The influence of measurement on the decay law

1. The influence of measurement on the decay law ICNFP 2014, Creta 5/8/2014 Francesco Giacosa in collaboration with Giuseppe Pagliara (INFN&University of Ferrara, Italy)

2. Outline • Decay law: general properties, Zeno effect, experimental evidence. • Measurement(s) on an exponentially decaying system • Conclusions and outlook Francesco Giacosa

3. Part 1: General discussion, Zeno effect, and exp. evidence Francesco Giacosa

4. Exponential decay law • : Number of unstable particles at the time t = 0. Confirmend in countless cases! • For a single unstable particle: is the survival probability for a single unstable particle created at t=0. (Intrinsic probabilty, see Schrödinger´s cat). For small times: Francesco Giacosa

5. Basic definitions Francesco Giacosa

6. Deviations from the exp. law at short times Taylor expansion of the amplitude: Francesco Giacosa

7. Lee Hamiltonian: definition |S> is the initial unstable state, coupled to an infinity of final states |k>. (Poincare-time is infinite. Irreversible decay). General approach, similar Hamiltonians used in many areas of Physics. Example/1: spontaneous emission. |S> represents an atom in the excited state, |k> is the ground-state plus photon. Example/2: pion decay. |S> represents a neutral pion, |k> represents two photons (flying back-to-back) Details in: F. Giacosa, Phys. Rev. A 88 (2013) 5, 052131 [arXiv:1305.4467 [quant-ph]]. Francesco Giacosa

8. Lee Hamiltonian: exponential limit If we measure only S, it is perfectly exponential: But: both conditions are non realistic! There is (i) a left threshold and (ii) a decrease of interaction strength for large energies!!! So, there are always (maybe small) deviations from the exp. decay. Francesco Giacosa

9. Lee Hamiltonian: non-exponential case Francesco Giacosa

10. The quantum Zeno-effect Survival probabilty after a single measurement at T Survival probability after N measurments at τ, 2, …, Nτ=T Zeno effect Francesco Giacosa

11. Experimental confirmation of the quantum Zeno effect - Itano et al (1) Francesco Giacosa

12. Experimental confirmation of non-exponential decays and Zeno /Anti-Zeno effects Same exp. setup, but with measurements in between Zeno effekt Anti-Zeno effect Francesco Giacosa

13. Comment on QFT Deviations from the exponential decay law for short and long times are well-established in QM But the very same arguments apply in Quantum Field Theory as well F. Giacosa and G. Pagliara, Deviation from the exponential decay law in relativistic quantum field theory: the example of strongly decaying particles, Mod. Phys. Lett. A 26 (2011) 2247[arXiv:1005.4817 [hep-ph]]. F. Giacosa, Non-exponential decay in quantum field theory and in quantum mechanics: the case of two (or more) decay channels, Found. Phys.42 (2012) 1262  [arXiv:1110.5923 [nucl-th]]. This is important because QFT is in the end the theoretical framework responsible for decays (particle creation and annihilation). Francesco Giacosa

14. Part 2: QZE induced by measurement(s) Francesco Giacosa

15. Bang-bang measurement in a finite band/1 Let us go back to the pure exponential case. So, no QZE should appear. Following discussion is based on: F.Giacosa and G. Pagliara, Pulsed and continuous measurements of exponentially decaying systems,arXiv:1405.6882 [quant-ph]. Francesco Giacosa

16. Bang-bang measurement in a finite band/2 Francesco Giacosa

17. Bang-bang measurement in a finite band/3 arXiv:1405.6882 Francesco Giacosa

18. Continuous measurement in a finite band/1 Let us now assume no collapse, but continuous evolution. In this case the whole ket is a superposition of all possible outcomes, In which the detector is now part of the game. The norm of the ket proportional to D0 gives us the no-click probability. At a practical level, the Hamiltonian is non-Hermitian with: Details in: arXiv:1405.6882 [quant-ph]. See also K. Koshino and A. Shimizu, Phys. Rept. 412 (2005) 191. Francesco Giacosa

19. Continuous measurement in a finite band/2 arXiv:1405.6882 Francesco Giacosa

20. Conclusions and outlook Francesco Giacosa

21. Conclusions and outlook Nonexponential decay is a general phenomenon. The question is if it is strong to be ‚seen‘ in natural systems. For nonexponential decay the QZE applies, but in the exponential limit it doesn‘t. However, we can have the QZE even in the exponential limit and pulsed measurements if the detector is not perfect (i.e., it measures the final state only in a certain range). A continuous measurement generates also a QZE! But in a different way than the bang-bang case. Outlook: investigate the difference between bang-bang and cont. meauserements. Connection to experiment. Francesco Giacosa

22. Thank You! Francesco Giacosa

23. Time evolution and energy distribution (1) Francesco Giacosa

24. Time evolution and energy distribution (2) Breit-Wigner distribution: • The Breit-Wigner energy distribution cannot be exact. • Two physical conditions for a realistic are: • Minimal energy: • Mean energy finite: Francesco Giacosa

25. A very simple numerical example Francesco Giacosa

26. The quantum Zeno effect: simple treatment Francesco Giacosa

27. Other experiments about Zeno Francesco Giacosa

28. GSI oscillations Measurement of weak decays of ions. Measurement was: But up to now: no accepted explanation of these oscillations! Oscillations very recently confirmed! arXiv:1309.7294 [nucl-ex]. Francesco Giacosa

29. Non-exponential case: a numerical example Francesco Giacosa