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Chinese Physics B

Enhancing von Neumann entropy by chaos in spin–orbit entanglement*

Chen-Rong Liu, Pei Yu, Xianzhang Chen, Hong-Ya Xu, Liang Huang, Ying‐Cheng Lai

Published Aug 23, 2019• 4 citations
Publisher

Abstract

For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin–orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin–orbit coupling regime, we find that classical chaos can significantly enhance spin–orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.

DOI
10.1088/1674-1056/ab3dff

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For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin–orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin–orbit coupling regime, we find that classical chaos can significantly enhance spin–orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.
This investigation delves into the dynamics of quantum correlations and coherence within a two-dimensional electron gas (2DEG) system, taking into account the influence of Rashba spin–orbit coupling (SOC). We utilize metrics such as logarithmic negativity ([Formula: see text]), local quantum uncertainty (LQU ([Formula: see text])), and relative entropy of coherence ([Formula: see text]) to specifically assess these quantum resources among electron spins within non-interacting electron gases. Our study investigates how the separation distance (R) between electrons and the intensity of Rashba SOC ([Formula: see text]), impact the behavior of quantum properties within the 2DEG system. We find that specific strengths of Rashba SOC can effectively regulate quantum correlations and coherence within this system. Particularly significant is our observation that optimal quantum indicators emerge when electron proximity is minimized, underscoring the substantial influence of electron distance on quantum characteristics. Conversely, as electron separation increases, these quantum metrics diminish. Therefore, by adjusting the Rashba parameter, we can enhance the resilience of these quantum measurements against increasing electron separations, providing valuable insights into the potential for controlling and manipulating quantum behavior in similar 2DEG systems.
We study the quantum entanglement caused by unitary operators that have classical limits that can range from the near integrable to the completely chaotic. Entanglement in the eigenstates and time-evolving arbitrary states is studied through the von Neumann entropy of the reduced density matrices. We demonstrate that classical chaos can lead to substantially enhanced entanglement. Conversely, entanglement provides a useful characterization of quantum states in higher-dimensional chaotic or complex systems. Information about eigenfunction localization is stored in a graded manner in the Schmidt vectors, and the principal Schmidt vectors can be scarred by the projections of classical periodic orbits onto subspaces. The eigenvalues of the reduced density matrices is sensitive to the degree of wave-function localization, and is roughly exponentially arranged. We also point out the analogy with decoherence, as reduced density matrices corresponding to subsystems of fully chaotic systems, are diagonally dominant.
Spin-orbital entanglement in quantum spin-orbital systems is quantified by a specifically reduced von Neumann entropy and is calculated for the ground state of a coupled spin-orbital chain with $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry. By analyzing the discontinuity and local extreme of the reduced entropy, we deduce a rich phase diagram describing quantum phase transitions in this system with complex correlations between multiple degrees of freedom.
We study the spatially chaoticity-dependent spin-motion entanglement of a spin-orbit (SO) coupled Bose-Einstein condensate with a source of ultracold atoms held in an optical superlattice. In the case of phase synchronization, we analytically demonstrate that (a) the SO coupling (SOC) leads to the generation of spin-motion entanglement; (b) the area of the high-chaoticity parameter region inversely relates to the SOC strength which renormalizes the chemical potential; and (c) the high-chaoticity is associated with the lower chemical potential and the larger ratio of the short-lattice depth to the longer-lattice depth. Then, we numerically generate the Poincaré sections to pinpoint that the chaos probability is enhanced with the decrease in the SOC strength and/or the spin-dependent current components. The existence of chaos is confirmed by computing the corresponding largest Lyapunov exponents. For an appropriate lattice depth ratio, the complete stop of one of (or both) the current components is related to the full chaoticity. The results mean that the weak SOC and/or the small current components can enhance the chaoticity. Based on the insensitivity of chaos probability to initial conditions, we propose a feasible scheme to manipulate the ensemble of chaotic spin-motion entangled states, which may be useful in coherent atom optics with chaotic atom transport.
In this paper, the mechanism of entanglement between electronic spin states and their spatial degrees of freedom in graphene is reported. From a calculation of the time evolution of von Neumann entropy, as a measure of entanglement, we show that the general behavior is oscillatory with characteristics depending on the external magnetic field, the Rashba spin–orbit coupling and the Landau states. The effect of these agents on the degree of entanglement is also discussed. It is shown that an increase in the magnetic field decreases the degree of entanglement, while an increase in Rashba spin–orbit coupling enhances the entanglement. Furthermore, for higher Landau levels the electronic states become more entangled. The material presented in this paper offers new means of controlling the entanglement of electronic states.
We consider the low-energy excitations of one-dimensional spin-orbital models which consist of spin waves, orbital waves, and joint spin-orbital excitations. Among the latter we identify strongly entangled spin-orbital bound states and spin-orbital quasiparticle states which appear as peaks in the von Neumann entropy spectral function introduced in this work. We present the scaling of the von Neumann entropy with system size and find a qualitatively different behavior for the bound state and the quasiparticle---the strong entanglement of these states is manifested by a universal logarithmic scaling of the von Neumann entropy with system size, while the entropy saturates for other spin-orbital excitations. We suggest that spin-orbital entanglement can be experimentally explored by the measurement of the dynamical spin-orbital correlations using resonant inelastic x-ray scattering, where strong spin-orbit coupling associated with the core hole plays a role.