arXiv:2401.04892 · Journal of Physics B Atomic Molecular and Optical Physics

Entanglement of a three-level atom interacting with two-modes field in a cavity

Alejandra del Río‐Lima, Freddy Jackson Poveda-Cuevas, Octavio Castaños

Published Aug 22, 2024• 4 citations

Abstract

Abstract The dynamics of an atom of three levels in Λ configuration interacting with a quantized field of two modes in a cavity is studied within the rotating wave approximation by considering experimental values of accessible hyperfine levels of alkali atoms. The Hamiltonian model is constructed on the basis of the direct product of the atomic states with Fock states of light. This simplified basis allows us to generalize the state of light to any quantum field. The interaction term of the Hamiltonian restricts the system to a 3D Hilbert space. The system’s time evolution results show some similarities with the effective two-level system, such as the presence of collapses and revivals and the atom-field entanglement. By an analysis of the statistics of the photons, we show that when the three-level atom is interacting with a coherent field of two modes, it is possible to control experimentally the statistics of the field to be super-Poissonian or sub-Poissonian by the choice of the initial atomic state.

DOI: 10.1088/1361-6455/ad717d

Related papers

Collapse-revival in entanglement and photon statistics: the interaction of a three-level atom with a two-mode quantized field in cavity optomechanics

Marziyeh Hassani Nadiki, Mohammad Kazem Tavassoly

Abstract In this paper the interaction of a three-level atom in V -configuration with a two-mode quantized field in cavity optomechanics is studied. To achieve the purpose, we first deduce the effective Hamiltonian and evaluate the explicit time-dependent form of the state vector of the whole system by choosing special initial conditions for atom, field and the oscillatory mirror. Interestingly, we can obtain the time evolution of atomic linear entropy, population inversion, quantum statistics and squeezing, both analytically and numerically. The results show that the entanglement between the atom and the subsystem of field and mirror, and all above-mentioned physical quantities can be appropriately controlled by the initial atom-field state condition, the parameters of cavity optomechanics as well as atom-field coupling strengths. In particular, the appearance of collapse-revival phenomenon in the entanglement and quantum photon statistics, also the full sub-Poissonian statistics in the two modes of field as well as in the mechanical mode of optomechanical system are noticeable features of the work.

Laser PhysicsNov 10, 201619 citations

ENTANGLEMENT AND PHOTON DYNAMICS IN THE INTERACTION BETWEEN TWO QUANTIZED ELECTROMAGNETIC FIELDS AND 3-LEVEL ATOMS

Behrooz Vaseghi, G. Rezaei, Reza Khordad +1 more

We study in this paper the dynamics of two electromagnetic (EM) fields and their entanglement in the interaction with a 3-level atom (Λ-configuration). We investigate the interaction when initially one of the fields is in a single mode coherent state, and the other one is in a Fock(number) state. We have calculated the mean photon numbers of the fields and their entanglement by means of the fields entropy as a measure of it. The results show the synchronization between entanglement beats and collapses-revivals of the fields, which cause the field in the Fock state (noncoherent) to behave coherently during the interaction. Also the results offer a way to generate coherent fields and achieve any desired degree of entanglement with specified dynamics via controlling the parameters of the atomic system.

International Journal of Quantum InformationFeb 1, 20111 citation

Entanglement of a general formalism Λ-type three-level atom interacting with a non-correlated two-mode cavity field in the presence of nonlinearities

A.‐S. F. Obada, A. A. Eied, G. M. Abd Al-Kader

We investigate the evolution of the atomic quantum entropy and the atom–field entanglement in a system of a Λ-configuration three-level atom interacting with a two-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a non-correlated two-mode squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are analysed.

Journal of Physics B Atomic Molecular and Optical PhysicsSep 17, 200811 citations

Dynamic Behavior of Lambda-Type Three-Level Atoms and Two-Mode Cavity Field

Huang Ting, Xiu‐Min Lin, Zhuo‐Liang Cao +1 more

A system comprising of Lambda-type three-level atoms and the two-mode cavity field is considered in this paper. Under the adiabatical approximation and the large detuning condition, the effective Hamiltonian of the system in the interaction picture can be given out. If the two identical three-level atoms pass through the cavity in turn, the entangled state atoms can be generated. When the interaction time is taken to an appropriate value, the maximally entangled states are created. At the same time, the dynamic behaviors of the system are studied in detail.

Communications in Theoretical PhysicsApr 1, 20062 citations

Interaction of a Λ-type three-level atom with a two-mode field and a two-mode Raman-coupled model

Zhang Zhi-ming, Lin-sheng He, Zhou Shi-kang

The Hamiltonian is derived for the interaction of a Λ-type three-level atom with a two-mode quantum cavity field from the general interaction Hamiltonian between a multi-level atom and a multi-mode radiation field, and it is reduced to an effective two-mode Raman-coupled model under a large detuning condition. We propose a modified effective Hamiltonian for the two-mode Raman-coupled model, find the time-dependent state vectors, and present the validity conditions for the involved interaction Hamiltonians. It is shown that in the study of the two-mode Raman-coupled model it is not enough to retain only the usually used effective Hamiltonian, one must also take into account the ac Stark shift of the atomic levels (at least one of the levels). Finally, we study the atomic dynamics in the interaction of a Λ-type three-level atom with a two-mode quantum cavity field and in the two-mode Raman-coupled model. We find that the number of collapse-revivals, the collapse time and the revival time show new characteristics.

Acta Physica Sinica (Overseas Edition)Feb 1, 19991 citation

A three-level atom interacting with a single mode cavity field: different configurations

N. H. Abdel-Wahab

In this paper, the problem of a three-level atom interacting with a single mode of the quantized electromagnetic cavity field is considered. The considered theoretical model describes the distinct configurations of a three-level atom. Also, this model includes a detuning and arbitrary forms of both the field and the intensity-dependent atom-field coupling. We obtain the general forms for both the constants of motion and the wavefunction when the atom is initially prepared in one of its states. We use this model for computing a number of statistical aspects of the three-level system. As an illustration, we use the model for studying the time evolution of the second-order correlation function when the atom is initially in an upper state and the field is considered in a coherent state.

Physica ScriptaJul 27, 200742 citations