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What NEC Did

What NEC Did. Engineered a two-state system Initialized the system Formed a superposition state Allowed the system to evolve Stopped the evolution Read out the final state. The Box. The box is 700x50x15nm; It has about 10 8 conduction electrons.

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What NEC Did

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  1. What NEC Did • Engineered a two-state system • Initialized the system • Formed a superposition state • Allowed the system to evolve • Stopped the evolution • Read out the final state

  2. The Box The box is 700x50x15nm; It has about 108 conduction electrons. e2/2C = 117mV; T=30mK, so kT = 3mV; for aluminum, D=230mV

  3. Scope of Talk • Tunneling • The wave function • Josephson’s equations and the squid • The Cooper pair box • Schrodinger equation solution • Josephson quasiparticle current

  4. Tunneling

  5. Josephson’s Equations

  6. Energy in a Junction . where Finally,

  7. Figure 6.1: Schematic of a two-junction squid. Current enters at the top, splits into two branches, and recombines at the bottom. The junctions are at a-b and d-c. A magnetic field B threads the loop formed by the two branches. The integration path is denoted C. Squid

  8. Energy of a Squid

  9. Junction Capacitor Vg Box Cj Cg Box,f Vg Rj Cooper Pair Box

  10. Energy of the Box

  11. Hamiltonian To arrive at the quantum mechanical Hamiltonian, note that These two exponents are just raising and lowering operators. H can be rewritten:

  12. Hamiltonian • For our system, we can safely consider only the two lowest energy states, • In that case,

  13. Junctions Capacitor Figure 9.1: The double junction Cooper pair box. Junction 2 has very high impedance, has very low critical current, and is voltage biased. Box 1 2 Vg Vb Josephson Quasiparticle Current (Averin and Aleshkin) Vb=650mV, EC=117mV, and R2=30MW Gqp=1.6x108sec-1, the lifetime is about 6ns.

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