Quantum information processing with individual neutral atoms in optical tweezers. Philippe Grangier. Institut d Optique, Palaiseau, France

Transcription

1 Quantum information processing with individual neutral atoms in optical tweezers Philippe Grangier Institut d Optique, Palaiseau, France

2 Outline Yesterday s lectures : 1. Trapping and exciting single atoms in optical tweezers 2. Driving, manipulating and moving individual atomic qubits Today s lecture : 3. Entanglement and two-qubit gates - Rydberg blockade as a way to entangle two atoms - Observation of Rydberg blockade between two atoms - Observation of the collective oscillation of two atoms - Entanglement of two atoms in the ground state

3 A possible architecture for a neutral atom-based QC (DTO / IARPA coll. with Bill Phillips, Trey Porto, Ivan Deutsch, Poul Jessen...) Storage 2-qubit gates Quantum measurement Lattices Array of dipole traps (hologram, micro-lenses) Tweezer / lattices (optical cavity) Natural link = moving optical tweezer Requires «long» coherence time of a qubit in a moving tweezer, and a good way to perform two-qubit gate

4 Two atoms at your fingertips N. Schlosser et al, Nature 411, 124 (21) PRL 89, 235 (22) Resolution of the imaging system: 1 micron / pixel Beam 1 Beam 2 4 µm

5 Outline 1. Trapping and exciting single atoms in optical tweezers 2. Driving, manipulating and moving individual atomic qubits 3. Towards entanglement and two-qubit gates : - Rydberg blockade as a way to entangle two atoms - Observation of Rydberg blockade between two atoms - Observation of the collective oscillation of two atoms - Entanglement of two atoms in the ground state

6 Detecting and "heralding" two single trapped atoms Dipole trap 1 lens Atom A Vacuum Atom B Dipole trap 2 flurorescence B (cps/ms) times (ms) CCD fluorescence A (cps/ms) μm times (sec)

7 Distance and size of the "single atom clouds" Dipole trap 1 Depth =.5 mk T = 7 μk Vacuum f r = 8 khz f z = 16 khz Dipole trap 2 2 nm R = 3-2 μm 8 nm

8 D 5P 1/2 Initialization (opt. pumping) Raman Detection time (fluorescence) 2 Results :, 1, 1,,, 1,, Probability P(1) : 1 1 Population in F = 1 (%) Raman transition : Rabi oscillation Duration of Raman pulse (μs) π Pulse = 99% efficiency 1

9 Creating entanglement... A B ( A + 1 A ) ( B + 1 B ) = A, B + A,1 B + 1 A, B + 1 A,1 B State-dependent operation Measurement Filtering A, B + A,1 B + 1 A, B - 1 A,1 B A,1 B + 1 A, B

10 Proposals for creating entanglement / gates Several protocols adapted to single atoms in tweezers «Deterministic» entanglement «Conditional» entanglement Dipole-dipole (Rydberg blockade) s-wave collision (also in optical lattices) d 2 /R 3 Entanglement induced by a Bell measurement R ~ 2 μm A B r r Mainz, NIST, Slow, sensitive to motional state (OK for BEC!) 1 1 U. Wisconsin, Palaiseau Fast, insensitive in ΔR JQI, Munich, Barcelona No «direct» coupling, but hard to scale

11 Perspective for conditional entanglement A B 1 1 Entanglement swapping projects onto A,1 B - 1 A, B A,ν A,ν 2 B,ν B,ν 2 PRA 73, (26) Requires - Triggered emission of single photons - Two photon interferences - Excellent stability of the expt (very low production rate) Implemented with trapped ions (Chris Monroe et al.)

12 Deterministic entanglement using Rydberg excitation d 4 /R 6 R ~ 2-5 μm D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R.Côté, and M. D. Lukin PRL 85, 228 (2) r 1 V dd r 1 Two atoms separated by few microns and excited to Rydberg states will interact very strongly (dipole-dipole coupling) This strong interaction may inhibit to excite both atoms : «Rydberg blockade» The blockade effect can be used to entangle the atoms, and to design very fast (sub-µs) quantum gates

13 Interaction between Rydberg atoms «Accidental» degeneracy (Förster interaction) R ~ 3 μm In general (no electric field) : van der Waals interaction E 6p1/2 58d3/2 56f5/2 dipole-dipole interaction e.g.: n = 58, R = 3 μm ΔE 5 MHz n = 58, R = 3 μm ΔE 1 MHz T. G. Walker and M. Saffman Phys. Rev. A 77, (28)

14 «Rydberg blockade» 2E V Energy E or A A + B Insensitive to exact V, i.e. distance between atoms! 18

15 Observations of Rydberg blockade in atomic ensembles Tong et al. PRL 93, p. 631 (24) Singer et al. PRL 93, p (24) Afrousheh et al. PRL 93, p (24) Cubel Liebisch et al. PRL 95, p (25) Vogt et al. PRL 97, p. 833 (26) Vogt et al. PRL 99, p. 732 (27) MOT Heidemann et al. PRL 99, p (27) BEC In these experiments many atoms in the sample : sensitive to <V int > over random inter-atomic distances Two individual atoms in dipole traps : E. Urban et al, Nature Physics 5, 11 (29) [U. Wisconsin] A. Gaëtan et al, Nature Physics 5, 115 (29) [Paris Sud]

16 Outline 1. Trapping and exciting single atoms in optical tweezers 2. Driving, manipulating and moving individual atomic qubits 3. Towards entanglement and two-qubit gates : - Rydberg blockade as a way to entangle two atoms - Observation of Rydberg blockade between two atoms - Observation of the collective oscillation of two atoms - Entanglement of two atoms in the ground state

17 Deterministic Rydberg excitation 58D3/2 σ +, nm M F = 3, M J = 3/2 B = 9 G 5P1/2 4 MHz M F = 2, M J = 1/2 D1 5S1/2 π, 795 nm M F = 2, M J = 1/2

18 Detection of Rydberg excitation Through loss of the atom.5 mk Excitation T = 7 μk Leave the trapping region (1 μm) in < 5 μsec Before Photo-ionization by dipole trap (81 nm) = 5 μsec Radiative decay to 5P 1/2 = 5 μsec Black-Body = 5 μsec

19 Deterministic Rydberg excitation Repeat 1 times the sequence Zeeman pumping in F = 2, M=2 6 μsec Excitation red + blue 1-4 ns Atom detection Check the presence of the atom Dipole trap Dipole trap time

20 Rabi oscillations on a single atom Also, U. Wisc. PRL, vol. 1, p (28) 1..8 Loss probability Duration of the excitation (ns) Two-photon Rabi oscillation between the ground and Rydberg state (58d 3/2)

21 Rabi oscillations on a single atom g Also, U. Wisc. PRL, vol. 1, p (28) 1..8 Loss probability r Duration of the excitation (ns)

22 Excitation of two atoms B 795 nm w = 2 µm R = 3-18 μm w = 1 µm 474 nm

23 «Blockade» range Two atoms excited to 58d 3/2 ; M J = 3/2 Δ=7 ΜΗz z r,r Blockade stops when R Energy Ω g,r Ω = 2π 7 MHz Rmax = 8 μm Ω g,g R

24 Experimental protocol 1. Trap 2 atoms in 2 tweezers and optically pump them 2. Excite the two atoms 3. Measure if they are still trapped after the excitation Repeat 1 times Atom A :, 1,, 1,,,, 1, 1, Atom B :, 1, 1, 1,,, 1, 1,, Extract P to excite no Rydberg s P of exciting two Rydberg s simultaneously P to excite only one Rydberg

25 Excitation of two atoms at R = 18 μm Two atom excitation probability Atom A without B Atom B without A Duration of the excitation (ns) Single atom Rabi oscillation between ground and Rydberg state

26 Excitation of two atoms at R = 18 μm The atoms are «independent» Two atom excitation probability Probability to excite A probability to excite B Duration of the excitation (ns) Measured probability to excite the two atoms

27 Excitation of two atoms at R = 3.6 μm 1. Atom A without B Excitation probability Atom B without A Duration of the excitation (ns)

28 Excitation of two atoms at R = 3.6 μm 1. Probability to excite 2 atoms at the same time Excitation probability BLOCKADE Duration of the excitation (ns) «Observation of collective excitation of two individual atoms in the Rydberg blockade regime», A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, Nature Physics 5, 115 (29).

29 Blockade at U. Wisconsin (M. Saffman) Two atoms only, Rydberg level n = 79, distance 1 µm Rabi oscillation for atom 1, atom 2 in ground state Rabi oscillation for atom 1, atom 2 in Rydberg state «Observation of Rydberg blockade between two individual atoms», E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, M. Saffman, Nature Physics 5, (29).

30 Outline 1. Trapping and exciting single atoms in optical tweezers 2. Driving, manipulating and moving individual atomic qubits 3. Towards entanglement and two-qubit gates : - Rydberg blockade as a way to entangle two atoms - Observation of Rydberg blockade between two atoms - Observation of the collective oscillation of two atoms - Entanglement of two atoms in the ground state

31 «Collective» Rabi oscillations Two-atom energy Blockade ΔE The probability to excite one atom in the blockade regime should oscillate 2 faster than the initial single atom Rabi frequency!

32 «Collective» Rabi oscillations One atom only : usual Rabi oscillations pr = sin 2 (ΩT/2), Two atoms, basis = g, g, 1 = ( g, r + r, g )/ 2, 2 = rr 2 p() = cos 4 (ΩT/2) H indépend. = hω 2 2 p(1) = 2 sin 2 (ΩT/2) cos 2 (ΩT/2) 2 p(2) = sin 4 (ΩT/2) = pr 2 2 p() = cos 2 ( 2 ΩT/2) H blockade = hω 2 p(1) = sin 2 ( 2 ΩT/2) p(2) = With two atoms the probability p(1) = sin 2 ( 2 ΩT/2) oscillates 2 faster than the single atom value pr = sin 2 (ΩT/2)!

33 Probability to excite only one atom (R = 3.6 μm) Excitation probability Probability to excite one atom with blockade Probability to excite one atom without the other one Duration of the excitation (ns) Frequency ratio = Also Heidemann, et al. PRL 99, p (27)

34 Probability to excite only one atom (R = 3.6 μm) Excitation probability Entangled state! But the Rydberg state leaves the trap? Duration of the excitation (ns)

35 Outline 1. Trapping and exciting single atoms in optical tweezers 2. Driving, manipulating and moving individual atomic qubits 3. Towards entanglement and two-qubit gates : - Rydberg blockade as a way to entangle two atoms - Observation of Rydberg blockade between two atoms - Observation of the collective oscillation of two atoms - Entanglement of two atoms in the ground state

36 58d 3/2 F = nm R = 3.6 µm s +, nm B = 9G 474 nm 5p 1/2 4 MHz F = 2 D1 s + +s -, 795 nm 5s 1/2 F = 2 ψ B = 1 2 ( 1, +,1 ) F = 1

37 Global Raman rotation on the two atoms ( 1, Ω) ψ B = 1 2 ( 1, +,1 ) ψ C = 1 2 (, 1,1 ) Raman oscillation at frequency 2 x Ω The visibility (contrast) of this oscillation tells how close the state is («fidelity») from the desired Bell state! Q. A. Turchette, D. Wineland et al., Phys. Rev. Lett. 81, 3631 (1998).

38 Repeat 1 times the sequence Zeeman pumping in F = 2, M=2 6 msec (65 ns) (1 ns) Atom detection Raman pulse Measure states of atom A and B Dipole trap Dipole trap time

39 1 8 6 Theory 4 2 5% 5% 1 P 11 P 1 P 1 P 8 Experiment % 34% 31% 29% oops P 11 P 1 P 1 P

40 Push-out beam Check presence of the atom 1 push-out beam push-out beam 1

41 x x x1 x xx ρ = Fm = < Φ ρ Φ > with Φ > =( 1 > + 1 > )/ 2 Fm = (a22 + a33 + a23 + a32)/2 P(2 atoms) = a11 + a22 + a33 + a44

42 It can be shown that P 11 (θ) = A + B cos(θ/2) + C cos(θ) where A, B, C can be obtained from the fit! Ideally B =, A = - C =1/4 : P 11 (θ) = ( 1 + cosθ )/4 Result of the analysis : * Probability to still have both atoms in the 2 qubits space at the end of the complete sequence = 61% * If both atoms are there, fidelity vs Bell state = 75% T. Wilk et al, Phys. Rev. Lett. 14, 152 (21) L. Isenhower et al, Phys. Rev. Lett. 14, 153 (21)

43 A r A B r 1 1 B 1, 1 with φ = k (Δr 2 -Δr 1 ) and k = kr + kb If pulses are short enough, atomic motion is frozen Δr n

44 1 Probability P1 + P1 ( % ) Duration of Raman pulse (μs) 5 6 Theory This gate IS fast! (PZ, 2 )

45 r Towards a phase gate r Jaksch, et al. PRL 85, 228 (2) 1 A B Phase π - excitation on A 2π - excitation on B π - excitation on A Blockade * Requires «adressability». Very fast gate * Can (easily?) be turned into a CNOT gate Full gate realized at U. Wisconsin : L. Isenhower et al, Phys. Rev. Lett. 14, 153 (21)

46 blockade over all the sample : W state decoherence control?

47 YOU? Philippe Grangier Janik Wolters Alpha Gaëtan Charles Evellin Tatjana Wilk Antoine Browaeys