PDF (double-sided) - Physics Department, UCSB - University of ...

other states using a classical excitation, one needs to change the spacing of the
energy levels, i.e. introduce a non-linearity into the potential. In general it is very
straightforward to make circuits behave in a non-linear fashion. In fact, almost all
circuits will show some kind of non-linear behavior if they are driven hard enough.
The problem here is to build a circuit that does so with only a single photon of
energy. Luckily, nature provides a way to achieve just that: The Josephson tunnel
junction [Josephson, 1962].
2.2.2 Josephson Tunnel Junctions
A Josephson tunnel junction is formed every time a superconducting lead is
interrupted by a thin barrier through which electrons can tunnel. The tunneling
provides a weak link between the two superconducting regions and allows the wave
functions of the superconducting order parameter on the two sides to interfere.
This leads to very interesting electrical characteristics of the junction that are
captured by the “Josephson Relations”, named after Brian Josephson who received
the Nobel Prize in 1973 for predicting them:
V (t) = Φ 0
2π
d
δ(t) (2.8)
dt
I(t) = I c sin δ(t) (2.9)
22