1. Single atom manipulations Benoît Darquié, Silvia Bergamini, Junxiang Zhang, Antoine Browaeys and Philippe Grangier Laboratoire Charles Fabry de l'Institut d'Optique Théorique et Appliquée UMR 8501 du CNRS 91 403 Orsay http://www.iota.u-psud.fr/~grangier/Quantum_optics.html

2. Introduction Experience : Context : Goals : –two neutral atoms –trapped in two different dipole traps –confinement :   m 3 –a few microns away from one another – entangle the atoms – make a quantum gate study and manipulation of an optical dipole trap for single atoms

3. Principle of a dipole trap Assumption : two-level atom, in a laser- field of frequency  L, with a red detuning :  =  L -   . Atoms are trapped in the high intensity regions The transition frequency is shifted to the blue laser-induced non-dissipative force associated with a potential energy with :- the Rabi frequency -  the lightshift For large detunings  hh |e |g atom in the laser field hLhL hh two-level atom

4. We use a magneto-optical trap as a reservoir of cooled atoms : - to trap and cool atoms - to induce the fluorescence of the atoms (which will allow us to observe them) Dipole trap Dipole force= non-dissipative force=> we previously have to cool atoms Focussing of a Titanium-Sapphire laser beam in the centre of this reservoir dipole trap Atoms are gathering at the focussing spot => dipole trap Dimensions of the trap = dimensions of the focussing spot

5. The microscope objective : MIGOU Position of the MOT Trapping beam Characteristics of MIGOU : – large numerical aperture : 0,7 – diffraction limited spot – large working distance ( ~ 1cm) – ultra high vacuum compatible waist of the beam < 1  m Double use of MIGOU : – to secure the focussing of the trapping beam in the center of the MOT – to collect the fluorescence of trapped atoms with a large efficiency ~5 cm

6. Experimental set-up Vacuum chamber MOT & dipole trap x y z Dipole trap beam Fluorescence CCD camera 780 nm filters Spatial filtering Computers Filtering pinhole Avalanche Photodiode

7. Pictures of the dipole trap on the CCD camera scaling of imaging system : 1 pixel = 1  m Continuous observation of the fluorescence of the dipole trap on the CCD caméra. One picture every 200 ms. Y X Fluorescence (CCD) X Y Fluorescence 10 000 counts (200 ms)

8. Images on the CCD camera 5  m Single atom regime 120 80 40 0 2520151050 Time (s) Counting rate (counts/10ms) 1 atom Background

9. Double trap MOT & dipole trap second trapping beam. 4  m What we observe on the CCD caméra In single atom regime, there are four likely configurations :

10. Temperature of the atoms and trap frequencies Goals : Requirements : –atom in the Lambe-Dicke regime :  << 1 we have to measure the temperature of the atoms and the trap frequencies – entangle the atoms – make a quantum gate

11. Oscillation frequencies : principle of the measurement We trap one atom. We switch off and on the dipole trap during  t 1.  If the atom is recaptured, it starts to oscillate in the trap. We wait for  t and then, we switch off and on the dipole trap during  t 2.  P(  t) is the probability to recapture the atom after the whole sequence. Dipole trap ON OFF tt tt P(  t)  oscillate at 2f osc. t1t1 t2t2

12. Oscillation frequencies : experimental results w 0 = 0.89  m P trap = 2 mW f r = 140 kHz, f z = 29 kHz } P trap = 1,9 mW Delay (  s)  t 1 = 2.5  s  t 1 = 1  s P trap = 1,5 mW

13. Temperature of the atom : time of flight experiments Time sequence: Objective MOT 1 : We trap one atom Trapping beam

14. Temperature of the atom : time of flight experiments Time sequence: Objective 1 : We trap one atom Trapping beam 2 : We switch off the MOT

15. Temperature of the atom : time of flight experiments Time sequence: 1 : We trap one atom 2 : We switch off the MOT 3 : The trapping beam is switched off during  t Objective Trapping beam MOT 4 : We check if the atom is still there  We measure the probability of recapturing the atom after  t.

16. Temperature of the atom : results T = 35  K P = 2 mW simulation with T = 140  K simulation with T = 35  K +

17. Conclusion and outlooks We are now able to evaluate the trap frequencies and the temperature of the atoms We need : –a better confinement –a smaller temperature Better confinement  retro-reflexion of the trapping beam, standing wave Smaller temperatures  Raman cooling Lamb-Dicke parameters :  r  0.5  z  2.5

18. Single atom manipulations Benoît Darquié, Silvia Bergamini, Junxiang Zhang, Antoine Browaeys and Philippe Grangier Laboratoire Charles Fabry de l'Institut d'Optique Théorique et Appliquée UMR 8501 du CNRS 91 403 Orsay http://www.iota.u-psud.fr/~grangier/Quantum_optics.html

19. Entanglement of two atoms |>|> |>|> probe beam   |>|> |>|> |>|> probe beam   |>|> Atome 1Atome 2 beam splitter detector of  -polarized light:

20. Entanglement of two atoms Excitation by a photon of the probe beam: detection of  -polarized ligt: |>|> |>|> probe beam   |>|> detection of  -polarized light: atoms behave as Young's slits  interferences projection onto the state:  entanglement

21. Plan of my talk Principle of the optical dipole trap Implementing a dipole trap A microscope objective : MIGOU Experimental set-up Pictures of the dipole trap Double dipole trap Temperature of the atoms Oscillation frequencies of the dipole trap Conclusion and outlooks