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Bulletin of Federal State University of Education Series Physics and Mathematics

Experimental test of the quantum Zeno effect using an scanning probe microscope

T. F. Kamalov, N. V. Evdokimov, Yu. T. Kamalov

Published Feb 24, 2025• 0 citations
Publisher

Abstract

Aim. To describe an experiment on direct experimental observation of the quantum Zeno effect. Methodology. The study requires a model of a scanning probe microscope-SPM. Results. The described theoretical estimates of the study give encouraging results of obtaining stable excited states of atoms by direct measurement of their excited states. Research implication lies in the prospect of obtaining stable excited states of atoms of various elements.

DOI
10.18384/2949-5067-2024-4-37-42

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Aim. To describe an experiment on direct experimental observation of the quantum Zeno effect. Methodology. The study requires a model of a scanning probe microscope-SPM. Results. The described theoretical estimates of the study give encouraging results of obtaining stable excited states of atoms by direct measurement of their excited states. Research implication lies in the prospect of obtaining stable excited states of atoms of various elements.
The quantum Zeno effect lies in the suppression of the quantum system’s evolution due to frequent successive measurements, which leads to the inhibition of transitions between quantum states. The paper presumes that a qubit can be found in an excited state |1) or in the non-excited state |0). The work aims to investigate how the quantum Zeno effect can be applied to the stable excited state of a qubit to prevent its spontaneous transition to the state |0). An As atom is exploited as the physical realization of a qubit, and it is suggested to register its quantum state using the scanning probe microscopy methods. The work demonstrates the condition necessary for the occurrence of the quantum Zeno effect in the system under study. Calculation results show that the diameter of the excited-state As atom orbit is 1.5 times larger than the diameter of an unexcited atom orbit. This ratio serves as an experimental criterion for identifying the state of a qubit.
Short pulses of a probe laser have been used in the past to measure whether a two-level atom is in its ground or excited state. The probe pulse couples the ground state to a third, auxiliary, level of the atom. The occurrence or absence of resonance fluorescence were taken to mean that the atom was found in its ground or excited state, respectively. In this paper we investigate to what extent this procedure results in an effective measurement to which the projection postulate can be applied, at least approximately. We discuss in detail the complications arising from an additional time development of the two-level system proper during a probe pulse. We extend our previous results for weak probe pulses to the general case and show that one can model an ideal (projection-postulate) measurement much better with a strong than a weak probe pulse. In an application to the quantum Zeno effect we calculate the slow-down of the atomic time development under n repeated probe pulse measurements and determine the corrections compared to the case of n ideal measurements.
We describe theoretically the effects of the quantum back action under the continuous optical measurement of electron spins in quantum dots. We consider the system excitation by elliptically polarized light close to the trion resonance, which allows for simultaneous spin orientation and measurement. We microscopically demonstrate that the nuclei-induced spin relaxation can be both suppressed and accelerated by the continuous spin measurement due to the quantum Zeno and anti-Zeno effects, respectively. Our theoretical predictions can be directly compared with the future experimental results and straightforwardly generalized for pump-probe experiments.
Itano and co-workers [Wayne M. Itano, D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, Phys. Rev. A 41, 2295 (1990)] have recently reported the experimental verification of the quantum Zeno effect, which is the inhibition of a quantum transition by frequent measurements. In this article, we offer an alternative interpretation of the quantum Zeno effect. We show that an analysis of the dynamics of the full three-level system gives the same result. There is no need to assume explicitly that the wave function has collapsed, nor even to assume that an ideal measurement has been made. In addition, we differentiate between what has been referred to as the quantum Zeno effect and what has been termed the quantum Zeno paradox. The former is the inhibition of induced transitions, and the latter is the, as yet experimentally unobserved, inhibition of spontaneous decay. Our interpretation, which emphasizes the ``measurement''-induced interruption of atomic-state coherences as the cause of inhibited quantum transitions, suggests a resolution to the quantum Zeno paradox. The theoretical limit of continuous observation is discussed.
The quantum Zeno effect is the inhibition of the free evolution of a system when that system is subject to a measurement process. The authors of one recent experiment study, W. M. Itano et al., [Phys. Rev. A 41, 2295 (1990)] claimed a demonstration of the quantum Zeno effect. This was done by performing discontinuous atomic-level measurements on a coherently evolving two-level atomic stystem. The measurement was implemented using a pulsed laser strong enough to saturate the two-level atomic system. In this paper, we examine the simpler case where the measurement laser is continuously on and does not saturate the two-level atomic system. In contrast to previous treatments, we show certain parameter regimes wherein an effective state reduction does occur. We ascertain the experimental parameter regimes under which a measurement can be said to have been performed. We show that, in some regimes, fully efficient photon detection does not give good information about the atomic-level populations and hence no measurement has been performed. Throughout, we emphasize that the design of an atomic level-measurement device requires more than the analysis of a mechanism for photon detection or of coherence loss. We gain insight into the operation of a particular measurement process by following the selective evolution of various systems using the quantum-trajectories approach.
We present a scheme for experimentally observing the quantum Zeno effect using the quantum-nondemolition measurement recently proposed by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)]. The Zeno effect refers to the freezing of the (unitary) free dynamics of a system by rapid measurements. We generalize the Zeno effect to be any change in the survival probability of an initial state induced by very rapid measurements, when such measurements are the dominant source of fluctuations in the system. We derive a master equation for the evolution of a cavity mode when the photon number is monitored by this method. This equation describes a phase-diffusion process. We propose that this measurement scheme be used to monitor the exchange of a single photon between the cavity and a single Rydberg atom. We show that for very rapid monitoring the free oscillation of the atomic inversion is disrupted and the atom can be trapped close to the initial excited state. This is the quantum Zeno effect.