Single atom manipulations Benot Darqui Silvia Bergamini Junxiang

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

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

Principle of a dipole trap Assumption : two-level atom, in a laserfield of frequency w. L, with a red detuning : d = w. L - w 0 < 0. laser-induced non-dissipative force associated with a potential energy For large detunings d : with : - the Rabi frequency - D the lightshift two-level atom |e hw 0 h. D hw. L |g atom in the laser field Atoms are trapped in the high intensity regions The transition frequency is shifted to the blue

Dipole trap Dipole force= non-dissipative force=> we previously have to cool atoms 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) Focussing of a Titanium-Sapphire laser beam in the centre of this reservoir Atoms are gathering at the focussing spot => dipole trap Dimensions of the trap = dimensions of the focussing spot dipole trap

The microscope objective : MIGOU Characteristics of MIGOU : ~5 cm – large numerical aperture : 0, 7 Trapping beam – diffraction limited spot – large working distance (~1 cm) Position – ultra high vacuum of the MOT compatible waist of the beam < 1 mm 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

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

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

Single atom regime Images on the CCD camera 5 mm Counting rate (counts/10 ms) 120 1 atom 80 40 Background 0 0 5 10 15 Time (s) 20 25

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

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

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

Oscillation frequencies : experimental results Ptrap = 1, 9 m. W Ptrap = 1, 5 m. W Delay (ms) Dt 1 = 1 ms • w 0 = 0. 89 mm • Ptrap = 2 m. W Dt 1 = 2. 5 ms } fr = 140 k. Hz , fz = 29 k. Hz

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

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

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

Temperature of the atom : results + P = 2 m. W simulation with T = 140 m. K simulation with T = 35 m. K

Conclusion and outlooks • We are now able to evaluate the trap frequencies and the temperature of the atoms Lamb-Dicke parameters : r 0. 5 z 2. 5 • We need : – a better confinement – a smaller temperature • Better confinement retro-reflexion of the trapping beam, standing wave • Smaller temperatures Raman cooling

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

Entanglement of two atoms probe beam p |2> probe beam s |0> |1> |0> Atome 1 p |2> s |1> Atome 2 beam splitter detector of p-polarized light:

Entanglement of two atoms probe beam |2> p s |0> |1> Excitation by a photon of the probe beam: detection of s-polarized ligt: atoms behave as Young's slits interferences detection of p-polarized light: projection onto the state: entanglement

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