Quantum Zeno effect with partial measurement and noisy dynamics

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.

arXiv:2006.13970Physical Review ResearchDec 24, 202019 citations

Quantum Zeno effect appears in stages

Kyrylo Snizhko, Parveen Kumar, Alessandro Romito

In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. The effect is conventionally controlled by the measurement frequency. Here we study the development of the Zeno regime as a function of the measurement strength for a continuous partial measurement. We show that the onset of the Zeno regime is marked by a cascade of transitions in the system dynamics as the measurement strength is increased. Some of these transitions are only apparent in the collective behavior of individual quantum trajectories and are invisible to the average dynamics. They include the appearance of a region of dynamically inaccessible states and of singularities in the steady-state probability distribution of states. These predicted dynamical features, which can be readily observed in current experiments, show the coexistence of fundamentally unpredictable quantum jumps with those continuously monitored and reverted in recent experiments.In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. The effect is conventionally controlled by the measurement frequency. Here we study the development of the Zeno regime as a function of the measurement strength for a continuous partial measurement. We show that the onset of the Zeno regime is marked by a cascade of transitions in the system dynamics as the measurement strength is increased. Some of these transitions are only apparent in the collective behavior of individual quantum trajectories and are invisible to the average dynamics. They include the appearance of a region of dynamically inaccessible states and of singularities in the steady-state probability distribution of states. These predicted dynamical features, which can be readily observed in current experiments, show the coexistence of fundamentally unpredictable quantum jumps with those continuously monitored and reverted in recent experiments.

Sep 29, 202062 citations

Quantum control for the Zeno effect with noise

Haorui Chen, Shengshi Pang

The quantum Zeno effect is a distinctive phenomenon in quantum mechanics, describing the nontrivial effect of frequent projective measurements on hindering the evolution of a quantum system. However, when subjected to environmental noise, the quantum system may dissipate, and the quantum Zeno effect no longer works. This research starts from the physical mechanism for the decay of the quantum Zeno effect in the presence of noise and investigates the effect of coherent quantum controls on mitigating the decrease of the survival probability that the system stays in the initial state induced by the noise. We derive the decay rate of the survival probability with and without coherent quantum controls in general, and show that when the frequency of the projective measurements is large but finite, proper coherent controls by sufficiently strong Hamiltonians can be designed to decrease the decay rate of the survival probability. A two-level quantum system suffering from typical unitary and nonunitary noise is then considered to demonstrate the effect of the proposed coherent quantum control scheme in protecting the quantum Zeno effect against the noise. The decay rate of the survival probability is obtained in the presence of noise, and the control Hamiltonian is further optimized analytically to minimize the decay rate by a variational approach. The evolution paths of the quantum system with the optimal coherent controls are illustrated numerically for different scenarios to explicitly show how the coherent control scheme works in lowering the decay of survival probability.The quantum Zeno effect is a distinctive phenomenon in quantum mechanics, describing the nontrivial effect of frequent projective measurements on hindering the evolution of a quantum system. However, when subjected to environmental noise, the quantum system may dissipate, and the quantum Zeno effect no longer works. This research starts from the physical mechanism for the decay of the quantum Zeno effect in the presence of noise and investigates the effect of coherent quantum controls on mitigating the decrease of the survival probability that the system stays in the initial state induced by the noise. We derive the decay rate of the survival probability with and without coherent quantum controls in general, and show that when the frequency of the projective measurements is large but finite, proper coherent controls by sufficiently strong Hamiltonians can be designed to decrease the decay rate of the survival probability. A two-level quantum system suffering from typical unitary and nonunitary noise is then considered to demonstrate the effect of the proposed coherent quantum control scheme in protecting the quantum Zeno effect against the noise. The decay rate of the survival probability is obtained in the presence of noise, and the control Hamiltonian is further optimized analytically to minimize the decay rate by a variational approach. The evolution paths of the quantum system with the optimal coherent controls are illustrated numerically for different scenarios to explicitly show how the coherent control scheme works in lowering the decay of survival probability.

arXiv:2402.13325Physical Review AJun 11, 20245 citations

Zeno effect of an open quantum system in the presence of 1/f noise

Shu He, Chen Wang, Liwei Duan +1 more

We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in a two-level system (TLS) interacting with an environment that has $1/f$ noise. Using a numerically exact method based on the thermofield dynamics theory and the matrix product states, we obtain exact evolutions of the TLS and bath (environment) under repetitive measurements at both zero and finite temperatures. At zero temperature, we observe a transition from a pure QZE in the short time scale to a QZE-QAZE crossover in the long time scale by considering the measurement-induced non-Markovian effect. At finite temperature, we exploit that the thermal fluctuation suppresses the decay of the survival probability in the short time scale, whereas it enhances the decay in the long time scale.We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in a two-level system (TLS) interacting with an environment that has $1/f$ noise. Using a numerically exact method based on the thermofield dynamics theory and the matrix product states, we obtain exact evolutions of the TLS and bath (environment) under repetitive measurements at both zero and finite temperatures. At zero temperature, we observe a transition from a pure QZE in the short time scale to a QZE-QAZE crossover in the long time scale by considering the measurement-induced non-Markovian effect. At finite temperature, we exploit that the thermal fluctuation suppresses the decay of the survival probability in the short time scale, whereas it enhances the decay in the long time scale.

arXiv:1710.02110Physical Review AFeb 20, 20187 citations

Stochastic quantum trajectories demonstrate the quantum Zeno effect in open spin 1/2, spin 1 and spin 3/2 systems

Sophia M. Walls, Julien M Schachter, Haocheng Qian +1 more

Abstract We investigate the quantum Zeno effect (QZE) in spin 1/2, spin 1 and spin 3/2 open quantum systems undergoing Rabi oscillations, revealing unexplored features for the spin 1 and spin 3/2 systems. The systems interact with an environment designed to perform continuous measurements of an observable, driving the systems stochastically towards one of the eigenstates of the corresponding operator. The system-environment coupling constant represents the strength of the measurement. Stochastic quantum trajectories are generated by unravelling a Markovian Lindblad master equation using the quantum state diffusion formalism. These are regarded as a more appropriate representation of system behaviour than consideration of the averaged evolution since the latter can mask the effect of measurement. Complete positivity is maintained and thus the trajectories can be considered as physically meaningful. The QZE is investigated over a range of measurement strengths. Increasing the strength leads to greater system dwell in the vicinity of the eigenstates of the measured observable and lengthens the time taken by the system to return to that eigenstate, thus the QZE emerges. For very strong measurement, the Rabi oscillations resemble randomly occurring near-instantaneous jumps between eigenstates. The trajectories followed by the quantum system are heavily dependent on the measurement strength which other than slowing down and adding noise to the Rabi oscillations, changes the paths taken in spin phase space from a circular precession into elaborate figures-of-eight. For spin 1 and spin 3/2 systems, the measurement strength determines which eigenstates are explored and the QZE is stronger when the system dwells in the vicinity of certain eigenstates compared to others.Abstract We investigate the quantum Zeno effect (QZE) in spin 1/2, spin 1 and spin 3/2 open quantum systems undergoing Rabi oscillations, revealing unexplored features for the spin 1 and spin 3/2 systems. The systems interact with an environment designed to perform continuous measurements of an observable, driving the systems stochastically towards one of the eigenstates of the corresponding operator. The system-environment coupling constant represents the strength of the measurement. Stochastic quantum trajectories are generated by unravelling a Markovian Lindblad master equation using the quantum state diffusion formalism. These are regarded as a more appropriate representation of system behaviour than consideration of the averaged evolution since the latter can mask the effect of measurement. Complete positivity is maintained and thus the trajectories can be considered as physically meaningful. The QZE is investigated over a range of measurement strengths. Increasing the strength leads to greater system dwell in the vicinity of the eigenstates of the measured observable and lengthens the time taken by the system to return to that eigenstate, thus the QZE emerges. For very strong measurement, the Rabi oscillations resemble randomly occurring near-instantaneous jumps between eigenstates. The trajectories followed by the quantum system are heavily dependent on the measurement strength which other than slowing down and adding noise to the Rabi oscillations, changes the paths taken in spin phase space from a circular precession into elaborate figures-of-eight. For spin 1 and spin 3/2 systems, the measurement strength determines which eigenstates are explored and the QZE is stronger when the system dwells in the vicinity of certain eigenstates compared to others.

arXiv:2209.10626Journal of Physics A Mathematical and TheoreticalApr 4, 20247 citations

Quantum Zeno effect at finite measurement strength and frequency

L. Lerner

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

We study the quantum Zeno effect (QZE) and quantum anti-Zeno effect (QAZE) in a two-level system (TLS) interacting with an environment that has

1/f

noise. Using a numerically exact method based on the thermofield dynamics theory and the matrix product states, we obtain exact evolutions of the TLS and bath (environment) under repetitive measurements at both zero and finite temperatures. At zero temperature, we observe a transition from a pure QZE in the short time scale to a QZE-QAZE crossover in the long time scale by considering the measurement-induced non-Markovian effect. At finite temperature, we exploit that the thermal fluctuation suppresses the decay of the survival probability in the short time scale, whereas it enhances the decay in the long time scale.

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