Rev. A 69, 030701 (2004) Variational parameters: C 6, C 8, a Sensitive to last bound states

Feshbach resonances III model potentials Variational parameters: C 6, C 8, a Sensitive to last bound states plus centrifugal potentials (e. g. )

closed channel Selection rules Possible couplings: 2 nd order coupling open channel Spin - Orbit Spin - Spin Selection rules: first order not allowed! second order Momentum conservation:

S=6 MS -2 -3 -4 -5 -6 g - wave d - wave -4 -5 -6 X S=2 S=4 MS -2 -3 -4 MS 0 -1 -2 -2 -3 -4 X s - wave -4 -5 -6 initial state (open channel) first order second order 3 resonances 8 resonances

Our resonances (observed by losses) individual calibration by RF

Comparison exp vs. theory Theory: A. Simoni E. Tiesinga NIST Deviation exp-theo 0. 6 G

What do we now about Chromium know? S=2 S=4 S=6 a 6= 112(14) a 0 a 4= 58(6) a 0 a 2= -7(20) a 0 C 6=733(70)a. u. C 8=75(+90/-75)a. u.

Outlook for a dipolar BEC Play the dipolar game n expansion of a dipolar gas n Collective excitations n stability of a dipolar condensate L. Santos et al. , PRL 85(9): 1791, 2000 n dipolar order H. Pu et al. , PRL, 87: 140405, 2001 n macroscopic spin tunneling H. Pu et al. , PRL 89: 0904001, 2002 n roton in the dispersion relation L. Santos et al. , Phys. Rev. Lett. 90, 250403 (2003)

Further outlook Trap fermion Lithography: I. Averbukh controlled single atom deposition? cw atom laser ?

The dragon tamers S. Hensler A. Griesmaier T. Koch M. Fattori Former members: J. Werner P. O. Schmidt A. Görlitz J. Stuhler ph. D students and postdocs wanted! Theory: K. Rzazewski S. Giovanazzi A. Simoni E. Tiesinga P. Pedri L. Santos