Experimental study of Efimov scenario in ultracold bosonic lithium Lev Khaykovich Physics Department, Bar-Ilan University, 52900 Ramat Gan, Israel FRISNO-11, Aussois, 28/3/2011

Outline Experimental approach - all optical BEC of lithium Exploring Feshbach resonances on F=1 state. Spontaneous spin purification. Universal quantum states in three body domain (scattering length a is the largest length scale in the system) Weakly bound Efimov trimers. Log periodic behavior of three-body recombination. Evidence of spin independent short range 3-body physics. Mapping between the scattering length and the applied magnetic field – direct association of Feshbach molecules. Conclusions – is the nonuniversal part of the theory nonuniversal?

Experimental system: bosonic lithium Why lithium? Compared to other atomic species available for laser cooling, lithium has the smallest range of van der Waals potential: Thus it is easier to fulfill the universal physics requirement: |a| >> r0

Experimental system: bosonic lithium What’s lithium? Bulk metal – light and soft Magneto-optically trapped atoms

All optical BEC: optical dipole trap Direct loading of an optical dipole trap from a MOT 0 order (helping beam) +1 order (main trap) Ytterbium Fiber Laser P = 100 W N=2x106 T=300 mK w0 = 31 mm U = 2 mK main trap Q = 19.50 * The helping beam is effective only when the main beam is attenuated helping beam w0 = 40 mm N. Gross and L. Khaykovich, PRA 77, 023604 (2008)

Tuning the s-wave scattering length Feshbach resonance A weakly bound state is formed for positive a – Feshbach molecule

Feshbach resonances on F=1 state Theoretical prediction for Feshbach resonances S. Kokkelmans, unpublished

Search for Feshbach resonances Atoms are optically pumped to F=1 state. Positions of Feshbach resonances from atom loss measurements: Narrow resonance: 845.8(7) G Wide resonance: 894.2(7) G From the whole zoo of possible resonances only two were detected.

Spontaneous spin purification Spin selective measurements to identify where the atoms are. Spin-flip collisions: |F=1, mF=0> N. Gross and L. Khaykovich, PRA 77, 023604 (2008)

Feshbach resonances on mF=0 state Theoretical prediction for Feshbach resonances This is not the absolute ground state!

Experimental playground Absolute ground state The one but lowest Zeeman state

Three-body universality: Efimov qunatum states

Quantum states near two-body resonance (Efimov scenario)

Universal three-body bound states even more weakly bound trimers weakly bound trimers

Universal three-body bound states Position of an Efimov state is nonuniversal. It is defined by a three-body parameter.

Experimental observables – Efimov resonances One atom and a dimer couple to an Efimov trimer Three atoms couple to an Efimov trimer Experimental observable - enhanced three-body recombination

Three-body recombination Release of binding energy causes loss which probes 3-body physics.

Manifistation of Efimov resonances One atom and a dimer couple to an Efimov trimer Three atoms couple to an Efimov trimer Enhanced three-body loss: collisions at much larger distance

Experimental observables – suppressed three-body recombination There are two paths for the 3- body recombination towards deeply bound state

Suppressed three-body recombination deeply bound molecule Two paths interfere destructively a certain scattering lengths – recombination minima.

Three-body recombination theory Loss rate from a trap: K3 – 3-body loss coefficient [cm6/sec] Dimension analysis: Full treatment:

Effective field theory Loss into deeply bound molecules Loss into shallow dimer Recombination minima Efimov resonances Braaten & Hammer, Phys. Rep. 428, 259 (2006)

Experimental results mf = 1; Feshbach resonance ~740G. a > 0: T= 2 – 3 mK a < 0: T= 1 – 2 mK mf = 1; Feshbach resonance ~740G. N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010).

Experimental results mf = 1; Feshbach resonance ~740G. a > 0: T= 2 – 3 mK a < 0: T= 1 – 2 mK mf = 1; Feshbach resonance ~740G. mf = 0; Feshbach resonance ~895G. N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010).

Experimentally demonstrated Efimov features This resonance This minimum

Experimentally demonstrated Efimov features Theses two resonances are related by 22.7

Experimentally demonstrated Efimov features Theses two resonances are related by 22

Experimentally demonstrated Efimov features This resonance This minimum This resonance

Summary of the results Fitting parameters to the universal theory: UT prediction: a+/|a-| = 0.96(0.3) The universal factor of 22.7 is confirmed across the region of Three-body parameter is the same (within the experimental errors) for both nuclear-spin subleves. N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, PRL 103, 163202 (2009); PRL 105, 103203 (2010).

the scattering length And the applied magnetic field Mapping between the scattering length And the applied magnetic field

Mapping between the scattering length and the applied magnetic field Bare state (non-universal) dimer: Feshbach molecule (universal dimer):

Universal two-body bound state There is only a small fraction of the wave function in the bound state. The size of the bound state increases. “Quantum halo states” The size of the bound state is that of a singlet potential: ~1.5 nm Progressive contamintion by the atomic continuum

Experimental probe Loss mechanism from the trap (release of binding energy): Deeply bound molecule

Mapping between the scattering length and the applied magnetic field Precise characterization of Feshbach resonances by rf-spectroscopy of universal dimers. A typical RF spectrum N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:1009.0926

Mapping between the scattering length and the applied magnetic field Precise characterization of Feshbach resonances by rf-spectroscopy of universal dimers. Solid (dashed) line – local (global) analysis N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:1009.0926

Mapping between the scattering length and the applied magnetic field Precise characterization of Feshbach resonances by rf-spectroscopy of universal dimers. Improved characterization of Li inter-atomic potentials. N. Gross, Z. Shotan, O. Machtey, S. Kokkelmans and L. Khaykovich, C.R. Physique 12, 4 (2011) ; arXiv:1009.0926

Conclusions For two different Fesbach resonances on two different nuclear-spin sublevles of the same atomic system we demonstrate: Universal scaling factor of 22.7 across the region of . Same positions of the Efimov features (within the experimental errors). First experimental indication that the nonuniversal part of the universal theory – the three-body parameter – might have some “universal” properties. New insight from Innsbruck group – for three different Feshbach resonances the Efimov features are the same!

People Bar-Ilan University, Israel Eindhoven University of Technology, The Netherlands Servaas Kokkelmans