Anti-Zeno effect

Figure 4.4 Frequency-domain representation of the dynamically controlled decoherence rate in various limits (Section 4.4). (a) Golden-Rule limit, (b) Anti-Zeno effect (AZE) limit (c) Quantum Zeno effect (QZE) limit. Here, F,( ) and G(w) are the modulation and bath spectra, respectively and F are the interval of change and width of G( ), respectively and is the interruption rate.

In the intermediate timescale of interventions, where the width of Ff co) is broader than the width (so that the GR is violated) but narrower than the width of G co) (so that the QZE does not hold), the overlap of Ff co) and G a>) grows as the rate of interruptions, or modulations, increases. This brings about the increase of relaxation rates R t) with the rate of interruptions, marking the anti-Zeno effect (AZE) [13,45, 67] (Eigure4.4b). Qn such timescales, more frequent interventions... 

This would accomplish the goal of DD [39,41 7, 79], Conversely, the increase of R due to a shift can be much greater than that achievable by repeated measurements, that is, the anti-Zeno effect [9,13-15]. In practice, however, AC Stark shifts are usually small for (cw) monochromatic perturbations, whence pulsed perturbations should often be used, resulting in multiple shifts as per Eq. (4.132). 

The prevailing view until recently has been that successive frequent measurements (interruptions of the evolution) known as the quantum Zeno effect must slow down the decay of any unstable system. A few years ago, Kofman et al. [Kofman 2000 Kofman 2001 (a)] showed that, in fact, the opposite is commonly true for decay into open-space continua the anti-Zeno effect (AZE), i.e., decay acceleration by frequent measurements1, is far more ubiquitous than the QZE [Milonni 2000 Seife 2000]. How can this conclusion be understood and what was missing in standard treatments that claimed the QZE universality The last paper of this part, by G. Kurizki et al. shows that ... 

The phenomenon known as the quantum Zeno effect takes place in a system which is subject to frequent measurements projecting it onto its (necessarily known) initial state if the time interval between two projections is small enough the evolution of the system is nearly "frozen". This effect, and its inverse (the anti-Zeno effect), have been widely investigated theoretically [Khalhn 1957-58 Winter 1961 Misra 1977 Fonda 1978 Kofman 1996 Kof-man 2000 Lewenstein 2000 Kofman 2001 (a) Schmidt 2003 / 2004] as well as experimentally [Cook 1988 Itano 1990 Wilkinson 1997 Fischer 2001], Generalizations have been proposed which employ incomplete measurements [Facchi 2002] in this setting, the Hilbert space is split into "Zeno subspaces" (degenerate multidimensional eigenspaces of the measured observable), and the state vector of the system is compelled by frequent measurements of the physical observable to remain in its initial Zeno subspace. The dynamics of the system in the Zeno subspaces has also been studied in different specific situations [Facchi 2001 (b)]. 

Abstract Decay acceleration by frequent measurements (interruptions of the coupling), known as the anti-Zeno effect is argued to be much more ubiquitous than its inhibition in one- or two-level systems coupled to reservoirs (continua). In multilevel systems, frequent measurements cause accelerated decay by destroying the multilevel interference, which tends to inhibit decay in the absence of measurements. 

The results of our numerical calculations based on Eqs. (7a) and (7b), which use the exact expressions for e(q), uq and vq instead of the HF approximation, clearly reveal a deviation from exponential decay for small times. Under such conditions, frequent measurements would accelerate the decay, causing the anti-Zeno effect (AZE). Alternatively, one may accelerate the decay by periodically modulating the coupling of the initial state to the continuum, [Kofman 2000 Kofman 2001 (a)], instead of repeated projective measurements. This can be done by changing the impurity velocity using a sequence of Bragg or Raman laser pulses [Stenger 1999 Steinhauer 2002],... 

ZENO AND ANTI-ZENO EFFECTS IN DRIVEN JOSEPHSON JUNCTIONS CONTROL OF MACROSCOPIC QUANTUM TUNNELING... 

Zeno and anti-Zeno effects in driven Josephson junctions... 

M. Lewenstein, K. Rzazewski, Quantum anti-Zeno effect, Phys. Rev. A 61 (2000) 022105. 

Decoherence in condensed phase typically slows down chemical reactions as has been exemplified by the non-radiative relaxation of solvated electrons [3,18,67]. In the case of an electron in water the difference in the rates of quantum decoherence induced in the electron subsystem by water and deuterated water explains the absence of a solvent isotope effect on the relaxation rate [18,67]. In rare instances, decoherence can enhance chemical reactivity. The SMF approach has been used to provide evidence for acceleration of a chemical reaction in a condensed phase due to the quantum anti-Zeno effect [55]. The mechanism indicates that the anti-Zeno effect involves both delocalization of the quantum dynamics and a feedback loop by coupling to the solvent. Believed to be the first example of the quantum anti-Zeno effect in chemistry, the observed phenomenon suggests the possibility of quantum control of chemical reactivity by choice of solvent. 

Kofman, A.G., Kurizki, G. Frequent observations accelerate decay The anti-Zeno effect. Zeit. Naturforsch. Sect. A 56, 83-90 (2001)... 

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