1. Quantum computing with Rydberg atoms Klaus Mølmer Coherence school Pisa, September 2012

2. Rydberg physics and Rydberg blockade Rydberg physics and quantum information - quantum computing - pure state quantum control of ensembles - quantum phase transitions Rydberg and many-body physics Rydberg physics and quantum (n.l.) optics Review paper: M. Saffman et al: Rev. Mod. Phys. 82, 2313–2363 (2010). Outline Johannes Robert Rydberg, 1854-1919 Albert Victor Bäcklund, 1845-1922

3. Rydberg atoms Large principal quantum numbers  Very large orbitals,  Large dipoles ~n 2  Long lifetimes Rydberg blockade ∆E ~ 1/ R 6 van der Waals ∆E ~ 1/ R 3 static or resonant dipole Neutral atoms interact weakly  Rydberg states ~100 kHz at few μm ~100 MHz at few μm

4. Rydberg blockade and quantum information Rydberg blockade gate: Jaksch et al, PRL 85, 2208 (2000) Saffman et al, Grangier et al

5. conditional gates on many targets Rydberg blockade and quantum information Long distance gates Multi-qubit gates in one operation See also: Rydberg Quantum Simulators, Weimer et al

6. = C-NOT C-NOT k multi-target C k -NOT multi-control EASY L. Isenhower, M. Saffman, K. Mølmer, Multibit C k -NOT quantum gates via Rydberg blockade, Quantum Inf Process 10, 755 (2011). 2k+3 pulses 5 pulses Rydberg blockade and quantum information

7. x Grover: 1) Σc x |x>  Σ (-1) f(x) c x |x> (-1) if x matches the “marked“ x 0 2) Inversion of c x about their mean. Rydberg blockade and quantum information

8. x 1/√N ~3/√N Repeat √N times Grover: 1) Σc x |x>  Σ (-1) f(x) c x |x> (-1) if x matches the “marked“ x 0 2) Inversion of c x about their mean. 1) Is every bit OK? Excite from ”wrong state”  change of sign, … and two errors do not cancel. 2) Change of sign of all states but the symmetric one |s> = Σ|x> = (|0> +| 1>) k Excite from ”wrong state” (|0> - |1>). Rydberg blockade and quantum information

9. 2k π-pulses One Grover step in 4k π-pulses 4k < 49k-149 one and two-bit gates Need √N Grover steps Mutual B ss small, ”ancilla” B sr big One Grover step in 8 π-pulses Klaus Mølmer, Larry Isenhower, Mark Saffman, Efficient Grover search with Rydberg blockade, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 184016 Rydberg blockade and quantum information

10. Missing atom = no Rydberg excitation 50 % chance: all remaining qubits are correct 50 % chance: all remaining qubits are random Filtering and majority vote determines all qubits in few trials Figure: Grover search with 40 atoms 20 atoms are lost in each trial After 10 trials, all 40 bits are guessed correctly with high probability. D. D. Bhaktavatsala Rao and KM in preparation Rydberg blockade and quantum information

11. Symmetric collective excitation of a single atom into different internal states: encoding bit value 1 … |N> |2> |1> |0> … E. Brion,et al, Phys. Rev. Lett. 99, 260501 (2007) |r> Rydberg blockade and ensemble qubits

12. … |N> |2> |1> |0> … Number of bits ~ number of states (linear scaling)!!! |r> |r’> Rydberg blockade and ensemble qubits

13. A 14 bit computer in a Cs cloud … and 127 bits (!) in a cloud of holmium. Rydberg blockade and ensemble qubits Ho 4 I 15/2 ground state contains 128 hyperfine states!!!

14. Distributed computing on different clouds with flying qubits Long distance quantum communication Multi-atom collective effects in light emission (phase matching and ”superradiance”). Directional single photon source (collective em.) Saffman and Walker, 2005. Rydberg ensemble qubits and light-matter interface

15. Repeater with on-board distillation Anne Nielsen and KM, PRA Line Pedersen and KM, PRA Combine multi-bit ensembles and single-photon interfaces: Entangled pulses on-demand

16. Quantum (atom) optics n atoms 0 or 1 atom N-n atoms |r> Quantum state of ground state occupation numbers: |n> -- second quantization, coupled oscillator, collective spins, … Spin squeezed states, Schrödinger cat states, NOON states Ressource states for clocks, magnetometers, navigation, light emission, quantum computing, QM tests, …

17. Quantum (atom) optics n atoms 0 or 1 atom Rydberg blockade:  blocks state transfer  non-linear coupling strengths Ω√n  Jaynes-Cummings simulator … many proposals by ”the usual suspects”. N-n atoms |r>

18. Quantum (atom) optics EIT, STIRAP=100 % transfer |g>  |r> |gg>  |gg>-|ee> … |g … g>  ??? D. Møller et al

19. Quantum (atom) optics n or n-1 atoms 0 or 1 atom Ω√n: |n,0>  |n-1,1> Jaynes-Cummings dynamics Eigenenergies: +/- Ω 2 √n N-n atoms |r> a + b + b + a = J x Eigenenergies : Ω 1 m x |e> |g> Adiabatic multi-atom ”dark state” |0,0> JC = |g N > ↨ |J x =0> Dicke state |J x =0> |r> if N is odd odd/even: phase  Schr. Cat. Quantum phase transition ?

20. Rydberg blockade and many body physics A resonant laser will only excite one atom, further excitation is blocked Partial suppression of excitation in large clouds Büchler, Zoller, Pupillo et al. Pohl, Demler, Lukin Rydberg dressing

21. Rydberg blockade and (non-lin.) quantum optics M. Fleischhauer, et al., Lukin et al C. Adams et al Saffman and Walker A. Kuzmich et al

22. Summary Rydberg blockade is one among many proposals for quantum information processing. Rydberg blocked ensembles has unique features: special multi-particle gates, long distance with selectivity Rydberg blocked ensembles are ”hybrid in a single system” (unique qubits, collective qubits, interface to light, microwaves, ….) Growing control capabilities, new ideas, new physics …