Coherent Quantum Phase Slip

1. Coherent quantum phase slip, Nature, 484, 355 (2012) 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 Oleg Astafiev NEC Smart Energy Research Laboratories, Japanand The Institute of Physical and Chemical Research (RIKEN), Japan

2. Outline • 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

3. Coherent Quantum Phase Slips (CQPS) • 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)

4. What is phase slip? Cooper pair tunneling Flux tunneling Space Superconductor Superconductor Superconductor Space Space Superconducting Wire Insulating Barrier Space Superconductor 2e F0 Josephson Effect: tunneling of Cooper pairs CQPS: tunneling of vortexes (phase slips)

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

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

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

8. Duality between CQPS and the Josephson Effect Mooij, Nazarov. Nature Physics2, 169-172 (2006) Josephson junction Phase-slip junction Z  Y L  C 0  2e The CQPS is completely dual to the Josephson effect

9. Exact duality Mooij, Nazarov. Nature Physics2, 169-172 (2006) [nq,f] = -i nq = normalized charge alongthe wire f = Phase across junction CQPS Voltage: Vc sin(2pnq) Kinetic Capacitance: 2e(2p Vc cos(2pnq))-1 Shapiro Step: DI =n2en Josephson Current: Ic sinf Kinetic Inductance: F0(2pIc cosf)-1 Shapiro Step: DV =nF0n Shapiro Step Shapiro Step IC VC Supercurrent CQPS voltage

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

11. The Phase-Slip Qubit Degeneracy 1 0 - - - - EL >> ECQPS + + + + 1 0 E 0 1 2 3 4 ext Magnrtic energy: EL >> kT ECQPS Phase-slip energy: CQPS qubit:

12. Duality to the charge qubit L  C 0  2e extqext Cg Cg Box C Vg EJ Reservoir Charge is quantized: 2eN Hamiltonian: The loop with phase-slip wire is dual to the charge qubit

13. Choice of materials • 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

14. 107 106 105 Sheet resistance R□ () 104 103 102 101 0 5 10 15 T (K) Superconductor-insulator transition(SIT) Requirements: high sheet resistance > 1 k InOx, TiN, NbN High resistance  high kinetic inductance The materials demonstratingSIT transition are the most promising for CQPS

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

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

17. B Transmission through the step-impedance resonator Z0 Z0 Z1 Current field the resonator 2nd Current amplitudes: maximal for evenzero for odd modes Z1 >> Z0 1st Transmission at 4th peak 4 3 5 250 MHz

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

19. Ip M I0  Current driven loop with CQPS ES |1 |0 RWA: Transitions can happen only when ES 0

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

21. = D E / h ( ) 2 + 2 d F 2 I E p s = h Wide range spectroscopy 2 fprobe + fres (3-photons) fprobe + fres (2 photons) fprobe Linear inductance!

22. Decoherence Gaussian peak  low frequency noise f = 260 MHz 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. NbN thin films R 2 k In MW measurements Tc 5 K L 1.6 nH/sq 20 different loops with wires of 20-50 nm width Many qubits can be identified General tendency: the higher resistance, the higher ES

24. NbN qubits Transmission amplitude f (GHz)

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