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International Journal of Modern Physics B

Rectify the effect of measurement in survival probability of the ground vibrational state in diatomic molecule

Bikram Nath, Sariful Rahaman, Chandan Kumar Mondal

Published Jul 10, 2019• 2 citations
Publisher

Abstract

We have proposed a methodology that uses secondary electromagnetic field to overcome the effect of measurement on quantum dynamics. Our aim is also to find out some characteristics of the used secondary (recovery) field. We have applied the methodology to reduce the quantum Zeno effect (ZE), a consequence of repeated measurements in survival probability of ground vibrational state. As the model systems, we choose HBr[Formula: see text] and HI. The study is done with variation in frequency, pulse shape and other parameters of the secondary field. In all cases, suitable secondary field for which the Zeno effect is minimum is found near 0 [Formula: see text] 1 vibrational transition frequency. Suitable time gap between the measurement and the application of secondary field depends on the shape of the secondary field. When the secondary field is optimized, the recovery is more than 90% which almost nullify the Zeno effect.

DOI
10.1142/s0217979219501777

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We have proposed a methodology that uses secondary electromagnetic field to overcome the effect of measurement on quantum dynamics. Our aim is also to find out some characteristics of the used secondary (recovery) field. We have applied the methodology to reduce the quantum Zeno effect (ZE), a consequence of repeated measurements in survival probability of ground vibrational state. As the model systems, we choose HBr[Formula: see text] and HI. The study is done with variation in frequency, pulse shape and other parameters of the secondary field. In all cases, suitable secondary field for which the Zeno effect is minimum is found near 0 [Formula: see text] 1 vibrational transition frequency. Suitable time gap between the measurement and the application of secondary field depends on the shape of the secondary field. When the secondary field is optimized, the recovery is more than 90% which almost nullify the Zeno effect.
Zeno and anti-Zeno effects in the evolution of the multi-photonic dissociation dynamics of the diatomic molecule HBr[Formula: see text] owing to repeated measurements demand if the system in the initial state have been studied. The effects have been calculated numerically for the case of vibrational population transfer and dissociation dynamics of HBr[Formula: see text] taking it as a model. We use time-dependent Fourier grid Hamiltonian (TDFGH) method as a mathematical tool in presence of intense radiation field as perturbation. The effects have been explored through a probable mechanism of population transfer from the ground vibrational state to the different upper vibrational states which ultimately go to the dissociation continuum. The results show significant differences in the mechanism of population transfer and the significant role of time interval of measurement ([Formula: see text] in Zeno and anti-Zeno effects. In case of survival probability of ground vibrational states, there is Zeno effect when the frequency of the laser to which the molecule is submitted is near the vibrational [Formula: see text] to [Formula: see text] resonance, while there is anti-Zeno effect if it is far from this resonance.
We have proposed the mathematical formulations of quantum Zeno and anti-Zeno effects at non-zero temperature on vibrational population transfer and dissociation of a diatomic system. The proposed formulation has been tested for diatomic systems HBr+ and HI using time-dependent Fourier grid Hamiltonian method. The effect of temperature on the dynamics is incorporated through the population distribution at different vibrational states following Boltzmann distribution formula. It has been found that with increase in temperature Zeno effect increases and anti-Zeno effect decreases in case of survival probability on ground vibrational state. In case of dissociation, with increase in temperature Zeno effect increases while anti-Zeno effect remains almost same.
When a quantum system undergoes a series of repeated measurements during its time evolution to check whether it remains in the initial state, the resulting state lifetime can decrease (the quantum Zeno effect) or increase (the quantum inverse Zeno effect) as the inter-measurement period increases. Several transitions between these two regimes may occur within the same system. A carefully chosen measurement period τ∗τ_\astτ∗​ (or rate r∗r_\astr∗​ in the case of a stochastic measurement protocol) brings the state lifetime to its global minimum. Here, we describe the upper and lower bounds on the optimized state lifetime, which are expressed in terms of characteristic time scales encoded in the state survival probability P(T)P(T)P(T), which is assumed to decrease monotonically to zero at large TTT. In addition, we analyze the bounds on the optimal measurement periods/rates and formulate sufficient conditions for observing the inverse Zeno effect. The analysis is also extended to states with non-monotonic survival functions. The results are illustrated numerically with an example of a system of optically trapped ultra-cold atoms.
Quantum Zeno effect can be applied to quantum information processing，and can reveal the nature of quantum measurement. In addition, it has also many potential applications. This suggests that studying the quantum Zeno effect has great theoretical and experimental significance. In this work, the system of a two-level atom interacting with a single mode field is considered and the dynamics of the system subjected to successive projection measurements is studied, and the quantum Zeno effect is presented. Moreover, the influence of the quantum Zeno effect on atomic population inversion is discussed. Based on Schrödinger equation, the survival probability of the initial state of the two-level atom subjected to frequently repeated measurements can be obtained. The survival probability depends on the time interval between measurements. It is seen that the exponential decay of the system under slowly frequent measurements is presented instead of the naturally oscillatory process. For slowly repeated measurements the atomic population inversion and the survival probability of initial state decline rapidly at the early time and then both of them become unchanged. As the time intervals of the measurements are sufficiently short, the quantum Zeno effect occurs. These results have also shown how the measurement can inhibit the atomic population inversion.
We study the quantum Zeno effect (QZE) induced by continuous partial measurement in the presence of short-correlated noise in the system Hamiltonian.We study the survival probability and the onset of the QZE as a function of the measurement strength and find that, depending on the noise parameters, the quantum Zeno effect can be enhanced or suppressed by the noise in different regions of parameter space.Notably, the conditions for the enhancement of the QZE are different when determined by the short-time or long-time behavior of the survival probability, or by the measurement strength marking the onset of the quantum Zeno regime.
We study the quantum Zeno effect (QZE) induced by continuous partial measurement in the presence of short-correlated noise in the system Hamiltonian. We study the survival probability and the onset of the QZE as a function of the measurement strength and find that, depending on the noise parameters, the quantum Zeno effect can be enhanced or suppressed by the noise in different regions of parameter space. Notably, the conditions for the enhancement of the QZE are different when determined by the short-time or long-time behavior of the survival probability, or by the measurement strength marking the onset of the quantum Zeno regime.