Vitaly Shumeiko Dept of Microtechnology and Nanoscience Chalmers University of Technology, Göteborg Sweden. Zeno regime in Macroscopic Quantum Tunneling. ESF Conference, Obergurgl, 6-9 June 2010. Background Aim : possibilities to slowdown quantum decay (MQT) of non-dissipative
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Dept of Microtechnology and Nanoscience
Chalmers University of Technology, Göteborg Sweden
Zeno regime in Macroscopic Quantum Tunneling
ESF Conference, Obergurgl, 6-9 June 2010
Aim: possibilities to slowdown quantum decay (MQT) of non-dissipative
state of current biased Josephson junctions by means of fast temporal
manipulations (Zeno regime)
Similar effect has been experimentally investigated with atoms trapped
in optical lattice, PRL 87, 040402, 2001
Dynamical control of MQT in Josephson junction has been theoretically
studied, PRL 92, 200403, 2004
Here we revisit this problem using different technique
Discussions: G. Kurizki, D. Dasari, A. Ustinov
MQT = tunnel switching from non-dissipative to dissipative current branch
Ψ(t) = exp (- iHt ) |0>
P(t) = exp (- Γt )
Ψ(tm) = exp (- iHtm ) |0> → |0>
Periodic watching: tm << 1/ΔU
P(t) ≈ exp (- Γzeno t )
Γzeno = (<H2> - <H>2 ) tm
Quantum Zeno effect
B. Misra and E. C. G. Sudarshan, J. Math. Phys. 18, 756 (1977)
P Facchi and S Pascazio, J. Phys. A: Math. Theor. 41 (2008) 493001
JJ is a meter itself
After escape, “particle” accelerates till threshold velocity, when
single particle tunneling channels opens;
Then JJ switches to dissipative branch = measurement
Before switching event – unitary evolution
∂tφ = 2eV = 4Δ
What is a measurement time?
tm ~ Δ/ωp2 >> 1/ ωp
JJ switching DOES NOT exhibit Zeno effect !
E = k2
E = k2
t1 << 1 /ΔU
t2 >> 1/ΔU
t2 >> 1/ΔU
= Zeno effect !
Correction~ (1 / ΔU t2) b
To achieve Zeno regime one has to open well for (short)
time intervals, t1<< 1/ΔU, then close for (long) time intervals
t2 >> 1/ΔU
The system measures itself. It gradually performs
projection on bound state during time >> 1/ΔU
Evolution is purely unitary!
Rapid modulation: t2 << 1 / ΔU
Decay from modulated well = decay from effective static well
E0 < Ueff
E0 > Ueff
Ueff =ΔUt1 /(t1+t2)
Studied: decay of a quantum state in quantum well into continuum
under rapid modulation of the barrier transparency (instant opening-closing)
Found: two distinctly different regimes: “incoherent” (Zeno) and coherent.
In both cases state evolution is purely unitary.
Incoherent regime: well is kept closed during time longer than inverse
level frequency. In this case, the leaking state is effectively projected on the
original bound state (self-measurement) leading to the Zeno effect – substantial
suppression of the decay rate.
Coherent regime: manipulation cycle (open-close) is shorter than inverse
level frequency. A finite fraction of the state stays in the well at t = ∞,
for ratio of open-close durations being smaller than certain critical value.