Although the quantum Zeno effect takes its name from Zeno's arrow paradox, the effect of frequently observing the position of a freely moving particle on its motion has not been analyzed in detail in the frame of standard quantum mechanics. We study the evolution of a moving free particle while monitoring whether it lingers in a given region of space, and explain the dependence of the lingering probability on the frequency of the measurements and the initial momentum of the particle. Stopping the particle entails the emergence of Schr\"odinger cat states during the observed evolution, closely connected to the high-order diffraction modes in Fabry-P\'erot optical resonators.
Although the quantum Zeno effect takes its name from Zeno's arrow paradox, the effect of frequently observing the position of a freely moving particle on its motion has not been analyzed in detail in the frame of standard quantum mechanics. We study the evolution of a moving free particle while monitoring whether it lingers in a given region of space, and explain the dependence of the lingering probability on the frequency of the measurements and the initial momentum of the particle. Stopping the particle entails the emergence of Schr"odinger cat states during the observed evolution, closely connected to the high-order diffraction modes in Fabry-P'erot optical resonators.
In 1977, Mishra and Sudarshan [J. Math. Phys. 18, 756 (1977)] showed that an unstable particle would never be found decayed while it was continuously observed. They called this effect the quantum Zeno effect (or paradox). Later it was realized that the frequent measurements could also accelerate the decay (quantum anti-Zeno effect). In this paper, we investigate the quantum Zeno effect using the definite model of the measurement. We take into account the finite duration and the finite accuracy of the measurement. A general equation for the jump probability during the measurement is derived. We find that the measurements can cause inhibition (quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the evolution, depending on the strength of the interaction with the measuring device and on the properties of the system. However, the evolution cannot be fully stopped.
The quantum Zeno effect is the suppression of unitary time evolution in quantum systems and can be caused by measurement or interactions with the environment. It is a feature of a systems under which time evolution of a particle can be slowed down by measuring it frequently enough. In other words, when a system is being constantly watched, it cannot change. Evolution of the system can be slowed down or even frozen by the act of frequent measurement or interaction with the environment. The name of the phenomena comes from Zeno’s arrow paradox, which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all. In this chapter, we will present results of a study conducted on a group of 45 judges adjudicating in criminal cases. We will analyse if preliminary rulings, interim orders and other numerous intermediate decisions related to the course of the criminal trial and affect the final judgement of the case. The findings show whether a quantum effect can be observed in the criminal trials.
The quantum Zeno effect consists in the hindrance of the evolution of a quantum system that is very frequently monitored and found to be in its initial state at every single measurement. On the basis of the correct formula for the survival probability, i.e. the probability of finding the system in its initial state at every single measurement, we critically analyze a recent proposal and experimental test, that make use of an oscillating system. PACS: 03.65.Bz, 42.50.-p 1 The seminal formulation of the quantum Zeno effect, due to Misra and Sudarshan [1], deals with the probability of observing an unstable system in its initial state throughout a time interval ∆ = [0, t]. The purpose of this note is to point out that the quantum Zeno effect has not been experimentally observed, yet, in its original formulation. Indeed, we shall argue that the interesting proposal by Cook [2], that makes use of a two-level system undergoing Rabi oscillations, as well as the beautiful experiment performed by Itano et al. [3], investigate the probability of finding the
Abstract. If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected “quantum Zeno subspace ” is called “quantum Zeno dynamics: ” for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.
If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.
Introduction Quantum theory predicts the striking and paradoxical result that when a system is continuously watched, it does not evolve! Although this effect was noticed much earlier by a number of people [146], [147], [148], [149], [150], it was first formally stated by Misra and Sudarshan [151] and given the appellation ‘Zeno's paradox’ because it evokes the famous paradox of Zeno denying the possibility of motion to a flying arrow. It is as startling as a pot of water on a heater that refuses to boil when continuously watched. This is why it is also called the ‘watched pot effect’. The effect is the result of repeated, frequent measurements on the system, each measurement projecting the system back to its initial state. In other words, the wave function of the system must repeatedly collapse. It is also necessary that the time interval between successive measurements must be much shorter than the critical time of coherent evolution of the system, called the Zeno time [152]. For decays this Zeno time is the time of coherent evolution before the irreversible exponential decay sets in, and is governed by the reciprocal of the range of energies accessible to the decay products. For most decays this is extremely short and hard to detect [153]. In the case of non-exponential time evolution, the relevant Zeno time can be much longer.