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The Journal of Chemical Physics

Effect of state-selective reactive decay on the evolution of quantum systems

Anatoly I. Shushin

Published Jul 22, 2010• 20 citations
Publisher

Abstract

The effect of state-selective reactive decay on the relaxation kinetics of quantum multistate systems is studied in detail in the Bloch-Redfield approach (BRA). The results are applied to the analysis of this effect in radical pair recombination kinetics. The BRA is shown to be able to describe quantitatively most important specific features of the recombination kinetics including those predicted by phenomenological treatment and by recently proposed approaches based on quantum measurement theories.

DOI
10.1063/1.3461133

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The effect of state-selective reactive decay on the relaxation kinetics of quantum multistate systems is studied in detail in the Bloch-Redfield approach (BRA). The results are applied to the analysis of this effect in radical pair recombination kinetics. The BRA is shown to be able to describe quantitatively most important specific features of the recombination kinetics including those predicted by phenomenological treatment and by recently proposed approaches based on quantum measurement theories.
The effect of state-selective reactive decay on the relaxation kinetics of quantum multistate systems is studied in detail in the Bloch-Redfield approach (BRA). The results are applied to the analysis of this effect in radical pair recombination kinetics. The BRA is shown to be able to describe quantitatively most important specific features of the recombination kinetics including those predicted by phenomenological treatment and by recently proposed approaches based on quantum measurement theories.
Manifestations of the chemical Zeno effect (slowing down of the quantum evolution of radical pairs as a result of spin-selective recombination of exchange-bounded radical pairs) are considered. In radical pairs created in singlet and random spin states, the chemical kinetics is described by the sum of kinetic evolution (exponential) and oscillatory functions. The kinetic function is a superposition of two exponential functions. Recombination monotonically decreases the amplitude of quantum beats in singlet radical pairs. The dependence of the amplitude of quantum beats in noncorrelated radical pairs on the recombination rate constant is not monotonic.
In the present work, we have shown that consistent derivation of the kinetic equations describing the electron spin-selective recombination of radical pairs confirms the conventional Haberkorn approach. The derivation has been based on considering the interaction of the reactive system (radical pair and product state) with the thermal bath. The consistency of this approach has also been substantiated by numerical simulations performed for the purely quantum mechanical model of the recombining radical pair. Finally, we have shown that the quantum Zeno effect on radical pair recombination is not an exclusive feature of the approach recently proposed by Kominis, as it should be present at any rate of the singlet-triplet dephasing in the radical pair, which always accompanies the recombination process.
The well-known magnetic or optical Bloch equations are extended to the case of unstable systems such as, e.g., spontaneously decaying particles and molecules undergoing chemical reactions or decaying from excited states back to states other than those involved in resonance. The modified equations are derived from a general theory of irreversible processes where quantum Markovian master equations and the corresponding completely positive dynamical semigroups dictate the time evolution of density operators. The results are of particular importance in those situations where decay occurs level-selectively and all relaxation and decay constants are of comparable order of magnitude. The obtained generalized Bloch equations are of direct applicability to problems of time-resolved magnetic or optical resonance spectroscopy.
In studies of the quantum Zeno and anti-Zeno effects, it is usual to consider rapid projective measurements with equal time intervals being performed on the system to check whether or not the system is in the initial state. These projective measurements are selective measurements in the sense that the measurement results are read out and only the case where all the measurement results correspond to the initial state is considered in the analysis of the effect of the measurements. In this paper, we extend such a treatment to consider the effect of repeated non-selective measurements - only the final measurement is required to correspond to the initial state, while we do not know the results of the intermediate measurements. We present a general formalism to derive the effective decay rate of the initial quantum state with such non-selective measurements. Importantly, we show that there is a difference between using non-selective measurements and the usual approach of considering only selective measurements only if we go beyond the weak system-environment coupling regime in models other than the usual population decay models. As such, we then apply our formalism to investigate the quantum Zeno and anti-Zeno effects for three exactly solvable system-environment models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems, and a large spin undergoing dephasing. Our results show that the quantum Zeno and anti-Zeno effects in the presence of non-selective measurements can differ very significantly as compared to the repeated selective measurement scenario.
In studies of the quantum Zeno and anti-Zeno effects, it is usual to consider rapid projective measurements with equal time intervals being performed on the system to check whether or not the system is in the initial state. These projective measurements are selective measurements in the sense that the measurement results are read out and only the case where all the measurement results correspond to the initial state is considered in the analysis of the effect of the measurements. In this paper, we extend such a treatment to consider the effect of repeated non-selective projective measurements - only the final measurement is required to correspond to the initial state, while we do not know the results of the intermediate measurements. We present a general formalism to derive the effective decay rate of the initial quantum state with such nonselective measurements. Importantly, we show that there is a difference between using non-selective projective measurements and the usual approach of considering only selective measurements only if we go beyond the weak system-environment coupling regime in models other than the usual population decay models. As such, we then apply our formalism to investigate the quantum Zeno and anti-Zeno effects for three exactly solvable system-environment models: a single two-level system undergoing dephasing, a single two-level system interacting with an environment of two-level systems and a large spin undergoing dephasing. Our results show that the quantum Zeno and anti-Zeno effects in the presence of non-selective projective measurements can differ very significantly as compared to the repeated selective measurement scenario.