Atom–atom entanglement dynamics enhancement via classically driven atoms coupled to a non-resonance single mode cavity field filled with nonlinear Kerr media
Entanglement dynamics of two identical non-interacting atoms (qubits) coupled individually with simultaneous classical and quantum fields are studied. The cavity field is filled with a nonlinear Kerr medium and initially prepared in a coherent state. The atoms are initially set up as a Bell-like pure state (BS). We present an approach for diagonalization of time-dependent nonlinear Hamiltonian of the system exactly. Connection between the change in the degree of entanglement and tomography of field state in phase space are also illustrated and interpreted. We demonstrate the possibility of atom–atom (qubit–qubit) entanglement optimization by suitably choosing initial interaction settings. Overall, we show that both classical driving amplitude and detuning as well as Kerr media and initial atomic states acts as the control parameters for the qubit–qubit entanglement. By adjusting of these parameters, accurately, entanglement can be enhanced noticeably and high degree of steady periodical entanglement can be generated. Moreover, starting with initial atomic BSs in presence of classical driving suppresses coherences randomness and considerably accompanied with (for specific values of detuning) slight decrease in their amplitudes. Furthermore, the addition of cross Kerr term suppresses degree of entanglement noticeably, where entanglement creation and enhancement could just be possible if cross Kerr effect is moved out from interaction. Our present approach promises the great advantage of being suitable for large quantum systems of various kinds of nonlinearities.
Entanglement dynamics of two identical non-interacting atoms (qubits) coupled individually with simultaneous classical and quantum fields are studied. The cavity field is filled with a nonlinear Kerr medium and initially prepared in a coherent state. The atoms are initially set up as a Bell-like pure state (BS). We present an approach for diagonalization of time-dependent nonlinear Hamiltonian of the system exactly. Connection between the change in the degree of entanglement and tomography of field state in phase space are also illustrated and interpreted. We demonstrate the possibility of atom–atom (qubit–qubit) entanglement optimization by suitably choosing initial interaction settings. Overall, we show that both classical driving amplitude and detuning as well as Kerr media and initial atomic states acts as the control parameters for the qubit–qubit entanglement. By adjusting of these parameters, accurately, entanglement can be enhanced noticeably and high degree of steady periodical entanglement can be generated. Moreover, starting with initial atomic BSs in presence of classical driving suppresses coherences randomness and considerably accompanied with (for specific values of detuning) slight decrease in their amplitudes. Furthermore, the addition of cross Kerr term suppresses degree of entanglement noticeably, where entanglement creation and enhancement could just be possible if cross Kerr effect is moved out from interaction. Our present approach promises the great advantage of being suitable for large quantum systems of various kinds of nonlinearities.
An analytical solution for a master equation describing the dynamics of a qubit interacting with a nonlinear Kerr-like cavity through intensity-dependent coupling is established. A superposition of squeezed coherent states is propped as the initial cavity field. The dynamics of the entangled qubit-cavity states are explored by negativity for different deformed function of the intensity-dependent coupling. We have examined the effects of the Kerr-like nonlinearity and the qubit-cavity detuning as well as the phase cavity damping on the generated entanglement. The intensity-dependent coupling increases the sensitivity of the generated entanglement to the phase-damping. The stability and the strength of the entanglement are controlled by the Kerr-like nonlinearity, the qubit-cavity detuning, and the initial cavity non-classicality. These physical parameters enhance the robustness of the qubit-cavity entanglement against the cavity phase-damping. The high initial cavity non-classicality enhances the robustness of the qubit-cavity entanglement against the phase-damping effect.
An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom–field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom–field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.
The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence o Abstract The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field. f Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.
In this work, the authors investigated the dynamics of entanglement of two identical two-level atoms (qubits) in the framework of the two-photon double Jaynes–Cummings model, taking into account the detuning between atoms and the double frequency of the field modes of the resonators, as well as the Kerr medium in both resonators. The authors derived the time dependence of the negativity parameter for the Bell initial states of the atoms and the vacuum states of the resonator fields. The results showed that detuning and Kerr nonlinearity leads to stabilization of the entanglement for all initial Bell-type atomic states. For some initial atomic entanglement states, the detuning and Kerr environment in the resonators can prevent the effect of sudden death of the atom-atom entanglement.
Abstract Cooperative atomic emission spectrum as a key probe of entanglement dynamics of an independent and a classically-pumped qubits pair is showed and investigated. The qubits are initially maximally-entangled while they penetrate a detuned, single-photon and coherent cavity embedded in nonlinear media. The system Hamiltonian; that is a nonlinear and a time-dependent system, is diagonalized and the time evolution unitary operator in an exact form is derived. Various characteristics are monitored while observations are theoretically documented—via tracing the field state tomography—and experimentally calibrated. Cooperation and decoherence as well as the statistics of the emitted radiation are discussed and analyzed in terms of the other phenomena. We show that, a measurement of the spectrum outputs represent a highly effective key calibration for entanglement attributes, where complete time dynamics may be predicted with a high considerable accuracy. The most striking feature realized is that, on high detuned interaction, a full matching of these phenomena outputs can be achieved regardless of the absence or presence or pumping. Once the pumping starts, a partial dephasing is encouraged, thus, the spectrum is inversely but slightly affected, nevertheless, matching remains highly closed. Within various surroundings of Kerr materials of different Kerr constants, that is an additional source of an effective dephasing, spectrum rapidly oscillates and so also entanglement that shows rapid Rabi oscillations during its fast degradation depending on the detuning width. However, on measuring the intracavity field state tomography, measurements confirm such a matching, that is, calibration is well documented.
Background. The need to implement controlled coupling between qubits, which are the logical elements of quantum devices such as quantum computers and quantum networks, requires, along with the use of traditional methods, the development of new, more effective ways to organize the interaction of qubits with the microwave fields of resonators used to generate and control the entanglement of qubits. As one of these methods, a method based on the influence of frequency-regulated radio frequency signals on a superconducting Josephson qubit connected by a large Josephson junction to a free qubit has been proposed. Aim. The influence of the Kerr medium of the resonator, in which one of the two qubits is placed, on their entanglement induced by the coherent or thermal frequency-regulated radio frequency field of the resonator is considered. Methods. To analyze the dynamics of the system under consideration, the solution of the quantum Liouville equation for the full density matrix is studied. An exact solution o this equation is found in the case of initial separable and entangled states of qubits. The exact solution of the evolution equation is used to calculate the criterion of qubit-qubit entanglement – cconcurrence. Numerical modeling of the concurrence was carried out for various states of qubits, coherent and thermal fields of the resonator, as well as various values of the intensity of the resonator field and the Kerr nonlinearity parameter. Results. It is shown that for separable initial states of qubits, the inclusion of Kerr nonlinearity reduces the maximum degree of entanglement of qubits. For an entangled initial state of qubits, the possibility of creating long-lived entangled states in the presence of Kerr nonlinearity is shown. Conclusion. The type of initial states of qubits and the range of values of the intensities of the resonator fields and the Kerr nonlinearity parameters have been established, for which the most effective control and operation of the evolution of qubits, as well as the degree of their entanglement, in the physical system under consideration, is possible.