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Technological issues of superconducting charge qubits Oleg Astafiev Tsuyoshi Yamamoto Yasunobu Nakamura Jaw-Shen Tsai Dmitri Averin NEC Tsukuba - SUNY at Stony Brook Yuri Pashkin RIKEN 30 March 2004 Quantum Technologies 2004 Vancouver, Canada - RIKEN

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Outline - introduction - electrostatic coupling - single-shot readout - T 1 and T 2 measurement - technological issues

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gate reservoir box ++++ - - a single artificial two-level system ~10 8 conduction electrons in the box n=01 Cooper-pair tunneling E = (C g V g – 2ne) 2 /2C Cooper-pair box M. Büttiker, 1987 V. Bouchiat et al, 1995

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Charge qubit based on Cooper-pair box eigenstates: charge states:, initialization coherent superposition read-out gate voltage energy EJEJ initial state coherent oscillations final state Y. Nakamura et al, 1999

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Josephson-quasiparticle cycle (Fulton et al., 1989) 2e Cooper-pair box detect the state initialize the system to e e + probe Final state read-out

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Capacitively coupled charge qubits pulse gate (common) dc gate 2 dc gate 1 probe 1 probe 2 reservoir 2 qubit 2 reservoir 1 qubit 1 1 m standard e-beam lithography + angle evaporation Cross Section capacitive coupling box 2box 1 I2I2 I1I1 V b2 V b1 VpVp V g1 V g2 I 1 and I 2 give info on charge states

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Hamiltonian charge basis E n1n2 = E c1 (n g1 –n 1 )² + E c2 (n g2 –n 2 )² + E m (n g1 –n 1 )(n g2 –n 2 ) E c1,2 = 4e²C Σ2,1 /2(C Σ1,2 C Σ2,1 – C m ²) 4e²C Σ2,1 /2C Σ1,2 C Σ2,1 n g1,2 = (C g1,2 V g1,2 + C p V p )/2e E m = 4e²C m /(C Σ1 C Σ2 – C m 2 ) I00>I10>I01>I11> I00> I10> I01> I11> E c1, E c2, E m E J1, E J2 initial state E J1,2 ~ E m < E c1,2 I00>

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Oscillations at the double degeneracy pulse gate d ｃ gate1 d ｃ gate2 1 0.5 0 1 0 n g2 n g1 0,0 0,1 1,0 1,1 n g1 (= n g2 ) time superposition of four charge states! I1I1 I2I2 X 0,1 1,0 0,0 1,1 E 00 = E 11 E 10 = E 01

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Quantum beatings operation point n g1 (= n g2 ) 0.5 0.45 p1p1 p2p2 time, ps 01000 + - 2f2f + 22 - 22

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Quantum beatings: experiment theoretically expected E J1 = 13.4 GHz E J2 = 9.1 GHz E m = 15.7 GHz 1 0.5 0 1 0 n g2 n g1 0,0 0,1 1,0 1,1 L R X - + 0.6 ns 2.5 ns E J1 E J2

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Single-shot readout 2( + E c ) EJEJ conventional readout reservoir probe permanently biased ! qp ~ 1/10 ns box EJEJ trap+SET readout reservoir trap kept unbiased during coherent evolution no qp relaxation! qp = 0 box

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Trap + SET readout box + trap galvanically isolated from the leads ! no qp relaxation ! no effect of the leads !

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Time trace SET signal control+readout derivative of SET signal

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Single-shot readout: coherent oscillations dead zones degeneracy

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no increase in T 2 Relaxation of coherent oscillations

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T 1 measurement create 1 state by NA -pulse move slowly along the upper band stay for time move slowly back repeat for different -pulse with probability exp(- /T 1 ) ngng E time

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T 1 measurement: experiment

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NEC Saclay Chalmers controlsubstrate pulse - waves pulse SiN x SiO 2 T1T1 T2T2 group 5 ns 1 s 1.8 s 100 ns 0.5 s readout RF-SET dc probe pulse probe trap+SET switching current Superconducting charge qubits

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What next? 1. Qubit readout: dc probe pulsed probe trap + SET 2. Qubit control: NA pulses -waves 3. Materials:qubit Al Nb? substrate SiN x SiO 2 4. Dependence of T 1 and T 2 on (1-3)

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Nb SET AlO x Barrier Nb island Nb lead

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UNIVERSITY OF NOTRE DAME Xiangning Luo EE 698A Department of Electrical Engineering, University of Notre Dame Superconducting Devices for Quantum Computation.

UNIVERSITY OF NOTRE DAME Xiangning Luo EE 698A Department of Electrical Engineering, University of Notre Dame Superconducting Devices for Quantum Computation.

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