Cooperativity of two cavity-coupled qubits: a multi-partite-entanglement approach

Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard the cooperative radiation as a manifested effect secondary to the intrinsic synchronization among the atoms and propose a time-resolved measure of synchronization on a cavity-coupled dual-qubit system using multipartite concurrence. Comparing the variation of the concurrence over time with that of an asynchronicity measure, we find that the synchronization between the qubits features a time delay characteristic to the initiation of superfluorescent pulses. The delay coincides with the duration for the qubits to establish cooperation and emit the collective radiation, after which the concurrence monotonically increases to a stationary value while the asynchronicity dives to a steady minimum. Furthermore, the establishment of synchronization is determined by the qubit-cavity coupling strength. Asynchronicity shows that synchronization is only possible when the coupling enters strong regime and sustains to a high level when the coupling becomes ultra-strong.Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard the cooperative radiation as a manifested effect secondary to the intrinsic synchronization among the atoms and propose a time-resolved measure of synchronization on a cavity-coupled dual-qubit system using multipartite concurrence. Comparing the variation of the concurrence over time with that of an asynchronicity measure, we find that the synchronization between the qubits features a time delay characteristic to the initiation of superfluorescent pulses. The delay coincides with the duration for the qubits to establish cooperation and emit the collective radiation, after which the concurrence monotonically increases to a stationary value while the asynchronicity dives to a steady minimum. Furthermore, the establishment of synchronization is determined by the qubit-cavity coupling strength. Asynchronicity shows that synchronization is only possible when the coupling enters strong regime and sustains to a high level when the coupling becomes ultra-strong.

arXiv:1606.07209Jun 23, 20161 citation

Synchronization of two cavity-coupled qubits measured by entanglement

Tiantian Huan, Ri‐Gui Zhou, Hou Ian

Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard cooperative radiations as a manifested effect secondary to the intrinsic synchronization among the two-level atoms and propose the entanglement measure, concurrence, as a time-resolved measure of synchronization. Modeled on two cavity-coupled qubits, the evolved concurrence monotonically increases to a saturated level. The finite duration required for the rising to saturation coincides with the time delay characteristic to the initiation of superfluorescence, showing the role of synchronization in establishing the cooperation among the qubits. We verify concurrence to be a good measure of synchronization by comparing it with asynchronicity computed from the difference between the density matrices of the qubits. We find that the feature of time delay agrees in both measures and is determined by the coupling regimes of the cavity-qubit interaction. Specifically, synchronization is impossible in the weak coupling regime.Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard cooperative radiations as a manifested effect secondary to the intrinsic synchronization among the two-level atoms and propose the entanglement measure, concurrence, as a time-resolved measure of synchronization. Modeled on two cavity-coupled qubits, the evolved concurrence monotonically increases to a saturated level. The finite duration required for the rising to saturation coincides with the time delay characteristic to the initiation of superfluorescence, showing the role of synchronization in establishing the cooperation among the qubits. We verify concurrence to be a good measure of synchronization by comparing it with asynchronicity computed from the difference between the density matrices of the qubits. We find that the feature of time delay agrees in both measures and is determined by the coupling regimes of the cavity-qubit interaction. Specifically, synchronization is impossible in the weak coupling regime.

Scientific ReportsJul 31, 202011 citations

Dynamics of quantum correlations and linear entropy in a multi-qubit-cavity system

Alexandra Olaya-Castro, Neil F. Johnson, Luis Quiroga

We present a theoretical study of the relationship between entanglement and entropy in multi-qubit quantum optical systems. Specifically we investigate quantitative relations between the concurrence and linear entropy for a two-qubit mixed system, implemented as two two-level atoms interacting with a single-mode cavity field. The dynamical evolutions of the entanglement and entropy are controlled via time-dependent cavity–atom couplings. Our theoretical findings lead us to propose an alternative measure of entanglement, which could be used to develop a much needed correlation measure for more general multi-partite quantum systems.We present a theoretical study of the relationship between entanglement and entropy in multi-qubit quantum optical systems. Specifically we investigate quantitative relations between the concurrence and linear entropy for a two-qubit mixed system, implemented as two two-level atoms interacting with a single-mode cavity field. The dynamical evolutions of the entanglement and entropy are controlled via time-dependent cavity–atom couplings. Our theoretical findings lead us to propose an alternative measure of entanglement, which could be used to develop a much needed correlation measure for more general multi-partite quantum systems.

arXiv:quant-ph/0311181Journal of Optics B Quantum and Semiclassical OpticsJul 28, 200415 citations

From Superradiance to Superabsorption: An Exact Treatment of Non-Markovian Cooperative Radiation

Ignacio González, Ángel Rivas

We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to $10^3$ emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to $10^3$ emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.

quant-pharXiv:2601.05989QuantumJan 12, 20260 citations

Periodic entanglement revivals of asynchronously excited cavity-coupled qubits

Tiantian Huan, Ri‐Gui Zhou, Franco Nori +1 more

In a multi-partite system, the multipartite concurrence of the entire system differs from the sum of the bipartite concurrences of its components. For a system with an even number of components, the relation between them is described by a monogamy inequality that compares the bipartite concurrences of two subsystems comprising even-number components and those of two subsystems comprising odd-number components. The difference between the even and the odd clusterings is exactly quantified by a polynomial invariant. We study the dynamic evolution of the polynomial invariant on three superconducting qubits inhomogeneously coupled to a circuit cavity. We show that in this quadripartite system, the non-negativity of the degree-4 invariant holds strictly over time and vanishes periodically. The magnitude of the invariant increases monotonically with the absolute coupling strength while the period of the vanishing and revival maximizes when the couplings among the qubits are inhomogeneous, showing the benefit of asynchronous qubit excitations in extending entanglement time.In a multi-partite system, the multipartite concurrence of the entire system differs from the sum of the bipartite concurrences of its components. For a system with an even number of components, the relation between them is described by a monogamy inequality that compares the bipartite concurrences of two subsystems comprising even-number components and those of two subsystems comprising odd-number components. The difference between the even and the odd clusterings is exactly quantified by a polynomial invariant. We study the dynamic evolution of the polynomial invariant on three superconducting qubits inhomogeneously coupled to a circuit cavity. We show that in this quadripartite system, the non-negativity of the degree-4 invariant holds strictly over time and vanishes periodically. The magnitude of the invariant increases monotonically with the absolute coupling strength while the period of the vanishing and revival maximizes when the couplings among the qubits are inhomogeneous, showing the benefit of asynchronous qubit excitations in extending entanglement time.

May 5, 20200 citations

Concurrence evolution of two qubits coupled with one-mode cavity separately

Weici Liu, Wang Fa-Qiang, Ruisheng Liang

The concurrence evolution of two qubits coupled with one-mode cavity separately is investigated exactly without adopting the rotating-wave approximation. The results show that for the resonant case, the concurrence evolution behaviour of the system is similar to that of the Markovian case when the coupling strength is weak, while the concurrence vanishes in a finite time and might revive fractional initial entanglement before it permanently vanishes when the coupling strength is strong. And for the detuning case, the entanglement could periodically recover after complete disentanglement. These results are quite different from those of system subjected to Jaynes–Cummings model.The concurrence evolution of two qubits coupled with one-mode cavity separately is investigated exactly without adopting the rotating-wave approximation. The results show that for the resonant case, the concurrence evolution behaviour of the system is similar to that of the Markovian case when the coupling strength is weak, while the concurrence vanishes in a finite time and might revive fractional initial entanglement before it permanently vanishes when the coupling strength is strong. And for the detuning case, the entanglement could periodically recover after complete disentanglement. These results are quite different from those of system subjected to Jaynes–Cummings model.

Chinese Physics BSep 1, 20103 citations

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emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.