Superinductor with Tunable Non-Linearity

1. 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 Superinductor with Tunable Non-Linearity

2. 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? Outline:

3. Why Superinductors? Superinductor: dissipationless inductor Z >> No extra dephasing Potential applications: • 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), • acisolation of the Josephson junctions in the electrical current standards based on Bloch oscillations. Impedance controls the scale of zero-point motion in quantum circuits:

4. Conventional “Geometric” Inductors 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: the fine structure constant

5. Tunable Nonlinear Superinductor Unit cell of the tested devices: asymmetric dc SQUID threaded by the flux . Josephson energy of a two cell device (classical approx., ) For the optimal EJL/EJS, the energy becomes “flat” at =1/20. - diverges, the phase fluctuations are maximized.

6. Kinetic Inductance This limitation does not apply to superconductors whose kinetic inductance is associated with the inertia of the Cooper pair condensate. Nanoscale superconducting wires: NbN films, d=5nm, R~0.9 k,L~1 nH Annunziata et al., Nanotechnology21, 445202 (2010). • InOx films, d=35nm, R~3 k,L~4 nH • Astafievet al., Nature 484, 355 (2012). Long chains of ultra-small Josephson junctions: (up to 0.3 H) Manucharyan et at., Science326, 113 (2009).

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

8. Inductance Measurements • Two coupled (via LC) 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 LC- resonator inductor resonator LK L LC CK C

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

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

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 the flux noise: Because the curvature (which controls the position of energy levels) has a minimum at full frustration, one expects that the flux noise does not affect the qubit in the linear order. 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 ~ 100m two-well potential almost linear inductor

14. Ladders with 24 unit cells (cont’d)

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

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