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Physical Review A

Quantum Zeno effect at finite measurement strength and frequency

L. Lerner

Published Nov 26, 2018• 4 citations
Publisher

Abstract

The evolution of a system subject to measurement is restricted to Zeno subspaces of the measurement Hamiltonian in the limit of strong measurements $k$ in a phenomenon known as the quantum Zeno effect (QZE). As the limit constrains QZE to the lowest orders of perturbation in $1/k$, we derive general expressions for the maximum probability leakage from Zeno subspaces for reversible interactions and leakage rates for irreversible interactions for both quantum decay and Lindblad measurement operators. We show that pulsed QZE can be expressed in the same Hamiltonian formulation as continuous QZE, and the two merge in the large-frequency $f$ limit. We derive a nonperturbative expression for pulsed QZE at finite $k$ and $f$, which reduces to previously known results for pulsed QZE at large $k$ and continuous QZE at large $f$.

DOI
10.1103/physreva.98.052132

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The evolution of a system subject to measurement is restricted to Zeno subspaces of the measurement Hamiltonian in the limit of strong measurements kkk in a phenomenon known as the quantum Zeno effect (QZE). As the limit constrains QZE to the lowest orders of perturbation in 1/k1/k1/k, we derive general expressions for the maximum probability leakage from Zeno subspaces for reversible interactions and leakage rates for irreversible interactions for both quantum decay and Lindblad measurement operators. We show that pulsed QZE can be expressed in the same Hamiltonian formulation as continuous QZE, and the two merge in the large-frequency fff limit. We derive a nonperturbative expression for pulsed QZE at finite kkk and fff, which reduces to previously known results for pulsed QZE at large kkk and continuous QZE at large fff.
Summary form only given. The quantum Zeno effect (QZE) is the striking possibility of inhibiting the decay of an unstable quantum state by sufficiently frequent measurements. This effect is currently believed to be universal, even though it has only been observed for oscillations between discrete states. Recently we showed that both the QZE and the inverse (anti-) Zeno effect (AZE) can be observed on spontaneous decay in cavities. We develop a general theory of evolution of quantum systems in the presence of frequent measurements. We consider both the ideal case of instantaneous projections of the wave function to the initial state and some possible measurement schemes. The considerations imply the impossibility of the continuous-observation limit necessary to stop quantum evolution (the quantum Zeno paradox). Indeed, this limit leads to an unbounded increase of the energy fluctuations of the system, which would cause the system to disintegrate. The present theory describes different measurement effects, including the QZE and AZE, and allows us to obtain the general criteria of their validity. In particular, we show that the AZE, rather than the QZE, is achievable for spontaneous decay of atoms in free space.
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.
If frequent measurements ascertain whether a quantum system is still in a given subspace, it remains in that subspace and a quantum Zeno effect takes place. The limiting time evolution within the projected subspace is called quantum Zeno dynamics. This phenomenon is related to the limit of a product formula obtained by intertwining the time evolution group with an orthogonal projection. By introducing a novel product formula, we will give a characterization of the quantum Zeno effect for finite-rank projections in terms of a spectral decay property of the Hamiltonian in the range of the projections. Moreover, we will also characterize its limiting quantum Zeno dynamics and exhibit its (not necessarily bounded from below) generator as a generalized mean value Hamiltonian.
Frequent Measurements on an unstable particle located at observable initial state freeze the particle on this state, known as quantum Zeno effect [1-14]. Measurements on an observable subspace further open the prelude of quantum Zeno dynamics [15-17]. These phenomena affect the results of quantum measurement that has been widely used in quantum information and quantum computation [18-21]. However, this common argument is insufficient when the initial state is coupled with a continuum reservoir. In such an irreversible system, intrinsic decay property destroys the frozen behavior. Although it has been proven that the decay rate of the initial state will be affected by measurements [7], the knowledge of detailed mechanisms for this measurement-dependent decay is still limited. In this work, we found based on three-subsystem perturbation theory that the indirect correlation between a continuum reservoir and a measurement apparatus through the interaction with a quantum system causes a Rabi-like inter-modulation among these subsystems. The indirect correlation effect from this combination drives the system into quantum Zeno and reactivation regions, which are dependent upon the Rabi strength, pulse duty, and its repetition rate. We also found that the dynamical changes of decay rate are quite different in continuous and pulsed measurements, and, thus, significantly affect the dynamics of the system.