Trapped Ions/Atoms: Quantum Networks Christian Vzquez, David - PowerPoint PPT Presentation

Δ Δ 2 g Ω C Ω C 2 g 6 μ m 6 μ m Ritter et al., Nature 484, 195 (2012) Trapped Ions/Atoms: Quantum Networks Christian Vázquez, David Nadlinger Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 1

This Talk ‣ Quantum Networks: Why? How? ‣ Two Entanglement Generation Experiments: Moehring et al., “Entanglement of single-atom quantum bits at a distance”, Nature 449, 68 (2007) Ritter et al., “An elementary quantum network of single atoms in optical cavities”, Nature 484, 195 (2012) ‣ Results/Comparison ‣ Perspectives Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 2

Why Quantum Networks? Large number of ions in one trap is not feasible: ‣ 1D string -> requirements on trap potential ‣ Heating rate increases linearly ‣ Mechanical mode density increases State of the art: ~15 qubits ‣ Entanglement of 14 ions Monz et al., Phys. Rev. Lett. 106, 130506 (2011) ‣ Simulations using long chains (~20 ions) C. Monroe and J. Kim, Science 339, 1164 (2013) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 3

Why Quantum Networks? k systems of n qubits: ‣ With classical links: d = k 2 n (dim. of state space) With quantum links: d = 2 nk ‣ Multiple qubit entanglement -> State transfer, information sharing J. Kimble, Nature 453, 1023 (2008) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 4

Requirements for Quantum Networks We infer the following requirements. For Nodes: ‣ Receiving, storing, releasing quantum information For Channels: ‣ Faithfully transmit quantum state between nodes Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 5

Linking Ion Traps “Quantum CCD” Photons Kiepinski, Monroe, Wineland, Nature 417, 709 (2002) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 6

Entangling Atoms using Photons Heralded entanglement gen. using beamsplitter: Moehring et al. (2007) C. Monroe and J. Kim, Science 339, 1164 (2013) Cavity QED: Ritter et al. (2012) H. Kimble, Nature 453, 1023 (2008) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 7

Entangling Atoms using Photons Heralded entanglement gen. using beamsplitter: Moehring et al. (2007) C. Monroe and J. Kim, Science 339, 1164 (2013) Cavity QED: Ritter et al. (2012) H. Kimble, Nature 453, 1023 (2008) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 8

Moehring (2007): Exp. Setup ������ re PMT B F = 0 PBS 3 D[3/2] 1/2 2.2 GHz F = 1 Yb + Beam 1 m 2 P 1/2 935.2 nm F = 1 splitter ������ re 2.1 GHz F = 0 B PBS 369.5 nm Repump Yb + Laser PMT F = 2 2 D 3/2 B = 0.55 mT 0.86 GHz F = 1 Excitation Laser 2 S 1/2 F = 1 Qubit Levels 12.6 GHz F = 0 Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 9

� |1,1 > |1,0 > |1,–1 > 2 P 1/2 2.1 GHz |0,0 > � – �������� | � > � | � > |1,0 > |1, 1 > 2 S 1/2 |1,0 > | > |1,–1 > 12.6 GHz |0,0 > |0,0 > | > ���������������� Discard ���������� > |F=1 > | � > | � > | > | > ���� 2 S 1/2 |F=1 2 P 1/2 ( - ) / � 2 Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 10

50/50 (non-polarizing) beam splitter: a a a a - + - b b b b atom photon 1 Consider input state | �� | � � � | �� | � � � � (| �� | � � � | �� | � � 2 1 2(| � | � + | � | � � | � | � � | � | � ) symmetric symmetric symmetric antisymmetric 1 1 ± ± where | � � | � � ± | � � | � � | � � | � � ± | � � | � � � 2 � 2 Detecting 2 coincident photons projects atoms into , | � coincident photons “herald” entanglement creation! Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 11

Entangling Atoms using Photons Heralded entanglement gen. using beamsplitter: Moehring et al. (2007) C. Monroe and J. Kim, Science 339, 1164 (2013) Cavity QED: Ritter et al. (2012) H. Kimble, Nature 453, 1023 (2008) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 12

State Transfer, Entangl. Creation Ideal state transfer follows from adequate Raman pulses: photonic wave packet determined by Ω i (t) Cirac, Zøller, Kimble, Mabuchi, Phys. Rev. Lett . 78, 3221 (1997) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 13

Ritter (2012): Entangl. Sequence Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 14

Ritter (2012): Entangl. Sequence Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 15

Ritter (2012): Entangl. Sequence Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 16

Ritter (2012): Entangl. Sequence Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 17

Ritter (2012): Entangl. Sequence Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 18

Ritter (2012): Entangl. Sequence Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 19

Ritter (2012): Entangl. Sequence Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 20

State Tomography ‣ Moehring (2007): Only correlations in unrotated basis ‣ Ritter (2012): Full state tomography 5 4 . 0 4 4 . 0 0.5 0.4 Detection probability 7 0 . 0 4 0 . 0 0.3 0.2 0 Re( ρ ) 0.1 1 RR 4 . 0 0 – �� �� �� �� RL 1 4 . 0 – Detected states –0.5 LR LL LR LL RL RR Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 21

Local rotations: fidelity oscillates ‣ Moehring (2007): Microwave pulses, di ff erent phase ‣ Ritter (2012): Extra B field applied for 12.5 µs 1.0 100 Fidelity with respective Bell state (%) 0.8 Probability for odd parity 80 0.6 60 0.4 40 20 0.2 0 0 20 40 60 0 –40 –20 0 20 40 60 80 100 Pulse delay ( � s) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 22

Comparison Moehring (2008) Ritter (2012) Excitation to upper state Stimulated Raman Photon creation with short pulse process (STIRAP) Interference at 50/50 Raman process at target Photon use beam splitter atom F = 65 ± 3% Fidelity to target state F = 85 ± 1.3 % Success probability of p = 3.6 ∙ 10 -9 p = 0.02 entanglement scheme Rate of R = 0.118 min -1 R = 1800 min -1 entanglement creation Coincidence detection Entanglement heralding None Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 23

Perspectives N x N optical ELU crossconnect switch ELU ELU ‣ Review: ELU C. Monroe and J. Kim, Science 339, 1164 (2013) ‣ Entanglement by single photon detection Slodi č ka et al., PRL 110, 083603 (2013) ‣ Atom/photon quantum gates Reiserer et al., Nature 508, 237 (2014) Tiecke et al., Nature 508, 241 (2014) Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 24

Conclusion ‣ To build large-scale quantum systems, we need to create entanglement between distant nodes ‣ Two approaches for entangling atoms/ions discussed: ‣ Heralded entanglement creation using beam splitter (probabilistic) ‣ Atom-cavity nodes allowing deterministic interaction with photons Quantum Systems for Information Technology, Spring Term 2014 Christian Vázquez, David Nadlinger | 09. 05. 2014 | 25