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

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

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

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

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

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

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

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

9. 9 Optical dipole force recoil dipole interaction scatters photon between initial and refracted beams maximum recoil momentum kk k-  kk+  k 

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

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

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

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

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

15. 15 Optical forces POSITIONVELOCITY continuous wave magneto-optic dipole Sisyphus dynamical (cavity) Doppler VSCPT modulated c.w. stochastic adiabatic pulsed time-of-arrival Raman interferometric TRAPPINGCOOLING

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

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

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

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

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

21. 21 Magneto-optical trap RCP LCP anti-Helmholtz coils Zeeman tuning in inhomogeneous magnetic field provides position-dependent absorption red-detuned laser beams also produce Doppler cooling sweep frequency towards resonance for coldest trapped sample typical values: 10 7 atoms, 10μK

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

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

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

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

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

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

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

29. 29 Amplification of cooling     velocity selective excitation t pzpz spontaneous emission

30. 30 Stimulated scattering: focussing and trapping München

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

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

33. 33 plane of coincidence Stimulated scattering: focussing and trapping Freegarde et al, Opt Commun 117 262 (1995) rectangular Sech 2 Gaussian rectangular Sech 2 FORCEHEATING Gaussian

34. 34 Stimulated scattering: focussing and trapping Freegarde et al, Opt Commun 117 262 (1995) Goepfert et al, Phys Rev A 56 R3354 (1997) rectangular Sech 2 Gaussian rectangular Sech 2 FORCEHEATING Gaussian EXPERIMENTAL DEMONSTRATION 852 nm transition in Cs 30 ps, 80 MHz sech 2 pulses from Tsunami stimulated force ~10x max spontaneous force

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

36. 36 Stimulated scattering: interferometry   ψψ ‘spin echo’, Ramsey spectroscopy excitation probability depends on ψ

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

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

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