Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Plasma Physics in Strong-Field Regimes

Yuan Shi [email protected]

Lawrence Livermore National Laboratory Princeton University

Marshall Rosenbluth Thesis Talk 62nd Annual Meeting of APS DPP November 12, 2020

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Acknowledgment

Thesis advisors: Nathaniel J. Fisch and Hong Qin Collaborators: Qing Jia, Matthew R. Edwards, Jianyuan Xiao, Julia M. Mikhailova, Renaud Gueroult, Jean-Marcel Rax, Alessandro R. Castelli, Xian Wu, Ilon Joseph, Vasily Geyko, Frank R. Graziani, Stephen B. Libby, Jeffrey B. Parker, Yaniv J. Rosen, Luis A. Martinez, Jonathan L DuBois, John D. Moody, Bradley B. Pollock, Eleanor R. Tubman, David J. Strozzi Hui Chen, Ryan Lau, Lili Manzo Funding: The Ph.D. thesis work was supported by NNSA Grant No. DE-NA0002948, AFOSR Grant No. FA9550-15-1-0391, DOE Research Grant No. DEAC02-09CH11466. This work was performed under the auspices of US DOE by LLNL under Contract DE-AC52-07NA27344. Y.S. is current supported by the Lawrence Fellowship through LLNL-LDRD under Project No. 19-ERD-038. Yuan Shi Strong-Field Plasma Physics Astrophysics Neutron stars: B ∼ 1012−14 G, E ∼ 1012−14 V/m ◦ Strong B fields quantize particles’ perpendicular momentum ◦ Strong E fields accelerate e−e+ plasma to relativistic energy I Probe interstellar medium, test gravitational physics ...

Laboratory Laser-target interactions: B ∼ 106−9 G, E ∼ 109−13 V/m ◦ Strong B fields alter laser-plasma interactions ... ◦ Strong lasers probe quantum electrodynamics (QED) effects ... I Control coupling in magneto-inertial confinement fusion I Improve plasma-based sources of particles and radiations

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Strong fields: Where do we find them? What’s new? Why do they matter?

Yuan Shi Strong-Field Plasma Physics ◦ Strong B fields quantize particles’ perpendicular momentum ◦ Strong E fields accelerate e−e+ plasma to relativistic energy I Probe interstellar medium, test gravitational physics ...

Laboratory Laser-target interactions: B ∼ 106−9 G, E ∼ 109−13 V/m ◦ Strong B fields alter laser-plasma interactions ... ◦ Strong lasers probe quantum electrodynamics (QED) effects ... I Control coupling in magneto-inertial confinement fusion I Improve plasma-based sources of particles and radiations

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Strong fields: Where do we find them? What’s new? Why do they matter? Astrophysics Neutron stars: B ∼ 1012−14 G, E ∼ 1012−14 V/m

Yuan Shi Strong-Field Plasma Physics I Probe interstellar medium, test gravitational physics ...

Laboratory Laser-target interactions: B ∼ 106−9 G, E ∼ 109−13 V/m ◦ Strong B fields alter laser-plasma interactions ... ◦ Strong lasers probe quantum electrodynamics (QED) effects ... I Control coupling in magneto-inertial confinement fusion I Improve plasma-based sources of particles and radiations

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Strong fields: Where do we find them? What’s new? Why do they matter? Astrophysics Neutron stars: B ∼ 1012−14 G, E ∼ 1012−14 V/m ◦ Strong B fields quantize particles’ perpendicular momentum ◦ Strong E fields accelerate e−e+ plasma to relativistic energy

Yuan Shi Strong-Field Plasma Physics Laboratory Laser-target interactions: B ∼ 106−9 G, E ∼ 109−13 V/m ◦ Strong B fields alter laser-plasma interactions ... ◦ Strong lasers probe quantum electrodynamics (QED) effects ... I Control coupling in magneto-inertial confinement fusion I Improve plasma-based sources of particles and radiations

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Strong fields: Where do we find them? What’s new? Why do they matter? Astrophysics Neutron stars: B ∼ 1012−14 G, E ∼ 1012−14 V/m ◦ Strong B fields quantize particles’ perpendicular momentum ◦ Strong E fields accelerate e−e+ plasma to relativistic energy I Probe interstellar medium, test gravitational physics ...

Yuan Shi Strong-Field Plasma Physics ◦ Strong B fields alter laser-plasma interactions ... ◦ Strong lasers probe quantum electrodynamics (QED) effects ... I Control coupling in magneto-inertial confinement fusion I Improve plasma-based sources of particles and radiations

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Strong fields: Where do we find them? What’s new? Why do they matter? Astrophysics Neutron stars: B ∼ 1012−14 G, E ∼ 1012−14 V/m ◦ Strong B fields quantize particles’ perpendicular momentum ◦ Strong E fields accelerate e−e+ plasma to relativistic energy I Probe interstellar medium, test gravitational physics ...

Laboratory Laser-target interactions: B ∼ 106−9 G, E ∼ 109−13 V/m

Yuan Shi Strong-Field Plasma Physics I Control coupling in magneto-inertial confinement fusion I Improve plasma-based sources of particles and radiations

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Strong fields: Where do we find them? What’s new? Why do they matter? Astrophysics Neutron stars: B ∼ 1012−14 G, E ∼ 1012−14 V/m ◦ Strong B fields quantize particles’ perpendicular momentum ◦ Strong E fields accelerate e−e+ plasma to relativistic energy I Probe interstellar medium, test gravitational physics ...

Laboratory Laser-target interactions: B ∼ 106−9 G, E ∼ 109−13 V/m ◦ Strong B fields alter laser-plasma interactions ... ◦ Strong lasers probe quantum electrodynamics (QED) effects ...

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Strong fields: Where do we find them? What’s new? Why do they matter? Astrophysics Neutron stars: B ∼ 1012−14 G, E ∼ 1012−14 V/m ◦ Strong B fields quantize particles’ perpendicular momentum ◦ Strong E fields accelerate e−e+ plasma to relativistic energy I Probe interstellar medium, test gravitational physics ...

Laboratory Laser-target interactions: B ∼ 106−9 G, E ∼ 109−13 V/m ◦ Strong B fields alter laser-plasma interactions ... ◦ Strong lasers probe quantum electrodynamics (QED) effects ... I Control coupling in magneto-inertial confinement fusion Improve plasma-based sources of particles and radiations Yuan Shi I Strong-Field Plasma Physics Theories • Classical: incorporate background B-fields in laser-plasma physics ... • Quantum: develop first-principle models for collective QED effects ...

Simulations • Classical/semi-classical: add fields, source/scattering terms ... • Quantum/relativistic: develop lattice-gauge simulations ...

Experiments ◦ Sources for strong fields, drivers and targets 1 ◦ Diagnose fields, radiations, and particles ...

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to study plasma physics in strong-field regimes?

Yuan Shi Strong-Field Plasma Physics Simulations • Classical/semi-classical: add fields, source/scattering terms ... • Quantum/relativistic: develop lattice-gauge simulations ...

Experiments ◦ Sources for strong fields, drivers and targets 1 ◦ Diagnose fields, radiations, and particles ...

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to study plasma physics in strong-field regimes? Theories • Classical: incorporate background B-fields in laser-plasma physics ... • Quantum: develop first-principle models for collective QED effects ...

Yuan Shi Strong-Field Plasma Physics Experiments ◦ Sources for strong fields, drivers and targets 1 ◦ Diagnose fields, radiations, and particles ...

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to study plasma physics in strong-field regimes? Theories • Classical: incorporate background B-fields in laser-plasma physics ... • Quantum: develop first-principle models for collective QED effects ...

Simulations • Classical/semi-classical: add fields, source/scattering terms ... • Quantum/relativistic: develop lattice-gauge simulations ...

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to study plasma physics in strong-field regimes? Theories • Classical: incorporate background B-fields in laser-plasma physics ... • Quantum: develop first-principle models for collective QED effects ...

Simulations • Classical/semi-classical: add fields, source/scattering terms ... • Quantum/relativistic: develop lattice-gauge simulations ...

Experiments ◦ Sources for strong fields, drivers and targets 1 ◦ Diagnose fields, radiations, and particles ...

1e.g. C. Goyon, B. B. Pollock, D. P. Turnbull et al., PRE 95, 033208 (2017). Yuan Shi Strong-Field Plasma Physics Magnetized processes: largely unexplored at oblique angles • Many more waves & possibilities: hybrid, Alfv´en,Bernstein ... ◦ EM waves nondegenerate, scatter from all plasma waves ◦ Plasma waves couple nonlinearly among themselves I Complicated and largely unexplored, but important for magnetic/inertial fusion, laser technology, astrophysics ...

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

µ µ µ Coherent three-wave interactions k1 = k2 + k3 Unmagnetized processes: decades of research • Only two plasma waves: Langmuir wave (P), acoustic wave (S) ◦ Processes involve electromagnetic waves (EM): Raman: EM↔ EM + P, Brillouin: EM↔ EM + S two-plasmon decay: EM↔ P + P parametric decay: EM↔ P + S, EM decay: P↔ EM + S ◦ Processes involve plasma waves only: Langmuir decay: P↔ P + S, acoustic decay: S↔ S + S

Yuan Shi Strong-Field Plasma Physics I Complicated and largely unexplored, but important for magnetic/inertial fusion, laser technology, astrophysics ...

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

µ µ µ Coherent three-wave interactions k1 = k2 + k3 Unmagnetized processes: decades of research • Only two plasma waves: Langmuir wave (P), acoustic wave (S) ◦ Processes involve electromagnetic waves (EM): Raman: EM↔ EM + P, Brillouin: EM↔ EM + S two-plasmon decay: EM↔ P + P parametric decay: EM↔ P + S, EM decay: P↔ EM + S ◦ Processes involve plasma waves only: Langmuir decay: P↔ P + S, acoustic decay: S↔ S + S Magnetized processes: largely unexplored at oblique angles • Many more waves & possibilities: hybrid, Alfv´en,Bernstein ... ◦ EM waves nondegenerate, scatter from all plasma waves ◦ Plasma waves couple nonlinearly among themselves

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

µ µ µ Coherent three-wave interactions k1 = k2 + k3 Unmagnetized processes: decades of research • Only two plasma waves: Langmuir wave (P), acoustic wave (S) ◦ Processes involve electromagnetic waves (EM): Raman: EM↔ EM + P, Brillouin: EM↔ EM + S two-plasmon decay: EM↔ P + P parametric decay: EM↔ P + S, EM decay: P↔ EM + S ◦ Processes involve plasma waves only: Langmuir decay: P↔ P + S, acoustic decay: S↔ S + S Magnetized processes: largely unexplored at oblique angles • Many more waves & possibilities: hybrid, Alfv´en,Bernstein ... ◦ EM waves nondegenerate, scatter from all plasma waves ◦ Plasma waves couple nonlinearly among themselves I Complicated and largely unexplored, but important for magnetic/inertial fusion, laser technology, astrophysics ... Yuan Shi Strong-Field Plasma Physics Brute-force: very complicated!!! −→ Operator formalism: elegant & general

◦ Previously, magnetizedΓ known only for collimated waves kB0 or ⊥B0

◦ Linear waves already complicated byB 0, nonlinear coupling even more so • Operator formalism: package complicated algebra into well-motivated operators

Schematics: find general formulaΓ from cold-fluid model

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to compute three-wave coupling coefficientΓ?

Yuan Shi Strong-Field Plasma Physics Schematics: find general formulaΓ from cold-fluid model

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to compute three-wave coupling coefficientΓ? Brute-force: very complicated!!! −→ Operator formalism: elegant & general

◦ Previously, magnetizedΓ known only for collimated waves kB0 or ⊥B0

◦ Linear waves already complicated byB 0, nonlinear coupling even more so • Operator formalism: package complicated algebra into well-motivated operators

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to compute three-wave coupling coefficientΓ? Brute-force: very complicated!!! −→ Operator formalism: elegant & general

◦ Previously, magnetizedΓ known only for collimated waves kB0 or ⊥B0

◦ Linear waves already complicated byB 0, nonlinear coupling even more so • Operator formalism: package complicated algebra into well-motivated operators

Schematics: find general formulaΓ from cold-fluid model

Yuan Shi Strong-Field Plasma Physics 1st order: well-known linear waves (1) • Eigenmodes can be found from E-field equation DkEk = 0. Dispersion tensor ij 2 2 2 ij 2 i j X 2 ij Dk = (ωk − c k )δ + c k k − ωps Fs,k. s • Forcing operator F related to linear susceptibility and Hamiltonian of linear waves 2 2 ωps 1 ∂ X ωps ∂ s χ = − , = D = 2 − F s,k ω2 Fs,k H ω ∂ω I ω ∂ω k s

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Compute couplingΓ from perturbation theory Perturbative solution • Expand near equilibrium, solve order by order, Z = E, B, vs , ns 2 Z = Z0 + λZ1 + λ Z2 + ... • Nonlinearities cause secular terms, remove by multi-scale expansion of spacetime µ µ µ µ 2 (a) µ µ (a) x = x(0) + x(1)/λ + x(2)/λ + . . . , ∂ν x(b) = δν δ(b)

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Compute couplingΓ from perturbation theory Perturbative solution • Expand near equilibrium, solve order by order, Z = E, B, vs , ns 2 Z = Z0 + λZ1 + λ Z2 + ... • Nonlinearities cause secular terms, remove by multi-scale expansion of spacetime µ µ µ µ 2 (a) µ µ (a) x = x(0) + x(1)/λ + x(2)/λ + . . . , ∂ν x(b) = δν δ(b) 1st order: well-known linear waves (1) • Eigenmodes can be found from E-field equation DkEk = 0. Dispersion tensor ij 2 2 2 ij 2 i j X 2 ij Dk = (ωk − c k )δ + c k k − ωps Fs,k. s • Forcing operator F related to linear susceptibility and Hamiltonian of linear waves 2 2 ωps 1 ∂ X ωps ∂ s χ = − , = D = 2 − F s,k ω2 Fs,k H ω ∂ω I ω ∂ω k s Yuan Shi Strong-Field Plasma Physics s Γ fromS q,p: vector eqs. ⇒ scalar eqs. ◦ Action conservation: property of forcing operator

⇒ 3-wave eqs. dt a1 = −Γa2a3/ω1 ...

s 1 • Scattering strengthsΘ = (cki · s,j ej )(ei · e ) i,jl ωj F Fs,l l

1 † • Normalized by wave energy u = 2 e He

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

2nd-order equation ⇒ coupling coefficientΓ Secular-free 2nd-order equations 1

Quasimodes Envelope Advection z }| { z }| { 2 s (2) (1) i Zs ωps Θ X iθk X iθk X i(θq+θq0 ) s X E e + i ω d E e = e S 0 ←→ Γ= Dk k kHk (1) k q,q 1/2 2 0 4Ms (u1u2u3) k∈K2 k∈K1 s,q,q ∈K1 s

1Y. Shi, H. Qin, and N. J. Fisch, Phys. Rev. E 96, 023204 (2017). Yuan Shi Strong-Field Plasma Physics s 1 • Scattering strengthsΘ = (cki · s,j ej )(ei · e ) i,jl ωj F Fs,l l

1 † • Normalized by wave energy u = 2 e He

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

2nd-order equation ⇒ coupling coefficientΓ Secular-free 2nd-order equations 1

Quasimodes Envelope Advection z }| { z }| { 2 s (2) (1) i Zs ωps Θ X iθk X iθk X i(θq+θq0 ) s X E e + i ω d E e = e S 0 ←→ Γ= Dk k kHk (1) k q,q 1/2 2 0 4Ms (u1u2u3) k∈K2 k∈K1 s,q,q ∈K1 s

s Γ fromS q,p: vector eqs. ⇒ scalar eqs. ◦ Action conservation: property of forcing operator

⇒ 3-wave eqs. dt a1 = −Γa2a3/ω1 ...

1Y. Shi, H. Qin, and N. J. Fisch, Phys. Rev. E 96, 023204 (2017). Yuan Shi Strong-Field Plasma Physics 1 † • Normalized by wave energy u = 2 e He

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

2nd-order equation ⇒ coupling coefficientΓ Secular-free 2nd-order equations 1

Quasimodes Envelope Advection z }| { z }| { 2 s (2) (1) i Zs ωps Θ X iθk X iθk X i(θq+θq0 ) s X E e + i ω d E e = e S 0 ←→ Γ= Dk k kHk (1) k q,q 1/2 2 0 4Ms (u1u2u3) k∈K2 k∈K1 s,q,q ∈K1 s

s Γ fromS q,p: vector eqs. ⇒ scalar eqs. ◦ Action conservation: property of forcing operator

⇒ 3-wave eqs. dt a1 = −Γa2a3/ω1 ...

s 1 • Scattering strengthsΘ = (cki · s,j ej )(ei · e ) i,jl ωj F Fs,l l

1Y. Shi, H. Qin, and N. J. Fisch, Phys. Rev. E 96, 023204 (2017). Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

2nd-order equation ⇒ coupling coefficientΓ Secular-free 2nd-order equations 1

Quasimodes Envelope Advection z }| { z }| { 2 s (2) (1) i Zs ωps Θ X iθk X iθk X i(θq+θq0 ) s X E e + i ω d E e = e S 0 ←→ Γ= Dk k kHk (1) k q,q 1/2 2 0 4Ms (u1u2u3) k∈K2 k∈K1 s,q,q ∈K1 s

s Γ fromS q,p: vector eqs. ⇒ scalar eqs. ◦ Action conservation: property of forcing operator

⇒ 3-wave eqs. dt a1 = −Γa2a3/ω1 ...

s 1 • Scattering strengthsΘ = (cki · s,j ej )(ei · e ) i,jl ωj F Fs,l l

1 † • Normalized by wave energy u = 2 e He

1Y. Shi, H. Qin, and N. J. Fisch, Phys. Rev. E 96, 023204 (2017). Yuan Shi Strong-Field Plasma Physics • Via upper-hybrid-like waves (P): favor exact backscattering, k3 effect dominants

• Via lower-hybrid-like waves (F): favor ⊥ scattering, e− and i + interference exactly cancel scattering at special angles

• Via Alfv´en-like waves (A): favor backward, but suppress exact backscattering

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

CouplingΓ ⇒ growth rate M Magnetized scattering is anisotropic

Example: perpendicular pump laser 1

1Experiments in preparation at OMEGA, B. B. Pollock, E. R. Tubman, J. D. Moody, and Y. Shi (2021). Yuan Shi Strong-Field Plasma Physics • Via lower-hybrid-like waves (F): favor ⊥ scattering, e− and i + interference exactly cancel scattering at special angles

• Via Alfv´en-like waves (A): favor backward, but suppress exact backscattering

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

CouplingΓ ⇒ growth rate M Magnetized scattering is anisotropic

Example: perpendicular pump laser 1 • Via upper-hybrid-like waves (P): favor exact backscattering, k3 effect dominants

1Experiments in preparation at OMEGA, B. B. Pollock, E. R. Tubman, J. D. Moody, and Y. Shi (2021). Yuan Shi Strong-Field Plasma Physics • Via Alfv´en-like waves (A): favor backward, but suppress exact backscattering

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

CouplingΓ ⇒ growth rate M Magnetized scattering is anisotropic

Example: perpendicular pump laser 1 • Via upper-hybrid-like waves (P): favor exact backscattering, k3 effect dominants

• Via lower-hybrid-like waves (F): favor ⊥ scattering, e− and i + interference exactly cancel scattering at special angles

1Experiments in preparation at OMEGA, B. B. Pollock, E. R. Tubman, J. D. Moody, and Y. Shi (2021). Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

CouplingΓ ⇒ growth rate M Magnetized scattering is anisotropic

Example: perpendicular pump laser 1 • Via upper-hybrid-like waves (P): favor exact backscattering, k3 effect dominants

• Via lower-hybrid-like waves (F): favor ⊥ scattering, e− and i + interference exactly cancel scattering at special angles

• Via Alfv´en-like waves (A): favor backward, but suppress exact backscattering

1Experiments in preparation at OMEGA, B. B. Pollock, E. R. Tubman, J. D. Moody, and Y. Shi (2021). Yuan Shi Strong-Field Plasma Physics First-of-the-kind demonstration on real quantum processors ◦ Convenient mapping use action basis ◦ Hamiltonian matrix block tridiagonal • Customized gates better than standard

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Quantum simulation of three-wave interactions 1 Classical problem ⇐ Quantum problem ˆ √ ˆ ˆ† 0 0 ◦ Promote to operators Ai = ωi ai ,[Ai (t), Aj (t )] = δij δ(t − t ) ˆ R ∗ ˆ ˆ† ˆ† ˆ† ˆ ˆ √ ◦ Interaction Hamiltonian HI = dt(ig A1A2A3 − ig A1A2A3), g =Γ / ω1ω2ω3 • Heisenberg eq. ⇔ quantum 3-wave eqs.

1Y. Shi, A. Castelli, X. Wu et al. arXiv:2004.06885. See more details at NP12.00001, APS DPP 2020. Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Quantum simulation of three-wave interactions 1 Classical problem ⇐ Quantum problem ˆ √ ˆ ˆ† 0 0 ◦ Promote to operators Ai = ωi ai ,[Ai (t), Aj (t )] = δij δ(t − t ) ˆ R ∗ ˆ ˆ† ˆ† ˆ† ˆ ˆ √ ◦ Interaction Hamiltonian HI = dt(ig A1A2A3 − ig A1A2A3), g =Γ / ω1ω2ω3 • Heisenberg eq. ⇔ quantum 3-wave eqs.

First-of-the-kind demonstration on real quantum processors ◦ Convenient mapping use action basis ◦ Hamiltonian matrix block tridiagonal • Customized gates better than standard

1Y. Shi, A. Castelli, X. Wu et al. arXiv:2004.06885. See more details at NP12.00001, APS DPP 2020. Yuan Shi Strong-Field Plasma Physics Why/what is pulse compression? Magnetized pulse compression • Generate high-intensity ◦ Mediated by magnetized waves short pulses for: ◦ Suppress competing effects · Inertial confinement fusion by B-field and angles · Single-molecule imaging · Additive manufacturing • Enable higher intensity and ... wider frequency ranges ◦ Chirped pulse amplification Optical regime ∼ 1 eV Unfocused ∼ 1014 W/cm2 ◦ Raman/Brillouin compression Frequency . 100 eV 18 2 Unfocused . 10 W/cm

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Application: improve laser pulse compression by magnetization

Yuan Shi Strong-Field Plasma Physics Magnetized pulse compression ◦ Mediated by magnetized waves ◦ Suppress competing effects by B-field and angles • Enable higher intensity and wider frequency ranges ◦ Chirped pulse amplification Optical regime ∼ 1 eV Unfocused ∼ 1014 W/cm2 ◦ Raman/Brillouin compression Frequency . 100 eV 18 2 Unfocused . 10 W/cm

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Application: improve laser pulse compression by magnetization

Why/what is pulse compression? • Generate high-intensity short pulses for: · Inertial confinement fusion · Single-molecule imaging · Additive manufacturing ...

Yuan Shi Strong-Field Plasma Physics Magnetized pulse compression ◦ Mediated by magnetized waves ◦ Suppress competing effects by B-field and angles • Enable higher intensity and wider frequency ranges

◦ Raman/Brillouin compression Frequency . 100 eV 18 2 Unfocused . 10 W/cm

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Application: improve laser pulse compression by magnetization

Why/what is pulse compression? • Generate high-intensity short pulses for: · Inertial confinement fusion · Single-molecule imaging · Additive manufacturing ... ◦ Chirped pulse amplification Optical regime ∼ 1 eV Unfocused ∼ 1014 W/cm2

Yuan Shi Strong-Field Plasma Physics Magnetized pulse compression ◦ Mediated by magnetized waves ◦ Suppress competing effects by B-field and angles • Enable higher intensity and wider frequency ranges

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Application: improve laser pulse compression by magnetization

Why/what is pulse compression? • Generate high-intensity short pulses for: · Inertial confinement fusion · Single-molecule imaging · Additive manufacturing ... ◦ Chirped pulse amplification Optical regime ∼ 1 eV Unfocused ∼ 1014 W/cm2 ◦ Raman/Brillouin compression Frequency . 100 eV 18 2 Unfocused . 10 W/cm

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Application: improve laser pulse compression by magnetization

Why/what is pulse compression? Magnetized pulse compression • Generate high-intensity ◦ Mediated by magnetized waves short pulses for: ◦ Suppress competing effects · Inertial confinement fusion by B-field and angles · Single-molecule imaging · Additive manufacturing • Enable higher intensity and ... wider frequency ranges ◦ Chirped pulse amplification Optical regime ∼ 1 eV Unfocused ∼ 1014 W/cm2 ◦ Raman/Brillouin compression Frequency . 100 eV 18 2 Unfocused . 10 W/cm

Yuan Shi Strong-Field Plasma Physics Fundamental reason: change laser-plasma interactions • Magnetization allows tuning of coupling & phase matching 1 ◦ B0 and θ = hk, B0i control growth rate ◦ Select interaction channel by frequency tunning • Magnetization suppresses competing processes 2 ◦ Damping: collisionless νL ∝ ne , collisional νi ∝ ne ◦ Modulational instabilities: growth rate γM ∝ ne ◦ Wave breaking: more resilient with larger B0 ◦ Wakefield: larger fraction to particles if ne too small Practical reason: relax engineering constraints Extra controls ⇒ further optimization ⇒ potentially better performance

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Why magnetic field helps?

1Y. Shi and N. J. Fisch, Phys. Plasmas 26, 072114 (2019). Yuan Shi Strong-Field Plasma Physics • Magnetization suppresses competing processes 2 ◦ Damping: collisionless νL ∝ ne , collisional νi ∝ ne ◦ Modulational instabilities: growth rate γM ∝ ne ◦ Wave breaking: more resilient with larger B0 ◦ Wakefield: larger fraction to particles if ne too small Practical reason: relax engineering constraints Extra controls ⇒ further optimization ⇒ potentially better performance

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Why magnetic field helps? Fundamental reason: change laser-plasma interactions • Magnetization allows tuning of coupling & phase matching 1 ◦ B0 and θ = hk, B0i control growth rate ◦ Select interaction channel by frequency tunning

1Y. Shi and N. J. Fisch, Phys. Plasmas 26, 072114 (2019). Yuan Shi Strong-Field Plasma Physics Practical reason: relax engineering constraints Extra controls ⇒ further optimization ⇒ potentially better performance

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Why magnetic field helps? Fundamental reason: change laser-plasma interactions • Magnetization allows tuning of coupling & phase matching 1 ◦ B0 and θ = hk, B0i control growth rate ◦ Select interaction channel by frequency tunning • Magnetization suppresses competing processes 2 ◦ Damping: collisionless νL ∝ ne , collisional νi ∝ ne ◦ Modulational instabilities: growth rate γM ∝ ne ◦ Wave breaking: more resilient with larger B0 ◦ Wakefield: larger fraction to particles if ne too small

1Y. Shi and N. J. Fisch, Phys. Plasmas 26, 072114 (2019). Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Why magnetic field helps? Fundamental reason: change laser-plasma interactions • Magnetization allows tuning of coupling & phase matching 1 ◦ B0 and θ = hk, B0i control growth rate ◦ Select interaction channel by frequency tunning • Magnetization suppresses competing processes 2 ◦ Damping: collisionless νL ∝ ne , collisional νi ∝ ne ◦ Modulational instabilities: growth rate γM ∝ ne ◦ Wave breaking: more resilient with larger B0 ◦ Wakefield: larger fraction to particles if ne too small Practical reason: relax engineering constraints Extra controls ⇒ further optimization ⇒ potentially better performance

1Y. Shi and N. J. Fisch, Phys. Plasmas 26, 072114 (2019). Yuan Shi Strong-Field Plasma Physics • Compress KrF ω0~ = 5 eV 13 2 I1 = 10 W/cm B0 = 5 MG L ∼ 0.1 m tM ∼ 1 ns ⇒ 0.1ps

• Compress x-ray ω0~ = 250 eV 18 2 I1 = 10 W/cm B0 = 1.5 GG L ∼ 0.1 mm tM ∼ 1 ps ⇒ 1fs

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Upper-hybrid mediation: B-field relaxes limiting effects

Yuan Shi Strong-Field Plasma Physics • Compress x-ray ω0~ = 250 eV 18 2 I1 = 10 W/cm B0 = 1.5 GG L ∼ 0.1 mm tM ∼ 1 ps ⇒ 1fs

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Upper-hybrid mediation: B-field relaxes limiting effects

• Compress KrF ω0~ = 5 eV 13 2 I1 = 10 W/cm B0 = 5 MG L ∼ 0.1 m tM ∼ 1 ns ⇒ 0.1ps

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Upper-hybrid mediation: B-field relaxes limiting effects

• Compress KrF ω0~ = 5 eV 13 2 I1 = 10 W/cm B0 = 5 MG L ∼ 0.1 m tM ∼ 1 ns ⇒ 0.1ps

• Compress x-ray ω0~ = 250 eV 18 2 I1 = 10 W/cm B0 = 1.5 GG L ∼ 0.1 mm tM ∼ 1 ps ⇒ 1fs

Yuan Shi Strong-Field Plasma Physics Expand regime of applicability • Enable compression of lasers of higher frequency ◦ Reduce damping by substituting ne with B0

Increase output pulse intensity I2 • Output pulse more intense u than unmagnetized maximum I2 ◦ Suppress competing instabilities, delay saturation, slower amplification

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Upper-hybrid mediation: B-field improves pulse compression 1

1 Yuan Shi Y. Shi, H. Qin, and N. J. Fisch, Phys. Rev. E 95, 023211 (2017). Strong-Field Plasma Physics Increase output pulse intensity I2 • Output pulse more intense u than unmagnetized maximum I2 ◦ Suppress competing instabilities, delay saturation, slower amplification

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Upper-hybrid mediation: B-field improves pulse compression 1

Expand regime of applicability • Enable compression of lasers of higher frequency ◦ Reduce damping by substituting ne with B0

1 Yuan Shi Y. Shi, H. Qin, and N. J. Fisch, Phys. Rev. E 95, 023211 (2017). Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Upper-hybrid mediation: B-field improves pulse compression 1

Expand regime of applicability • Enable compression of lasers of higher frequency ◦ Reduce damping by substituting ne with B0

Increase output pulse intensity I2 • Output pulse more intense u than unmagnetized maximum I2 ◦ Suppress competing instabilities, delay saturation, slower amplification

1 Yuan Shi Y. Shi, H. Qin, and N. J. Fisch, Phys. Rev. E 95, 023211 (2017). Strong-Field Plasma Physics • B0 < Bopt: slower amplification, delayed saturation ⇒ higher output intensity • B0 > Bopt: wakefield limits further growth, increased energy transfer to particles

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

1D PIC validation: upper-hybrid compression in optical regime 1-µm laser pulse compression 1

◦ Increase B0, decrease ne , fixed ω3 and Te 14 2 Fixed pump: 1.0 µm, I10 = 3.5 × 10 W/cm 13 2 Fixed seed : 1.1 µm, I20 = 1.8 × 10 W/cm

1 Yuan Shi Q. Jia, Y. Shi, H. Qin, and N. J. Fisch, Phys. Plasmas 24, 093103 (2017). Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

1D PIC validation: upper-hybrid compression in optical regime 1-µm laser pulse compression 1

◦ Increase B0, decrease ne , fixed ω3 and Te 14 2 Fixed pump: 1.0 µm, I10 = 3.5 × 10 W/cm 13 2 Fixed seed : 1.1 µm, I20 = 1.8 × 10 W/cm

• B0 < Bopt: slower amplification, delayed saturation ⇒ higher output intensity • B0 > Bopt: wakefield limits further growth, increased energy transfer to particles

1 Yuan Shi Q. Jia, Y. Shi, H. Qin, and N. J. Fisch, Phys. Plasmas 24, 093103 (2017). Strong-Field Plasma Physics Low frequencies Strong coupling

• Resonant Ωe ∼ ω0 ⇒ intense short pulse Large growth rate, similar to Raman Wide bandwidth, overlapping ∼MHD waves Small detuning, pump ∼ seed frequency

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

1D PIC validation: mediation by low-frequency waves 1

1-µm laser amplification

◦ Select θ = hk, B0i and B0 to tune: Phase matching. Interaction strength.

1M. R. Edwards, Y. Shi, J. M. Mikhailova, and N. J. Fisch, Phys. Rev. Lett. 123, 025001 (2019). Yuan Shi Strong-Field Plasma Physics • Resonant Ωe ∼ ω0 ⇒ intense short pulse Large growth rate, similar to Raman Wide bandwidth, overlapping ∼MHD waves Small detuning, pump ∼ seed frequency

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

1D PIC validation: mediation by low-frequency waves 1

1-µm laser amplification

◦ Select θ = hk, B0i and B0 to tune: Phase matching. Low frequencies Interaction strength. Strong coupling

1M. R. Edwards, Y. Shi, J. M. Mikhailova, and N. J. Fisch, Phys. Rev. Lett. 123, 025001 (2019). Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

1D PIC validation: mediation by low-frequency waves 1

1-µm laser amplification

◦ Select θ = hk, B0i and B0 to tune: Phase matching. Low frequencies Interaction strength. Strong coupling

• Resonant Ωe ∼ ω0 ⇒ intense short pulse Large growth rate, similar to Raman Wide bandwidth, overlapping ∼MHD waves Small detuning, pump ∼ seed frequency

1M. R. Edwards, Y. Shi, J. M. Mikhailova, and N. J. Fisch, Phys. Rev. Lett. 123, 025001 (2019). Yuan Shi Strong-Field Plasma Physics X-ray pulsars B ∼ 1012 G • Quantum: ~Ωe > kB T • Relativistic ~Ωe ∼ 10 keV ⇒ Anharmonic spectrum 1

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Even stronger fields: relativistic-quantum regime

• Quantum: ∆H & kB T , Up 2 • Relativistic: H & me c

1W. A. Heindl, W. Coburn, D. E. Gruber, et al., AIP Conf. Proc. 510(1):173, (2000). Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Even stronger fields: relativistic-quantum regime

12 • Quantum: ∆H & kB T , Up X-ray pulsars B ∼ 10 G 2 • Relativistic: H & me c • Quantum: ~Ωe > kB T • Relativistic ~Ωe ∼ 10 keV ⇒ Anharmonic spectrum 1

1W. A. Heindl, W. Coburn, D. E. Gruber, et al., AIP Conf. Proc. 510(1):173, (2000). Yuan Shi Strong-Field Plasma Physics First-principle model: QED plasma theory • QED plasma theory: add background fields, fluctuations on plasma background ◦ Usual quantum field theory: fluctuations on vacuum background ◦ Tree-level QED effects ⇐ classical field equations ◦ Quantum loop effects ⇐ path integrals, higher-order diagrams

Toy model: scalar-QED • φ = φ0 +ϕ, Aµ = A¯µ +Aµ. Plasma effects in φ0 and A¯µ, dynamical backgrounds ∗ µ 2 ∗ 1 µν L = (Dµφ) (D φ) − m φ φ − FµνF | {z } 4 | {z } Charged Bosons EM Fields Dµ=∂µ−iqAµ ◦ Scalar-QED: spin-0 charged bosons interact with EM fields Usual plasma models ignore spin/statistics of charged particles

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to model relativistic-quantum plasmas?

Yuan Shi Strong-Field Plasma Physics Toy model: scalar-QED • φ = φ0 +ϕ, Aµ = A¯µ +Aµ. Plasma effects in φ0 and A¯µ, dynamical backgrounds ∗ µ 2 ∗ 1 µν L = (Dµφ) (D φ) − m φ φ − FµνF | {z } 4 | {z } Charged Bosons EM Fields Dµ=∂µ−iqAµ ◦ Scalar-QED: spin-0 charged bosons interact with EM fields Usual plasma models ignore spin/statistics of charged particles

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to model relativistic-quantum plasmas? First-principle model: QED plasma theory • QED plasma theory: add background fields, fluctuations on plasma background ◦ Usual quantum field theory: fluctuations on vacuum background ◦ Tree-level QED effects ⇐ classical field equations ◦ Quantum loop effects ⇐ path integrals, higher-order diagrams

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

How to model relativistic-quantum plasmas? First-principle model: QED plasma theory • QED plasma theory: add background fields, fluctuations on plasma background ◦ Usual quantum field theory: fluctuations on vacuum background ◦ Tree-level QED effects ⇐ classical field equations ◦ Quantum loop effects ⇐ path integrals, higher-order diagrams

Toy model: scalar-QED • φ = φ0 +ϕ, Aµ = A¯µ +Aµ. Plasma effects in φ0 and A¯µ, dynamical backgrounds ∗ µ 2 ∗ 1 µν L = (Dµφ) (D φ) − m φ φ − FµνF | {z } 4 | {z } Charged Bosons EM Fields Dµ=∂µ−iqAµ ◦ Scalar-QED: spin-0 charged bosons interact with EM fields Usual plasma models ignore spin/statistics of charged particles

Yuan Shi Strong-Field Plasma Physics • Vacuum polarization response: pair creation/annihilation in vacuum x x0 Σµν (x, x0) = µ ν + µ ν 2,vac x • Collective plasma response: excitation/de-excitation of background fields x x0 µν 0 x Σ2,bk (x, x ) = µ ν + µ ν

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Lowest order: linear wave propagation Waves in scalar-QED plasmas 1 • Path integral over charged particles ⇒ wave effective action 1 Γ = − F F µν + A ΣµνA +O(e3) 4 µν µ 2 ν | {z } | {z } Vacuum Linear Response µν µν µν Σ2 =Σ2,vac+Σ2,bk

1 Yuan Shi Y. Shi, N. J. Fisch, and H. Qin, Phys. Rev. A 94, 012124 (2016). Strong-Field Plasma Physics • Collective plasma response: excitation/de-excitation of background fields x x0 µν 0 x Σ2,bk (x, x ) = µ ν + µ ν

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Lowest order: linear wave propagation Waves in scalar-QED plasmas 1 • Path integral over charged particles ⇒ wave effective action 1 Γ = − F F µν + A ΣµνA +O(e3) 4 µν µ 2 ν | {z } | {z } Vacuum Linear Response µν µν µν Σ2 =Σ2,vac+Σ2,bk • Vacuum polarization response: pair creation/annihilation in vacuum x x0 Σµν (x, x0) = µ ν + µ ν 2,vac x

1 Yuan Shi Y. Shi, N. J. Fisch, and H. Qin, Phys. Rev. A 94, 012124 (2016). Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Lowest order: linear wave propagation Waves in scalar-QED plasmas 1 • Path integral over charged particles ⇒ wave effective action 1 Γ = − F F µν + A ΣµνA +O(e3) 4 µν µ 2 ν | {z } | {z } Vacuum Linear Response µν µν µν Σ2 =Σ2,vac+Σ2,bk • Vacuum polarization response: pair creation/annihilation in vacuum x x0 Σµν (x, x0) = µ ν + µ ν 2,vac x • Collective plasma response: excitation/de-excitation of background fields x x0 µν 0 x Σ2,bk (x, x ) = µ ν + µ ν

1 Yuan Shi Y. Shi, N. J. Fisch, and H. Qin, Phys. Rev. A 94, 012124 (2016). Strong-Field Plasma Physics • Quantum effects: cold resonances Open gaps between Bernstein waves Classically, no gap when cold Quantum uncertainty∼thermal fluctuation • Relativistic effects: anharmonic spectrum Redshift cyclotron resonances In this example ω5 ∼ 4Ωe Classical is harmonic ω5 ≈ 5Ωe

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Observable: anharmonic cyclotron lines of x-ray pulsars 1

Perpendicular wave propagation k ⊥ B0

Cold e− gas ωpe Ωe ~ = 0.7, 2 = 0.1 Ωe me c

1Y. Shi, N. J. Fisch, and H. Qin, Phys. Rev. A 94, 012124 (2016). Yuan Shi Strong-Field Plasma Physics • Relativistic effects: anharmonic spectrum Redshift cyclotron resonances In this example ω5 ∼ 4Ωe Classical is harmonic ω5 ≈ 5Ωe

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Observable: anharmonic cyclotron lines of x-ray pulsars 1

Perpendicular wave propagation k ⊥ B0 • Quantum effects: cold resonances Open gaps between Bernstein waves Classically, no gap when cold Quantum uncertainty∼thermal fluctuation

Cold e− gas ωpe Ωe ~ = 0.7, 2 = 0.1 Ωe me c

1Y. Shi, N. J. Fisch, and H. Qin, Phys. Rev. A 94, 012124 (2016). Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Observable: anharmonic cyclotron lines of x-ray pulsars 1

Perpendicular wave propagation k ⊥ B0 • Quantum effects: cold resonances Open gaps between Bernstein waves Classically, no gap when cold Quantum uncertainty∼thermal fluctuation • Relativistic effects: anharmonic spectrum Redshift cyclotron resonances In this example ω5 ∼ 4Ωe Classical is harmonic ω5 ≈ 5Ωe

Cold e− gas ωpe Ωe ~ = 0.7, 2 = 0.1 Ωe me c

1Y. Shi, N. J. Fisch, and H. Qin, Phys. Rev. A 94, 012124 (2016). Yuan Shi Strong-Field Plasma Physics 2 2 mΩ mωp m0 nR/L = 1 − ω2 − 2m ω2 ∓ ω r 0  2 2 2 mΩ mωp m0 2mωp ± 2 + 2 ± ∓ 3 ω 2m0ω ω ω • Quantum effects: p 2 zero-point energy m0 = m + eB0 • Relativistic effects: frequency shifts Ω ∼ rest mass m I Observable for radio pulsars near cutoff, compounded with mechanical-optical rotation

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Observable: anomalous Faraday rotation of radio pulsars 1

Parallel wave propagation k k B0

◦ Rotation angle per vacuum wavelength λ0

λ0dφ/dz = π(nL − nR )

1 Yuan Shi R. Gueroult, Y. Shi, J.-M. Rax, and N. J. Fisch, Nat. Commun. 10, 3232 (2019). Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Observable: anomalous Faraday rotation of radio pulsars 1

Parallel wave propagation k k B0

◦ Rotation angle per vacuum wavelength λ0

λ0dφ/dz = π(nL − nR ) 2 2 mΩ mωp m0 nR/L = 1 − ω2 − 2m ω2 ∓ ω r 0  2 2 2 mΩ mωp m0 2mωp ± 2 + 2 ± ∓ 3 ω 2m0ω ω ω • Quantum effects: p 2 zero-point energy m0 = m + eB0 • Relativistic effects: frequency shifts Ω ∼ rest mass m I Observable for radio pulsars near cutoff, compounded with mechanical-optical rotation

1 Yuan Shi R. Gueroult, Y. Shi, J.-M. Rax, and N. J. Fisch, Nat. Commun. 10, 3232 (2019). Strong-Field Plasma Physics • QED predicts ω-dependence of θ˙ = dθ/dz, differs from classical • Difference largest near cutoff, 2 δ → Ωe ~/me c when ω → ∞ • Observable for large B0 small ne

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Can we observe QED effects in lab? Corrections to Faraday rotation

Yuan Shi Strong-Field Plasma Physics • Observable for large B0 small ne

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Can we observe QED effects in lab? Corrections to Faraday rotation • QED predicts ω-dependence of θ˙ = dθ/dz, differs from classical • Difference largest near cutoff, 2 δ → Ωe ~/me c when ω → ∞

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Can we observe QED effects in lab? Corrections to Faraday rotation • QED predicts ω-dependence of θ˙ = dθ/dz, differs from classical • Difference largest near cutoff, 2 δ → Ωe ~/me c when ω → ∞ • Observable for large B0 small ne

Yuan Shi Strong-Field Plasma Physics • Existing numerical methods valid in semi-classical limit ◦ QED-PIC: particle-in-cell + QED source terms ◦ Quantum fluid: hydro + quantum pressure/sources • What existing methods cannot do? energy-momentum conservation, radiation reaction nonlocal interactions, quantum interference ... How to simulate QED plasmas? ◦ Inspired by lattice quantum chromodynamics (QCD): commonly used for quark-gluon matter • First-principle lattice QED plasma simulations: large n0 small e, classical fields dominate path integral

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Beyond perturbative regime: QED plasma simulations Why do we need QED plasma simulations? ◦ Ultra-intense lasers interact with targets in QED regime 1

1 Yuan Shi H. Chen, S. C. Wilks, D. D. Meyerhofer et al., Phys. Rev. Lett. 105, 015003 (2010). Strong-Field Plasma Physics How to simulate QED plasmas? ◦ Inspired by lattice quantum chromodynamics (QCD): commonly used for quark-gluon matter • First-principle lattice QED plasma simulations: large n0 small e, classical fields dominate path integral

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Beyond perturbative regime: QED plasma simulations Why do we need QED plasma simulations? ◦ Ultra-intense lasers interact with targets in QED regime 1 • Existing numerical methods valid in semi-classical limit ◦ QED-PIC: particle-in-cell + QED source terms ◦ Quantum fluid: hydro + quantum pressure/sources • What existing methods cannot do? energy-momentum conservation, radiation reaction nonlocal interactions, quantum interference ...

1 Yuan Shi H. Chen, S. C. Wilks, D. D. Meyerhofer et al., Phys. Rev. Lett. 105, 015003 (2010). Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Beyond perturbative regime: QED plasma simulations Why do we need QED plasma simulations? ◦ Ultra-intense lasers interact with targets in QED regime 1 • Existing numerical methods valid in semi-classical limit ◦ QED-PIC: particle-in-cell + QED source terms ◦ Quantum fluid: hydro + quantum pressure/sources • What existing methods cannot do? energy-momentum conservation, radiation reaction nonlocal interactions, quantum interference ... How to simulate QED plasmas? ◦ Inspired by lattice quantum chromodynamics (QCD): commonly used for quark-gluon matter • First-principle lattice QED plasma simulations: large n0 small e, classical fields dominate path integral

1 Yuan Shi H. Chen, S. C. Wilks, D. D. Meyerhofer et al., Phys. Rev. Lett. 105, 015003 (2010). Strong-Field Plasma Physics Variational algorithm & discretization by exterior calculus ◦ 0-form φ lives on vertices ◦ 1-form A lives on edges ◦ 2-form F lives on faces P • Discrete action Sd = ∆V c Ld • Variations of Sd ⇒ discretized eqs. Local charge conservation exactly satisfied ⇒ ∇·B=0, ∂t B=−∇×E exactly satisfied

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Classical-statistical regime: solve field equations Toy model: scalar-QED plasma • Leading order behavior described by classical field equations µ 2 ◦ Klein-Gordon’s Equation: (DµD + m )φ = 0 µν ν ◦ Maxwell’s Equation : ∂µF = j

Yuan Shi Strong-Field Plasma Physics Local charge conservation exactly satisfied ⇒ ∇·B=0, ∂t B=−∇×E exactly satisfied

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Classical-statistical regime: solve field equations Toy model: scalar-QED plasma • Leading order behavior described by classical field equations µ 2 ◦ Klein-Gordon’s Equation: (DµD + m )φ = 0 µν ν ◦ Maxwell’s Equation : ∂µF = j Variational algorithm & discretization by exterior calculus ◦ 0-form φ lives on vertices ◦ 1-form A lives on edges ◦ 2-form F lives on faces P • Discrete action Sd = ∆V c Ld • Variations of Sd ⇒ discretized eqs.

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Classical-statistical regime: solve field equations Toy model: scalar-QED plasma • Leading order behavior described by classical field equations µ 2 ◦ Klein-Gordon’s Equation: (DµD + m )φ = 0 µν ν ◦ Maxwell’s Equation : ∂µF = j Variational algorithm & discretization by exterior calculus ◦ 0-form φ lives on vertices ◦ 1-form A lives on edges ◦ 2-form F lives on faces P • Discrete action Sd = ∆V c Ld • Variations of Sd ⇒ discretized eqs. Local charge conservation exactly satisfied ⇒ ∇·B=0, ∂t B=−∇×E exactly satisfied

Yuan Shi Strong-Field Plasma Physics 0 1 0 1/2 • Initial conditions φs , φs ; As+l/2, As 1 • 0-th step: As+l/2 from Gauss’s law 2 0 ∂t ∇ · A = −∇ A − ρ 1st order, easier than Poisson’s equation • Time advance: need gauge fixing, observables gauge-independent ◦ Gauge condition: n−1/2 n n+1/2 (As , As+l/2) → As ◦ Klein-Gordon equation: n−1 n n n±1/2 n+1 (φs , φs ; As+l/2, As ) → φs ◦ Maxwell-Amp`ere’slaw: 1 ∆t <∆x <1/H, Compton scale n−1 n n± 2 n n+1 (A l , A l , As ; φs ) → A l qA∆<2π, no topological mode s+ 2 s+ 2 s+ 2

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric scheme: explicit, parallelizable

Yuan Shi Strong-Field Plasma Physics 1 • 0-th step: As+l/2 from Gauss’s law 2 0 ∂t ∇ · A = −∇ A − ρ 1st order, easier than Poisson’s equation • Time advance: need gauge fixing, observables gauge-independent ◦ Gauge condition: n−1/2 n n+1/2 (As , As+l/2) → As ◦ Klein-Gordon equation: n−1 n n n±1/2 n+1 (φs , φs ; As+l/2, As ) → φs ◦ Maxwell-Amp`ere’slaw: 1 ∆t <∆x <1/H, Compton scale n−1 n n± 2 n n+1 (A l , A l , As ; φs ) → A l qA∆<2π, no topological mode s+ 2 s+ 2 s+ 2

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric scheme: explicit, parallelizable 0 1 0 1/2 • Initial conditions φs , φs ; As+l/2, As

Yuan Shi Strong-Field Plasma Physics • Time advance: need gauge fixing, observables gauge-independent ◦ Gauge condition: n−1/2 n n+1/2 (As , As+l/2) → As ◦ Klein-Gordon equation: n−1 n n n±1/2 n+1 (φs , φs ; As+l/2, As ) → φs ◦ Maxwell-Amp`ere’slaw: 1 ∆t <∆x <1/H, Compton scale n−1 n n± 2 n n+1 (A l , A l , As ; φs ) → A l qA∆<2π, no topological mode s+ 2 s+ 2 s+ 2

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric scheme: explicit, parallelizable 0 1 0 1/2 • Initial conditions φs , φs ; As+l/2, As 1 • 0-th step: As+l/2 from Gauss’s law 2 0 ∂t ∇ · A = −∇ A − ρ 1st order, easier than Poisson’s equation

Yuan Shi Strong-Field Plasma Physics ◦ Klein-Gordon equation: n−1 n n n±1/2 n+1 (φs , φs ; As+l/2, As ) → φs ◦ Maxwell-Amp`ere’slaw: 1 ∆t <∆x <1/H, Compton scale n−1 n n± 2 n n+1 (A l , A l , As ; φs ) → A l qA∆<2π, no topological mode s+ 2 s+ 2 s+ 2

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric scheme: explicit, parallelizable 0 1 0 1/2 • Initial conditions φs , φs ; As+l/2, As 1 • 0-th step: As+l/2 from Gauss’s law 2 0 ∂t ∇ · A = −∇ A − ρ 1st order, easier than Poisson’s equation • Time advance: need gauge fixing, observables gauge-independent ◦ Gauge condition: n−1/2 n n+1/2 (As , As+l/2) → As

Yuan Shi Strong-Field Plasma Physics ∆t <∆x <1/H, Compton scale qA∆<2π, no topological mode Yuan Shi Strong-Field Plasma Physics

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric scheme: explicit, parallelizable 0 1 0 1/2 • Initial conditions φs , φs ; As+l/2, As 1 • 0-th step: As+l/2 from Gauss’s law 2 0 ∂t ∇ · A = −∇ A − ρ 1st order, easier than Poisson’s equation • Time advance: need gauge fixing, observables gauge-independent ◦ Gauge condition: n−1/2 n n+1/2 (As , As+l/2) → As ◦ Klein-Gordon equation: n−1 n n n±1/2 n+1 (φs , φs ; As+l/2, As ) → φs ◦ Maxwell-Amp`ere’slaw: 1 n−1 n n± 2 n n+1 (A l , A l , As ; φs ) → A l s+ 2 s+ 2 s+ 2 Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric scheme: explicit, parallelizable 0 1 0 1/2 • Initial conditions φs , φs ; As+l/2, As 1 • 0-th step: As+l/2 from Gauss’s law 2 0 ∂t ∇ · A = −∇ A − ρ 1st order, easier than Poisson’s equation • Time advance: need gauge fixing, observables gauge-independent ◦ Gauge condition: n−1/2 n n+1/2 (As , As+l/2) → As ◦ Klein-Gordon equation: n−1 n n n±1/2 n+1 (φs , φs ; As+l/2, As ) → φs ◦ Maxwell-Amp`ere’slaw: 1 ∆t <∆x <1/H, Compton scale n−1 n n± 2 n n+1 (A l , A l , As ; φs ) → A l qA∆<2π, no topological mode s+ 2 s+ 2 s+ 2

Yuan Shi Strong-Field Plasma Physics • Relativistic intensity a = eE/me cω > 1: ponderomotive snow-plow, wakefield acceleration, splashing from boundaries 2 • Quantum intensity a > mc /~ω: + pair production by wakefield and backscattered laser, pair annihilation

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric example 1: x-ray laser + 1D plasma slab Plasma response: wakefield acceleration → Schwinger pair production

1 Yuan Shi Y. Shi, J, Xiao, H. Qin, and N. J. Fisch, Phys. Rev. E, 97, 053206 (2018). Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric example 1: x-ray laser + 1D plasma slab Plasma response: wakefield acceleration → Schwinger pair production • Relativistic intensity a = eE/me cω > 1: ponderomotive snow-plow, wakefield acceleration, splashing from boundaries 2 • Quantum intensity a > mc /~ω: + pair production by wakefield and backscattered laser, pair annihilation

1 Yuan Shi Y. Shi, J, Xiao, H. Qin, and N. J. Fisch, Phys. Rev. E, 97, 053206 (2018). Strong-Field Plasma Physics • Relativistic intensity a = eE/me cω > 1: plasma wave excitation, frequency downshift, Raman scattering, harmonics 2 • Quantum intensity a > mc /~ω: + spectral broadening, radiation generation through pair recollision

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric example 1: x-ray laser + 1D plasma slab EM fields response: parametric instability → radiation generation

1 Yuan Shi Y. Shi, J, Xiao, H. Qin, and N. J. Fisch, Phys. Rev. E, 97, 053206 (2018). Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Numeric example 1: x-ray laser + 1D plasma slab EM fields response: parametric instability → radiation generation • Relativistic intensity a = eE/me cω > 1: plasma wave excitation, frequency downshift, Raman scattering, harmonics 2 • Quantum intensity a > mc /~ω: + spectral broadening, radiation generation through pair recollision

1 Yuan Shi Y. Shi, J, Xiao, H. Qin, and N. J. Fisch, Phys. Rev. E, 97, 053206 (2018). Strong-Field Plasma Physics Pulse compression: magnetic fields improve performance • Competing effects suppressed, more effective interaction channels enabled ⇒ Possible to produce more intense short laser pulses in wider frequency ranges Waves in QED plasmas: modified by relativistic quantum effects • Interpretation of Faraday rotation and cyclotron absorption corrected for pulsars ⇒ Possible to extract more accurate information from astrophysical observations Lattice QED simulation: novel numerical tool for plasma physics • Pair creation/annihilation and radiation generation demonstrated at quantum intensity ⇒ Possible to model laboratory strong-field QED physics from first-principle

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Summary: plasma physics in strong-field regimes Three-wave interactions: richer physics due to magnetization • Coupling at oblique angles quantified, enhancement/suppression identified ⇒ Possible to use B-field to better control laser-plasma interactions

Yuan Shi Strong-Field Plasma Physics Waves in QED plasmas: modified by relativistic quantum effects • Interpretation of Faraday rotation and cyclotron absorption corrected for pulsars ⇒ Possible to extract more accurate information from astrophysical observations Lattice QED simulation: novel numerical tool for plasma physics • Pair creation/annihilation and radiation generation demonstrated at quantum intensity ⇒ Possible to model laboratory strong-field QED physics from first-principle

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Summary: plasma physics in strong-field regimes Three-wave interactions: richer physics due to magnetization • Coupling at oblique angles quantified, enhancement/suppression identified ⇒ Possible to use B-field to better control laser-plasma interactions Pulse compression: magnetic fields improve performance • Competing effects suppressed, more effective interaction channels enabled ⇒ Possible to produce more intense short laser pulses in wider frequency ranges

Yuan Shi Strong-Field Plasma Physics Lattice QED simulation: novel numerical tool for plasma physics • Pair creation/annihilation and radiation generation demonstrated at quantum intensity ⇒ Possible to model laboratory strong-field QED physics from first-principle

Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Summary: plasma physics in strong-field regimes Three-wave interactions: richer physics due to magnetization • Coupling at oblique angles quantified, enhancement/suppression identified ⇒ Possible to use B-field to better control laser-plasma interactions Pulse compression: magnetic fields improve performance • Competing effects suppressed, more effective interaction channels enabled ⇒ Possible to produce more intense short laser pulses in wider frequency ranges Waves in QED plasmas: modified by relativistic quantum effects • Interpretation of Faraday rotation and cyclotron absorption corrected for pulsars ⇒ Possible to extract more accurate information from astrophysical observations

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

Summary: plasma physics in strong-field regimes Three-wave interactions: richer physics due to magnetization • Coupling at oblique angles quantified, enhancement/suppression identified ⇒ Possible to use B-field to better control laser-plasma interactions Pulse compression: magnetic fields improve performance • Competing effects suppressed, more effective interaction channels enabled ⇒ Possible to produce more intense short laser pulses in wider frequency ranges Waves in QED plasmas: modified by relativistic quantum effects • Interpretation of Faraday rotation and cyclotron absorption corrected for pulsars ⇒ Possible to extract more accurate information from astrophysical observations Lattice QED simulation: novel numerical tool for plasma physics • Pair creation/annihilation and radiation generation demonstrated at quantum intensity ⇒ Possible to model laboratory strong-field QED physics from first-principle

Yuan Shi Strong-Field Plasma Physics Introduction Magnetized three-wave Pulse compression Waves in QED plasma Lattice QED simulation Summary

References

Shi Y., Plasma Physics in Strong Field Regimes, Ph.D. Thesis, Princeton University (2018).

Chen H., S. C. Wilks, D. D. Meyerhofer et al., Phys. Rev. Lett. 105, 015003 (2010). Edwards M. R., Y. Shi, J. M. Mikhailova, and N. J. Fisch, Phys. Rev. Lett. 123, 025001 (2019). Goyon C., B. B. Pollock, D. P. Turnbull et al., PRE 95, 033208 (2017). Gueroult R., Y. Shi, J.-M. Rax, and N. J. Fisch, Nat. Commun. 10, 3232 (2019). Heindl W. A., W. Coburn, D. E. Gruber, et al., AIP Conf. Proc. 510(1):173, (2000). Jia Q., Y. Shi, H. Qin, and N. J. Fisch, Phys. Plasmas 24, 093103 (2017). Shi Y., N. J. Fisch, and H. Qin, Phys. Rev. A 94, 012124 (2016). Shi Y., H. Qin, and N. J. Fisch, Phys. Rev. E 95, 023211 (2017). Shi Y., H. Qin, and N. J. Fisch, Phys. Rev. E 96, 023204 (2017). Shi Y., H. Qin, and N. J. Fisch, Phys. Plasmas 25, 055706 (2018). Shi Y. and N. J. Fisch, Phys. Plasmas 26, 072114 (2019). Shi Y., A. Castelli, X. Wu et al. arXiv:2004.06885 (2020).

Yuan Shi Strong-Field Plasma Physics