Compton Source of Twisted Photons

Transcription

1 Compton Source of Twisted Photons Andrei Afanasev The George Washington University Washington, DC LDRS 2015 International Meeting on Laser-Driven Radiation Sources for Nuclear Applications George Washington University, Washington, DC, Dec 13-15, 2015

2 Questions Addressed. How do optical vortices excite atoms (and nuclei)?. Are there any differences in excitation of higher-angular momentum states (compared to plane waves)?. Are (Orbital Angular Momentum) OAM beams more efficient for exciting high OAM?

3 Introduction. Photons carry linear momentum p=ħk (k=wave vector). Photons carry both spin angular momentum (SAM) and orbital angular angular momentum (OAM) may be separated in paraxial approximation. Circularly polarized plane-wave photons carry J z =±ħ along the propagation direction z (Beth s experiment, 1936). Heitler, Quantum Theory of Radiation (1954): larger J z possible if the EM wave is constrained in the transverse plane (cylindrical waves). Spherical waves: expansion in terms of angular momentum eigenfunctions, position dependence of vector potential A µ (x) contains OAM information. Beams of light with azimuthal beam dependence exp(ilϕ) (e.g, Laguerre-Gaussian modes) can carry large values of OAM (Allen et al, 1992). Review: Yao, Padgett, Advances in Optics and Photonics 3, (2011) and references therein

4 Orbital vs Spin Angular Momentum (from Yao 11 review) Quantization of light beams having azimuthal phase dependence exp(ilϕ) leads to a concept of twisted photons G. Molina-Terriza, J.Torres, L. Torner, Twisted Photons, Nature Physics, May 2007.

5 Twisted Photons. Quantization of light beams having azimuthal phase dependence exp(ilϕ) lead to a concept of twisted photons G. Molina-Terriza, J.Torres, L. Torner, Twisted Photons, Nature Physics, May The typical transverse intensity pattern of a light beam with orbital angular momentum, (a) theory (b) experiment. The light beam exhibits a dark spot in the center, and a ring-like intensity profile. (c) Azimuthal dependence of beam phase results in a helical wavefront. (d) Orientation of the local momentum of the beam has a vortex pattern (hence another name, an optical vortex).

6 Generation of Light Beams with Orbital Angular Momentum. A diffraction grating with fork dislocation centered on the beam axis, could convert the fundamental Gaussian mode from any laser into a helically phased mode [V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, Laser-beams with screw dislocations in their wave-fronts, JETP. Lett. 52, (1990).] Commonly accepted method for producing helically phased beams.. Spiral Phase Plates: Gaussian beam is passed through optical media, with azimuthal dependence in thickness

7 Generation of Twisted Photons with Helical Undulators. E. Hemsing, A. Marinelli, and J. B. Rosenzweig, Generating Optical Orbital Angular Momentum in a High-Gain Free-Electron Laser at the First Harmonic, Phys. Rev. Lett. 106, (2011).. AA, Mikhailichenko, On Generation of Photons Carrying Orbital Angular Momentum in the Helical Undulator, E-print: arxiv Considered properties of synchrotron radiation by charged particles passing through a helical undulator. Shown that all harmonics higher than the first one radiated in a helical undulator carry OAM. Large K-factors favor large values of OAM for generated radiation.

8 Helical Undulators. AA, Mikhailichenko, On Generation of Photons Carrying Orbital Angular Momentum in the Helical Undulator, E-print: arxiv

9 Transfer of Angular Momentum. From Yao et al (2011): for optical wavelengths, transfer of Orbital AM differs from Spin AM.. Common misconception: magnetic quantum numbers of the excited state are not affected by OAM

10 Atomic Excitations with High-L Photons. Twisted photons may enhance (relatively) atomic transitions with large transfer of angular momentum. Picon et al, Photoionization with orbital angular momentum beams, Opt. Express 18, 3660 (2010): OAM of light is passed to internal degrees of freedom of an atom placed in the center of an optical vortax. Afanasev, Carlson, Mukherjee, Off-axis excitation of hydrogenlike atoms by twisted photons, Phys. Rev. A 88, (2013); Two properties of twistedlight absorption, JOSA B 31, 2721 (2014); HM Scholz-Marggraf, S Fritzsche, VG Serbo, A Afanasev, A Surzhykov, Phys. Rev. A 90, (2014)

11 Twisted Photon State. For Bessel beam vector potential and plane-wave expansion we use formalism from Jaregui PRA 70, (2004) and Jentschura&Serbo, PRL 106, (2011). Use plane-wave expansion. Plane wave:. Twisted wave:

12 Fields of the Twisted Wave. Vector potential Magnetic field. Poynting vector

13 Transverse Beam Profile. OAM light beam is characterized with a special transverse profile (example from AA, Carlson, Mukherjee,). Intensity dip on the beam axis, with transverse size > wavelength

14 Atomic Photoexcitation. Interaction Hamiltonian:. Matrix element of the transition:. b- an impact parameter w.r.t. the atomic center

15 Matrix Element of Photoexcitation. Photo-excite a hydrogen atom from the ground to the state with a principal quantum number n f, OAM l f, and OAM projection m f. Incoming twisted photon is defined by AM projection m γ, energy ω and a pitch angle θ k (with κ=k perp ). Matrix element:. Atomic factors

16 Calculation Results. Matrix elements as a function of an impact parameter b

17 Normalized transition probabilities. Fermi s Golden Rule: Squared amplitudes times phase space volume - > excitation rates. Cross section: transition probability per photon. Need to divide squares of above amplitudes by the photon flux. Reminder: local photon flux is zero at optical vortex center. But we see some amplitudes nonzero at the center (for Δm=m γ ) => singularity!. Example of photon flux as a function of impact parameter b:

18 Normalized Transition Probabilities: Electric Dipole. Surprise or not? Rates for standard electric-dipole transitions scale with the (local) photon flux 20 Relative probability (per photon) to excite L=1 state σ 1 S 2 P (Λ=1,m γ =3)/σ 1 S 2 P (Λ=1,m γ =1) b/λ

19 Normalized Transition Probabilities: Higher Multipoles. Higher multipoles are generated more efficiently for OAM photons near the optical vortex center. Singularity occurs when magnetic quantum number of excited state matches total AM projection of a twisted photon. 10x enhancement at b~0.4 wavelength! 50 Relative probability (per photon) to excite L=3 state 40 σ 1 S 4 F (Λ=1,mγ=3)/σ 1 S 4 F (Λ=1,PW) b/λ

20 Helicity Asymmetry. Flip photon helicity Λ, keep the OAM projection the same =>. Results a different twisted photon state with m γ è m γ -2Λ. Photoabsorption cross sections are different for a given impact parameter => (parity-conserving) helicity asymmetry; physics reason: flipping helicity affects local photon flux. The largest asymmetry is near the center of optical vortex. Asymmetry is zero after averaging over the impact parameter b. May be observed for small-size targets or near-field geometry

21 Experiments with Atoms. New results from Mainz University, Germany posted 23Nov2015, C.T. Schmiegelow et al Confirmed our theoretical arguments

22 How to Generate Twisted Photons in MeV-GeV?. Serbo et al proposal (2010): Compton backscattering. U.D. Jentschura V.G. Serbo, Generation of High-Energy Photons with Large Orbital Angular Momentum by Compton Backscattering. Phys.Rev.Lett. 103 (2011) ; Compton Upconversion of Twisted Photons: Backscattering of Particles with Non-Planar Wave Functions. Eur.Phys.J. C71 (2011) 1571.

23 Twisted Photons for Nuclei vs Atoms. For atomic transitions photon OAM is preferably transferred to internal degrees of freedom if the target is near the center of an optical vortex. The nuclear transitions of different multipolarity can be controlled by generating a twisted gamma-ray beam. For example, strength of E1 vs E2 transition. Enforce population of high OAM, longer-lived states in nuclei. A step toward a gamma laser?. Quantum Core area of efficient OAM transfer appears large, at a fraction of the twisted-photon wavelength

24 Summary. Considered atomic photoexcitation with twisted photons. Results in excitation of states with a range of quantum numbers, different from plane waves. Effect is relative suppression of lower-multipole transitions. Extending the same approach to photo-nuclear transitions (e.g., E1 vs E2 strengths). Plan experiments with existing Compton sources