1. Coherent Quantum Phase Slip Oleg Astafiev NEC Smart Energy Research Laboratories, Japan and The Institute of Physical and Chemical Research (RIKEN), Japan RIKEN/NEC: O. V. Astafiev, S. Kafanov, Yu. A. Pashkin, J. S. Tsai Rutgers: L. B. Ioffe Jyväskylä: K. Yu. Arutyunov Weizmann: D. Shahar, O. Cohen Coherent quantum phase slip, Nature, 484, 355 (2012)

2.  Introduction. Phase slip (PS) and coherent quantum phase slip (CQPS)  Duality between CQPS and the Josephson Effect  CQPS qubits  Superconductor-insulator transition (SIT) materials  Experimental demonstration of CQPS Outline

3.  Very fundamental phenomenon of superconductivity (as fundamental as the Josephson Effect)  Exactly dual to the Josephson Effect Flux interference (SQUID)  Charge interference Charge tunneling  Flux tunneling Applications  Quantum information Qubits without Josephson junctions  Metrology Current standards (dual to voltage standards) Coherent Quantum Phase Slips (CQPS)

4. Flux tunneling SpaceSpace Superconductor Superconductor Superconducting Wire WireSuperconducting  Cooper pair tunneling SuperconductorSuperconductor Space Space InsulatingBarrierInsulatingBarrier2e What is phase slip? Josephson Effect: tunneling of Cooper pairs CQPS: tunneling of vortexes (phase slips)

5. Superconductivity does not exist in 1D-wires: Thermally activated phase slips I V Phase-slips at T close to T c are known for long time Width  coherence length  Phase can randomly jump by 2 

6. Thermally activated phase slips Quantum phase slip V T kT    Thermally activated and Quantum phase slip Signature of QPS? At T = 0: Phase slips due to quantum fluctuations(?) Are phase slips possible at T = 0?

7. Incoherent quantum process  coherent quantum process Quantum Phase Slip (QPS)  Coherent QPS Spontaneous emission: Open space  infinite number of modes I Dissipative transport measurements: P = IV Coherent coupling to a single mode: Resonator, two-level system  single mode Nanowire in a closed superconducting loop   incoh <  

8. Duality between CQPS and the Josephson Effect Josephson junctionPhase-slip junction The CQPS is completely dual to the Josephson effect Z  Y L  C  0  2e Mooij, Nazarov. Nature Physics 2, 169-172 (2006)

9. Exact duality Josephson Current: I c sin  Kinetic Inductance:   (2  I c cos  ) -1 Shapiro Step:  V = n   CQPS Voltage: V c sin(2  n q ) Kinetic Capacitance: 2e(2  V c cos(2  n q )) -1 Shapiro Step:  I = n2e  = Phase across junction n q = normalized charge along the wire Mooij, Nazarov. Nature Physics 2, 169-172 (2006) ICICICIC VCVCVCVC Shapiro Step [n q,  ] = -i Supercurrent CQPS voltage

10. Flux is quantized: N  0 A loop with a nano-wire Hamiltonian: The loop with phase-slip wire is dual to the charge qubit (PS qubit proposed by Mooij J. E. and Harmans C.J.P.M ）

11. Magnrtic energy: Phase-slip energy: E CQPS E         Degeneracy >> kT 0 2314 The Phase-Slip Qubit  ext ELEL >> E CQPS ELEL CQPS qubit: 00 11 00 11

12. Charge is quantized: 2eN Duality to the charge qubit Hamiltonian: The loop with phase-slip wire is dual to the charge qubit EJEJ Reservoir Box C CgCg VgVg CgCg L  C  0  2e  ext  q ext

13.  Loops of usual (BCS) superconductors (Al, Ti) did not show qubit behavior  BCS superconductors become normal metals, when superconductivity is suppressed  Special class of superconductors turn to insulators, when superconductivity is suppressed  Superconductor-insulator transition (SIT)  High resistive films in normal state  high kinetic inductance Choice of materials

14. Superconductor-insulator transition (SIT) InO x, TiN, NbN Requirements: high sheet resistance > 1 k  High resistance  high kinetic inductance 10 7 10 6 10 5 10 4 10 3 10 2 10 1 051015 T (K) Sheet resistance R □ (  ) The materials demonstrating SIT transition are the most promising for CQPS

15. 40 nm EsEs N0N0 (N+1)  0 E  ext (N+1/2)  0 Gold ground-planes InO x 5  m 0.5 mm InO x MW in MW out Amorphous InO x film: R □ = 1.7 k  The device Step-impedance resonator: High kinetic inductance

16. Measurement circuit Network Analyzer -20 dB Isolator resonator Phase-slip qubit Coil Low pass filters output input 4.2 K 1 K 40 mK

17. Transmission through the step-impedance resonator 1st 2nd Z0Z0 Z1Z1 Z0Z0 Current field the resonator Current amplitudes: maximal for even zero for odd modes 3 4 5 250 MHz BB Z 1 >> Z 0 Transmission at 4 th peak

18.  f = 260 MHz 0 -5 arg(t) (mrad) Two-tone spectroscopy We measure transmission through the resonator at fixed frequency f res Another frequency f probe is swept The fitting curve: I p = 24 nA, E S /h = 4.9 GHz

19. Current driven loop with CQPS Transitions can happen only when E S  0 M IpIp I0I0  |1  |0  RWA: ESES

20. The result is well reproducible Three identical samples show similar behavior with energies 4.9, 5.8 and 9.5 GHz After “annealing” at room temperature InO x becomes more superconducting. The samples were loaded three times with intervals about 1 months. Es is decreased with time.

21. f probe 2 f probe + f res (3-photons)  h EI hE sp 2 2 2 /       f probe + f res (2 photons) Wide range spectroscopy Linear inductance!

22. Decoherence  f = 260 MHz Gaussian peak  low frequency noise Total PS energy: Potential fluctuations along the chain of Josephson junctions leads to fluctuations of energy and decoherence Potential equilibration (screening) in the wire? Mechanism of decoherence?

23. L  1.6 nH/sq NbN thin films R  2 k  In MW measurements T c  5 K Many qubits can be identified 20 different loops with wires of 20-50 nm width General tendency: the higher resistance, the higher E S

24. NbN qubits f (GHz) Transmission amplitude

25. Conclusion  We have experimentally demonstrated Coherent Quantum Phase Slip  Phase-slip qubit has been realized in thin highly resistive films of InO x and NbN  Mechanism of decoherence in nano-wires is an open question