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Laser-driven Ps excitation in the Aegis antimatter experiment

This talk outlines the Aegis experiment, which focuses on gravity measurement using laser-driven Ps excitation. The experiment aims to study the properties of antimatter, specifically antihydrogen, through precision spectroscopy.

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Laser-driven Ps excitation in the Aegis antimatter experiment

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  1. AEgIS Spectroscopy Antimatter Interferometry Experiment Gravity Laser-driven Ps excitation in the Aegis antimatter experiment Marco G. Giammarchi and Fabrizio Castelli Dipartimento di Fisica dell’Universita’ di Milano Istituto Nazionale Fisica Nucleare - Milano Outline of talk: • The Physics of Aegis • The production of a H beam • The gravity measurement • Positronium energy levels in magnetic field • Positronium laser excitation AEGIS: AD-6 Experiment http://aegis.web.cern.ch/aegis/ Varenna - July 2009

  2. Antimatter history in a slide • 1928: relativistic equation of the ½ spin electron (Dirac) • 1929: electron sea and hole theory (Dirac) • 1931: prediction of antimatter (Dirac, Oppenheimer, Weyl) • 1932: discovery of positron in cosmic rays (Anderson) • 1933: discovery of e-/e+ creation and annihilation (Blackett, Occhialini) • 1937: symmetric theory of electrons and positrons • 1955: antiproton discovery (Segre’, Chamberlain, Wiegand) • 1956: antineutron discovery (Cork, Lambertson, Piccioni, Wenzel) • 1995: creation of high-energy antihydrogen (CERN, Fermilab) • 2002: creation of 10 K antihydrogen (Athena, Atrap) Future: study of Antimatter properties ! Varenna - July 2009

  3. AEGIS Collaboration CERN, Geneva, Switzerland M. Doser, D. Perini, T. Niinikoski, A. Dudarev, T. W. Eisel, R. Van Weelderen, F. Haug, L.. Dufay-Chanat, J. L.. Servai LAPP, Annecy, France. P. Nédélec, D. Sillou Queen’s U Belfast, UK G. Gribakin, H. R. J. Walters INFN Firenze, Italy G. Ferrari, M. Prevedelli, G. M. Tino INFN Genova, University of Genova, Italy C. Carraro, V. Lagomarsino, G. Manuzio, G. Testera, S. Zavatarelli INFN Milano, University of Milano, Italy I. Boscolo, F. Castelli, S. Cialdi, M. G. Giammarchi, D. Trezzi, A. Vairo, F. Villa INFN Padova/Trento, Univ. Padova, Univ. Trento, Italy R. S. Brusa, D. Fabris, M. Lunardon, S. Mariazzi, S. Moretto, G. Nebbia, S. Pesente, G. Viesti INFN Pavia – Italy University of Brescia, University of PaviaG. Bonomi, A. Fontana, A. Rotondi, A. Zenoni MPI- K, Heidelberg, Germany C. Canali, R. Heyne, A. Kellerbauer, C. Morhard, U. Warring Kirchhoff Institute of Physics U of Heidelberg, Germany M. K. Oberthaler INFN Milano, Politecnico di Milano, Italy G. Consolati, A. Dupasquier, R. Ferragut, F. Quasso INR, Moscow, Russia A. S. Belov, S. N. Gninenko, V. A. Matveev, A. V. Turbabin ITHEP, Moscow, RussiaV. M. Byakov, S. V. Stepanov, D. S. Zvezhinskij New York University, USA H. H. Stroke Laboratoire Aimé Cotton, Orsay, FranceL. Cabaret, D. Comparat University of Oslo, Norway O. Rohne, S. Stapnes CEA Saclay, France M. Chappellier, M. de Combarieu, P. Forget, P. Pari INRNE, Sofia, Bulgaria N. Djourelov Czech Technical University, Prague, Czech Republic V. Petráček, D. Krasnický ETH Zurich, Switzerland S. D. Hogan, F. Merkt Institute for Nuclear Problems of the Belarus StateUniversity, Belarus G. Drobychev Qatar University, Qatar I. Y. Al-Qaradawi Varenna - July 2009

  4. AD (Antiproton Decelerator) at CERN 3 x 107 antiprotons / 100 sec 6 MeV 104 p / 100 sec Varenna - July 2009

  5. Physics with Antimatter is at the very foundation of Modern Physics: CPT Physics (second phase of Aegis, not covered here) WEP (Weak Equivalence Principle, first phase of Aegis, approved by CERN) WEP: Weak Equivalence Principle The trajectory of a falling test body depends only on its initial position and velocity and is independent of its composition (a form of WEP) All bodies at the same spacetime point in a given gravitational field will undergo the same acceleration (another form of WEP) • Direct Methods: measurement of gravitational acceleration of H and Hbar in the Earth gravitational field • High-precision spectroscopy: H and Hbar are test clocks (this is also CPT test) Varenna - July 2009

  6. WEP tests on matter system 10-18 10-16 10-14 10-12 10-10 10-8 10-6 10-4 10-2 1700 1800 1900 2000 Gravitational Physics: Weak Equivalence Principle (WEP) Any violation of WEP implies either that the theory is in error or that there is a new force acting • No direct measurements on gravity effects on antimatter • “Low” precision measurement (1%) will be the first one Gravity in the Solar System Matter limit Period of pendula Torsion measurement Can be done with a beam of Antiatoms flying to a detector! AEGIS first phase L H g Varenna - July 2009

  7. (B) e+ p p + Ps* H + e- Production Methods I. ANTIPROTON + POSITRON (exp.demonstration: ATHENA and ATRAP) (A) p + e+ H + hn p + e+ + e+ H + e+ • EXPERIMENTAL RESULTS: • TBR seems to be the dominant process (highly exicited antihydrogen) • Warm antihydrogen atoms (production when vantiproton~ vpositron) II. ANTIPROTON + RYDBERG POSITRONIUM (exp.demonstration: ATRAP) • PROMISING TECHNIQUE: • Control of the antihydrogen quantum state • Cold antihydrogen atoms (vantihydrogen~ vantiproton) Production Method in AEGIS Varenna - July 2009

  8. Method II: Antiproton + Rydberg Ps (ATRAP) 104 antiprotons 108 e+ Method I: Antiproton + Positron (ATHENA) C. H. Storry et al., First Laser-Controlled AntihydrogenProduction, Physical Review Letters 93, 263401 (2004) • Spontaneous radiative recombination • Three body recombination Two-stage Rydberg charge exchange 14 ± 4 antihydrogen atoms In Aegis: Antiproton + Rydberg Ps (obtained by Ps and laser excited) • Large cross section • Quantum states of antihydrogen related to Ps quantum number • Reaction suitable for cold antihydrogen production (cold antiprotons!) Varenna - July 2009

  9. Moire’ deflectometer and detector AEGIS experimental strategy 1) Produce ultracold antiprotons (100 mK) 2) Accumulate e+ 3) Form Ps by interaction of e+ with porous target 4) Laser excite Ps to get Rydberg Ps 5) Form Rydberg cold (100 mK) antihydrogen 6) Form a beam using an inhomogeneous electric field to accelerate the Rydberg antihydrogen 7) The beam flies toward the deflectometer which introduces a spatial modulation in the distribution of the Hbar arriving on the detector 8) Extract g from this modulated distribution Cold antiprotons Porous target e+ Varenna - July 2009

  10. Use of 108 positrons in a bunch 500 sec accumulation time A few comments on AEGIS strategy (and timing) to produce Antihydrogen: • Source and moderator • Trap • Accumulator (Surko-type) Bunch of 20 ns and 1 mm beam spot Catch p from AD, degrade the energy An antihydrogen production shot every 500 sec Cool down the p with e- 500 sec accumulation time (a few AD shots, 105 p) Avoid the problem of a particle trap able to simultaneously confine charged particles (Penning trap) and Antihydrogen (by radial B gradients). • Have a charged particle trap only g measurement • Form a neutral (antihydrogen) beam • Confine only neutrals (future) (CPT physics) Varenna - July 2009

  11. e+ Vacuum Solid Positron beam Positronium emission Ps Ps Ps Ps Positronium yield from materials: requirement of 10% (reemitted, cold) out of 108 in ortho-Ps. (lectures by R. Brusa and A. Dupasquier) Silicon nanochannel material: 10-15 nm pores: max o-Ps formation observed 50% Velocity of reemitted Ps: 5 x 104 m/s (corresponding to thermalized at 100 K) Laser excitation of the Positronium to Rydberg states (more on this later on) Varenna - July 2009

  12. Ultracold Antiprotons • The CERN AD (Antiproton Decelerator) delivers 3 x 107 antiprotons / 80 sec Antiprotons Production GeV Deceleration MeV Trapping keV Cooling eV • Antiprotons catching in cylindrical Penning traps after energy degrader • Catching of antiprotons within a 3 Tesla magnetic field, UHV, 4 Kelvin, e- cooling • Stacking several AD shots (104/105 subeV antiprotons) • Transfer in the Antihydrogen formation region (1 Tesla, 100 mK) • Resistive cooling based on high-Q resonant circuits • Sympathetic cooling with laser cooled Os- ions • Cooling antiprotons down to 100 mK • 105 antiprotons ready for Antihydrogen production U. Warring et al., PRL 102 (2009) 043001 Varenna - July 2009

  13. AEgIS in short Acceleration of antihydrogen. Formation of antihydrogen atoms The antihydrogen beams will fly (with v~500 m/sec) through a Moire’ deflectometer • Positronium: 107 atoms • Antiprotons: 105 • Antihydrogen: 104/shot The vertical displacement (gravity fall) will be measured on the last (sensitive) plane of the deflectometer Antiprotons Positrons Such measurement would represent the first direct determination of the gravitational effect on antimatter Varenna - July 2009

  14. Antihydrogen detector How do we know that this works? Intermediate level: need to know that we are producint Antihydrogen! Ps converter e+ Bunch Ps* Antiprotons Antihydrogen monitor Antiproton Catching Zone (3 T) Antihydrogen Formation Zone (1 T) Deflectometer Varenna - July 2009

  15. 192 CsI (pure) Crystals 2 Layers of Si strips (r,f) and pads (z) The Athena Anti-hydrogen detector GOALVertex from tracking of charged particlesIdentification of 511 keV gammasTime and space coincidence of tracks + gammas DESIGN Compact (radial thickness ~ 3 cm,length ~ 25 cm)Large solid angle (~ 80 %)High granularityOperation at T ~ 140 K, B = 3 Tesla Time Resolution ~ 5 ms (CsI decay time ~ 1 ms) Space Resolution ~ 4 mm (Vertex reconstruction s ) C. Regenfus, NIM A 501, 65 (2003). Varenna - July 2009

  16. Antihydrogen (Stark) acceleration Rydberg antihydrogen is accelerated or decelerated by electric field Stark acceleration Stark acceleration of hydrogen atoms”, E. Vliegen and F. Merkt, Journ. Phys. B 39 (2006) L241 The energy levels of an H (anti)atom in an electric field F are given to first order, in atomic units, by E = excitation energy n = principal quantum number k = quantum number which runs from -(n-1-|m|) to (n-1-|m|) m = azimuthal quantum number If the excited atoms are moving in a region where the amplitude of the electric field is changing then their internal energy changes accordingly (to conserve total energy), they are accelerated or decelerated Varenna - July 2009

  17. Atoms (1/ms-1) Horizontal velocity (m/s) no acceleration - electric fields of few 100 V/cm are used (limited by field ionization) - Δv of few 100 m/s within about 1 cm can be achieved acceleration Effect of the magnetic field (e.g. 1 T) acceleration inside 1T acceleration n’ = quantum number which runs from -(n-1)/2, -(n-3)/2 to (n-3)/2, (n-1)/2 γ = magnetic field in atomic units Horizontal velocity (m/s) Varenna - July 2009

  18. AEgIS realistic numbers: - horizontal flight path L ~ 1 m - horizontal velocity vz ~ 500 m/s vertical deflection ~ 30 μm Gravity Measurement Seems easy: • antihydrogen has a radial velocity (related to the temperature) • any anti-atom falls by 30 μm, but, in addition it can go up or down by few cm • beam radial size after 1 m flight ~ several cm (poor beam collimation) 1 cm Downward shift by 30 μm DISPLACEMENT DUE TO GRAVITY HARD TO MEASURE THIS WAY Varenna - July 2009

  19. Let us collimate! Position sensitive detector cm An aperture of 100 μm Now displacement easily detectable. At the price of a huge loss in acceptance Acceptance can be increased by having several holes. In doing so new possible paths show up L2 L1 Let us collimate! cm If L1 = L2 the new paths add up to the previous information on the 3rd plane Varenna - July 2009

  20. Based on a totally geometric principle, the device is insensitive to a bad collimation of the incoming beam (which however will affect its acceptance) Moiré Deflectometry is an interferometry technique, in which the object to be tested (either phase object or secular surface) is mounted in the course of a collimated beam followed by a pair of transmission gratings placed at a distance from each other. The resulting fringe pattern, i.e., the moiré deflectogram, is a map of ray deflections corresponding to the optical properties of the inspected object. Varenna - July 2009

  21. The final plane will be made of Silicon Strip detectors with a spatial resolution of about 10-15 μm Now, this is NOT a quantum deflectometer, because: α dg L So, it is a classical device if dg>> 10 μm Varenna - July 2009

  22. silicon μ-strip detector 20 cm 20 cm AEgIS requirements (for the achievement of the 1% measurement accuracy) - area 20x20 cm2 - 10-13 μm resolution for the reconstruction of the annihilation point - high efficiency - to work around 140 K g-measurement position sensitive detector ➠ EVENT SIMULATION (Geant 3.21) - generate randomly an impact point (inside 20x20 cm2) - generate antiproton at rest on the detector surface ➠ force annihilation - simulate/track the interaction of annihilation by-products in the silicon detector DETECTOR SIMULATION - 8000 silicon strips - 20 cm long - 25μm pitch - 300μm thick corresponding to 20x20 cm2 area, 300μm thick silicon slab ... 8000 strips 25 μm wide ... g-measurementpositionSensitiveDetector (gSD) MEASURING THE ANNIHILATION POINT WITH GREAT PRECISION IS ESSENTIAL Varenna - July 2009

  23. annihilation hit position on the final detector (in a units) annihilation hit position on the final detector (in a units, modulo grating period a) moiré deflectometer X counts (a.u.) solid grating slits shadow Z Grating transparency = 30% (total transmission 9%) -5 -4 -3 -2 -1 0 1 2 3 4 5(x/a) 0 0.25 0.5 0.75 1 x/a ]a counts (a.u.) Moiré deflectometer Suppose: - L = 40 cm - grating period a = 80 μm - grating size = 20 cm (2500 slits) - gravity beam horizontal velocity vz = 600 m/s vz = 250 m/s fringe shift slit slit Fringe shift ! Varenna - July 2009

  24. Measuring g: • Measure arrival time: difference between Stark acceleration and arrival time on the microstrip detector 2) Events enter different histograms according to velocity 3) Every histogram gets fitted to find the phase shift at that velocity g 1% accuracy in g measurement in a month of AD data taking Varenna - July 2009

  25. The accuracy of the g measurement • Systematic error on <T2>: about 0.5 % error in the mean axial position of the beam • sT2/T2 : can be as large as 20-30% • Radial extent of the beam : no contribution to the systematic errors • Antihydrogen radial velocity: no contribution to the systematic errors • Vertical alignement between the two gratings and the detector: influence d0 few micron stability, absolute position unimportant (mount an optical interferometer on a small area of the grating system ) • Grating- grating distance and detector-2° grating distance: max diff 2 grating periods); influence on the contrast • Radiative decay during the fligth: the vertical velocity changes due to atom recoil decreases contrast; max fraction of decaying atoms 60% • Magnetic gradient :10 Gauss/m gives a force equal to mg (for antihydrogen in fundamental state) • Systematic effects studied by repeating the measurement with the grating system rotated by 90 degrees (switch off gravity) Varenna - July 2009

  26. Out beam is not monochromatic (T varies quite a lot) T2 v counts (a.u.) counts (a.u.) ms2 m/s ➠ Moiré deflectometer fringe shift of the shadow image T = time of flight = [tSTARK - tDET] (L~ 1 m, v ~ 500 m/s ➠T ~ 2 ms) Binning antihydrogens with mean velocity of 600-550-500-450-400-350-300-250-200 m/s, and plotting δ as a function of ➠ δ (a.u.) g comes from the fit time of flight T (s) Varenna - July 2009

  27. Now, before moving on to more serious problems, we would like to thank the organizers for this pleasant time here Varenna - July 2009

  28. - + AEGIS AEGIS Positronium Laser Excitation to Rydberg Levels in Magnetic Field (an intriguing topic of atomic physics) F. Castelli and M.G. Giammarchi Varenna - July 2009

  29. Outline The structure of Positronium (Ps) energy levels in magnetic fields • Experiments and theory: only n = 1,2 and weak fields • Moving Ps in strong magnetic fields: • Zeeman and diamagnetic effects • motional Stark effect – the most effective! • Energy splitting and mixing of n-sublevels, physical consequences Efficient Ps laser excitation to high-n (Rydberg) levels: tailoring of laser pulses for maximizing the efficiency • Two possible paths of excitation with two laser pulse • Line broadening: Doppler and motional Stark effects • Theory of incoherent excitation and determination of saturation fluence • Laser pulses energy and bandwidth, efficiency • Modeling of excitation dynamics and Conclusions Varenna - July 2009

  30. Ps energy levels for n = 1,2: tests on quantum electrodynamics para-Ps (singlet states S=0) ortho-Ps (triplet states S=1) Theory: A.Rich, Rev. Mod. Phys. 53, 127 (1981) A.Pineda, J.Soto, PRD 59, 016005 (1998) Experiments: with Doppler free high resolution spectroscopy and microwave fields S.Chu, A.P.Mills, J.Hall, PRL 52,1689 (1984); A.P.Mills et al, PRL 34, 1541 (1975); Ziock et al, J.Phys.B 23, 329 (1990) Ghz 1.1 · 10-4 eV Fine structure: spin-orbit, hyperfine, relativistic interactions, and weak magnetic fields 8.5 · 10-4 eV (203,4 Ghz) long living state short living state Varenna - July 2009

  31. tested?! continuum high n ~1.69 eV ~730 nm n=2 5.10 eV 243 nm n=1 high-n energy levels of Ps : Rydberg levels Only one experiment on n > 13 Rydberg states; two ns laser pulses , large bandwidth, weak magnetic field (Ziock et al, PRL 64, 2366 (1990)) • Theory of Ps in strong magnetic field: an open question!! •  Ps is the lightest atom: strong velocity effects • moving Ps is equivalent to Ps in crossing B and E field • lack of symmetry, no separable hamiltonian  perturbative methods Varenna - July 2009

  32. Ps in magnetic field B~ 1 T : theory two particles with Coulomb interaction (4n2 degeneration) diamagnetic (or quadratic Zeeman) fine structure  1/n3(negligible for n ≥ 2) Zeeman motional Stark quantum numbers n,l,m,s…? Varenna - July 2009

  33. (1) linear Zeeman effect • Interaction with magnetic dipoles from orbital angular momentum L • (e+ and e- have equal mass and opposite charge  opposite magnetic dipole moment) no energy contribution from orbital motion! b) Interaction with magnetic dipoles associated to spins (only S = 0 and S = 1, ms = 0) independent from n Excited states obtained via optical excitation: selection rules S = 0, ms = 0; EZ = 0 in the transition  (Zeeman effect is not relevant) Varenna - July 2009

  34. (1) linear Zeeman effect • Interaction with magnetic dipoles from orbital angular momentum L • (e+ and e- have equal mass and opposite charge  opposite magnetic dipole moment) no energy contribution from orbital motion! b) Interaction with magnetic dipoles associated to spins (only S = 0 and S = 1, ms = 0) independent from n Excited states obtained via optical excitation: selection rules S = 0, ms = 0; EZ = 0 in the transition  (Zeeman effect is not relevant) (2) diamagnetic (quadratic Zeeman) effect (R.H. Garstang, Rep. Prog. Phys. 40, 105 (1977)) Varenna - July 2009

  35. (3) Moving Ps: motional Stark effect transformation of e.m. fields in Ps rest frame (up to first order in vPs / c) laboratory frame Ps rest frame Varenna - July 2009

  36. breaking of the axial symmetry around the B axis! complete mixing of l , m substates of a n manifold l , m are no longer good quantum numbers No known proper quantum numbers for this problem! (3) Moving Ps: motional Stark effect transformation of e.m. fields in Ps rest frame (up to first order in vPs / c) laboratory frame Ps rest frame induced electric field acting on moving Ps Varenna - July 2009

  37. with the transverse electric field:  Stark effect depends on Ps center of mass velocity vPS(T) ( on the temperature of Ps cloud) Theory of Stark effect: maximum splitting of n2 (l,m mixed) substates  Varenna - July 2009

  38. with the transverse electric field:  Stark effect depends on Ps center of mass velocity vPS(T) ( on the temperature of Ps cloud) Theory of Stark effect: maximum splitting of n2 (l,m mixed) substates  Ps : the lightest atom motional Stark effect is largerly the dominant contribution to sublevel splitting energy for Rydberg Ps Varenna - July 2009

  39. assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)  comparison with H Varenna - July 2009

  40. assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)  comparison with H  ionization of Rydberg red states n > 27 (ionization for n > 87) Minimum electric field for Rydberg ionization (Gallagher, Rep. Prog. Phys. 51, 143 (1988) Varenna - July 2009

  41. assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)  comparison with H  ionization of Rydberg red states n > 27 (ionization for n > 87) Minimum electric field for Rydberg ionization (Gallagher, Rep. Prog. Phys. 51, 143 (1988)  for n < 40 for n > 6 for n > 46 Varenna - July 2009

  42. l,m mixing interleaving of n-manifolds n2 sublevels motional Stark electric field strength assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)  comparison with H atoms  ionization of Rydberg red states n > 27 (ionization for n > 87) Minimum electric field for Rydberg ionization (Gallagher, Rep. Prog. Phys. 51, 143 (1988)  for n < 40 for n > 6 for n > 46  for n > 18 interleaving of different n-sublevel manifolds! Energy difference between neighboring unperturbed n-levels Varenna - July 2009

  43. moving Rydberg Ps in magnetic field: max. energy splitting contributes and sublevel structure energy difference between adjacent n Zeeman energy, only for spins diamagnetic energy, axial symmetry motional Stark energy, no symmetry Varenna - July 2009

  44. motional Stark effect • strong mixing of of n-manifolds containing n2 sub-states • optical resonance line broadening ? • no l,m quantum numbers  no electric dipole selection rules for interaction with e.m. radiation  all sublevels interacting weak dependence on T and B Varenna - July 2009

  45. continuum Two possible strategies for Ps Rydberg excitation to n  (20  30), using two resonant laser pulses with time length of a few ns (the single pulse laser excitation 1 high n requires   180 nm !) continuum high n high n ~0.75 eV ~1650 nm ~1.69 eV ~730 nm n=3 n=2 6.05 eV 205 nm 5.10 eV 243 nm n=1 n=1 AEGIS AEGIS Rydberg laser excitation of Ps tested?!  tailoring of laser pulsescharacteristics (pulse energy, bandwidth,…) for maximization of excitation efficiency Varenna - July 2009

  46. moving Ps atom: all optical resonances are broadened by Doppler effect Assuming a Maxwellian thermal distribution of Ps atoms velocity along the laser direction: spectral Gaussian lineshape centered on Ps resonance at rest 0  Ps atoms resonant at  total Ps atoms resonant frequency of Ps with velocity v (first order in v/c) Varenna - July 2009

  47. Doppler effect (inhomogeneous broadening) motional Stark effect (~homogeneous broadening) high excitation efficiency requires large laser bandwidth to cover the lineshape! relevant contributes to lineshape in B field: Varenna - July 2009

  48. Doppler effect (inhomogeneous broadening) motional Stark effect (~homogeneous broadening) high excitation efficiency requires large laser bandwidth to cover the lineshape! relevant contributes to lineshape in B field: laser pulse intensity profile basic characteristics of laser pulses: time length Lof some ns, Gaussian spectral profiles FWHM = L coherence time ( phase coherence) tcoh L (Fourier analysis) ns laser pulse phase ns Varenna - July 2009

  49. Doppler effect (inhomogeneous broadening) motional Stark effect (~homogeneous broadening) high excitation efficiency requires large laser bandwidth to cover the lineshape! relevant contributes to lineshape in B field: laser pulse intensity profile basic characteristics of laser pulses: time length Lof some ns, Gaussian spectral profiles FWHM = L coherence time ( phase coherence) tcoh L (Fourier analysis) ns laser pulse phase with large bandwidth, tcoh << L (rapidly varying laser pulse phase) incoherent excitation ns max. efficiency with incoherent excitation: 50% population equally distributed on interacting levels i.e. saturation of transition (neglecting any decay process, like spontaneous emission) Varenna - July 2009

  50. Modeling incoherent excitations Theory of incoherent excitation from level a to level b: definition of a cross-section lineshape function (normalized to 1) Einstein B coefficient for absorption  (B.W.Shore,The theory of coherent excitations, Wiley (1990)) Varenna - July 2009

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