Vacuum-decay time in strong external fields

Abstract

We consider dynamics of vacuum decay and particle production in the context of short pulse laser experiments. We identify and evaluate the invariant "materialization time," τ , the timescale for the conversion of an electromagnetic field energy into particles, and we compare to the laser related time scales.In the past decade high intensity short pulse laser technology has advanced rapidly [1], pulses achieved intensities of 10 26 W/m 2 [2,3]. With subsequent concentration by coherent harmonic focusing allowing a further gain in intensity of around six orders of magnitude [4], laser technology is nearing the scale of rapid vacuum instability, cǫ 0 E 2 0 /4π = 4.65×10 33 W/m 2 , where E 0 ≡ m 2 c 3 /e = 1.32 × 10 18 V/m. The study of vacuum instability with laser pulses involves dynamics on a timescale set by the pulse length, which at optical frequencies implies that the fields are in existence for ∼ 10 −15 s, and may reach ∼ 10 −18 s when coherent harmonic focusing is used.The vacuum state of quantum electrodynamics (QED) is metastable in the presence of electrical fields of any strength, but only in proximity of E 0 does the effect occur on an observable time scale [5,6], as we exhibit below. Specifically, we investigate whether the laser pulse timescale allows the vacuum in strong fields to relax, thereby admitting the new vacuum to experimental investigation using pulsed lasers. The dynamics of 'false' vacuum decay have been studied in the context of spontaneous positron creation in heavy ion collisions [7,8,9] and cosmological models [10,11,12]. The QED vacuum decay has not been directly observed in heavy ion collision experiments, due to the relatively long time scale of vacuum decay dynamics as compared to competing processes. However, particle production in strong fields has found a fertile field in quantum chromodynamics [13,14].Considerable effort went into generalizing the Euler-Heisenberg-Schwinger (EHS) [5,6] pair production mechanism for a variety of large-scale (compared toλ e = /m e c = 3.86 × 10 −13 m) space-and time-dependent field configurations [15,16,17] and to incorporating back reaction [13,18,19,20,21]. A stable, modified vacuum state has only been obtained when the field fills a finite spacetime domain [18]. The perturbative vacuum is also stable for an ideal plane wave (laser) field of arbitrary strength, and thus many investigations have focused on understanding pair production in optimized pulsed laser field configurations [22,23,24,25,26,27,28,29,30,31,32]. More recently it has been also noted that in the interaction of laser pulses with thin foils, the charge seperation effect due to a much greater electron mobility helps in achieving longitudinal electrical fields of comparable strength as are present in the laser pulse, a phenomenon used in laser-ion acceleration [33]. We thus address in this work the general circumstance of a spatially homogeneous electrical field.In all laboratory experiments supercritical fields (fields capable of spontaneous particle production) will be strongl...

Extremely high-intensity laser interactions with fundamental quantum systems

“…The classical motion of an electron (electric charge e < 0 and mass m) in an arbitrary external electromagnetic field F µν (x) is determined by the Lorentz equation mdu µ /ds = eF µν u ν , where u µ = dx µ /ds is the electron four-velocity and s its proper time (Landau and Lifshitz, 1975). If the external field is a plane wave, the field tensor F µν (x) depends only on the dimensional phase φ = (n 0 x), where n µ 0 = (1, n 0 ), with n 0 being the unit vector along the propagation direction of the wave.…”

“…Since a plane-wave field depends only on φ, the canonical momenta p ⊥ (φ) + eA(φ) and p − (φ) are conserved as they are the conjugated momenta to the cyclic coordinates x ⊥ and t + x , respectively. For p µ (φ 0 ) = p µ 0 = (ε 0 , p 0 ) = mγ 0 (1, β 0 ) being the initial condition for the electron's four-momentum at a given phase φ 0 , the above-mentioned conservation laws already allow to write the electron's four-momentum at an arbitrary phase φ as (Landau and Lifshitz, 1975) …”

Time evolution of the QED vacuum in a uniform electric field: Complete analytic solution by spinorial decomposition

“…The initial conditions that interest us most are those of the QED vacuum and we describe the time evolution in this case. Our solution clarifies the mechanism responsible for pair production and may explain some details of the vacuum decay studied recently [17].…”

“…Still, even for an arbitrary H(q) the precession equations have some special properties implied by the O(3) symmetry that will enable us to find their solutions. In the next section we proceed directly to the solution of the equations (17). In the Appendix we explain the grouptheoretic foundations of this solution.…”

Vacuum Structure and Dark Energy

“…2m is the energy stability gap, 2/m the width of the tunneling barrier, and e the coupling charge. β −1 ≃ 0.1 suffices to induce just one decay event in a macroscopic volume, while full collapse of the vacuum ensues for β −1 → 1 [8]. As dark energy is a long wavelength phenomenon, we study the long-wavelength limit of QED in prescribed external fields of arbitrary strength with small values of the charge e 2 /4π 2 = α/π.…”