Introduction to Josephson Tunneling and Macroscopic Quantum
Tunneling Marc Manheimer November 5, 1999 Slide 2 Outline Review of
Josephson Tunneling. Derivation of tilted washboard potential.
Thermal lifetime (Fulton & Dunkleberger). Macroscopic Quantum
Tunneling (Voss&Webb). More recent work. Slide 3 November 5,
1999 Basic Tunnel Junction i v NIN Tunneling Slide 4 November 5,
1999 NIS Tunneling Slide 5 November 5, 1999 SIS Tunneling Slide 6
November 5, 1999 SIS Tunneling No current flows at T=0 until the
gap voltage is exceeded. It takes 2 to break a Cooper pair, and
leave it at the Fermi level, and another 2 to bring it to the
conduction band in the second metal. ( per electron) The tunneling
current is given by: Slide 7 November 5, 1999 The superconducting
condensate is described by a Schrodinger equation, with
wavefunction: The phase of the wavefunction plays an important role
in Josephson tunneling. The Wavefunction Slide 8 November 5, 1999
Josephson Tunneling In 1962, Josephson predicted... A zero voltage
super current: An evolving phase difference, if a voltage is
maintained across a junction: Metal 1Metal 2 Oxide barrier Slide 9
November 5, 1999 Simple Derivation Impose a voltage between the two
superconductors Couple two superconductors Substitute the pair
density Separate real and imaginary We get Josephsons relationships
with: Slide 10 November 5, 1999 Slide 11 Josephson Energy One can
derive the coupling free energy stored in the junction by
integrating the electrical work done by a current source in
changing the phase: With a convenient reference for : Slide 12
November 5, 1999 RSJ Model I c sin iv + _ C R Tilted Washboard
Potential I Slide 13 November 5, 1999 The Potential Tilted
Washboard Potential II Slide 14 November 5, 1999 Mechanical
Analogue mg Tilted Washboard Potential III Slide 15 November 5,
1999 Slide 16 Slide 17 Measured the effect of thermal noise on the
lifetime of the zero voltage state. They scanned junction current,
lowering the potential barrier, until the junction made the
transition into the finite voltage state. The thermal lifetime is
given by: The probability of switching to the finite voltage state
is: Fulton &Dunkleberger Slide 18 November 5, 1999 Fulton &
Dunkleberger H(K) Slide 19 November 5, 1999 Slide 20 Metastable
state separted from a continuum. Two macroscopically
distinguishable states. Frequency of small oscillations high enough
that Barrier height variable. Experimentally describable in
classical terms. Desired System Properties for QMT Slide 21
November 5, 1999 Verify thermal switching at high T As T 0, the
switching rate becomes dominated by quantum tunneling. Voss &
Webb Caldeira and Leggett fix the parameters, at T=0. Slide 22
November 5, 1999 Misc Parameters I c =1.6 I c =160n 2x10 11 sec -1
7x10 10 sec -1 3.2x10 -3 eV ~35K 3.2x10 -4 eV ~3.5K For Fulton
& Dunkleberger: For Voss & Webb: Slide 23 November 5, 1999
Voss & Webb An interesting aside, is that V&W write the
barrier as: Also, V&W determined x=I/I c by fitting to the
exponential. Slide 24 November 5, 1999 Voss & Webb w/o zero
point subtraction Incl zero point subtraction Slide 25 November 5,
1999 Voss & Webb Slide 26 November 5, 1999 Note: Curves change
with T in MQT regime, as Ic continues to change. Slide 27 November
5, 1999 Slide 28 Slide 29 Finite Temperature MQT Subsequnt to
V&W, several groups developed a finite T model. MQT increases
with T. Washburn, Webb, Voss & Faris, published a follow-on
which verifies predictions. PRL54, p2712 (1985). Groups at Berkeley
and SUNY/SB also verified predictions. Slide 30 November 5, 1999
WWV&F Slide 31 November 5, 1999 WWV&F
