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Scientific Reports

Quantum Fisher information of atomic system interacting with a single cavity mode in the presence of Kerr medium

Nour Zidan, H. F. Abdel-Hameed, NASSER METWALLY

Published Feb 25, 2019• 16 citations
Publisher

Abstract

The quantum Fisher information of an atomic system interacting with a single cavity mode in the presence of Kerr medium is discussed. It is shown that quantum Fisher information for an initial separable atomic system is larger than that depicted for the initial entangled atomic system. For initial vacuum state of the cavity mode, the quantum Fisher information with respect to the Kerr medium and the phase decoherence parameter is larger than that displayed for the detuning parameter. Both phase decoherence and Kerr medium have the same effect on the decay of quantum Fisher information, while they have an opposite effect on its maximum values.

DOI
10.1038/s41598-019-39183-5

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Results in Physics•Nov 12, 2021•3 citations
The quantum Fisher information of an atomic system interacting with a single cavity mode in the presence of Kerr medium is discussed. It is shown that quantum Fisher information for an initial separable atomic system is larger than that depicted for the initial entangled atomic system. For initial vacuum state of the cavity mode, the quantum Fisher information with respect to the Kerr medium and the phase decoherence parameter is larger than that displayed for the detuning parameter. Both phase decoherence and Kerr medium have the same effect on the decay of quantum Fisher information, while they have an opposite effect on its maximum values.
We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) for N-level atomic system interacting with a coherent field in the presence of Kerr (linear and non-linear medium) and Stark effects. It is observed that the Stark and Kerr effects play a prominent role during the time evolution of the quantum system. The evolving quantum Fisher information (QFI) is noted as time grows under the non-linear Kerr medium contrary to the QE for higher dimensional systems. The effect of non-linear Kerr medium is greater on the QE as we increase the value of Kerr parameter. However, QFI and QE maintain their periodic nature under atomic motion. On the other hand, linear Kerr medium has no prominent effects on the dynamics of N-level atomic system. Furthermore, it has been observed that QFI and QE decay soon under the influence of Stark effect. In short, the N-level atomic system is found prone to the change of the Kerr medium and Stark effect for higher dimensional systems.
We have investigated numerically the dynamics of quantum Fisher information (QFI) and quantum entanglement (QE) of a two moving two-level atomic systems interacting with a coherent and thermal field in the presence of intrinsic decoherence (ID) and Kerr (non-linear medium) and Stark effects. The state of the entire system interacting with coherent and thermal fields is evaluated numerically under the influence of ID and Kerr (nonlinear) and Stark effects. QFI and von Neumann entropy (VNE) decrease in the presence of ID when the atomic motion is neglected. QFI and QE show an opposite response during its time evolution in the presence of a thermal environment. QFI is found to be more susceptible to ID as compared to QE in the presence of a thermal environment. The decay of QE is further damped at greater time-scales, which confirms the fact that ID heavily influences the system’s dynamics in a thermal environment. However, a periodic behavior of entanglement is observed due to atomic motion, which becomes modest under environmental effects. It is found that a non-linear Kerr medium has a prominent effect on the VNE but not on the QFI. Furthermore, it has been observed that QFI and QE decay soon under the influence of the Stark effect in the absence of atomic motion. The periodic response of QFI and VNE is observed for both the non-linear Kerr medium and the Stark effect in the presence of atomic motion. It is observed that the Stark, Kerr, ID, and thermal environment have significant effects during the time evolution of the quantum system.
In this paper, we have proposed the numerical calculations to study the quantum entanglement (QE) of moving two-level atom interacting with a coherent and the thermal field influenced by intrinsic decoherence (ID), Kerr medium (non-linear) and the Stark effect. The wave function of the complete system interacting with a coherent and the thermal field is calculated numerically affected by ID, Kerr (non-linear) and Stark effects. It has been seen that the Stark, Kerr, ID and the thermal environment have a significant effect during the time evolution of the quantum system. Quantum Fisher information (QFI) and QE decrease as the value of the ID parameter is increased in the thermal field without the atomic movement. It is seen that QFI and von Neumann entropy (VNE) show an opposite and periodic response in the presence of atomic motion. The non-linear Kerr medium has a more prominent and significant effect on the QE as the value of the Kerr parameter is decreased. At smaller values of the non-linear Kerr parameter, the VNE increases, however, QFI decreases, so QFI and VNE have a monotonic connection with one another. As the value of the Kerr parameter is increased, the effect of non-linear Kerr doesn’t stay critical on both QFI and QE. However, a periodic response of QE is seen because of the atomic movement which becomes modest under natural impacts. Moreover, it has been seen that QFI and QE rot soon at the smaller values of the Stark parameter. However, as the value of the Stark parameter is increased, the QFI and QE show periodic response even when the atomic movement is absent.
We investigated numerically the dynamics of quantum Fisher information (QFI) and entanglement for three- and four-level atomic systems interacting with a coherent field under the effect of Stark shift and Kerr medium. It was observed that the Stark shift and Kerr-like medium play a prominent role during the time evolution of the quantum systems. The non-linear Kerr medium has a stronger effect on the dynamics of QFI as compared to the quantum entanglement (QE). QFI is heavily suppressed by increasing the value of Kerr parameter. This behavior was found comparable in the cases of three- and four-level atomic systems coupled with a non-linear Kerr medium. However, QFI and quantum entanglement (QE) maintain their periodic nature under atomic motion. On the other hand, the local maximum value of QFI and von Neumann entropy (VNE) decrease gradually under the Stark effect. Moreover, no prominent difference in the behavior of QFI and QE was observed for three- and four-level atoms while increasing the value of Stark parameter. However, three- and four-level atomic systems were found equally prone to the non-linear Kerr medium and Stark effect. Furthermore, three- and four-level atomic systems were found fully prone to the Kerr-like medium and Stark effect.
A quantum cavity filled with a nonlinear medium (Kerr like medium) and contains a 2-mode field interacting with time dependence of 2-qubit is investigated. Part of the two qubits interact in the form of an amplifier, while the other is in the form of a ladder. The constants of motion are calculated by using the Heisenberg differential equation. Moreover, the analytical solution is calculated by solving the Schrodinger differential equations. Some statistical quantities are calculated to identify the features of the proposed model. The effective of the nonlinear term on the phenomena of collapse and revival are discussed through atomic population. The amount of entanglement between the quantum subsystem, whether it is between the 2-qubit and the cavity field, or between the 2-qubit together are calculated using the linear entropy and the concurrence. The results indicated that there is a superstructure between the atomic population and the linear entropy, concurrence. The intensity of oscillations decreases for the entanglement between the field and the two qubits when the Kerr like medium of the Hamiltonian system is included. The nonclassical distribution of the quantum system decreases after taking Kerr like medium into account.
The nonlinearity effect on the various formed quantum correlations between two atoms interacting locally with a bimodal cavity is explored in this work. The local quantum Fisher information, local quantum uncertainty, and negativity are used to investigate the quantum correlation’s sensitivity to the cavity modes characteristics. It is demonstrated that when the ratio of the Stark shift of the two modes increases, the atomic quantum correlations rise. During the time intervals of sudden death negativity entanglement, the three two-atom correlation quantifiers reveal that the two-atom system can contain local Fisher information and local uncertainty correlations. The Stark shift may be utilized to amplify the produced atomic correlation, while the Kerr-like medium can be used to suppress it. The regularity, the amount of generated atomic correlations, and their immunity to the Stark shift as well as the Kerr-like medium non-linearities are improved when the mean photon number is increased. As a result, the cavity modes’ nonlinear parameters might be utilized as a controller to optimize atomic quantum correlations.