Italian National Research Council Institute for Photonics and Nanotechnologies Elettronica quantistica con dispositivi Josephson: dagli effetti quantistici macroscopici al qubit Fabio Chiarello IFN-CNR Rome, Italy "Effetto Josephson: in memoria di Antonio Barone Conferenza SIF, Napoli, 21/9/2012 fabio.chiarello @ ifn.cnr.it SIF Conference, Effetto Josephson: in memoria di Antonio Barone, Sep. 2012
Josephson effect Two superconducting electrodes separated by a thin insulating barrier L i L Le R i R Re Josephson s equations V VR VL R L Symbol
Realistic Josephson junction model RCSJ model I Mechanical equivalent du M M d U I b I0 bcos H 2 p 2M U M C b 1/ RC p M CV b
JJ potential JJ potential U I b I0 bcos I Inclination Modulation For different current biases:
Population of state 1> Josephson junction as an artificial atom Anharmonic potential: JJ used as an Artificial atom Manipulated by microwave pulses, using NMR techniques - Qubit for Quantum computing I mw mw John M. Martinis et al., 2002 J. Lisenfeld et al., 2007
rf SQUID Potential Rf SQUID scheme Potential shape parabola + cosine Flux Symmetric double well for Hamiltonian ( is an equivalent position ) Kinetic energy Potential Unbalancing controlled by x
dc SQUID Small superconducting loop interrupted by two identical JJs i 0, C 0 i 0, C 0 l I 0, C For behaves approximately like a single junction with:
Double SQUID rf SQUID with the single JJ replaced by a dc SQUID Unbalancing controlled by x Barrier height controlled by c
Gradiometricity Flux bias c Different samples: CNR, VTT, PTB, Hypres, MIT Typical: L=85pH, l=5ph, J=8mA, C=0.35pF 1/100 coupling Flux bias x Readout SQUID Junctions 100mm 1 m 0 discrimination
double SQUID characteristics
Manipulation with flux pulses State preparation:?? Phase rotation: e Population rotation: W
Manipulation and readout of the double SQUID state S. Poletto et al., NJP 11, 013009 (2009) M. G. Castellano et al., NJP 12, 043047 (2010)
Observation of coherent oscillations Experimental observation of coherent oscillations (at 30mK) Nb/AlOx/Nb standard technology (Hypres, MIT) Dt - High oscillation frequency: 10GHz 22GHz (new result: up to 60GHz!) - Large number of visible oscillations (~200) S. Poletto, F. Chiarello, M. G. Castellano, et al., New J. Phys. 11, 013009 (2009)
Oscillations for different pulse heights - Oscillation frequency tuned by c (in the single well case) c
Decay times Decay time t*: time necessary to reduce the oscillations amplitude to 1/e=0.368 t* Optimal point
Decay shapes The decay shape changes with the oscillation frequency F Chiarello, E Paladino et Al., NJP 2012 11.6GHz 20.9GHz This behavior is explained by noise dominated by low frequency components
Adiabaticity Required Landau-Zener transitions between levels 0 1 (avoiding transitions to upper levels...) c pulse with risetime t R t R t R Populations for different risetimes (simulation): t R = 3.2ns t R = 1ns t R = 0.32ns t R = 0.1ns 0 0 0 1 1 2 2 1 0 t time s 0 t time s 0 t time s 0 t time s Increasing rates upper (unwanted) levels involved
Adiabaticity For the sudy of adiabaticity used just one part of the complete manipulation: 1. Single well, only fundamental level populated initially 2. Fast transition, single double well t R?? The result depends on the unbalancing: S-shape curve
Peaks
Resonant activation Presence of peaks: resonances between left-righ levels t R =1.34ns 1 2 0 t R =1.14ns 2 3 1 0
Risetime/flux pattern - Test on the capability to tune up the adiabaticity - Interesting quantum effect, based on Landau-Zener and Resonant Activation
Coupling of double SQUID qubits Coupling of qubits Coupling of two qubits by a superconducting transformer Switchable Coupling of two qubits by a tunable superconducting transformer M. G. Castellano et al, App. Phys. Lett. 86, 152504 (2005)
Coupling schemes Coherent bus Neural network XOR of input signals Experimental results (incoherent regime, T = 4.2K)
SQUID neural network Errors (%) Squares Circles = examples = real results after learning Training (genetic algorithm) 60 50 40 30 20 10 0 0 2 4 6 8 10 Generation
Conclusions double SQUID manipulated by fast pulses very high operation frequency (up to 60GHz): a lot of operation possible in short coherence time problem: subnanosecond electronics... Decoherence mechanisms Main decoherence source: low frequency fluctuations Transition between two distinc regimes Probe of the noise features Tests on adiabaticity Possibility to verify the correct operation of the qubit Presence of resonance peaks: combined effect of Landau-Zener transitions and resonant activation