1. Superinductor with Tunable Non-Linearity M.E. Gershenson M.T. Bell, I.A. Sadovskyy, L.B. Ioffe, and A.Yu. Kitaev * Department of Physics and Astronomy, Rutgers University, Piscataway NJ * Caltech, Institute for Quantum Information, Pasadena CA

2. Outline: Superinductor: why do we need it? Our Implementation of the superinductor Microwave Spectroscopy and Rabi oscillations Potential Applications - A new fully tunable platform for the study of quantum phase transitions?

3. Impedance controls the scale of zero-point motion in quantum circuits: -reduction of the sensitivity of Josephson qubits to the charge noise, -Implementation of fault tolerant computation based on pairs of Cooper pairs and pairs of flux quanta (Kitaev, Ioffe), -ac isolation of the Josephson junctions in the electrical current standards based on Bloch oscillations. Potential applications: Why Superinductors?

4. Conventional “Geometric” Inductors the fine structure constant Geometrical inductance of a wire: ~ 1 pH/  m. Hence, it is difficult to make a large (1  H  6 k  @ 1 GHz) L in a planar geometry. Moreover, a wire loop possesses not only geometrical inductance, but also a parasitic capacitance, and its microwave impedance is limited:

5. Tunable Nonlinear Superinductor For the optimal E JL /E JS, the energy becomes “flat” at  =1/2  0. - diverges, the phase fluctuations are maximized. Unit cell of the tested devices: asymmetric dc SQUID threaded by the flux .

6. Kinetic Inductance Manucharyan et at., Science 326, 113 (2009). Long chains of ultra-small Josephson junctions: (up to 0.3  H) Nanoscale superconducting wires: InOx films, d=35nm, R  ~3 k , L  ~4 nH Astafiev et al., Nature 484, 355 (2012). NbN films, d=5nm, R  ~0.9 k , L  ~1 nH Annunziata et al., Nanotechnology 21, 445202 (2010).

7. Tunable Nonlinear Superinductor (cont’d) I cell 2 cells 4 cells 6 cells Optimal depends on the ladder length. two-well potential

8. Inductance Measurements CKCK LCLC L C LC- resonator inductor resonator LKLK Two coupled (via L C ) resonators: -decoupling from the MW feedline -two-tone measurements with the LC resonance frequency within the 3-10 GHz setup bandwidth. 1-11 GHz 3-14 GHz

9. Dev1 Dev2 Dev3 Dev4 Multiplexing: several devices with systematically varied parameters. “Manhattan pattern” nanolithography Multi-angle deposition of Al On-chip Circuitry

10. Devices with 6 unit cells Hamiltonian diagonalization - for the ladders with six unit cells 4.5 4.3

11. Rabi Oscillations a non-linear quantum system in the presence of an resonance driving field. 1 The non-linear superinductor shunted by a capacitor represents a Qubit. Damping of Rabi oscillations is due to the decay (coupling to the LC resonator and the feedline).

12. Mechanisms of Decoherence Decoherence due to Aharonov-Casher effect: fluctuations of offset charges on the islands + phase slips. The phase slip rate is negligible (for the junctions in the ladder backbone ).

13. Ladders with 24 unit cells almost linear inductor ~ 100  m two-well potential

14. Ladders with 24 unit cells (cont’d) Number of unit cells 243.150.4614.50.154.650.8163 000

15. Ladders with 24 unit cells (cont’d) - this is the inductance of a 3- meter-long wire! quasi-classical modeling

16. Double-well potential crit. point A new fully tunable platform for the study of quantum phase transitions?

17. Summary Our Implementation of the superinductor Microwave Spectroscopy and Rabi oscillations - Rabi time up to 1.4  s, limited by the decay Potential Applications - Quantum Computing - Current standards - Quantum transitions in 1D