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Chinese Physics B

Analytical and robust generation of two-excitation entangled states in a driven two-atom system

Li‐Bao Fan, Gengbiao Lu, Xiaobing Luo, Yu 裕 Guo 郭

Published May 20, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/ae7058

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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.
Abstract High-fidelity entangled-state generation in driven two-atom systems is often optimized at a nominal transition frequency, which can produce control pulses that are fragile against detuning errors and experimental imperfections. To address this limitation, we develop a sampled-detuning quantum optimal-control approach in which different detuning values are treated as control scenarios driven by a common laser field. Time-domain equality constraints, including zero pulse area and fixed fluence, are incorporated directly into the pulse update. The resulting constraint-projected update provides a common ascent direction for the sampled detuning objectives while preserving the imposed pulse constraints. Numerical simulations show that the optimized robust pulses maintain a high target-state population over a wider detuning interval than resonant Gaussian pulses and conventional single-objective optimal pulses. The results further reveal a fluence-bandwidth trade-off for robust plateau formation. Frequency-domain analysis indicates that the enhanced robustness is associated with optimized off-resonant spectral components, and the robustness window can be tuned by selecting the sampled-detuning training range.
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.
Abstract We develop a scheme for deterministic generation of an entangled state between two atoms on different Rydberg states via a chirped adiabatic passage, which directly connects the initial ground and target entangled states and also does not request the normally needed blockade effect. The occupancy of intermediate states suffers from a strong reduction via two pulses with proper time-dependent detunings and the electromagnetically induced transparency condition. By solving the analytical expressions of eigenvalues and eigenstates of a two-atom system, we investigate the optimal parameters for guaranteeing the adiabatic condition. We present a detailed study for the effect of pulse duration, changing rate, different Rydberg interactions on the fidelity of the prepared entangled state with experimentally feasible parameters, which reveals a good agreement between the analytic and full numerical results.
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.
This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes–Cummings model. For some particular field states, coherent and squeezed states, the transformation between the two bare bases, related by the unitary transformation, becomes particularly simple. It is shown how to generate (the highly non-classical) entangled coherent states of the two modes, both in the zero and large detuning cases. An advantage of the zero detuning case is that the preparation is deterministic and no atomic measurement is needed. For the large detuning situation, a measurement is required, leaving the field in either of two orthogonal entangled coherent states.