We utilize the band structure of a mesoscopic Josephson junction to construct low noise ampli- The noise temperature is estimated to be around 1 Kelvin, but it is realistic to achieve T N < 0.1 Kelvin. These devices provide quantum-electronic building blocks that will be useful in low-noise, The quantum behavior of a superconducting junction is described by the Schrödingerwhere ϕ is the phase difference of the order parameter across the junction,denotes the Coulomb energy set by the junction capacitance C, and the Josephson coupling energy E J =h 2e I C is given by the critical current I C of the junction. From this Mathieu equation, energy bands (see Fig. 1) should be formed in a similar fashion as for electrons in a periodic potential (9). In the limit of small Josephson coupling, E J /E C << 1, the width of the lowest band is nearly equal to E C , while the gap between the first and second band is given by E J . In the strongly superconducting case, E J /E C 1, the band width becomes exponentially small with exp(− 8E J /E C ) and the gap grows as Zener tunneling occurs when the junction leaves its ground state at the Brillouin zone boundary by tunneling through the forbidden energy gap without a change of charge. As the bias current increases, the probability to cross the band gap by Zener tunneling grows according to the formula (whereI C , the probability of Zener tunneling becomes substantial.Relaxation downwards from higher bands can be induced either by intrinsic mechanism at rate Γ ↓ or by external quasiparticle injection Γ ext . If Γ ↓ << Γ ext , then external, active control of the junction dynamics can be achieved. Γ ↓ is a strong function of the environmental impedance R C , and it can be made small when R C R Q and when T is small (11).In order to go beyond the regime of Coulomb blockade of Cooper pairs (12) and to have a supercurrent I flowing in the JJ, the biasing voltage has to satisfy V bias >the maximum slope of the lowest band (see point A in Fig. 1). Then the junction will propagate along the lowest level and perform Bloch oscillations in a periodic fashion at f B .When the current increases, the probability to cross the band gap by Zener tunneling grows.By selecting the ratio of E J /E C and the current I properly, one can tune the probability ratio P Zener /P Bloch so that the state of the junction will tunnel into the second band after a few Bloch oscillations, N on average.| max , the maximum slope of the second band, then the state of the Josephson junction will become stationary on the higher band after Zener tunneling.If there is no intrinsic relaxation (Γ ↓ → 0), the junction will not relax and it will remain stationary, i.e., Coulomb blockaded on the higher band (sitting, e.g., at point B in Fig. 1).
3Consequently, there will be no supercurrent in the JJ before relaxation takes place due to externally-induced quasiparticle tunneling which is indicated by the slanted arrow in Fig (Fig. 2).To estimate the current gain β of the BOT, the relaxation rate due to the base current ...