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 $f$ .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 $f$.

Physical Review ANov 26, 20184 citations

Quantum Zeno effect by general measurements

Kazuki Koshino, Akira Shimizu

arXiv:quant-ph/0411145Physics ReportsApr 27, 2005224 citations

Large-time limit of the quantum Zeno effect

Paolo Facchi A, Marilena Ligabò

If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, t∝Nα. The limit survival probability exhibits a sudden jump from 1 to 0 at α=1/2, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for α≥1, the limit probability becomes sensitive to the spectral properties of the initial state and to the arithmetic properties of the measurement periods.If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, t∝Nα. The limit survival probability exhibits a sudden jump from 1 to 0 at α=1/2, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for α≥1, the limit probability becomes sensitive to the spectral properties of the initial state and to the arithmetic properties of the measurement periods.

arXiv:1702.04284Journal of Mathematical PhysicsMar 1, 20176 citations

Quantum Zeno effect induced by quantum-nondemolition measurement of photon number

M. J. Gagen, Gerard J Milburn

Measurements performed on a system will alter the dynamics of that system, and in the strong-measurement limit, can theoretically freeze the free evolution completely. This is the quantum Zeno effect. We utilize quantum-nondemolition photon-counting techniques to realize the Zeno effect on the evolution of either a two-level Jaynes-Cummings atom interacting with a resonant cavity mode, or on two electromagnetic modes configured as a multilevel parametric frequency converter. These systems interact with another electromagnetic cavity mode via a quadratic coupling system based on four-wave mixing and constructed so as to be a nondemolition measurement of the photon number. This mode is then coupled to the environment through the cavity mirrors. This measurement is shown to be a measurement of system populations, which generates the desired Zeno effect and in the strong-measurement limit will freeze the free dynamics of the system.Measurements performed on a system will alter the dynamics of that system, and in the strong-measurement limit, can theoretically freeze the free evolution completely. This is the quantum Zeno effect. We utilize quantum-nondemolition photon-counting techniques to realize the Zeno effect on the evolution of either a two-level Jaynes-Cummings atom interacting with a resonant cavity mode, or on two electromagnetic modes configured as a multilevel parametric frequency converter. These systems interact with another electromagnetic cavity mode via a quadratic coupling system based on four-wave mixing and constructed so as to be a nondemolition measurement of the photon number. This mode is then coupled to the environment through the cavity mirrors. This measurement is shown to be a measurement of system populations, which generates the desired Zeno effect and in the strong-measurement limit will freeze the free dynamics of the system.

Physical Review AApr 1, 199217 citations

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