Linear and nonlinear quantum Zeno and anti-Zeno effects in a nonlinear optical coupler

Abstract

Quantum Zeno and anti-Zeno effects are studied in a symmetric nonlinear optical coupler, which is composed of two nonlinear (χ (2) ) waveguides that are interacting with each other via the evanescent waves. Both the waveguides operate under second harmonic generation. However, to study quantum Zeno and anti-Zeno effects one of them is considered as the system and the other one is considered as the probe. Considering all the fields involved as weak, a completely quantum mechanical description is provided, and the analytic solutions of Heisenberg's equations of motion for all the field modes are obtained using a perturbative technique. Photon number statistics of the second harmonic mode of the system is shown to depend on the presence of the probe, and this dependence is considered as quantum Zeno and anti-Zeno effects. Further, it is established that as a special case of the momentum operator for χ (2) − χ (2) symmetric coupler we can obtain momentum operator of χ (2) − χ (1) asymmetric coupler with linear (χ (1) ) waveguide as the probe, and in such a particular case, the expressions obtained for Zeno and anti-Zeno effects with nonlinear probe (which we referred to as nonlinear quantum Zeno and anti-Zeno effects) may be reduced to the corresponding expressions with linear probe (which we referred to as the linear quantum Zeno and anti-Zeno effects). Linear and nonlinear quantum Zeno and anti-Zeno effects are rigorously investigated, and it is established that in the stimulated case, we may switch between quantum Zeno and anti-Zeno effects just by controlling the phase of the second harmonic mode of the system or probe.

Quantum Zeno effect and nonclassicality in a PT -symmetric system of coupled cavities

“…1) can be considered as a system-probe configuration, where one of the cavities (considered system) is under a constant influence of the other cavity (probe). The occurrence of QZE and QAZE in the system-probe setting can be studied by defining Zeno parameter, introduced in [83,84],…”

Lower Order and Higher Order Entanglement in Four‐Wave Mixing Process

“…Keeping these facts in mind, in the present paper, we investigate the possibilities of observing lower order and higher order intermodal entanglement in FWM process associated with a cascade system under the framework of Sen‐Mandal perturbative approach that is known to provide analytic expressions for time evolution of field operators with greater accuracy compared to the traditionally used short‐time solution . This is well established in earlier works ([] and references therein). In what follows, we report a perturbative solution (using the Sen‐Mandal approach) for the Heisenberg's equations of motion for various modes present in the Hamiltonian of the FWM process.…”

Quantum Zeno effect in self-sustaining systems: suppressing phase diffusion via repeated measurements

“…We have numerically solved the stochastic Langevin equations (14) with the initial phase difference θ − = θ 1 −θ 2 = π/2 and we show the results in Fig. 6.…”

“…One striking and well-known example is the so-called quantum Zeno effect, which predicts that frequent measurements can freeze quantum dynamics [4]. In recent years, several in-depth explorations have been performed both theoretically and experimentally [5][6][7][8][9][10][11][12][13][14][15][16][17][18] and different mechanisms related to the Zeno effect have been investigated such as the nonmonotonic dissipation process caused by a structured reservoir, the renormalization effect due to a strong system-detector interaction [8], or its connection with the opposite phenomenon of the anti-Zeno effect [5,6,12,14,[19][20][21]. In quantum information processing it has been related to decoherence-free subspaces [22] and to decoherence control strategies [23][24][25][26][27].…”