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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 dipole interaction Coulomb interaction U coul (r) short range isotropic long range anisotropic this talk long range isotropic q1 q2 4πε0 r Dipolar systems magnetic dipoles electric dipoles Chromium Hetero-nuclear molecules [Ar]3d54s1 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 70Yb Cr - element properties isotopic distribution 3 Bosons (I=0): 52Cr (83.8%), 50Cr (4.3%), (2.4%) 1 Fermion (I=3/2): 53Cr (9.5%) versatile level scheme electronic configuration 54Cr [Ar]3d54s1 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 L << kBT Spin reservoir (large S) Cv~NkB D << Phonon reservoir Cv<<NkB coupling Adiabatic demagnetization cooling of a trapped gas? e.g. S=3 L >> kB T Spin reservoir (large S) >> trap Phonon reservoir Demagnetising collisions Cv<<NkB Cv~NkB Single demagnetization step (kBT>>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 dipole interaction? elastic scattering only! 7S 3 mJ=+3 mJ=-3 „high field seeker“ optical dipole trap Strength of elastic dipole-dipole interaction 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.: CaH, NH3, CrRb eJ.ddWerner ~100 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 T<Tc lifetime of the condensate t~400msec n0i= 2×1015 cm-3 t~6 sec n0i= 2×1014 cm-3 Cr S=3, mS=-3 L3 10−29 cm6 s−1 (upper limit) Rb F=2, mF=2 L3 = 1.8 × 10−29 cm6 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 nK T=625nK exp. A. Griesmaier, et al. PRL 94, 160401 (2005) * S. Giorgini, L. P. Pitaevskii, and S. Stringari, Phys. Rev. A 54, R4633 (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 nTF(r) perturbation by dipole interaction: parabolic density profile B Fdd(r) dipole-dipole interaction & aspect ratio y B z B z aspect ratio time of flight r y/rz<1 smaller aspect ratio ! r y/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, S208 (2003). dipolar coupling in fluids Ferrofluids ~ 2-20 nm Strength of elastic dipole-dipole interaction 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 Skip Feshbach Quantum numbers - notation atomic electrons s,l molecular electrons S,L S=2 S=4 S=6 centrifugal potentials (e.g. 4) molecular nuclei Cr2 ab initio potentials: Z. Pavlovic et al., PRA 69, 030701 (2004) FRs: couplings & selection rules Possible couplings: 2nd 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 4 d - wave -4 -5 -6 2 X MS S=2 -2 -3 -4 -2 -3 -4 X -4 -5 -6 initial state (open channel) MS 0 -1 -2 m M S 0 first order 3 resonances second order 8 resonances s - wave 0 S=4 } 11 How to see the FR resonance B Feshbach resonances in 52Cr • 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 2 S=6 4 S=4 4 S=2 4 not yet ass. exp. vs. theory /Br ~ 210-4 /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 a6= 112(14) a0 a4= 58(6) a0 a2= -7(20) a0 C6=733(70) a.u. C8=75(+90/-75) a.u. summary Cr-BEC with 105 atoms new twist: dipole-dipole interaction dipolar effects visible in Cr Feshbach resonances all 11 FR up to 2nd order dipole- dipole interactions detected (+3) theo. & exp. fit a6,a4,a2,C6,C8 outlook experimental set up tuning of contact interaction tuning of dipole-dipole interaction field compensation play the dipolar game ! excitations stability and ground state of condensate Roton-Maxon dispersion Supersolid relation new quantum phase transitions ... unstable stable pancake Checkerboard Further outlook Demagnetization cooling Trap fermion (see Poster Villetaneuse) Lithography: controlled single atom deposition? Cr3+:Al203 Cr3+:LiSAF Cr3+:LiNb03 Cr:GaN cw atom laser ? More projects…. postdocs & phd students welcome !!!