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arXiv:1504.07387

A weak-value interpretation of the Schwinger mechanism of massless/massive pair productions

Kazuhiro Yokota, Nobuyuki Imoto

Published Apr 28, 2015• 0 citations
arXivHTMLPDF

Abstract

According to the Schwinger mechanism, a uniform electric field brings about pair productions in vacuum; the relationship between the production rate and the electric field is different, depending on the dimension of the system. In this paper, we make an offer of another model for the pair productions, in which weak values are incorporated: energy fluctuations trigger the pair production, and a weak value appears as the velocity of a particle there. Although our model is only available for the approximation of the pair production rates, the weak value reveals a new aspect of the pair production. Especially, within the first order, our estimation approximately agrees with the exponential decreasing rate of the Landau-Zener tunneling through the mass energy gap. In other words, such tunneling can be associated with energy fluctuations via the weak value, when the tunneling gap can be regarded as so small due to the high electric field.

DOI
10.48550/arxiv.1504.07387

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According to the Schwinger mechanism, a uniform electric field brings about pair productions in vacuum; the relationship between the production rate and the electric field is different, depending on the dimension of the system. In this paper, we make an offer of another model for the pair productions, in which weak values are incorporated: energy fluctuations trigger the pair production, and a weak value appears as the velocity of a particle there. Although our model is only available for the approximation of the pair production rates, the weak value reveals a new aspect of the pair production. Especially, within the first order, our estimation approximately agrees with the exponential decreasing rate of the Landau-Zener tunneling through the mass energy gap. In other words, such tunneling can be associated with energy fluctuations via the weak value, when the tunneling gap can be regarded as so small due to the high electric field.
In the context of quantum electrodynamics, a strong electric field can trigger the production of particle-antiparticle pairs, a phenomenon known as the Schwinger effect. In practical experimental scenarios, producing a pair requires quantum tunneling of particles over a long distance, thus suppressing the production rate and making this process very challenging to observe. Here we report an experimental investigation, in a cold-atom quantum simulator, of the effect of the external background field on pair production from the infinite-mass vacuum in a 1+1D U(1) lattice gauge theory in its quantum link model formulation, which we address through a genuine out-of-equilibrium protocol. The ability to tune the background field allows us to study pair production in a favorable regime of a large production rate. Furthermore, we probe the time evolution of the model in the zero fermion mass limit. We find that the energy spectrum of the time-evolved observables displays excitation peaks analogous to the (massive) bosonic modes of the Schwinger model and whose phenomenology can be interpreted as a string inversion mechanism. Our Letter opens the door to quantum-simulation experiments that can controllably tune the production of pairs and manipulate their far-from-equilibrium dynamics.
Abstract The creation of particle–antiparticle pairs from vacuum by a large electric field is at the core of quantum electrodynamics. Despite the wide acceptance that this phenomenon occurs naturally when electric field strengths exceed E c ≈ 1018 V m−1, it has yet to be experimentally observed due to the limitations imposed by producing electric fields at this scale. The high degree of experimental control present in ultracold atomic systems allow experimentalists to create laboratory analogs to high-field phenomena. Here we emulated massive relativistic particles subject to large electric field strengths, thereby quantum-simulated particle–antiparticle pair creation, and experimentally explored particle creation from ‘the Dirac vacuum’. Data collected from our analog system spans the full parameter regime from low applied field (negligible pair creation) below the Sauter–Schwinger limit, to high field (maximum rate of pair creation) far in excess of the Sauter–Schwinger limit. In our experiment, we perform direct measurements on an analog atomic system and show that this high-field phenomenon is well-characterized by Landau–Zener tunneling, well known in the atomic physics context, and we find full quantitative agreement with theory with no adjustable parameters.
We quantum-simulated particle-antiparticle pair production with a bosonic quantum gas in an optical lattice by emulating the requisite 1d Dirac equation and uniform electric field. We emulated field strengths far in excess of Sauter-Schwinger's limit for pair production in quantum electrodynamics, and therefore readily produced particles from "the Dirac vacuum" in quantitative agreement with theory. The observed process is equivalently described by Landau-Zener tunneling familiar in the atomic physics context.
We investigate entropy of electron-positron pair production in time-dependent Sauter pulse electric field. Both cases of pair longitudinal momentum only and full momentum consideration are examined. We further examine three types of entropy, one is the usual entanglement entropy SES_{\text{E}}SE​, the other two extensions are thermal distribution entropy SThS_{\text{Th}}STh​, and that with the chemical potential correction, STh,CPS_{\text{Th,CP}}STh,CP​. For short pulse, SES_{\text{E}}SE​ is higher than SThS_{\text{Th}}STh​ and vice versa for long pulse. The chemical potential causes the single-particle average thermal distribution entropy STh,CPN\frac{S_{\text{Th,CP}}}{N}NSTh,CP​​ to exhibit non-monotonic behavior, similar to the single-particle average entanglement entropy SEN\frac{S_{\text{E}}}{N}NSE​​ in the short-pulse range. In the full momentum case, we calculate the thermal distribution entropy STh, US_{\text{Th, U}}STh, U​ via introducing the Unruh temperature as the local effective temperature. We find that both STh, US_{\text{Th, U}}STh, U​ and SES_{\text{E}}SE​ saturate asymptotically to the constant while the former has a larger asymptotic value. The results presented in this study reveals that the different entropies have some delicate relationships among them.
The two-level pairing model was investigated in the framework of the Schwinger representation. It has been shown that zero-point fluctuations, which are important in the crossover region, are well described by certain coherent states which conserve the constants of motion. These so-called conserving approximations provide excellent descriptions of the ground-state energy and of the first excitation energy over the whole range of coupling constant values. The description of the ground-state energy provided by the Glauber coherent state is also reasonable, but not so good. Although the Glauber coherent state fails to provide the description of the excitation energy around the critical point, its performance in the strong coupling limit is very good both for the description of the ground-state energy and of the first excitation energy. The present results also show that already at the mean-field level, the bosonic description in the independent particle approximation incorporates important correlation corrections to the conventional mean-field description based on the fermionic realization of the su (2) algebra (BCS theory).
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.