2. 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

3. The Box The box is 700x50x15nm; It has about 10 8 conduction electrons. e 2 /2C = 117  V; T=30mK, so kT = 3  V; for aluminum,  =230  V

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

5. Tunneling

6. Josephson’s Equations

7. Energy in a Junction. Finally, where

8. Squid 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.

9. Energy of a Squid

10. Cooper Pair Box VgVg Box Capacitor Junction RjRj CgCg Box,  CjCj VgVg

11. Energy of the Box

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

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

19. Josephson Quasiparticle Current Figure 9.1: The double junction Cooper pair box. Junction 2 has very high impedance, has very low critical current, and is voltage biased. Capacitor Junctions VgVg VbVb Box 1 2 V b =650  V, E C =117  V, and R 2 =30M   qp =1.6 x 10 8 sec -1, the lifetime is about 6ns. (Averin and Aleshkin)