RYDBERG BLOCKADE IN AN ARRAY OF OPTICAL TWEEZERS

Transcription

1 4th GDR - IQFA Paris 7 November 20, 2013 RYDBERG BLOCKADE IN AN ARRAY OF OPTICAL TWEEZERS Sylvain Ravets, Henning Labuhn, Daniel Barredo, Lucas Beguin, Aline Vernier, Florence Nogrette, Thierry Lahaye, Antoine Browaeys

2 Quantum information with neutral atoms Quantum state engineering for quantum information, metrology, simulation (entangled states interaction) Isolate and control single atoms: Optical lattices d ~ 500 nm Arrays of optical tweezers d ~ a few microns Interaction: Rydberg atoms Rb + e Rb + e J. F. Sherson et al., Nature 467, (2010) W. S. Bakr et al., Nature 462, (2009) M. Saffman et al., Rev. Mod. Phys. 82, (2010) V vdw d ~ μm

3 n ~ Rydberg blockade Large dipole-dipole interaction (d ~ n 2 e a 0 ) ~ 100 nm Rb + e 1 atom 2 atoms If Rabi coupling, : no excitation of BLOCKADE D. Jaksch, et al., Phys. Rev. Lett. 85, (2000) M. D. Lukin, et al., Phys. Rev. Lett. 87, (2001)

4 Collective excitation 1 atom 2 atoms COLLECTIVE EXCITATION of coupling to with

5 OUR SETUP Production of arrays of traps Control of the electric field

6 Single atoms in optical tweezers Vacuum chamber Dipole trap at 850 nm Aspheric lenses NA = 0.50 Single-mode fiber MOT T = 30 µk 1 um trap Dichroic mirror Single photon detector (avalanche photodiode) Only one atom trapped due to light-assisted collisions Detection: collect fluorescence (780 nm) on avalanche photodiode Schlosser et al., Nature 411, 1024 (2001) Sortais et al., PRA 75, (2007)

7 Photons per 10 ms Single atoms in optical tweezers Fluorescence signal Time Light-assisted collisions prevent N-atom trapping (N > 1) Non deterministic single-atom source

8 Arrays of optical tweezers APD SLM optical tweezers fiber Spatial Light Modulator (liquid crystals) Reconfigurable phase hologram Iterative algorithm to obtain the desired intensity pattern Bergamini et al., JOSAB 21, 1889 (2004)

9 Multi-atom pictures Fluorescence on a CCD in the Multi-atom regime (~ few tens of atoms per trap): 40 mm

10 Control of static electric fields Polarizability: α n=82 ~ 3 GHz / (V/cm) 2 Atomic beam Avoid patch charges: ITO conductive coating on aspheric lenses 2 x 4 electrodes ODT beam ITO coating Control of E-field: 8 electrodes (compensation, control of interaction) See also: Löw, et al., J. Phys. B: At. Mol. Opt. Phys. 45 (2013)

11 Rb + e Rb + e V vdw d ~ μm MEASURING THE INTERACTION BETWEEN TWO ATOMS From full blockade to partial blockade

12 Excitation probability Single atom Rydberg excitation 850nm dipole trap 475nm 475 nm nd 3/2 795 nm 5P 1/2 795nm 1.0 5S 1/2 58D 3/2 level One atom excitation probability (Rabi oscillation) Y. Miroshnychenko, et al., PRA 82, (2010) Early results at Wisconcsin: PRL 100, (2008) Duration of Rydberg excitation (ns) 2000

13 Excitation of 2 atoms Two traps, two avalanche photodiodes, two counters Trigger experiment on the presence of one atom in each trap Blockade: no multiple excitation 1 Collective excitation to rg + gr 2 ( ) (faster) 8 μm A C 795 nm 475 nm 2 atoms

14 Excitation probability 2 atoms Rydberg blockade A Exc. prob. atom A only D 3/ Duration of Rydberg excitation (ns) 2000

15 Excitation probability 2 atoms Rydberg blockade A B R 1.0 Exc. prob. atom A only Exc. prob. atom A & B BLOCKADE 58D 3/2 R = 5 mm U vdw / h = 25 MHz Duration of Rydberg excitation (ns) E. Urban, et al., Nature Physics 5, 110 (2009) A. Gaëtan, et al., Nature Physics 5, 115 (2009) L. Beguin, et al. PRL 110, (2013) 2000

16 Excitation probability 2 atoms Rydberg blockade A B R Exc. prob. atom A only Exc. prob. atom A & B Exc. prob. atom A OR B 1.0 Freq. ratio = D 3/2 R = 5 mm U vdw / h = 25 MHz Duration of Rydberg excitation (ns) 2000

17 Notion of partial blockade : Partial blockade 2 characteristic frequencies, Ω and U/ħ

18 Notion of partial blockade R (mm) p 4p 6p 8p Pulse area Wt L. Beguin, et al. PRL 110, (2013) 0 0 2p 4p 6p 8p Pulse area Wt

19 U vdw vs distance 53D 3/2 62D 3/2 82D 3/2 Interaction entre 2 atomes uniques 1/R 6 law (logarithmic scale)

20 U vdw vs distance x50 Theory curves: direct diagonalization (dipole-dipole interaction) No adjustable parameter! L. Beguin, et al. PRL 110, (2013)

21 θ TESTING THE ANISOTROPY OF THE INTERACTION Anisotropy of the interaction Consequences on a 3-atom chain

22 U vdw vs θ (preliminary) θ S state: isotropic interaction d=12μm 82S 1/2 θ (degrees) θ d=12μm 82D 3/2 θ (degrees) D state: stronger but anisotropic interaction (quantization axis fixed by the setup)

23 Energy Excitation of a 3-atom chain 3 traps, 3 photon counters Trigger experiment on the presence of one atom in each trap Blockade: no multiple excitation 1 Collective excitation to rgg + grg + ggr 3 ( ) rrr (faster) 4 μm A B C 795 nm rrg rgr grr Blockade rgg grg ggr 475 nm ggg

24 Excitation probabilities Excitation probabilities 3-atom blockade P rgg +P grg +P ggr P rrg +P rgr +P grr P rrr No 3-atom excitation for various geometries: Blockade works! 0 π 2π 3π 4π Pulse area Ωτ (rad) Probability to excite atom A or B or C P rgg +P grg +P ggr P rrg +P rgr +P grr P rrr Collective excitation of: 1 3 ( rgg + grg + ggr ) 0 π 2π 3π 4π Pulse area Ωτ (rad)

25 Excitation probabilities 3-atom blockade A B C P rgg +P grg +P ggr P 1at Frequency ratio = 1.7 ~ 3 0 π 2π 3π 4π Pulse area Ωτ (rad) Collective excitation

26 TUNING THE INTERACTION Förster resonances for two atoms

27 Tuning the interaction: Förster resonance Rb + In general: vdw interaction e e Rb + nd,nd (n-2)p,(n+2)f D(n) n = 59, R = 4 mm DE 10 MHz In some specific cases, it is possible to cancel D(n)

28 Tuning the interaction: Förster resonance Rb + e Rb + e In general: vdw interaction nd,nd (n-2)p,(n+2)f D(n) Förster resonance (tunable) Tune D(n) with an E-field 59d 3/2 + 59d 3/2 57p 1/2 + 61f 5/2 pf E (MHz) dd n = 59, R = 4 mm DE 10 MHz In some specific cases, it is possible to cancel D(n) gg F (V/cm)

29 Spectroscopy of the doubly excited states 59D 3/2 level (close to Förster resonance) d=8 μm We add a ~ 22 mv/cm electric field to reach the resonance pf dd E (MHz) δ P double excitation F ~ 22 mv/cm gg F (V/cm) δ/2π (MHz)

30 Control voltage (V) Control voltage (V) Varying the field (preliminary) (No adjustable parameter) δ/2π (MHz) d 2 /R 3 Förster resonance δ/2π (MHz) Enhance or switch the interaction by changing the electric field J. Niepper, et al., PRL 108, (2012)

31 1/ Δ (arb. units) Tuning the interaction (preliminary) n = Control voltage (V) Can control the interaction over two orders of magnitude

32 Perspectives Experiments with arrays of a few atoms: Geometry of array Electric field control of interaction Three-atom entanglement (GHZ, W) Addressability of single atoms: implementing CNOT gate D. Jaksch, et al., Phys. Rev. Lett. 85, (2000) M. D. Lukin, et al., Phys. Rev. Lett. 87, (2001) D. Moeller, et al., Phys. Rev. Lett. 100, (2008) Deterministic loading M. Saffman, et al., PRA 66, (2002) T. Grünzweig, et al., Nature Physics 6, (2010) M. Ebert, et al., arxiv: (2013)