In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.
In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits negativity. The resultsof numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.
Background. To operate a quantum computer, a set of universal gates must be implemented, such as a two-cubit gate of the controlled negation type plus one-cubit spins. As a universal alternative, three-cubic-bit gates may be used. In this regard, it seems very relevant to investigate the dynamics of three-qubit systems in microwave resonators, in particular to study the most efficient schemes for generating, controlling, and monitoring entangled qubit states. Aim. To investigate the features of the dynamics of entangled pairs of qubits for a system in which two qubits are locked in a single-mode resonator and interact with the thermal field mode, and the third qubit is in a free state. Methods. To analyze the dynamics of the considered system, the solution of the quantum Liouville equation for the full density matrix is investigated. The exact solution of the above equation in the case of initial biseparable states of the qubits is found. The exact solution of the evolution equation is used to calculate the criterion of entanglement of qubit pairs – negativity. Numerical simulations of negativity for biseparable qubit states as well as different values of the thermal field intensity of the resonator have been carried out. Results. It is shown that for intense thermal fields of the resonator the effect of instantaneous death of entanglement is observed, while the time intervals between death and revival of entanglement of qubits depend essentially on the choice of their initial biseparable state. It is found that for one of the biseparable states, entanglement of qubits trapped in the resonator does not occur at any field intensities of the resonator. Conclusion. It is found that the peculiarities of the dynamics of entanglement of qubits, in particular the time intervals between the death and birth of entangled qubits, are determined by the choice of the initial biseparable state of qubits, as well as by the values of the field intensity of the resonator. The results obtained can be used to effectively control and manage the degree of qubit entanglement in three-qubit systems in microwave resonators.
The article studies the dynamics of pairwise entanglement of three qubits, two of which are trapped in a resonator and interact with a single-mode ideal resonator through single-photon transitions, and the third qubit is outside the resonator. This takes into account the dipole-dipole coupling between the isolated qubit and the qubit in the resonator. We have found a solution to the quantum nonstationary Schrodinger equation for the total wave function of the system for the initial separable and biseparable states of qubits and the thermal initial state of the resonator field. Using these solutions, the criterion of entanglement of qubit pairs - negativity is calculated. The results of numerical simulation of the negativity criterion have shown that the including of a small dipole-dipole coupling between an isolated and one of the trapped qubits can lead to significant entanglement of qubit pairs for all initial states. There is a transition of entanglement from one pair of atoms to other pairs of atoms during the evolution of the system. It is also shown that for some separable and biseparable states, the dipole-dipole interaction can suppress the effect of sudden death of entanglement.
In this paper, we study the dynamics of a system consisting of two identical qubits interacting non-resonantly with a single-mode field of an ideal resonator in the presence of direct dipole-dipole and Ising interactions between the qubits. In the representation of "dressed" states, we find an exact solution of the quantum time Liouville equation for the full density matrix of the system under consideration for the initial separable and entangled states of the qubits and the thermal initial state of the resonator field. Based on the exact solution, the criterion for qubit entanglement, negativity, is calculated. The results of numerical modeling of negativity show that the inclusion of dipole-dipole and Ising coupling in the case of separable initial states of qubits can lead to a significant increase in the maximum degree of their entanglement, and in the case of entangled initial states of qubits, to stabilization of the initial entanglement. For the model with resonant interaction of qubits and the resonator field, direct interaction of qubits can also lead to the disappearance of the sudden death of entanglement effect.
In this paper, a three-qubit Tavis-Cummings model with two independent lossless single-mode resonators is considered. It is assumed that the initial states of the resonator fields are thermal fields and the qubits are in genuine entangled W- and GHZ-type states. For the model under study and the specified initial states of the resonator fields and qubits, we have exactly solved the quantum Liouville equation for the full density matrix. The full density matrix was used to calculate the entanglement parameters - negativity and fidelity. The computer simulation results showed that in the investigated model, the entanglement for all initial qubit states breaks down rapidly with increasing intensity of the thermal fields of the resonators compared to the previously investigated three-qubit models. Moreover, a sudden death of entanglement is observed even for vacuum resonator fields.
In this work, we have studied the dynamics of entanglement of two identical superconducting qubits resonantly interacting with the one-mode field of a coplanar microwave cavity without loss through single-photon transitions in the presence of third- and fifth-order nonlinearities. Based on the solution of the equation of evolution of the system for the Fock initial states of the cavity field, the criterion of qubits entanglement negativity is calculated. The results of the negativity calculation show that for the initial separable states, the cavity nonlinearity can lead to a significant increase in the maximum degree of qubit entanglement. It is shown that for the initial entangledstates of qubits and intense cavity fields, taking into account nonlinearities leads to stabilization of the degree of entanglement of qubits in the cavity and contributes to the disappearance of the effect of the entanglement sudden death of qubits.
In this paper, we investigated the dynamics of entanglement of two qubits interacting non-resonantly with the thermal field of a one-mode lossless resonator, taking into account the Ising-type direct interaction between qubits. Based on the exact solution of the quantum Liouville equation, we found the density matrix of the system under consideration. With its help, the reduced qubit-qubit density matrix was calculated and the entanglement criteriоn of the two-qubit system, Pres-Horodeсki parameter, was found. It was shown that for the resonance model and separable initial states of qubits, the direct interaction of qubits leads to a significant increase in the maximum degree of their entanglement. It was also found that for the nonresonant interaction between qubits and field, the increase of the maximum degree of entanglement of qubits is much greater than that due to direct interaction. For the original entangled Bell-type state of the qubits, the direct interaction was found to lead to the vanishing of the effect of the sudden death of entanglement in the case of a resonant qubit-field interaction and, conversely, to an increase in this effect for a nonresonant interaction.