Quantum Optics with Electrical Circuits: Circuit QED

Transcription

1 Quantum Optics with Electrical Circuits: Circuit QED Eperiment Rob Schoelkopf Michel Devoret Andreas Wallraff David Schuster Hannes Majer Luigi Frunzio Andrew Houck Blake Johnson Emily Chan Jared Schwede Joe Schreier Jerry Chow NSF/Keck Foundation Yale Center for Quantum Information Physics Yale Institute for Nanoscience and Quantum Engineering Theory SMG Jay Gambetta Jens Koch Terri Yu Lev Bishop Daniel Rubin David Price Aashish Clerk (McGill) R. Huang (Taipei) Aleandre Blais (Sherbrooke) K. Moon (Yonsei) Joe Chen (Cornell) Cliff Cheung (Harvard)

2 Overview Fundamental Physics: cavity QED with SC microwave circuits Etreme strong atom-photon coupling Non-linear quantum optics with small atom and photon numbers Focus on quantum particle nature of microwaves Quantum Measurements Josephson bifurcation amplifier -- QND measurements of qubits and photons Quantum Computation: Focus on optimal qubit design with high symmetries and long coherence times 1D cavities as quantum bus for communication via real and virtual photons 2

3 A Circuit Analog for Cavity QED Circuit Quantum Electrodynamics L = λ ~ 2.5 cm λ 2.5 cm out transmission line cavity DC + 6 GHz in 6 3 mode volume: 10 λ dispersive coupling enhanced by μm 3 6 Q = 10 Cross-section 10 photons of travel mode: 10 Ekilomet B ers while - in the + + resonator! - CPW optical fiber 10 μm (if superconducting) Artificial atom A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, PRA 69, (2004) 3

4 4 SCALABLE ARCHITECTURE: The Importance of Communicating with Photons X: individual qubits cavity buses switch -able coupling photon on demand logical qubits cavity swapping crossbar bus

5 The transmon: Optimizing the Cooper Pair Bo Qubit to Maimize T μm E J /E C = 1 E J /E C = 5 E J /E C = 10 E J /E C = 50 Energy Design Goals: Eliminate sensitivity to charge noise Retain anharmonicity of qubit energy levels Increase coupling to cavity N g (gate charge) Ref: cond-mat/ and Phys. Rev. A (2007) 5

6 Coherence Time at Flu Insensitive Point Ramsey eperiment at 7.5 GHz Q φ ~ 100,000 NO Echo: T * 2 = 2.05 ± 0.1μs T1 = 1.5μs = + * T2 2T1 T φ T φ = μs 6μs consistent with ~ 20 khz of residual charge dispersion at E J /E C = 50 6

7 Single-Shot Readout of Transmon Histograms of single shot msmts. Integrated probabilities e g e g Measurement with ~ 5 photons in cavity; SNR ~ 4 in one qubit lifetime (T 1 ) T1 ~ 300 ns, low Q cavity on sapphire 7

8 Resolving individual photon numbers using ac Stark shift of qubit transition frequency 17 coherent input power = 10 Watts Coherent state is produced by a laser or a microwave generator. Coherent state n 2 Poisson distribution P ( n) λ ( n) = n! n e n Thermal state is digitally synthesized noise (blackbody radiation) Thermal state n 2 Bose-Einstein distribution Average cavity photon number is n=2 in both cases. P th ( n) = ( n) n n+ ( n + 1) 1 8

9 Single Photons on Demand Temporal separation reduces collection efficiency Single Photon Fock State: 90% emission efficiency 40% collection efficiency Superposition State: 60% emission efficiency 15% collection efficiency 9

10 Fluorescence Tomography Apply pulse about arbitrary qubit ais Qubit state mapped on to photon superposition σˆ z a + a a a Qubit (all of the above are data) 10

11 Cavity as quantum bus for two qubit gates Interaction via virtual photon echange H J gg 2 ( + + σ ) 1σ2 σ1σ2 = J Δ Δ 1 2 =

12 12

13 (first generation with T < 200 ns) 1 Multipleed Readout: 2 classical bits of information 13

14 Rabi flop qubit 1 Rabi flop qubit 2 Very little cross talk 1 14 (first generation with T < 200 ns)

15 Avoided Qubit-Qubit Crossing 15

16 State Transfer (Using first generation transmon with short T2=100 ns.) Background due to off-resonant driving by the Stark tone 16

17 Design for Si Qubits Coupled on a Single Bus Q1 Q2 Q3 In Out Q4 Q5 Q6 Sample bo with 8 20 GHz connections Si flu lines to address each qubit, plus one input and one output port for control and measurement 17

18 Main New Results New regime of Cooper-pair bo: the transmon - charge noise and parity problems are SOLVED - T2 > 1 μs & limited by T1, no significant 1/f dephasing - T1 is partially understood and now 10 longer Using microwave photons to communicate quantum information! Converted quantum info to flying qubit photon on demand Demonstrated two qubit swapping via cavity bus Two kinds of multipleed readout demonstrated: cavity bifurcation amplifier (CBA) and cavity QED Readout fidelity still not optimized, limited by relaation 18

19 The End 19

20 Nb Coming Soon: Individual Addressing of Qubits: Fast Flu Bias Lines Short-circuited CPW line for fast flu control I bias Readout & coupling bus Nb Al transmons 20

21 Purcell Effect Controls T 1 : Low Q cavity can enhance rate of spontaneous emission of photon from qubit qubit cavity qubit cavity κ g = + Δ 2 γ γ κ Intrinsic non-radiative decay rate Cavity enhanced decay rate

22 T1 Times Eplained Eplained by Purcell Effect Sapphire Q = 100 Sapphire Q = 100 loss tangent Q=70,000 Silicon Q =

23 LONG TERM GOAL: SCALABLE ARCHITECTURE superconducting transmission-line cavity as quantum bus for 2-bit operations frequency-selective RF pulses for 1 and 2-bit operations Cooper-pair bo qubits multipleed cavity Josephson bifurcation amplifiers for readout of individual qubits module scalable to 10 s of qubits if coherence and fidelity allow (may be simpler than two superconducting wiring layers and one dielectric isolation 23 layer)