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Fortschritte der Physik

Generation of Entanglement in a System of Two Dipole-Interacting Atoms by Means of Laser Pulses

Igor Bargatin, B. A. Grishanin, Виктор Николаевич Задков

Published May 1, 2000• 0 citations
Publisher

Abstract

Effectiveness of using laser field to produce entanglement between two dipole-interacting identical two-level atoms is considered in detail.The entanglement is achieved by driving the system with a carefully designed laser pulse transferring the system's population to one of the maximally entangled Dicke states in a way analogous to population inversion by a resonant π-pulse in a two-level atom.It is shown that for the optimally chosen pulse frequency, power and duration, the fidelity of generating a maximally entangled state approaches unity as the distance between the atoms goes to zero.

DOI
10.1002/(sici)1521-3978(200005)48:5/7<637::aid-prop637>3.3.co;2-#

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Effectiveness of using laser field to produce entanglement between two dipole-interacting identical two-level atoms is considered in detail.The entanglement is achieved by driving the system with a carefully designed laser pulse transferring the system's population to one of the maximally entangled Dicke states in a way analogous to population inversion by a resonant π-pulse in a two-level atom.It is shown that for the optimally chosen pulse frequency, power and duration, the fidelity of generating a maximally entangled state approaches unity as the distance between the atoms goes to zero.
Effectiveness of using laser field to produce entanglement between two dipole-interacting identical two-level atoms is considered in detail. The entanglement is achieved by driving the system with a carefully designed laser pulse transferring the system's population to one of the maximally entangled Dicke states in a way analogous to population inversion by a resonant π-pulse in a two-level atom. It is shown that for the optimally chosen pulse frequency, power and duration, the fidelity of generating a maximally entangled state approaches unity as the distance between the atoms goes to zero.
We present a quantum optimal control theory study combined with theoretical analysis to determine a pulsed laser field, capable of generating a maximally entangled state in two trapped two-level atoms. By expanding the time-dependent unitary operator to the first leading term of Magnus expansion, we reexamine the pulse area theorem for the trapped atoms driven by an arbitrarily temporary field. Due to the dipole-dipole interaction blockade, we find that the two trapped atoms described by a three-level ladder system can be reduced into an equivalent two-level model by using narrow-bandwidth pulses, leading to an analytical solution for generating the maximally entangled state. We also solve a highly constrained optimization problem to search for optimal laser pulses with broad bandwidths. A zero pulse-area constraint is employed to remove the dc offset of the optimized laser pulses, and a fixed fluence limitation combined with a constant pulse-area constraint at the resonant frequency of the equivalent two-level system are utilized to restrict the unitary evolution of quantum systems by the first leading term of Magnus expansion. This work provides a potentially useful approach to find all-optical control schemes for generating the maximally entangled state by using ultrafast laser pulses while satisfying multiple strict limitations.
Abstract We discuss the problem of creation of entangled states in a system of two two‐level atoms which are separated by an arbitrary distance r12 and interact with each other via the dipole‐dipole interaction and both are driven by a laser field. The entangled antisymmetric state of the system is included throughout, even for small inter‐atomic separations. Different mechanisms leading to effective transfer of population to the antisymmetric state are identified. The steady‐state values of concurrence which is a measure of entanglement are calculated showing that perfect entanglement can be reached in case of two non‐identical atoms.
We explore the possibilities of creating radiatively stable entangled states of two three-level dipole-interacting atoms in a \ensuremath{\Lambda} configuration by means of laser biharmonic continuous driving or pulses. We propose three schemes for generation of entangled states which involve only the lower states of the \ensuremath{\Lambda} system, not vulnerable to radiative decay. Two of them employ coherent dynamics to achieve entanglement in the system, whereas the third one uses optical pumping, i.e., an essentially incoherent process.
Abstract We propose a high-fidelity and robust scheme for generating two-excitation Bell entangled states in a driven system of two dipole-dipole coupled two-level atoms. By exploiting the cascade structure of the collective states and applying a Morris-Shore transformation, the dynamics is reduced to an effective two-level system, enabling an analytical derivation of pulse area conditions for deterministic entanglement generation. The protocol is implemented in two sequential stages, allowing complete population transfer from the ground state to the maximally coherent superposition of the zero- and double-excitation states. To enhance robustness against pulse area and detuning errors, we replace single pulse pairs with composite pulse sequences featuring tailored phase patterns. Numerical simulations demonstrate substantial enlargement of high-fidelity regions, with different phase sequences providing different robustness profiles against pulse area and detuning errors. Our results provide a simple and analytically tractable route toward robust entanglement generation in driven atomic platforms.
We describe a mechanism for a controlled generation of a pure Bell state with correlated atoms that involve two or zero excitations. The mechanism inhibits transitions into singly excited collective states of a two-atom system by shifting them from their unperturbed energies. The shift is accomplished by the dipole-dipole interaction between the atoms. The creation of the Bell state is found to be dependent on the relaxation of the atomic excitation. When the relaxation is not present or can be ignored, the state of the system evolves harmonically between a separable to the maximally entangled state. We follow the temporal evolution of the state and find that the concurrence can be different from zero only in the presence of the dipole-dipole interaction. Furthermore, in the limit of a large dipole-dipole interaction, the concurrence reduces to that predicted for an X state of the system. A general inequality is found which shows that the concurrence of an X-state system is a lower bound for the concurrence of the two-atom system. With the relaxation present, the general state of the system is a mixed state that under a strong dipole-dipole interaction reduces the system to an X-state form. We find that mixed states admit of lower level of entanglement, and the entanglement may occur over a finite range of time. A simple analytical expression is obtained for the steady-state concurrence which shows that there is a threshold value for the dipole-dipole interaction relative to the Rabi frequency of the driving field above which the atoms can be entangled over the entire time of the evolution.