Report

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 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? Why Superinductors? Superinductor: dissipationless inductor ℎ Z >> Q ≡ 2 ≈ 6.5Ω 2 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), - ac isolation of the Josephson junctions in the electrical current standards based on Bloch oscillations. Impedance controls the scale of zero-point motion in quantum circuits: 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: = ≈ 0 = 8 × ~0.4Ω 0 the fine structure constant 1 e 2 2 0 hc 1 137 Tunable Nonlinear Superinductor ≡ Unit cell of the tested devices: asymmetric dc SQUID threaded by the flux . Φ Δ = 2 Φ0 ℎ Φ0 ≡ ≈ 20 ∙ 2 2 Josephson energy of a two cell device (classical approx., ≪ ) = −5 × 2 5 −1 Φ − 1 2 Φ − 3 5 − 1 2 Φ + 3 5 . For the optimal EJL/EJS, the energy becomes “flat” at =1/20. 2 2 Φ - diverges, the phase fluctuations are maximized. 0 0 = . = = . = < . = 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: ℎ ∆ Φ0 = 2 = 8 2 2 1 Φ0 = 2 2 1 ℏ = ∆ NbN films, d=5nm, R~0.9 k, L~1 nH Annunziata et al., Nanotechnology 21, 445202 (2010). InOx films, d=35nm, R~3 k, L~4 nH Astafiev et al., Nature 484, 355 (2012). Long chains of ultra-small Josephson junctions: (up to 0.3 H) Manucharyan et at., Science 326, 113 (2009). Tunable Nonlinear Superinductor (cont’d) two-well potential I cell 2 cells 4 cells 6 cells Optimal ≡ depends on the ladder length. Inductance Measurements LC- resonator LK inductor resonator 3-14 GHz 1-11 GHz CK L LC C Two coupled (via LC) resonators: - decoupling feedline from the MW - two-tone measurements with the LC resonance frequency within the 3-10 GHz setup bandwidth. ≈ 6 − 7 2 ≈ 1 − 20 2 On-chip Circuitry “Manhattan pattern” nanolithography Multi-angle deposition of Al Dev1 Dev2 Multiplexing: several devices with systematically varied parameters. Dev3 Dev4 Devices with 6 unit cells Hamiltonian diagonalization o Device , K , K , K , K 1 3.5 0.46 15 0.15 2 3.5 0.46 14.3 0.15 o = 6 = Φ = 0 , Φ = Φ0 /2 , nH nH 4.3 4.5 3.7 150 4.1 4.3 3.8 310 ≡ ≈ 4.1 - for the ladders with six unit cells opt 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). Mechanisms of Decoherence Decoherence due to the flux noise: Because the curvature 2 J 2 (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 exp − JL CL ≅ 2.5 − 2.8 is negligible (for the junctions in the ladder backbone JL ≅ 100 CL ). Ladders with 24 unit cells ≈ 5.2 o = 24 ≈ 4.5 ~ 100m two-well potential almost linear inductor = 0 /2 = 3 Ladders with 24 unit cells (cont’d) ≈ 4.6 o = 24 = Number of unit cells JS , K 24 3.15 CS , K JL , ≈ 4.5 opt CL , K K 0.46 14.5 0.15 = ≡ JL JS 4.6 , , K Φ = 0 , K Φ = Φ0 /2 , fF nH nH nH 5 0.8 16 3 000 Ladders with 24 unit cells (cont’d) quasi-classical modeling = / = - this is the inductance of a 3meter-long wire! 3 = 50Ω > ≡ ℎ 2 2 Φ0 Φ= 2 crit. point Double-well potential ≈ 4.2 o = 24 ≈ 4.5 A new fully tunable platform for the study of quantum phase transitions? 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