Unruh effect & Schwinger mechanism in strong lasers? Ralf Schützhold Fachbereich Physik Universität Duisburg-Essen Unruh effect & Schwinger mechanism in strong lasers? p.1/14
Unruh Effect Uniformly accelerated detector experiences inertial vacuum state as thermal bath with Unruh temperature T Unruh = 2πk B c a = c 1 2πk B d horizon Similarities to Hawking radiation (black hole evaporation) However: Time-reversal invariance W. G. Unruh, Phys. Rev. D 14, 870 (1976). causally disconnected region ct future horizon d horizon trajectory past horizon x Unruh effect & Schwinger mechanism in strong lasers? p.2/14
Accelerated Scatterer Scattering in accelerated frame (thermal bath) causally disconnected region ct future horizon d horizon x trajectory past horizon Translation back into inertial frame Conversion of (virtual) quantum vacuum fluctuations into (real) particle pairs by non-inertial scattering Vacuum entanglement entangled pairs Compare: P. Chen and T. Tajima, Phys. Rev. Lett. 83, 256 (1999). E.g., strongly accelerated electrons... Unruh effect & Schwinger mechanism in strong lasers? p.3/14
Constant Electric Field (ȧ = 0) R. S., G. Schaller, and D. Habs, Phys. Rev. Lett. 97, 121302 (2006). Unruh radiation Larmor radiation blind spot: quantum (Unruh) radiation dominates within small forward cone with angle ( ) ( ) 1 E E 4 ϑ = O, P Unruh (ϑ) = O 1 γ E S E 4 S Schwinger limit E S = m 2 e/q e = O(10 18 V/m) Unruh effect & Schwinger mechanism in strong lasers? p.4/14
Alternative Set-up (ȧ 0) Laser beam with linear polarization and 10 18 W/cm 2 Counter-propagating electron pulse with γ = 1000 Laboratory frame: optical photons with energy 2.5 ev Rest frame of electrons: strongly boosted field E E S 300, ω = 5 kev m e 100 Emission of entangled EPR-pairs of photons: k + k = ω (resonance) perfectly correlated polarizations e Unruh Larmor Unruh effect & Schwinger mechanism in strong lasers? p.5/14
Lowest-order Diagrams One-photon Larmor k k qe qe q + q ω ω Two-photon Larmor qe ω k k qe q q ω +... Quantum radiation (Unruh): ω = k + k Thomson scattering p 2 e/(2m e ) ω low-energy re-summation of qe(q 2 e E ext ) n, cf. exp {i(k + k ) r e [qe ext ]} k k qe +... q q ω Unruh effect & Schwinger mechanism in strong lasers? p.6/14
Lowest-order Scaling Quantum (Unruh) radiation (cf. E 4 /E 4 S ) P Unruh = α2 QED 4π [ E E S ] 2 O ( ωt 30 ) Classical counterpart (Larmor) [ ] 2 qe P 1γ Larmor = α QED O mω ( ωt 2 ) One electron with γ = 300 after 100 cycles in Laser field with 10 18 W/cm 2 yields P Unruh = 4 10 11 and P 1γ Larmor = O(10 1 ) e.g., N e = 6 10 9... Unruh effect & Schwinger mechanism in strong lasers? p.7/14
Distinguishability Larmor monochromatic k = ω, Unruh not k + k = ω in rest frame of electron boost to lab frame γθ Unruh Larmor 2γω E Larmor (left), Unruh (right) 0 < E < 2MeV, 0 < ϑ < 1/100 monochromators apertures (e.g., blind spot) polarization filters R. S., G. Schaller, and D. Habs, Phys. Rev. Lett. 100, 091301 (2008). Unruh effect & Schwinger mechanism in strong lasers? p.8/14
Schwinger Mechanism Problem: non-perturbative imaginary part of Γ[A µ ] = i ln in out = ln[det{i(/ iq /A) m}] =? very few analytic solutions ( Dirac operator) e.g., E(t) = Ee z / cosh 2 (Ωt) 1D-scattering problem for E(t) = e z f(t) approximations: WKB, instanton for E(t) = E 0 f(t) or E(x) = E 0 f(x) (i.e., 1D) numerical techniques (Monte Carlo worldline) Keldysh parameter: non-perturbative vs multi-photon γ = mω qe P e + e { exp{ πes /E} : γ 1 (qe/[mω]) 4m/Ω : γ 1 Unruh effect & Schwinger mechanism in strong lasers? p.9/14
Assisted Schwinger Mechanism Strong & slow + weak & fast pulse ( experiment) E(t) = E cosh 2 (Ωt) e z + ε cosh 2 (ωt) e z Instanton action A inst tunnelling exponent Combined inst Keldysh parameter γ = mω qe 3.0 2.5 Enhancement for γ > π/2 R. S., H. Gies, G. Dunne, arxiv:0807.0754 2.0 1 2 3 4 5 Γ Unruh effect & Schwinger mechanism in strong lasers? p.10/14
Summary signatures of Unruh effect in near-future facilities N e = 6 10 9, γ = 300, 10 18 W/cm 2, 100 cycles ct future horizon causally disconnected region d horizon x trajectory past horizon detectability? spatial interference of many electrons? Schwinger mechanism? E E S = m 2 e/q e = O(10 18 V/m) R. S., G. Schaller, and D. Habs, Phys. Rev. Lett. 97, 121302 (2006). R. S., G. Schaller, and D. Habs, Phys. Rev. Lett. 100, 091301 (2008). R. S., H. Gies, G. Dunne, arxiv:0807.0754 Unruh effect & Schwinger mechanism in strong lasers? p.11/14
Acknowledgements EU-Extreme Light Infrastructure (ELI) Munich-Centre for Advanced Photonics (MAP) G. Schaller, D. Habs, F. Grüner, U. Schramm, P. Thirolf, J. Schreiber, F. Bell, etc. Unruh effect & Schwinger mechanism in strong lasers? p.12/14
Low-Energy Effective Action Spin- and energy-independent Thomson scattering L electron = m e 1 ṙ 2 q e ṙ A(r) Split A = A + A r = r + δr yields L = 1 2 ( E 2 B ) 2 g 2 A2 δ 3 (r [t] r) 1 ṙ 2 [t] Planar Thomson s-wave scattering with g = qe/m 2 e e δr r A A Unruh effect & Schwinger mechanism in strong lasers? p.13/14
Two-photon Amplitude Perturbation theory for small coupling g = q 2 e/m e out = 0 + k,λ,k,λ A k,λ,k,λ k,λ,k,λ + O(g 2 ) Two-photon amplitude of created pairs A k,λ,k,λ = e k,λ e k,λ 2iV dt g 1 ṙ 2 e[t] kk exp {i(k + k )t i(k + k ) r e [t]} Depends on electron s trajectory r e [t] Always entangled photon pairs e k,λ e k,λ Unruh effect & Schwinger mechanism in strong lasers? p.14/14