Vitaly Shumeiko Dept of Microtechnology and Nanoscience
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Transcript of Vitaly Shumeiko Dept of Microtechnology and Nanoscience
Vitaly Shumeiko
Dept of Microtechnology and NanoscienceChalmers 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 state of current biased Josephson junctions by means of fast temporal manipulations (Zeno regime)
Similar effect has been experimentally investigated with atoms trappedin optical lattice, PRL 87, 040402, 2001
Dynamical control of MQT in Josephson junction has been theoreticallystudied, PRL 92, 200403, 2004
Here we revisit this problem using different technique
Discussions: G. Kurizki, D. Dasari, A. Ustinov
Macroscopic Quantum Tunneling
eV2Δ
IS
S
JJ
MQT = tunnel switching from non-dissipative to dissipative current branch
Quantum Tunneling
P(t) = exp (- Γt )
Ψ(t) = exp (- iHt ) |0>
Free evolution
ΔU
- lnP
t
Periodic watching: tm << 1/ΔU
P(t) ≈ exp (- Γzeno t )
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
Quantum Tunneling
ΔU
Watching!
Ψ(tm) = exp (- iHtm ) |0> → |0> Projective measurement
Γzeno = (<H2> - <H>2 ) tm
- lnP
t1/ΔU
Zeno regime
JJ switching DOES NOT exhibit Zeno effect !
∂tφ = 2eV = 4Δ
After escape, “particle” accelerates till threshold velocity, when single particle tunneling channels opens;Then JJ switches to dissipative branch = measurementBefore switching event – unitary evolution
eV2Δ
I
tm ~ Δ/ωp2 >> 1/ ωp
What is a measurement time?
JJ is a meter itself
MQT: what is measured?
MQT: how to get Zeno regime?
static
dynamic
x x
ΔU
E = k2
t2 >> 1/ΔU
E0
completelyopen
MQT: periodic modulation
closed
ΔU
t1 << 1 /ΔU
E = k2
open closed open
|k1> |k2>
|k’>
|0>
|k’>
|k’>
openopen closed
Correction ~ (1 / ΔU t2) b
= Zeno effect !
destructive interferencet2 >> 1/ΔU
Conclusion
To achieve Zeno regime one has to open well for (short) time intervals, t1<< 1/ΔU, then close for (long) time intervalst2 >> 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(Kapitza regime)
ΔU
E
ΔU
E
Ueff
E0 < Ueff E0 > Ueff
Stay Go
C00
E’0
Ueff =ΔUt1 /(t1+t2)
Ueff
SUMMARY
Studied: decay of a quantum state in quantum well into continuumunder 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.