Anisotropic optical trapping of ultracold erbium atoms

Transcription

1 Anisotropic optical trapping of ultracold erbium atoms M. Lepers 1, J.-F. Wyart 1,2, and O. Dulieu 1 1 Laboratoire Aimé Cotton, CNRS, Univ. Paris-Sud, ENS Cachan, Orsay, France 2 LERMA, Observatoire de Paris-Meudon, Univ. Pierre et Marie Curie, Meudon, France Orsay, December

2 Ultracold atoms with a complex structure (1) Research on ultracold atoms & molecules mostly with alkali-metals Li, Na, K, Rb, Cs But more and more with alkaline-earth or closed-shell atoms Strontium, ytterbium, And also with complex atoms: transition metals, open-shell lanthanides Chromium; dysprosium, holmium, erbium, thulium Several bosonic and/or fermionic isotopes Spectrum made of strong and narrow lines Metrology, precision measurements Large magnetic dipole moment (up to 10 µ B 0.1 Debye for Dy) dipolar gases, correlated matter, quantum information 04/12/2013 Anisotropic optical trapping of ultracold erbium 2

3 Ultracold atoms with a complex structure (2) Ground-state electronic configuration: [Xe]4f n 6s 2 : n = 10 for Dy n = 14 for Yb Anisotropic optical trapping of ultracold erbium 3

4 Laser-cooling of erbium in Innsbruck I = 0 for 162,164,166,168,170 Er I = 7/2 for 167 Er Frisch et al., PRA 85, (2012) L = 5, S = 1, J = 6 [Xe]4f 12 6s 2 3 H 6 04/12/2013 Anisotropic optical trapping of ultracold erbium 4

5 Laser-cooling of erbium in Innsbruck I = 0 for 162,164,166,168,170 Er After narrow-line cooling, T = 15 µk Loading in a dipole trap for evaporative cooling Need to characterize the trapping conditions I = 7/2 for 167 Er Frisch et al., PRA 85, (2012) L = 5, S = 1, J = 6 [Xe]4f 12 6s 2 3 H 6 04/12/2013 Anisotropic optical trapping of ultracold erbium 5

6 Optical trapping of alkali-metal atoms In a laser beam of angular requency ω, electric field E and intensity I Due to 2 nd -order Stark effect, potential energy on atomic center of mass The beam also induces photon scattering 04/12/2013 Anisotropic optical trapping of ultracold erbium 6

7 Optical trapping of alkali-metal atoms In a laser beam of angular requency ω, electric field E and intensity I Due to 2 nd -order Stark effect, potential energy on atomic center of mass The beam also induces photon scattering Valid for atoms with an isotropic electronic distribution (S atoms) E E E Alkali metal, alkaline-earth, chromium Isotropic optical trapping 04/12/2013 Anisotropic optical trapping of ultracold erbium 7

8 Atomic polarizability α scal (ω) = scalar dynamic (ω) dipole polarizability (complex) For an atom in state βj> (J = 1/2 for alkalis) => Sum over all electric-dipole transitions β J β J 04/12/2013 Anisotropic optical trapping of ultracold erbium 8

9 Atomic polarizability α scal (ω) = scalar dynamic (ω) dipole polarizability (complex) For an atom in state βj> (J = 1/2 for alkalis) => Sum over all electric-dipole transitions β J β J Two-level atoms = detuning 04/12/2013 Anisotropic optical trapping of ultracold erbium 9

10 Optical trapping of erbium atoms In a linearly-polarized laser beam z E z θ E θ E z 04/12/2013 Anisotropic optical trapping of ultracold erbium 10

11 Optical trapping of erbium atoms In a linearly-polarized laser beam z E z θ E θ E z Anisotropic optical trapping 04/12/2013 Anisotropic optical trapping of ultracold erbium 11

12 Optical trapping of erbium atoms In a linearly-polarized laser beam α tens (ω) = tensor dynamic (ω) dipole polarizability z E z θ E θ E z Anisotropic optical trapping 04/12/2013 Anisotropic optical trapping of ultracold erbium 12

13 Optical trapping of erbium atoms In a linearly-polarized laser beam We need a list of transition energies and transition dipole moments. α tens (ω) = tensor dynamic (ω) dipole polarizability z E z θ E θ E z Anisotropic optical trapping 04/12/2013 Anisotropic optical trapping of ultracold erbium 13

14 Atomic spectral data Experimental data: FT spectroscopy, Lawler et al., JPB 43, (2010) «Incomplete» list of transitions = lower bound of α scal (ω 0) 04/12/2013 Anisotropic optical trapping of ultracold erbium 14

15 Atomic spectral data Experimental data: FT spectroscopy, Lawler et al., JPB 43, (2010) «Incomplete» list of transitions = lower bound of α scal (ω 0) Theoretical data: least-squares fitting method, Cowan codes Distinct radial and angular contributions to energy levels 1. Radial integrals (direct and exchange Coulombic, spin-orbit, ) are calculated ab initio (Relavistic Hartree-Fock) 2. The computed energy levels are fitted with known experimental levels 3. Radial integrals are adjusted to have the best agreement between calculated and experimental energies R.D. Cowan, The theory of atomic structure and spectra, Univ. California Press (1981) 04/12/2013 Anisotropic optical trapping of ultracold erbium 15

16 Results: Er spectrum Energy levels accessible from Er ground state (odd parity, J =5, 6, 7) Standard deviation: 65 cm -1 04/12/2013 Anisotropic optical trapping of ultracold erbium 16

17 Results: Er spectrum Energy levels accessible from Er ground state (odd parity, J =5, 6, 7) Standard deviation: 65 cm -1 9 predicted levels around cm -1! 04/12/2013 Anisotropic optical trapping of ultracold erbium 17

18 Results: trap depth Corresponding to λ = 1570 nm Ex: Li, α scal (0) = 164 a.u. a D.R. Lide. CRC handbook of chemistry and physics. CRC press (2012); purely ab initio b Chu et al., PRA 75, (2007) ; purely ab initio c A. Kiyotaka et al., Private comm. (2013) d with data from Lawler et al. Lepers et al., submitted to PRA (2013); arxiv: /12/2013 Anisotropic optical trapping of ultracold erbium 18

19 Results: trap depth Corresponding to λ = 1570 nm Ex: Li, α scal (0) = 164 a.u. Within experimental uncertainty a D.R. Lide. CRC handbook of chemistry and physics. CRC press (2012); purely ab initio b Chu et al., PRA 75, (2007) ; purely ab initio c A. Kiyotaka et al., Private comm. (2013) d with data from Lawler et al. Lepers et al., submitted to PRA (2013); arxiv: /12/2013 Anisotropic optical trapping of ultracold erbium 19

20 Results: trap depth Corresponding to λ = 1570 nm Ex: Li, α scal (0) = 164 a.u. a D.R. Lide. CRC handbook of chemistry and physics. CRC press (2012); purely ab initio b Chu et al., PRA 75, (2007) ; purely ab initio c A. Kiyotaka et al., Private comm. (2013) d with data from Lawler et al. Within experimental uncertainty The trapping potential is essentially isotropic. Lepers et al., submitted to PRA (2013); arxiv: /12/2013 Anisotropic optical trapping of ultracold erbium 20

21 Results: photon-scattering rate I = 1 GW/m² M J = -J 04/12/2013 Anisotropic optical trapping of ultracold erbium 21

22 Results: photon-scattering rate θ = 0 I = 1 GW/m² M J = -J 04/12/2013 Anisotropic optical trapping of ultracold erbium 22

23 Results: photon-scattering rate θ = 0 I = 1 GW/m² The photon-scattering rate is strongly anisotropic. M J = -J 04/12/2013 Anisotropic optical trapping of ultracold erbium 23

24 Conclusions & prospects Modeling of Er spectrum, transitions from the ground state 9 predicted levels around cm -1 List of transition energies and transition dipole moments Calculation of all the contributions to the polarizability at any frequency (real and imaginary parts, scalar, vector, tensor polarizabilities) Van der Waals long-range interaction: C 6 iso = 1670 a.u. Isotropic trap depth but anistropic photon-scattering rate Control trap losses for atoms and Fesbach molecules Collisions of Er 2 Feshbach molecules (G. Quéméner) Polarizability of Er excited states Polarizability of other lanthanides (Yb, Tm, Ho, Dy) Lepers et al., submitted to PRA (2013); arxiv: /12/2013 Anisotropic optical trapping of ultracold erbium 24

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