Quantum control for the Zeno effect with noise

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.