Entangling operations in nonlinear two-atom Tavis-Cummings models

Abstract

We derive an analytical approximate solution of the time-dependent state vector in terms of material Bell states and coherent states of the field for a generalized two-atom Tavis-Cummings model with nonlinear intensity-dependent matter-field interaction. Using this solution, we obtain simple expressions for the atomic concurrence and purity in order to study the entanglement in the system at specific interaction times. We show how to implement entangling atomic operations through measurement of the field. We illustrate how these operations can lead to a complete Bell measurement. Furthermore, when considering two orthogonal states of the field as levels of a third qubit, it is possible to implement a unitary three-qubit gate capable of generating authentic tripartite entangled states such as the Greenberger-Horne-Zeilinger state and the W state. As an example of the generic model, we present an ion-trap setting employing the quantized mode of the center-of-mass motion instead of the photonic field, showing that the implementation of realistic entangling operations from intrinsic nonlinear matter-field interactions is indeed possible.

Performance of entanglement purification including maximally entangled mixed states

“…One of these operations, M − , appears in matter-field interactions based on the Tavis-Cummings model [31]. The second operation, M + , has been recently investigated in physical systems of a similar nature, but presenting linear dependence in the eigenenergies [32,40]. Both operations, M ± , are non-unitary.…”

“…Moreover, for generic two-qubit states, these approaches rely on local random transformations, also known as twirling operations, that waste useful entanglement [28,29]. To circumvent the need for twirling operations and to find alternatives to the CNOT gate, the emergence of entangling operations, which naturally occur in physical systems, has been explored [30][31][32]. This approach has led to the development of alternative entanglement purification protocols [31] with more relaxed conditions for purifying arbitrary states.…”

Generating Bell states and Werner states of two qubits via optical field

“…With the development of experimental techniques in cavity quantum electrodynamics, it has become possible to control atom-light interactions precisely [89][90][91][92][93][94]. The generation of maximally entangled states has been realized in a series of TC models under different conditions [95][96][97][98][99][100][101], such as the TC model under large detuning conditions [95], the nonlinear two-atom TC model [101], the TC model with driven dissipation [99], and so on. Unlike the above studies, in this paper, we investigate how to control the initial state of the light field to control the two qubits in the direct product state to produce the maximally entangled state in the TC model under resonance conditions by an exact solution without any approximation.…”