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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 gate 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 ) p1p1 p2p2 time, ps + - 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 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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