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Vitaly Shumeiko Dept of Microtechnology and Nanoscience

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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Vitaly Shumeiko Dept of Microtechnology and Nanoscience

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  1. 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

  2. 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

  3. Macroscopic Quantum Tunneling I S JJ S eV 2Δ MQT = tunnel switching from non-dissipative to dissipative current branch

  4. Quantum Tunneling Free evolution ΔU Ψ(t) = exp (- iHt ) |0> P(t) = exp (- Γt ) - lnP t

  5. 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

  6. 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 2Δ What is a measurement time? tm ~ Δ/ωp2 >> 1/ ωp JJ switching DOES NOT exhibit Zeno effect !

  7. MQT: how to get Zeno regime? dynamic static

  8. MQT: periodic modulation E = k2 E = k2 completely open closed ΔU ΔU E0 x x t1 << 1 /ΔU t2 >> 1/ΔU open closed open

  9. destructive interference t2 >> 1/ΔU |k’> |k’> |k’> |k1> |k2> |0> closed open open = Zeno effect ! Correction~ (1 / ΔU t2) b

  10. 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!

  11. 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)

  12. 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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