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

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

2. Albert Victor Bäcklund, 1845-1922 Outline Johannes Robert Rydberg, 1854-1919 • 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).

3. Neutral atoms interact weakly ∆E ~ 1/ R6 van der Waals ∆E ~ 1/ R3 static or resonant dipole Rydberg atoms Large principal quantum numbers Very large orbitals, Large dipoles ~n2 Long lifetimes Rydberg blockade • Rydberg states ~100 kHz at few μm ~100 MHz at few μm

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

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

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

7. Rydberg blockade and quantum information Grover: 1) Σcx|x>  Σ (-1) f(x) cx |x> (-1) if x matches the “marked“ x0 2) Inversion of cxabout their mean. x

8. ~3/√N 1/√N x Repeat √N times Rydberg blockade and quantum information Grover: 1) Σcx|x>  Σ (-1) f(x) cx |x> (-1) if x matches the “marked“ x0 2) Inversion of cx 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>).

9. Rydberg blockade and quantum information 2k π-pulses Mutual Bss small, ”ancilla” Bsr big One Grover step in8π-pulses 2k π-pulses One Grover step in 4k π-pulses 4k < 49k-149 one and two-bit gates Need √N Grover steps Klaus Mølmer, Larry Isenhower, Mark Saffman, Efficient Grover search with Rydberg blockade, J. Phys. B: At. Mol. Opt. Phys. 44 (2011) 184016

10. Rydberg blockade and quantum information 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

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

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

13. Rydberg blockade and ensemble qubits A 14 bit computer in a Cs cloud … and 127 bits (!) in a cloud of holmium. Ho 4I15/2 ground state contains 128 hyperfine states!!!

14. Rydberg ensemble qubits and light-matter interface 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.

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

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

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

19. Quantum (atom) optics 0 or 1 atom |r> Ω√n: |n,0>  |n-1,1> Jaynes-Cummings dynamics Eigenenergies: +/- Ω2√n n or n-1 atoms |e> a+b + b+a = Jx Eigenenergies : Ω1mx N-n atoms |g> Quantum phase transition ? Adiabatic multi-atom ”dark state” |0,0>JC = |gN> ↨ |Jx=0> Dicke state |Jx=0> |r>ifN is odd odd/even: phase  Schr. Cat.

20. Rydberg dressing Pohl, Demler, Lukin 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.

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

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 …

23. The ice flake is on fire !!!