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Advanced Quantum Technologies

Predestined Steady‐State Entanglement under Pure Vacuum Noise

Yuebing Zhou, Jiawei Hu, Hongwei Yu

Published Dec 30, 2022• 0 citations
Publisher

Abstract

Abstract Ever since the seminal work by Yu and Eberly [Phys. Rev. Lett. 93 , 140404 (2004)], it has become widely accepted that nonlocal entanglement is more fragile than local coherence, in the sense that even under the influence of pure vacuum noise, the two‐qubit entanglement may end within a finite time, while the single‐qubit coherence always decays exponentially. By contrast, in this paper, it is shown that, for a pair of rotating qubits under pure vacuum noise with appropriate orbital radius and angular velocity, nonlocal entanglement as compared to local coherence is not only more resilient against vacuum noise to be preserved in the steady‐state for initially entangled states, but more importantly is also predestined to be created and be preserved for initially separable states. The generation of predestined entanglement here is essentially different from the dissipative steady‐state entanglement generation in existing schemes insofar as it is inevitably generated in pure vacuum instead of an elaborately designed environment.

DOI
10.1002/qute.202200159

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Abstract Ever since the seminal work by Yu and Eberly [Phys. Rev. Lett. 93 , 140404 (2004)], it has become widely accepted that nonlocal entanglement is more fragile than local coherence, in the sense that even under the influence of pure vacuum noise, the two‐qubit entanglement may end within a finite time, while the single‐qubit coherence always decays exponentially. By contrast, in this paper, it is shown that, for a pair of rotating qubits under pure vacuum noise with appropriate orbital radius and angular velocity, nonlocal entanglement as compared to local coherence is not only more resilient against vacuum noise to be preserved in the steady‐state for initially entangled states, but more importantly is also predestined to be created and be preserved for initially separable states. The generation of predestined entanglement here is essentially different from the dissipative steady‐state entanglement generation in existing schemes insofar as it is inevitably generated in pure vacuum instead of an elaborately designed environment.
In a recent paper Yu and Eberly [Phys. Rev. Lett. 93, 140404 (2004)] have shown that two initially entangled and afterward not interacting qubits can become completely disentangled in a finite time. We study transient entanglement between two qubits coupled collectively to a multimode vacuum field, assuming that the two-qubit system is initially prepared in an entangled state produced by the two-photon coherences, and find the unusual feature that the irreversible spontaneous decay can lead to a revival of the entanglement that has already been destroyed. The results show that this feature is independent of the coherent dipole-dipole interaction between the atoms but it depends critically on whether or not collective damping is present.
It was showed in [Phys. Rev. Lett. 125 090401 (2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob’s half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.
A system, comprised of a qubit pair coupled to a common cavity, is studied with the aim of establishing qubit entanglement. This study is the sequel of the paper Phys. Rev. A 111, 043705 (2025), where similar model was investigated for an initially vacuum cavity. In the present manuscript the cavity with finite initial occupancy is considered and the effect of asymmetric qubit cavity couplings is investigated. For a closed system scenario, the ratio of the qubit-cavity couplings shows a threshold beyond which no maximally-entangled qubit state is available. The threshold value is shown to depend on the excitation level of the cavity. For a driven-dissipative case steady state entanglement is shown to depend non-monotonically on the qubit drive. Intricate interplay of drive, dissipation, and coupling asymmetry is shown to be pivotal for steady-state entanglement generation.
We study the time evolution of two two-state systems (two qubits) initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherence.
Abstract The entanglement dynamics of a pair of three-level V-type atoms decaying spontaneously in a common vacuum reservoir is investigated. Under the condition that the decaying transitions in the atoms have parallel dipole moments, the effect of coherences induced by spontaneous emission is considered in the atomic dynamics. We show that vacuum-induced coherence (VIC) and collective effects in atomic decay play a significant role in the creation of entanglement. By using negativity as a measure of entanglement, we study the time evolution of entanglement for initial separable and generalized Dicke states as well as maximally entangled qutrit states. We show that the effects of VIC enhance the production of entanglement from initial separable states of the atoms. We also show that the entanglement can be protected in steady-state for atoms evolving from initial entangled states. The amount of entanglement that can be preserved is more in the presence of VIC than in its absence.
We investigate qubit entanglement dynamics in a two-qubit cavity system with stochastically fluctuating coupling strength, comparing white noise (Markovian) and Ornstein-Uhlenbeck noise (non-Markovian) processes. We analytically solve the system dynamics for both Fock and coherent cavity states and systematically characterize how initial qubit configurations affect entanglement generation and preservation. Our results reveal distinct dynamical regimes: in the Fock-state cavity, initial states in the single-excitation subspace generate robust qubit entanglement in decoherence-free subspaces, while initially entangled states in the double-excitation subspace exhibit inevitable decay without protective symmetries. For coherent cavities, we identify a critical photon-number threshold in the intermediate coherent-state amplitude regime where dynamics transition from low-frequency to high-frequency entanglement oscillations, while universal entanglement loss occurs at large amplitudes. Remarkable resilience against entanglement sudden death emerges under strong non-Markovian noise with long correlation times, where repeated revivals occur. These findings establish cavity photon statistics and environmental memory time as key control parameters for engineering qubit entanglement dynamics in qubit-cavity systems, revealing how system-environment correlations govern quantum information preservation.