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Frontiers in Optics

Sudden Freezing and Sudden Thawing of Entanglement in Multi-Party Jaynes-Cummings Dynamics

Yi Ding, Songbo Xie, Joseph H. Eberly

Published Jan 1, 2020• 0 citations
Publisher

Abstract

The dynamical responses of two qubits jointly interacting with the same cavity mode are studied. New dynamical quantum phenomena labeled Entanglement Sudden Freezing and Entanglement Sudden Thawing are discovered by analyzing the normalized Schmidt weights.
DOI
10.1364/fio.2020.fw1b.7

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In a system where two identical two-level atoms interact with their common one-mode cavity field, it is shown that entanglement can become abruptly frozen in time, remaining at a constant value for a period of time until it begins to thaw from this value from the entanglement sharing perspective [Ding et al., Phys. Rev. A 103, 032418 (2021)]. We generalize this exotic behavior of entanglement sharing dynamics to more general systems with arbitrary N qubits, instead of restricting to the atom-cavity mode interaction system. We also demonstrate methods to control the entanglement freezing time and freezing value, and we discover a nontrivial dynamics where entanglement is frozen permanently. In addition, we show that this phenomenon is not a coincidence but a universal feature in a variety of systems with a geometric explanation of the mechanisms.
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We investigate the dynamics of different configurations of entanglement in a one-dimensional N -site optical lattice chain. Entanglement freezing has so far been primarily associated with noisy or decoherence-induced processes. Remarkably, we show that this phenomenon also occurs in a fully coherent and lossless many-body system. By deriving exact analytical results, we demonstrate the emergence of permanent entanglement freezing in the thermodynamic limit ( N → ∞). Even more surprisingly, for finite N , where purely unitary dynamics would normally be expected to destroy such stationary behavior, the system still exhibits robust entanglement freezing over a finite time interval. This frozen behavior is subsequently followed by a phenomenon of entanglement “thawing," manifested as revivals of quantum correlations. Furthermore, alternating regimes of entanglement freezing and thawing appear during the time evolution. Our results reveal that entanglement freezing can arise intrinsically from coherent many-body dynamics, even in finite lossless systems, and provide analytical guidance for entanglement control in optical-lattice-based quantum information processing and photonic quantum technologies.
Entanglement freezing has been demonstrated existing in various noisy decoherence mechanisms. Here we explore its universality by investigating freezing behavior in a lossless multiparty system, i.e., an NNN-site optical lattice (or equivalently spin-chain) system. Interesting phenomenon of permanent entanglement freezing is found for the infinite-size case (N→∞N\rightarrow\inftyN→∞). As the multiparty system size reduces to finite NNN, the interesting behavior of dynamical entanglement "thawing" start to emerge. Especifically, alternative appearances of "freezing" and "thawing" can be identified as time evolves. Our results may provide useful guidance to entanglement control in quantum tasks.