Ultracold Chromium a dipolar quantum gas Quantum Optyks

Ultracold Chromium a dipolar quantum gas Quantum Optyks VI, Krynica 16. 6. 05 Tilman Pfau University of Stuttgart

Interacting quantum systems in atomic physics contact interaction van der Waals dipole interaction Coulomb interaction short range isotropic long range anisotropic this talk long range isotropic

Dipolar systems magnetic dipoles electric dipoles Chromium Hetero-nuclear molecules [Ar]3 d 54 s 1 S=3 Light induced dipoles Erbium, Europium … R. Löw, R. Gati, J. Stuhler and T. Pfau EPL, in press Rydberg atoms in E-field see poster d

Cr in periodic table of elements 70 Yb

Cr - element properties n isotopic distribution n 3 Bosons (I=0): 52 Cr (83. 8%), 50 Cr (4. 3%), 54 Cr (2. 4%) n 1 Fermion (I=3/2): 53 Cr (9. 5%) n versatile level scheme n electronic configuration n n [Ar]3 d 54 s 1 S=3 large magnetic moment 6 µB ! dipole-dipole interaction!

Cr BEC phase transition tof = 5 msec Decreasing T

The Dragontamers S. Hensler A. Griesmaier T. Koch M. Fattori Former members: J. Werner P. O. Schmidt A. Görlitz J. Stuhler Theory: K. Rzazewski S. Giovanazzi A. Simoni E. Tiesinga P. Pedri L. Santos

Was it worth all the trouble?

Dipole dipole scattering Exactly solvable in Born approximation S. Hensler, J. Werner, A. Griesmaier, P. O. Schmidt, A. Görlitz, T. Pfau, S. Giovanazzi, K. Rzazewski Appl. Phys. B 77, 765 (2003) elastic scattering spin relaxation collisions spin changing collisions

Dipolar relaxation atom number dipolar relaxation + spin changing collisions • Very good agreement between theory and experiment • no BEC in magnetic trap time [sec]

Demagnetization is a pain! BUT could it be useful? 1915: Einstein - de Haas for a quantum gas?

Adiabatic demagnetization cooling of a solid e. g. S=3 Einstein‘s model of a solid << k. BT Spin reservoir (large S) Cv~Nk. B << Phonon reservoir Cv<<Nk. B coupling

Adiabatic demagnetization cooling of a trapped gas? e. g. S=3 >> k. BT Spin reservoir (large S) >> Phonon reservoir Demagnetising collisions Cv<<Nk. B Cv~Nk. B

Single demagnetization step (k. BT>>hntrap) Continuous recycling

Would it work in ODT? S. Hensler, A. Greiner, J. Stuhler, T. Pfau, submitted Example: ntrap = 500 Hz Includes: 3 body losses heat rate due to pump photons BUT no reabsorption …

Elastic dipole interaction? elastic scattering only! 7 S 3 m. J=-3 „high field seeker“ optical dipole trap m. J=+3

Strength of elastic dipole-dipole interaction compare to contact interaction: tunable! contact interaction atoms d m Rb Na Cr tuning Rydberg atoms het. -nucl. molecules edd=0. 007 edd=0. 003 edd=0. 15 magnetic dipoles Feshbach resonance e. g. : Ca. H, NH 3, Cr. Rb edd~100 J. Werner et al. PRL 94, 183201 (2005) electric dipoles spinning polarization e. g. : Rb (n=40)* edd~108 S. Giovanazzi, A. Görlitz, T. P. PRL 89, 130401 (2002)

Evaporative cooling – phase space density gain

expansion T>Tc T<Tc

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

Condensate fraction ideal gas T=1. 1μK corr. for finite size and weak interaction* nx=581 Hz ny=406 Hz nz=138 Hz Tc~700 n. K T=625 n. K exp. A. Griesmaier, et al. PRL 94, 160401 (2005) * S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. A 54, R 4633 (1996)

Expansion driven by interaction T<Tc Cr edd=0. 15 time of flight

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

dipole-dipole interaction & aspect ratio y B z aspect ratio time of flight ry/rz<1 smaller aspect ratio ! ry/rz>1 Magnetostriction! larger aspect ratio !

dipolar expansion - magnetostriction 31 measurements nx=942 Hz ny=712 Hz nz=128 Hz J. Stuhler, A. Griemaier, T. Koch, M. Fattori, S. Giovanazzi, P. Pedri L. Santos, T. Pfau submitted Theory – No free parameters! S. Giovanazzi, A. Görlitz, and T. Pfau, J. Opt. B: Quantum Semiclass. Opt. 5, S 208 (2003).

dipolar coupling in fluids Ferrofluids ~ 2 -20 nm

Strength of elastic dipole-dipole interaction compare to contact interaction: tunable! contact interaction tuning atoms m Rb Na Cr edd=0. 007 edd=0. 003 edd=0. 15 magnetic dipoles Feshbach resonance spinning polarization

FRs: centrifugal terms & notation Quantum numbers - notation atomic electrons s, l molecular electrons S, L Skip Feshbach S=2 S=4 S=6 centrifugal potentials (e. g. ) molecular nuclei Cr 2 ab initio potentials: Z. Pavlovic et al. , PRA 69, 030701 (2004)

FRs: couplings & selection rules Possible couplings: 2 nd order Spin-Orbit Spin - Spin Selection rules: first order not allowed! second order angular momentum conservation:

expected FRs in Cr S=6 MS -2 -3 -4 -5 -6 g - wave d - wave -4 -5 -6 X S=4 MS S=2 -2 -3 -4 s - wave -4 -5 -6 initial state (open channel) 0 -1 -2 -2 -3 -4 first order 3 resonances second order 8 resonances X MS } 11

How to see the FR resonance B

Feshbach resonances in 52 Cr • expectation for collisions of ultracold, fully polarized Cr: 11 resonances (3 first order, 8 second order) • results (assignment by A. Simoni, E. Tiesinga): increasing B-field S=6 S=4 S=2 not yet ass.

exp. vs. theory D/Br ~ 2 10 -4 D/Br ≈ 0. 003 av. agreement of resonance despite 6 valence e-, Cr is positions better than 0. 6 G incl. not too complicated • no hyperfine interaction (I=0) only spin-spin interaction! J. Werner et al. PRL 94, 183201 (2005) • dipole-dipole interaction is dominant coupling mechanism

What do we know about Chromium now? 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.

summary n Cr-BEC with 105 atoms new twist: dipole-dipole interaction dipolar effects visible in Cr n Feshbach resonances n n all 11 FR up to 2 nd order dipole- dipole interactions detected (+3) theo. & exp. fit a 6, a 4, a 2, C 6, C 8

outlook n n experimental set up n tuning of contact interaction n tuning of dipole-dipole interaction n field compensation play the dipolar game ! n excitations n stability and ground state of condensate n Roton-Maxon dispersion Supersolid relation n new quantum phase transitions. . . unstable pancake Checkerboard

Further outlook Demagnetization cooling Trap fermion (see Poster Villetaneuse) Lithography: controlled single atom deposition? Cr 3+: Al 203 Cr 3+: Li. SAF Cr 3+: Li. Nb 03 Cr: Ga. N cw atom laser ?

More projects…. postdocs & phd students welcome !!!