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Optics Express

Entanglement freezing and thawing in one-dimensional optical lattice systems

Xiao‐Feng Qian, Chunlei Qu, Joseph H. Eberly

Published Jul 3, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1364/oe.590184

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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.
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.
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.
We show that bipartite entanglement in an one-dimensional quantum spin model undergoing time evolution due to local Markovian environments can be frozen over time. We demonstrate this by using a number of paradigmatic quantum spin models including the anisotropic XYXYXY model in the presence of a uniform and an alternating transverse magnetic field (ATXY), the XXZXXZXXZ model, the XYZXYZXYZ model, and the ${J}_{1}\ensuremath{-}{J}_{2}$ model involving the next-nearest-neighbor interactions. We show that the length of the freezing interval, for a chosen pair of nearest-neighbor spins, may remain independent of the length of the spin chain, for example, in paramagnetic phases of the ATXY model, indicating a scale invariance. Freezing of entanglement is found to be robust against a change in the environment temperature, the presence of disorder in the system, and whether the noise is dissipative or not dissipative. Moreover, we connect the freezing of entanglement with the propagation of information through a quantum many-body system, as considered in the Lieb-Robinson theorem. We demonstrate that the variation of the freezing duration exhibits a quadratic behavior against the distance of the nearest-neighbor spin pair from the noise source, obtained from exact numerical simulations, in contrast to the linear one as predicted by the Lieb-Robinson theorem.
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to examine driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary locally reduce the entropy of the many-body system. Surprisingly, the many-body entanglement is established by continuously evolving a locally dissipative Rydberg system towards the steady state, precisely as with optical pumping. We characterize the dynamics of multipartite entanglement in an one-dimensional lattice by way of quantum uncertainty relations, and demonstrate the long-range behavior of the stationary entanglement with finite-size scaling. Our work opens a route towards dissipative preparation of many-body entanglement with unprecedented scaling behavior.
We study the real-time dynamics of a quantum Ising chain driven periodically by instantaneous quenches of the transverse field between $+{\ensuremath{\Gamma}}_{0}$ and ${\ensuremath{\Gamma}}_{0}$ back and forth in equal intervals of time. Two interesting phenomena are reported and analyzed. (i) We observe dynamical many-body freezing (DMF), i.e., strongly nonmonotonic freezing of the response with respect to the driving parameters (pulse width and height) resulting from coherent suppression of dynamics of all quasiparticle modes. For certain combinations of the pulse height and the period, maximal freezing (DMF peaks) is observed, where a massive collapse of the entire Floquet spectrum occurs and the many-body system remains frozen extremely close to the initial state for all time. (ii) Second, away from the freezing peak, we observe the emergence of a distinct oscillation with a single nontrivial frequency, which can be much lower than the driving frequency. This remarkable slow oscillation involving many high-energy modes dominates the response in the limit of long observation time. We identify this slow oscillation as the unique survivor of destructive quantum interference between the many-body modes. The oscillation tends to decay algebraically with time to a constant value. All the key features are demonstrated analytically with numerical evaluations for specific results.