1. Varenna - July 2009 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 A E g I SA E g I S Antimatter Experiment Gravity Interferometry Spectroscopy 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/

2. Varenna - July 2009 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 !

3. Varenna - July 2009 AEGIS Collaboration LAPP, Annecy, France. P. Nédélec, D. Sillou 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 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 Pavia G. 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, Russia V. M. Byakov, S. V. Stepanov, D. S. Zvezhinskij New York University, USA H. H. Stroke Laboratoire Aimé Cotton, Orsay, France L. 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

4. Varenna - July 2009 AD (Antiproton Decelerator) at CERN 3 x 10 7 antiprotons / 100 sec6 MeV10 4 p / 100 sec

5. Varenna - July 2009 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 1.Direct Methods: measurement of gravitational acceleration of H and Hbar in the Earth gravitational field 2.High-precision spectroscopy: H and Hbar are test clocks (this is also CPT test) 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)

6. Varenna - July 2009 10 -18 10 -16 WEP tests on matter system 10 -14 10 -12 10 -10 10 -4 10 -6 10 -8 10 -2 170019001800 2000 Matter limit Gravitational Physics: Weak Equivalence Principle (WEP) No direct measurements on gravity effects on antimatter “Low” precision measurement (1%) will be the first one Can be done with a beam of Antiatoms flying to a detector! AEGIS first phase g H L Period of pendula Torsion measurement Gravity in the Solar System Any violation of WEP implies either that the theory is in error or that there is a new force acting

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

8. Varenna - July 2009 Method I: Antiproton + Positron (ATHENA) 10 4 antiprotons 10 8 e + Spontaneous radiative recombination Three body recombination 14 ± 4 antihydrogen atoms Method II: Antiproton + Rydberg Ps (ATRAP) Two-stage Rydberg charge exchange C. H. Storry et al., First Laser-Controlled Antihydrogen Production, Physical Review Letters 93, 263401 (2004) 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!)

9. Varenna - July 2009 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 e+ Porous target Moire’ deflectometer and detector AEGIS experimental strategy

10. Varenna - July 2009 A few comments on AEGIS strategy (and timing) to produce Antihydrogen: 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 Form a neutral (antihydrogen) beam g measurement Confine only neutrals (future) (CPT physics) Source and moderator Trap Accumulator (Surko-type) Bunch of 20 ns and 1 mm beam spot Use of 10 8 positrons in a bunch 500 sec accumulation time Catch p from AD, degrade the energy Cool down the p with e - 500 sec accumulation time (a few AD shots, 10 5 p) An antihydrogen production shot every 500 sec

11. Varenna - July 2009 Ps VacuumSolid Positron beam Ps Positronium emission e+ Positronium yield from materials: requirement of 10% (reemitted, cold) out of 10 8 in ortho-Ps. Velocity of reemitted Ps: 5 x 10 4 m/s (corresponding to thermalized at 100 K) Laser excitation of the Positronium to Rydberg states (more on this later on) (lectures by R. Brusa and A. Dupasquier) Silicon nanochannel material: 10-15 nm pores: max o-Ps formation observed 50%

12. Varenna - July 2009 Ultracold Antiprotons The CERN AD (Antiproton Decelerator) delivers 3 x 10 7 antiprotons / 80 sec 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 (10 4 /10 5 subeV antiprotons) Transfer in the Antihydrogen formation region (1 Tesla, 100 mK) Cooling antiprotons down to 100 mK 10 5 antiprotons ready for Antihydrogen production Antiprotons ProductionGeV DecelerationMeV TrappingkeV CoolingeV Resistive cooling based on high-Q resonant circuits Sympathetic cooling with laser cooled Os - ions U. Warring et al., PRL 102 (2009) 043001

13. Varenna - July 2009 Such measurement would represent the first direct determination of the gravitational effect on antimatter A E g I S in short Acceleration of antihydrogen. Formation of antihydrogen atoms Antiprotons Positrons The antihydrogen beams will fly (with v~500 m/sec) through a Moire’ deflectometer The vertical displacement (gravity fall) will be measured on the last (sensitive) plane of the deflectometer Positronium: 10 7 atoms Antiprotons: 10 5 Antihydrogen: 10 4 /shot

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

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

16. Varenna - July 2009 Antihydrogen (Stark) acceleration Stark acceleration Stark acceleration of hydrogen atoms”, E. Vliegen and F. Merkt, Journ. Phys. B 39 (2006) L241 Rydberg antihydrogen is accelerated or decelerated by electric field 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

17. Varenna - July 2009 - 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 Horizontal velocity (m/s) Atoms (1/ms -1 ) no acceleration acceleration Effect of the magnetic field (e.g. 1 T) 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) acceleration inside 1T

18. Varenna - July 2009 Gravity Measurement Seems easy: DISPLACEMENT DUE TO GRAVITY HARD TO MEASURE THIS WAY 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) AEgIS realistic numbers: - horizontal flight path L ~ 1 m - horizontal velocity v z ~ 500 m/s vertical deflection ~ 30 μm 1 cm Downward shift by 30 μm

19. Varenna - July 2009 An aperture of 100 μm Now displacement easily detectable. At the price of a huge loss in acceptance cm Let us collimate! Position sensitive detector Acceptance can be increased by having several holes. In doing so new possible paths show up cm Let us collimate! L1L1 L2L2 If L 1 = L 2 the new paths add up to the previous information on the 3 rd plane

20. Varenna - July 2009 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.interferometrycollimatedfringe

21. Varenna - July 2009 So, it is a classical device if d g >> 10 μm 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: dgdg α L

22. Varenna - July 2009 AEgIS requirements (for the achievement of the 1% measurement accuracy) - area 20x20 cm 2 - 10-13 μm resolution for the reconstruction of the annihilation point - high efficiency - to work around 140 K g-measurement position Sensitive Detector (gSD) MEASURING THE ANNIHILATION POINT WITH GREAT PRECISION IS ESSENTIAL EVENT SIMULATION (Geant 3.21) - generate randomly an impact point (inside 20x20 cm 2 ) - 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 - 25 μ m pitch - 300 μ m thick corresponding to 20x20 cm 2 area, 300 μ m thick silicon slab... 8000 strips 25 μ m wide... 20 cm g-measurement position sensitive detector ➠ silicon μ -strip detector

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

24. Varenna - July 2009 Measuring g: 1)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

25. Varenna - July 2009 The accuracy of the g measurement  Systematic error on : about 0.5 % error in the mean axial position of the beam   T2 /T 2 : 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  0 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)

26. Varenna - July 2009 M o i r é deflectometer fringe shift of the shadow image T = time of flight = [t STARK - t DET ] (L~ 1 m, v ~ 500 m/s ➠ T ~ 2 ms) Out beam is not monochromatic (T varies quite a lot) v counts (a.u.) m/s ➠ counts (a.u.) ms 2 T2T2 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.) time of flight T (s) ➠ g comes from the fit

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

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

29. Varenna - July 2009 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

30. Varenna - July 2009 para-Ps (singlet states S=0) ortho-Ps (triplet states S=1) Ghz Ps energy levels for n = 1,2: tests on quantum electrodynamics 8.5 · 10 -4 eV (203,4 Ghz) 1.1 · 10 -4 eV 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) long living state short living state Fine structure: spin-orbit, hyperfine, relativistic interactions, and weak magnetic fields

31. Varenna - July 2009 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)) n=2 continuum n=1 5.10 eV 243 nm high n ~1.69 eV ~730 nm tested?! 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

32. Varenna - July 2009 two particles with Coulomb interaction (4n 2 degeneration) Zeeman motional Stark diamagnetic (or quadratic Zeeman) Ps in magnetic field B ~ 1 T : theory fine structure  1/n 3 (negligible for n ≥ 2) quantum numbers n,l,m,s…?

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

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

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

36. Varenna - July 2009 (3) Moving Ps: motional Stark effect Ps rest frame laboratory frame transformation of e.m. fields in Ps rest frame (up to first order in v Ps / c) 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! induced electric field acting on moving Ps

37. Varenna - July 2009 with the transverse electric field:  Stark effect depends on Ps center of mass velocity v PS (T) (  on the temperature of Ps cloud) Theory of Stark effect: maximum splitting of n 2 (l,m mixed) substates 

38. Varenna - July 2009 with the transverse electric field:  Stark effect depends on Ps center of mass velocity v PS (T) (  on the temperature of Ps cloud) Theory of Stark effect: maximum splitting of n 2 (l,m mixed) substates  Ps : the lightest atom motional Stark effect is largerly the dominant contribution to sublevel splitting energy for Rydberg Ps

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

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

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

42. Varenna - July 2009 assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)  ionization of Rydberg red states n > 27 Minimum electric field for Rydberg ionization (Gallagher, Rep. Prog. Phys. 51, 143 (1988)    Energy difference between neighboring unperturbed n-levels for n > 6 for n > 18 interleaving of different n-sublevel manifolds!  comparison with H atoms (ionization for n > 87) for n < 40 for n > 46 motional Stark electric field strength l,m mixing interleaving of n-manifolds n 2 sublevels

43. Varenna - July 2009 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

44. Varenna - July 2009 motional Stark effect  strong mixing of of n-manifolds containing n 2 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

45. Varenna - July 2009 Rydberg laser excitation of Ps n=2 continuum n=1 5.10 eV 243 nm high n ~1.69 eV ~730 nm n=3 continuum n=1 6.05 eV 205 nm high n ~0.75 eV ~1650 nm tested?! 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 !) tailoring of laser pulses characteristics (pulse energy, bandwidth,…) for maximization of excitation efficiency 

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

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

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

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

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

51. Varenna - July 2009 Modeling incoherent excitations Excitation probability for unit time: with spectral radiation intensity and bandwidth  E L   Saturation fluence: total pulse energy for unit target area; with a F SAT pulse  43% of atoms in excited state; F SAT defined from rate equations (max excitation 50% when laser fluence   ) Theory of incoherent excitation from level a to level b : definition of a cross-section  (B.W.Shore,The theory of coherent excitations, Wiley (1990)) Einstein B coefficient for absorption lineshape function (normalized to 1) 

52. Varenna - July 2009 Modeling Ps excitation to Rydberg levels: determination of fluence, energy and bandwidth for laser pulses 1) transitions 1  2 and 2  high n comparison of broadening of optical transitions lineshapes, for both excitation paths (reference B field = 1T, reference temperature = 100 K) motional Stark Doppler: 2) transitions 1  3 and 3  high n (nm)  D (nm)  MS (nm) 1  2 2430.0540.85·10 -3 2  n >15 7300.16> 0.9 (nm)  D (nm)  MS (nm) 1  3 2050.0451.8·10 -3 3  n >15 16500.36> 4.0

53. Varenna - July 2009 1) transitions 1  2 and 2  high n comparison of broadening of optical transitions lineshapes, for both excitation paths (reference B field = 1T, reference temperature = 100 K) motional Stark Doppler: 2) transitions 1  3 and 3  high n low n excitation  Doppler high n excitation  motional Stark dominant contribution to lineshape:  (nm)  D (nm)  MS (nm) 1  2 2430.0530.85·10 -3 2  n >16 7300.16> 0.9 (nm)  D (nm)  MS (nm) 1  3 2050.0441.8·10 -3 3  n >16 16500.36> 4.0 Modeling Ps excitation to Rydberg levels: determination of fluence, energy and bandwidth for laser pulses

54. Varenna - July 2009 Fluence and energy of laser pulses : low n excitations 1  2,3 Absorption cross section (Doppler lineshape): Einstein coeff. Saturation fluence, with laser bandwidth = Doppler linewidth  D As expected F SAT proportional to  D matrix element of electric dipole allowed transition (  polarization vector)

55. Varenna - July 2009 Fluence and energy of laser pulses : high n excitations 2,3  n AEGIS useful range of Rydberg n-levels is in a region of dominant motional Stark lineshape ionization limit line broadenings for transition to Rydberg states (from n = 3) (  n+1,n : energy diff. in nm between adjacent n levels) useful range  strong mixing of of n-manifolds and n 2 sub-states in 17 < n < 27  assume quasi-continuum of energy levels: a Rydberg level band  a large band interacting  rapidly growing saturation fluence ??  assuming uniform distribution of energy sublevels  density of energy sublevels per unit angular frequency

56. Varenna - July 2009 Generalization of the theory of incoherent excitation cross sectionexcitation probability  E L = laser energy bandwidth (  Doppler bandwidth, not critical) B MS (  ) = absorption Einstein coeff. for excitation of a single sublevel

57. Varenna - July 2009 Generalization of the theory of incoherent excitation number of interleaved unperturbed n levels under MS energy width number of sub-states of a n-manifold angular frequency MS width An expression for  (  ) in the full mixed range n > 17 independent from Ps velocity and B ! cross sectionexcitation probability  E L = laser energy bandwidth (  Doppler bandwidth, not critical) B MS (  ) = absorption Einstein coeff. for excitation of a single sublevel

58. Varenna - July 2009 from definition of Einstein coeff  unknown normalized wavefunction of a mixed single sublevel assuming full l,m mixing: and using electric dipole selection rules (with sum on final quantum numbers l = 0, 2)

59. Varenna - July 2009 Scaling of B MS coefficient and excitation probability Rydberg state wave functions scale as n -3/2  sublevel density  (  ) scale as n 5  W n is independent from n, Ps velocity and B ! from definition of Einstein coeff  unknown normalized wavefunction of a mixed single sublevel assuming full l,m mixing: and using electric dipole selection rules (with sum on final quantum numbers l = 0, 2)

60. Varenna - July 2009 Scaling of B MS coefficient and excitation probability Rydberg state wave functions scale as n -3/2  sublevel density  (  ) scale as n 5  from definition of Einstein coeff  unknown normalized wavefunction of a mixed single sublevel assuming full l,m mixing: and using electric dipole selection rules (with sum on final quantum numbers l = 0, 2) W n is independent from n, Ps velocity and B !

61. Varenna - July 2009 Finally: saturation fluence of laser pulses, excitations 2,3  n in full mixed range ( note the independence from laser bandwidth ) (F.Castelli et al, PRA 78, 052512 (2008)) fast growing of saturation fluence for l,m mixing ~constancy of saturation fluence for interleaving of n-manifolds useful excitation range limited by ionization losses an example of Rydberg excitation dependence on Ps temperature   

62. Varenna - July 2009 Ps time length 5 ns, transverse Gaussian profile, spot size FWHM =  r = diameter of Ps cloud, peak fluence = 4 F SAT (with a security factor) bandwidth =  D pulse energy 1  2 243 nm0.054 nm 4.4  J 2  n =25 730 nm0.16 nm1.5 mJ Energy of laser pulses (reference case B = 1T, T = 100K) bandwidth =  D pulse energy 1  3 205 nm0.045 nm 32  J 3  n =25 1664 nm0.36 nm 350  J 1) transitions 1  2 and 2  high n2) transitions 1  3 and 3  high n (see the poster of F.Villa for this laser R&D)

63. Varenna - July 2009 Ps time length 5 ns, transverse Gaussian profile, spot size FWHM =  r = diameter of Ps cloud, peak fluence = 4 F SAT (with a security factor) bandwidth =  D pulse energy 1  2 243 nm0.054 nm 4.4  J 2  n =25 730 nm0.16 nm1.5 mJ Energy of laser pulses (reference case B = 1T, T = 100K) bandwidth =  D pulse energy 1  3 205 nm0.045 nm 32  J 3  n =25 1664 nm0.36 nm 350  J 1) transitions 1  2 and 2  high n2) transitions 1  3 and 3  high n What about the theoretical efficiency for these two-step processes of incoherent excitation towards Rydberg states? high-n excitation expected at 33% (population equally distributed on three interacting levels, and neglecting of decay processes,like spontaneous emission or collisions) (see the poster of F.Villa for this laser R&D)

64. Varenna - July 2009 testing the theory: a model for excitation dynamics  multilevel Bloch equation system, derived from a density matrix formulation  inclusion of population losses (spontaneous decay and photoionization)  cross section between level bands = cross section between single unperturbed levels  fluence and bandwidth as tabulated  phases of laser pulses modeled as “random walk” with step = coherence time Plot of population dynamics in a single realization of the process excitation probability from numerical experiments: 1  2  25 24% 1  3  25 30% The difference is mainly due to the higher spontaneous decay rate of level n =2

65. Varenna - July 2009 Conclusions ♫ Development of a “first order” analysis of the energy level structure of a moving Ps atom in magnetic field; ♫ Formulation of a generalized theory of incoherent excitation, for application in sublevel full mixing cases; ♫ Determination of laser pulse characteristics, to the goal of maximum efficiency in Ps excitation for AEGIS

66. Varenna - July 2009 Conclusions ♫ Development of a “first order” analysis of the energy level structure of a moving Ps atom in magnetic field; ♫ Formulation of a generalized theory of incoherent excitation, for application in sublevel full mixing cases; ♫ Determination of laser pulse characteristics, to the goal of maximum efficiency in Ps excitation for AEGIS Possible improvements ♫ Detailed description of Ps energy levels; ♫ Refinement of the incoherent excitation theory; ♫ More realistic modelization of excitation dynamics ♫ Experimental tests on Ps Rydberg excitation ?

67. Varenna - July 2009 M o i r é deflectometer new position-sensitive detector (to detect antihydrogen annihilation) upgraded version Collimation of the beam with a classical

68. Varenna - July 2009 Monte Carlo Choice of the production point Choice of velocity Choice of grating characteristics Tracking Summing up the period of the grating Reference model: L = 30 cm Size of gratings : 20 x 20 cm 2 Pitch of grating 100 μm Opening fraction 30%

69. Varenna - July 2009 Production point Velocity distribution Hitting the first plane Getting out from first plane

70. Varenna - July 2009 Action of the second plane Third plane g no-g

71. Varenna - July 2009 Gravity No gravity

72. Varenna - July 2009 Δ o (calculated experimentally) Suppose: - L = 40 cm - grating period a = 80 μm - grating size = 20 cm (2500 slits) - no gravity M o i r é deflectometer X Z Grating transparency = 30% (total transmission 9%) moiré deflectometer annihilation hit position on the final detector (in x/a units, modulo grating period a) 0 0.25 0.5 0.75 1 x/a counts (a.u.) slit solid counts (a.u.) ]a]a -5 -4 -3 -2 -1 0 1 2 3 4 5 (x/a) annihilation hit position on the final detector (in x/a units) grating slits shadow fringes depends on the alignement between the gratings, and on the alignment between them and the center of the antihydrogen cloud. It is indepentend to the radial antihydrogen velocity and profile

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

74. Varenna - July 2009 M o i r é deflectometer fringe shift of the shadow image T = time of flight = [t STARK - t DET ] (L~ 1 m, v ~ 500 m/s ➠ T ~ 2 ms) Out beam is not monochromatic (T varies quite a lot) v counts (a.u.) m/s ➠ counts (a.u.) ms 2 T2T2 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.) time of flight T (s) ➠ g comes from the fit