Light and Matter

1. School of Physics & Astronomy University of Southampton Light and Matter Controlling matter with light Tim Freegarde

2. Mechanical effect of the photon • electromagnetic waves carry momentum emission • momentum flux (Maxwell stress tensor) defined by absorption • photons carry momentum

3. Mechanical effect of the photon • electromagnetic waves carry momentum emission emission • momentum flux (Maxwell stress tensor) defined by absorption absorption • photons carry momentum

4. where is photon absorption rate Optical scattering force • each absorption results in a well-defined impulse emission emission • isotropic spontaneous emission causes no average recoil • average scattering force is therefore absorption absorption

5. photons carry energy • visible photon • photons carry momentum • visible photon • momentum flux • sunlight Mechanical effect of the photon Cosmos 1, due for launch early 2004 © Michael Carroll, The Planetary Society

6. photons carry energy • visible photon • photons carry momentum • visible photon • momentum flux • sunlight Solar sails and comet tails Comet Hale-Bopp, 1997 Cosmos 1, due for launch early 2004 © Malcolm Ellis © Michael Carroll, The Planetary Society

7. energy and momentum are conserved Acousto-optic modulation • Fraunhofer diffraction condition crystal phonon • Bragg diffraction condition • Doppler shift transducer

8. 1 • high 0 G=0.050 freq • low Optical dipole force • force is gradient of dipole potential towards high intensity • depends upon real part of susceptibility towards low intensity

9. maximum recoil k-Dk k+Dk Dw momentum k Optical dipole force recoil • dipole interaction scatters photon between initial and refracted beams

10. Optical tweezers Controlled rotation of small glass rod Trapping and rotation of microscopic silica spheres © Kishan Dholakia, University of St Andrews

11. Diffracting atoms E M Rasel et al, Phys Rev Lett 75 2633 (1995)

12. electromagnetic waves carry momentum where is photon absorption rate • maximum absorption rate is Optical scattering force emission • photon absorption gives a well-defined impulse • isotropic spontaneous emission causes no average recoil absorption • average scattering force is therefore

13. electromagnetic waves carry momentum emission TRAPPING absorption Optical forces • forces therefore accompany radiative interactions • position-dependent interaction gives position-dependent force

14. electromagnetic waves carry momentum TRAPPING COOLING Optical forces • forces therefore accompany radiative interactions • position-dependent interaction gives position-dependent force • velocity-dependent interaction gives velocity-dependent force

15. Optical forces

16. momentum k Doppler cooling • use the Doppler effect to provide a velocity-dependent absorption • photon absorption gives a well-defined impulse • red-detuned photon reduces momentum • spontaneous emission gives no average impulse

17. momentum k Doppler cooling • use the Doppler effect to provide a velocity-dependent absorption • photon absorption gives a well-defined impulse • red-detuned photon reduces momentum • spontaneous emission gives no average impulse • illuminate from both (all) directions • sweep wavelength to cool whole distribution

18. atomic beam red-detuned (s-) laser beam Zeeman slowing • opposite circular polarizations see opposite shifts in transition frequency in presence of longitudinal magnetic field ZEEMAN EFFECT • Zeeman / Faraday effect tapered solenoids

19. red-detuned laser beam accelerating ions Optical ion speed limiter • electrostatic acceleration cancelled by radiation pressure deceleration

20. LCP Magneto-optical trap RCP RCP RCP RCP anti-Helmholtz coils RCP RCP LCP

21. LCP Magneto-optical trap • Zeeman tuning in inhomogeneous magnetic field provides position-dependent absorption • red-detuned laser beams also produce Doppler cooling RCP RCP RCP • sweep frequency towards resonance for coldest trapped sample RCP anti-Helmholtz coils • typical values: 107 atoms, 10μK LCP

22. spatial part of eigenfunctions given by and energy 0 Quantum description of atomic polarization • full time-dependent eigenfunctions therefore • any state of the two-level atom may hence be written

23. write time-dependent Schrödinger equation for two-level atom • spatial part of eigenfunctions given by and insert energy of interaction with oscillating electric field reduce to coupled equations for a(t) and b(t) Quantum description of atomic polarization • full time-dependent eigenfunctions therefore • any state of the two-level atom may hence be written

24. write time-dependent Schrödinger equation for two-level atom • spatial part of eigenfunctions given by and • full time-dependent eigenfunctions therefore insert energy of interaction with oscillating electric field • any state of the two-level atom may hence be written reduce to coupled equations for a(t) and b(t) Quantum description of atomic polarization

25. write time-dependent Schrödinger equation for two-level atom • solve for initial condition that, at , • solutions are insert energy of interaction with oscillating electric field reduce to coupled equations for a(t) and b(t) where is the Rabi frequency Rabi oscillations

26. solve for initial condition that, at , • solutions are where is the Rabi frequency Rabi oscillations

27. RABI OSCILLATION • time Pi-pulses • coherent emission as well as absorption • half-cycle of Rabi oscillation provides complete population transfer between two states

28. experiences opposite impulse p p Coherent deflection • two photon impulses • atom returned to initial state Kazantsev, Sov Phys JETP 39 784 (1974)

29. p p p pz t p p p spontaneous emission Amplification of cooling velocity selective excitation

30. Stimulated scattering: focussing and trapping München

31. München Garching plane of coincidence Stimulated scattering: focussing and trapping • first bus is more likely to be heading towards plane of coincidence

32. first pulse excites …………………. photon absorbed • second pulse stimulates decay… photon emitted Stimulated scattering: focussing and trapping plane of coincidence • coherent process – can be repeated many times • spontaneous emission only in overlap region

33. rectangular Sech2 Gaussian FORCE HEATING rectangular plane of coincidence Sech2 Gaussian Freegarde et al, Opt Commun 117 262 (1995) Stimulated scattering: focussing and trapping

34. EXPERIMENTAL DEMONSTRATION • 852 nm transition in Cs • 30 ps, 80 MHz sech2 pulses from Tsunami • stimulated force ~10x max spontaneous force rectangular Sech2 Gaussian FORCE HEATING rectangular Sech2 Gaussian Freegarde et al, Opt Commun 117 262 (1995) Goepfert et al, Phys Rev A 56 R3354 (1997) Stimulated scattering: focussing and trapping

35. RABI OSCILLATION • time • pure states become Atom interferometry p/2 pulses • quarter Rabi cycles • atomic beam-splitters

36. Stimulated scattering: interferometry • excitation probability depends on ψ • ‘spin echo’, Ramsey spectroscopy Dψ p/2 p/2

37. p p • coherent sequence of operations on atomic/molecular sample • pulses form mirrors of atom/molecule interferometer • velocity-dependent phase: p/2 impulses add or cancel • short pulses  spectral insensitivity z p/2 p/2 M Weitz, T W Hänsch, Europhys Lett 49 302 (2000) t Stimulated scattering: interferometric cooling

38. VELOCITY-DEPENDENT PHASE • variation of phase with kinetic energy: where ,  Dψ • hence velocity-dependent impulse and cooling… Stimulated scattering: interferometric cooling

39. Light and Matter • next Monday 5 Jan: Q & A Thursday 9 Jan: problem sheet 3 : • for handouts, links and other material, see http://www.phys.soton.ac.uk/quantum/phys3003.htm