Elastic and inelastic dipolar effects in chromium Bose-Einstein condensates Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France Former PhD students and post-docs: T. Zanon, R. Chicireanu, A. Pouderous Former members of the group: J. C. Keller, R. Barbé B. Pasquiou O. Gorceix P. Pedri B. Laburthe L. Vernac E. Maréchal G. Bismut Q. Beaufils A. Crubellier (LAC)

Dipole-dipole interactions -Intersites effects in optical lattices Inguscio (Bloch oscillations) -Use for quantum computing Polar molecules, de Mille Blockade and entanglement of Rydberg atoms (Browaeys) -Checkerboard phases (Lewenstein) (Resembles ionic Wigner cristals) Non local meanfield Non local correlations -Strong correlations in 1D and 2D dipolar systems (Astrakharchik) Chromium : S=3 Long range interactions - 2-body physics (thermalization of polarized fermions) -Static and dynamic properties of BECs Stuttgart, Villetaneuse

Inelastic dipolar effects - Feshbach resonances due to dipole-dipole interactions (Stuttgart, Villetaneuse) Anisotropic dipole-dipole interactions Spin degree of freedom coupled to orbital degree of freedom - Dipolar relaxation (Stuttgart, Villetaneuse) - Spinor physics; spin dynamics (Stamper-Kurn)

How to make a Chromium BEC in 14s and one slide ? 425 nm 427 nm 650 nm 7S37S3 5 S,D 7P37P3 7P47P4  An atom: 52 Cr N = T=120 μK (1) (2) Z  An oven  A small MOT  A dipole trap  A crossed dipole trap  All optical evaporation  A BEC (Rb=10 9 or 10 ) (Rb=780 nm) Oven at 1350 °C (Rb 150 °C)  A Zeeman slower

Similar results in Stuttgart PRL 95, (2005) Modification of BEC expansion due to dipole-dipole interactions TF profile Eberlein, PRL 92, (2004) Striction of BEC (non local effect) Parabolic ansatz is still a good ansatz Full symbols : experiment Empty squares : numerical

Collective excitations in dipolar BECs (parametric excitation) « Quadrupole » (intermediate) « Quadrupole » (lower) « Monopole » Smaller effect (4%), but (possibly) better spectroscopic accuracy Ongoing experiment …

When dipolar mean field beats local contact meanfield (i.e. e dd >1), implosion of (spherical) condensates Stuttgart: d-wave collapse Pfau, PRL 101, (2008) Anisotropic explosion pattern reveals dipolar coupling. (Breakdown of self similarity) And…, Tc, solitons, vortices, Mott physics, 1D or 2D physics, breakdown of integrability in 1D… (Tune contact interactions using Feshbach resonances (i.e. e dd >1) Nature. 448, 672 (2007) >

Other fascinating phenomena when dipolar mean field beats magnetic field Ueda, PRL 96, (2006) Similar theoretical results by Santos and Pfau. Some differences and open questions Meanfield picture : Spin(or) precession (Majorana flips) Spin degree of freedom released, with creation of orbital momentum (vortices) Analog of the Einstein –de Haas effect Dipole inelastic interactions modify the (already rich) S=3 spinor physics, and, most noticeably, its dynamics Santos and Pfau PRL 96, (2006) At the heart of the Einstein-de Haas effect with Cr BECs : dipolar relaxation

What is dipolar relaxation ? - Only two channels for dipolar relaxation in m=3: Rotate the BEC ? (Einstein-de-Haas) rotation ! Need of an extremely good control of B close to 0

Dipolar relaxation in a Cr BEC Fit of decay gives  Produce BEC m=-3 detect BEC m=-3 Rf sweep 1Rf sweep 2 BEC m=+3, vary time See also Shlyapnikov PRL 73, 3247 (1994) Never observed up to now Remains a BEC for ~30 ms Born approximation Pfau, Appl. Phys. B, 77, 765 (2003)

Interpretation Zero coupling Determination of scattering lengths S=6 and S=4 Gap ~

New estimates of Cr scattering lengths Collaboration Anne Crubellier (LAC, IFRAF)

- The 2-body loss parameter is always twice smaller in the BEC than in thermal gases - Effect of thermal (HBT-like) correlations DR in a BEC accounted for by a purely s-wave theory. No surprise, as the pair wave-function in a BEC is purely l=0 What about DR in thermal gases ? Dipole-dipole interactions are long-range: all partial waves may contribute The dip in DR is as strong for thermal gases and BECs Partial waves l>0 do not contribute to dipolar relaxation

Perspectives : - no DR in fermionic dipolar mixtures - use DR as a non-local probe for correlations Red : l=0 Blue: l=2 Green : l=4 Magenta: l=6 Overlap calculations Anne Crubellier (LAC, IFRAF) All partial waves contribute to elastic dipolar collisions … but … For large enough magnetic fields, only s-wave contributes to dipolar relaxation (because the input and output wave functions always oscillate at very different spatial frequencies) Overlap Magnetic field

Towards Einstein-de-Haas ? (i) Go to very tightly confined geometries (BEC in 2D or 3D optical lattices) (ii) Modify output energy (rf fields) Energy to nucleate a « mini-vortex » in a lattice site Ideas to ease the magnetic field control requirements Create a gap in the system: B now needs to be controlled around a finite non-zero value (~300 kHz) Below E v no dipolar relaxation allowed. Resonant dipolar relaxation at E v.

(i) Reduction of dipolar relaxation in reduced dimension (2D gaz) Load the BEC in a 1D Lattice (retro-reflected Verdi laser) Produce BEC m=-3 detect m=-3 Rf sweep 1Rf sweep 2 BEC m=+3, vary time Load optical lattice Lose BEC (2D thermal gas) Band mapping Dipolar relaxation in reduced dimension (2D) 1st BZ

Strong reduction of dipolar relaxation when !!! !!! but instead Prospect : go to 2D or 3D optical lattices

(ii) Controlling the output energy in dipolar relaxation: rf-assisted dipolar relaxation Within first order Born approximation: (B rf parallel to B) Calculation by Paolo Pedri (IFRAF post-doc, now joined our group) Coll. Anne Crubellier (LAC) See also Verhaar, PRA (1996) Never observed Similar mechanism than dipolar relaxation Gap ~ Without rf, no DR in m=-3

Dipolar relaxation between dressed states, to control: Coupling: Output energy Prospect: operate at to observe resonant DR

Conclusion Rapid and simplified production of (slightly dipolar) Cr BECs (BECs in strong rf fields)Collective excitations (rf association) (d-wave Feshbach resonance) dipolar relaxation rf-assisted relaxation dipolar relaxation in reduced dimensions (MOT of 53 Cr) Optical lattice and low-D physics (breakdown of integrability in 1D) DR as a probe for correlations Einstein-de-Haas effect Spinor diagram Production of a (slightly) dipolar Fermi sea Load into optical lattices – superfluidity ? Perspectives

Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaboration: Anne Crubellier (Laboratoire Aimé Cotton) B. Pasquiou O. Gorceix Q. Beaufils Paolo PedriB. Laburthe L. Vernac J. C. Keller E. Maréchal G. Bismut

Why Bessel functions ? (Floquet analysis) Modulate the eigenenergy of an eigenstate: e.g. different Zeeman states Pillet PRA, 36, 1132 (1987) Phase modulation -> Bessel functions Arimondo PRL (2007)) Q. Beaufils et al., arXiv: arXiv: rf association Rydberg in  -waves Shaken lattice