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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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slide1
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

slide2

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 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

slide3

Macroscopic Quantum Tunneling

I

S

JJ

S

eV

MQT = tunnel switching from non-dissipative to dissipative current branch

slide4

Quantum Tunneling

Free evolution

ΔU

Ψ(t) = exp (- iHt ) |0>

P(t) = exp (- Γt )

- lnP

t

slide5

Quantum Tunneling

Watching!

Ψ(tm) = exp (- iHtm ) |0> → |0>

ΔU

Projective

measurement

Periodic watching: tm << 1/ΔU

P(t) ≈ exp (- Γzeno t )

Zeno regime

Γzeno = (<H2> - <H>2 ) tm

- lnP

t

Quantum Zeno effect

1/ΔU

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

slide6

MQT: what is measured?

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

I

∂tφ = 2eV = 4Δ

eV

What is a measurement time?

tm ~ Δ/ωp2 >> 1/ ωp

JJ switching DOES NOT exhibit Zeno effect !

slide8

MQT: periodic modulation

E = k2

E = k2

completely

open

closed

ΔU

ΔU

E0

x

x

t1 << 1 /ΔU

t2 >> 1/ΔU

open

closed

open

slide9

destructive interference

t2 >> 1/ΔU

|k’>

|k’>

|k’>

|k1>

|k2>

|0>

closed

open

open

= Zeno effect !

Correction~ (1 / ΔU t2) b

slide10

Conclusion

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!

slide11

Rapid modulation: t2 << 1 / ΔU

Decay from modulated well = decay from effective static well

(Kapitza regime)

E

E

E0 < Ueff

E0 > Ueff

ΔU

ΔU

Ueff

E’0

Ueff

Stay

Go

C00

Ueff =ΔUt1 /(t1+t2)

slide12

SUMMARY

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.

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