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arXiv:2009.12449 · Physical Review A

Sudden freezing and thawing of entanglement sharing in a shrunken volume

Yi Ding, Songbo Xie, Joseph H. Eberly

Published Mar 16, 2021• 11 citations

Abstract

Restriction to the one-excitation context allows two identical two-level atoms and their common one-mode cavity field to exhibit previously unreported features of three-party entanglement during fully coherent evolution. We find entanglement showing dynamical behavior in the form of nonanalytic slope discontinuities in the time record. Specifically, the entanglements of the system can become abruptly frozen in time, remaining at a constant value, and can subsequently suddenly begin thawing from this value. We calculate the onset timing of such sudden freezings and sudden thawings under several different initial conditions. The conditions producing permanent freezing of entanglement are found. We also identify a nontrivial upper limit for the sum of three individual bipartite entanglements, which exposes the concept of entanglement ``volume'' and the volume shrinkage that accompanies the entanglement sharing. Further analysis of these freezing and thawing processes reveals quantitative and qualitative constraints on entanglement sharing of three qubits.

DOI: 10.1103/physreva.103.032418

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Restriction to the one-excitation context allows two identical two-level atoms and their common one-mode cavity field to exhibit previously unreported features of three-party entanglement during fully coherent evolution. We find entanglement showing dynamical behavior in the form of nonanalytic slope discontinuities in the time record. Specifically, the entanglements of the system can become abruptly frozen in time, remaining at a constant value, and can subsequently suddenly begin thawing from this value. We calculate the onset timing of such sudden freezings and sudden thawings under several different initial conditions. The conditions producing permanent freezing of entanglement are found. We also identify a nontrivial upper limit for the sum of three individual bipartite entanglements, which exposes the concept of entanglement ``volume'' and the volume shrinkage that accompanies the entanglement sharing. Further analysis of these freezing and thawing processes reveals quantitative and qualitative constraints on entanglement sharing of three qubits.

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.

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

N

-site optical lattice (or equivalently spin-chain) system. Interesting phenomenon of permanent entanglement freezing is found for the infinite-size case (

N\rightarrow\infty

). As the multiparty system size reduces to finite

N

, 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.

We investigate entanglement dynamics of bipartite as well multipartite systems beyond Markov approximation. We study two pairs of cavity–reservoir systems, modeled as four qubits and track the change of entanglement among cavity–cavity qubits, reservoir–reservoir qubits, and also for genuine entanglement of all four qubits. For cavity–cavity qubits, we find that non-Markovianity prolongs the life of entanglement besides collapse/revival phenomenon. For reservoir–reservoir qubits, entanglement sudden birth is delayed accordingly along with oscillations. For all four qubits, with a specific initial state, we find that genuine entanglement develops gradually, reaches to a maximum constant value and then freezes at this value for some time before decaying. This sudden change in dynamics of genuine entanglement occurs for a time window where neither cavities nor reservoirs are entangled. In contrast to Markov process, sudden change phenomenon may be recurrent in non-Markovian regime.