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arXiv:1812.08534 · Physical Review A

Schwinger effect of a relativistic boson entangled with a qubit

Yujie Li, Qingqing Mao, Yu Shi

Published Mar 25, 2019• 15 citations
arXivHTMLPDF

Abstract

We use the concept of quantum entanglement to analyze the Schwinger effect on an entangled state of a qubit and a boson mode coupled with the electric field. As a consequence of the Schwinger production of particle-antiparticle pairs, the electric field decreases both the correlation and the entanglement between the qubit and the particle mode. This work exposes a profound difference between bosons and fermions. In the boson case, entanglement between the qubit and the antiparticle mode cannot be caused by the Schwinger effect on the preexisting entanglement between the qubit and the particle mode, though correlation can. In the fermion case, both can.

DOI
10.1103/physreva.99.032340

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We use the concept of quantum entanglement to analyze the Schwinger effect on an entangled state of a qubit and a boson mode coupled with the electric field. As a consequence of the Schwinger production of particle-antiparticle pairs, the electric field decreases both the correlation and the entanglement between the qubit and the particle mode. This work exposes a profound difference between bosons and fermions. In the boson case, entanglement between the qubit and the antiparticle mode cannot be caused by the Schwinger effect on the preexisting entanglement between the qubit and the particle mode, though correlation can. In the fermion case, both can.
We analyze entanglement generated by the Schwinger effect using a mode-by-mode formalism for scalar and spinor QED in constant backgrounds. Starting from thermal initial states, we derive compact, closed-form results for bipartite entanglement between particle-antiparticle partners in terms of the Bogoliubov coefficients. For bosons, thermal fluctuations enhance production but suppress quantum correlations: the logarithmic negativity is nonzero only below a (mode-dependent) critical temperature TcT_cTc​. At fixed TTT, entanglement appears only above a critical field EentangE_{\text{entang}}Eentang​. For fermions, we observe a qualitatively different pattern: the fermionic logarithmic negativity is non-vanishing at finite temperature, and is monotonically suppressed by thermal noise. As a function of the electric field, it is non-monotonic, featuring a temperature-independent optimal field strength E∗E_*E∗​ and decreasing on both sides of the maximum. We give quantitative estimates for analog experiments, where our entanglement criteria convert directly into concrete temperature and electric field constraints. These findings identify realistic regimes where the quantum character of Schwinger physics may be tested in the laboratory.
We study the charge resolved structure of the pairwise mode entanglement produced by the Schwinger effect. Using the U(1)U(1)U(1) electric charge of quantum electrodynamics, we decompose the entanglement of the reduced density matrices of momentum modes into individual charge sectors, applying the symmetry resolved entanglement entropy to the pure bipartition reductions and the charge imbalance resolved negativity to the mixed particle-antiparticle pair. For a constant electric field we obtain closed form results for every mode pairing, with all field dependence controlled by the single pair production probability ∣β∣2=e−πμ|β|^2=e^{-πμ}∣β∣2=e−πμ. For the particle, particle and antiparticle antiparticle pairs the entanglement entropy within each charge sector is field independent, so that the field acts only by redistributing statistical weight among the sectors; for the mixed particle antiparticle pair the populated sector additionally carries a field dependent entropy. The vacuum created pair is the richest case: its resolved negativity is distributed over three imbalance sectors and is transported from one sector to the next as the field increases, the sectors contributing equally only at the critical field. The entanglement across a fixed momentum bipartition, by contrast, is frozen at its initial value because pair creation conserves the sector charge. Symmetry resolution thus refines the total entanglement measures into a sector resolved picture, exposing where in charge space the entanglement of the Schwinger mechanism resides and how the electric field moves it, information beyond that contained in the total measures or in particle number distributions.
We analyze the correlations of the vacuum state of a charged scalar field by constructing localized observables in two disjoint regions. We consider a time-dependent homogeneous electric field and examine the time evolution of correlations by relating it with the particle-antiparticle creation through the Schwinger effect. Our results show that the electric field increases the mixedness of the states and enhances total correlations, while the distillable entanglement among the regions decreases, vanishing at a finite time for sufficiently intense pulses within the non-perturbative pair-production regime. We also discuss the effect of anisotropy induced by the external background, showing that the distribution of correlations acquires a nontrivial directional dependence.
We analyze the spins of a Schwinger particle pair in a spatially uniform but time dependent electric field. The particle pair's spins are in the maximally entangled Bell state only if the particles' momenta are parallel to the electric field. However if transverse momentum is present, the spins are not in the maximally entangled Bell state. The reason is that the pair is created by the external field, which also carries angular momentum, and the particle pair can take away some of this external angular momentum.
Abstract Quantum entanglement is a typical nonclassical correlation. Here, we use this concept to analyze quantum entanglement for continuous variables generated by the Schwinger pair production for constant and pulsed electric fields. An initial two-mode entangled state evolves into a three-mode entangled state through a Gaussian channel of the Schwinger effect, which encodes the information about the Schwinger effect. By detecting the entanglement of the output three-mode state, we obtain the optimal parameters for easier to generate particle–antiparticle pairs. We find that the generated 1 → 2 entanglement is more sensitive to the parameters than the generated 1 → 1 entanglement. Therefore, we should choose the generated 1 → 2 entanglement to extract information. We argue that extracting the optimal parameters from quantum entanglement may guide future experiments.
The Schwinger process in strong electric fields creates particles and antiparticles that are entangled. The entropy of entanglement between particles and antiparticles has been found to be equal to the statistical Gibbs entropy of the produced system. Here we study the effect of quantum interference in sequences of electric pulses, and show that quantum interference suppresses the entanglement entropy of the created quantum state. This is potentially relevant to quantum-enhanced classical communications. Our results can be extended to a wide variety of two-level quantum systems.