Berry phase from a quantum Zeno effect

Facchi, Paolo; Klein, A. G.; Pascazio, Saverio; Schulman, L. S.

doi:10.1016/s0375-9601(99)00323-0

Cited by 40 publications

(37 citation statements)

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“…At the same time, the dynamics of system B becomes unitary in this limit, and this is an example of the so-called "quantum Zeno dynamics" [12]. However, we stress that our interest lies in a different situation: we keep the time interval τ between measurements finite and nonvanishing.…”

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confidence: 97%

Purification through Zeno-Like Measurements

2003

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A series of frequent measurements on a quantum system (Zeno-like measurements) is shown to result in the "purification" of another quantum system in interaction with the former. Even though the measurements are performed on the former system, their effect drives the latter into a pure state, irrespectively of its initial (mixed) state, provided certain conditions are satisfied.PACS numbers: 03.65.XpIt is well known that unstable particles or quantum states display a peculiar behavior at short and long times [1]. Phenomenologically, they are known to decay exponentially and this is well confirmed experimentally [2]. Short-time deviations were only observed very recently [3]. The deviations from the familiar exponential decay law are unavoidable consequences of the quantum dynamics both at short and long times, and the derivation of the exponential decay law itself is not a trivial matter in quantum mechanics. These deviations reflect the unitarity of the time evolution operator or the time reversal symmetry of the Schrödinger equation at short times and the lower boundedness of the Hamiltonian or the stability of the vacuum at long times. See, e.g., Ref.[1] for a review.The quantum behavior of unstable states at short times has been one of the central issues of investigation and discussion in recent years, since it is closely connected to the so-called quantum Zeno effect (QZE) [4,5], where the act of measurement [6] (usually represented by the von Neumann projection or the generalized spectral decomposition [7]) affects in an essential way the dynamics of the measured system and results in a hindrance of the decay process. The first attempt at the experimental observation of the QZE in an atomic transition process [8], following Cook's theoretical work [9], has triggered heated discussions on this subject. Furthermore, another exciting experiment has been reported very recently: the observation of the QZE (and also of the inverse QZE [10]) in an atomic tunneling process [11], which is the first experimental observation of the (inverse) QZE in a truly unstable quantum system, unlike in the previous experiment [8] performed on an oscillating system.In this Letter, we will shed new light on another (and so far not well explored) feature of the quantum dynamics with measurements, closely related to the QZE. Notice first that the system under consideration cannot be considered completely isolated and usually interacts with other systems. Therefore, it would be interesting and maybe more realistic to consider the case where the measurement, represented by a von Neumann projection for simplicity, is not performed on the total system, but only on the system of interest. Here, we consider such measurements and address the following point: How does a series of frequent measurements on a system affect the dynamics of another system in interaction with the former? Under frequent measurements performed only on the former system, the latter evolves away from its initial state. We shall show that such measurements can result i...

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confidence: 97%

Purification through Zeno-Like Measurements

2003

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“…This is an example of the so-called "quantum Zeno dynamics." 12,14,15) We are however interested in a different situation: we repeat the measurement with a nonvanishing (not necessarily small) τ . The probability P (τ ) (N ) would decay out completely for such a finite τ , but we are interested in the asymptotic behavior of the state of system B, ρ In order to clarify the evolution of system B under the Zeno-like measurement on system A, let us consider the eigenvalue problem of the projected time-evolution operator V φ (τ ).…”

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confidence: 99%

“…We let the total system evolve with the Hamiltonian (14) and confirm repeatedly at regular intervals τ that oscillator a is in the coherent state |α . The time-evolution operator (between adjacent measurements), e −iHτ , is calculated exactly to be (15) in terms of the τ -dependent functions…”

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confidence: 99%

Purification of Quantum State Through Zeno-Like Measurements

2003

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We present a novel procedure to purify quantum states, i.e., purification through Zeno-like measurements. By simply repeating one and the same measurement on a quantum system, one can purify another system in interaction with the former. The conditions for the (efficient) purification are specified on a rather general setting, and the framework of the method possesses wide applicability. It is explicitly demonstrated on a specific setup that the purification becomes very efficient by tuning relevant parameters.KEYWORDS: purification of quantum states, quantum Zeno effect, repeated measurement One cannot observe a quantum system without any disturbance on the object, and the dynamics of the quantum system is affected by the measurement. An interesting manifestation of this effect is the "quantum Zeno effect" (QZE):1-3) if one repeats measurement very frequently in order to ascertain whether a system remains in the initial state, the evolution of the system is slowed down and totally hindered in the limit of infinite frequency. Or conversely, one can also accelerate the decay of an unstable state by repeating the measurement less frequently than a critical frequency (inverse QZE). 4)These are typical examples of the effects of measurement on quantum dynamics.In this article, we present another interesting effect of measurement on quantum dynamics when the measurement is repeated as in the case of the (inverse) QZE: purification of quantum state through Zeno-like measurements.5) We show in the following that a series of measurements on a quantum system indirectly affects the dynamics of another system in interaction with the former, and the latter (initially in any mixed state) is driven into a pure state, provided certain conditions are satisfied. The state of the latter system is purified through the repeated measurement on the former.In the ideas of quantum information and computation, quantum coherence plays crucial roles.6, 7) It is hence one of the important issues to be addressed how to maintain and/or recover quantum coherence, and various schemes have been proposed attacking this subject. 6-14)The work presented here contributes to this issue and provides a novel method to purify quantum states (i.e., to recover quantum coherence), which is simple compared to the standard purification techniques 6, 9, 10) and the framework is rather general.Let a total system A+B be described by a Hamiltonian of the formwhere H A(B) is a free Hamiltonian of system A(B) and H int is an interaction between A and B. We prepare system A in a pure state |φ at time t = 0, while the initial state of system B, denoted by ρ B , can be arbitrary * E-mail address: yuasa@hep.phys.waseda.ac.jp † E-mail address: hiromici@waseda.jp (a mixed state). The total system starts to evolve from the initial statewith the Hamiltonian (1), and we check the state of system A at time t = τ . If it is confirmed that system A remains in its initial state |φ , the state of the total system is projected by a projection operatorand restarts to evolve. We ...

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“…A special kind of experimentations which attract many discussions by many authors (Aharono and Vardi, 1980;Bixon, 1982;Chiu et al, 1977;Facchi et al, 1999;Giulini et al, 1996;Itano et al, 1990;Kofman and Kurizki, 1996;Kurizki et al, 1995;Misra and Sudarshan, 1977;Pascazio and Namiki, 1994;Peres, 1989;Peres and Ron, 1990;Simonius, 1978;Wilkinson et al, 1997) are those in which a large number of experiments are involved. Among these one may note the special role played by those in which the time duration of each of the involved experiments tends to become infinitesimally small.…”

Section: Introductionmentioning

confidence: 99%

The Effects of Related Experiments

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2005

Int J Theor Phys

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The effects of the experiment itself on the obtained results and, especially, the influence of a large number of experiments is extensively discussed in the literature. We show that the important factor that stands as the basis of these effects is that the involved experiments are related and not independent and detached from each other. This relationship takes, as shown here, different forms for different situations and is found in entirely different physical regimes such as the quantum and classical ones.

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Berry phase from a quantum Zeno effect

Cited by 40 publications

References 19 publications

Purification through Zeno-Like Measurements

Purification through Zeno-Like Measurements

Purification of Quantum State Through Zeno-Like Measurements

The Effects of Related Experiments

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