Transcript n 2 - (INFN) - Sezione di Milano

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
AEgIS
Spectroscopy
Antimatter
Interferometry
Experiment
Gravity
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
Varenna - July 2009
AEGIS: AD-6 Experiment
http://aegis.web.cern.ch/aegis/
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
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
AD (Antiproton Decelerator) at CERN
3 x 107 antiprotons / 100 sec
6 MeV
Varenna - July 2009
104 p / 100 sec
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)
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)
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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
10-18
WEP tests on matter system
10-16
10-14
10-12
Gravity in the Solar System
10-10
10-8
Matter limit  1013
Period of pendula
10-6
10-4
Torsion measurement
10-2
1700
1800
1900
Can be done with a beam of Antiatoms flying to a detector!
L
H
g
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2000
AEGIS
first
phase
Production Methods
I. ANTIPROTON + POSITRON (exp.demonstration: ATHENA and ATRAP)
(A)
(B)
e+
p+
e+
H + hn
p + e+ + e+
H + e+
p
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)
p + Ps*
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H + eProduction
Method in AEGIS
Method I: Antiproton + Positron (ATHENA)
104 antiprotons
Method II: Antiproton + Rydberg Ps (ATRAP)
C. H. Storry et al., First Laser-Controlled Antihydrogen Production,
Physical Review Letters 93, 263401 (2004)
108 e+
• Spontaneous radiative recombination
Two-stage
Rydberg
charge
exchange
• Three body recombination
14 ± 4 antihydrogen atoms
In Aegis: Antiproton + Rydberg Ps (obtained by Ps and laser excited)
*
p  ( Ps)  H  e 
*
   a 2 n4
0
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•
Large cross section
•
Quantum states of antihydrogen related to
Ps quantum number
•
Reaction suitable for cold antihydrogen
production (cold antiprotons!)
Moire’ deflectometer and detector
AEGIS experimental strategy
1) Produce ultracold antiprotons (100 mK)
Cold antiprotons
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
*
p  ( Ps)  H  e
*
Porous target
e+

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
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A few comments on AEGIS strategy (and timing) to produce Antihydrogen:
Use of 108 positrons in a bunch
• Source and moderator
Bunch of 20 ns and 1 mm beam spot
• Trap
500 sec accumulation time
Catch p from AD, degrade the energy
Cool down the p with e-
• Accumulator (Surko-type)
An antihydrogen production
shot every 500 sec
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
• Form a neutral (antihydrogen) beam
g measurement
• Confine only neutrals (future)
(CPT physics)
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Vacuum
Positronium yield from materials:
requirement of 10% (reemitted, cold)
out of 108 in ortho-Ps.
Solid
Positron beam
(lectures by R. Brusa and A. Dupasquier)
Ps
Silicon nanochannel material: 10-15
nm pores: max o-Ps formation
observed 50%
e+
Ps
Ps
Ps
Velocity of reemitted Ps: 5 x 104 m/s
(corresponding to thermalized at 100 K)
Positronium emission
Laser excitation of the Positronium to Rydberg states (more on this later on)
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Ultracold Antiprotons
•The CERN AD (Antiproton Decelerator)
delivers 3 x 107 antiprotons / 80 sec
Antiprotons
•Antiprotons catching in cylindrical
Penning traps after energy degrader
Production
GeV
Deceleration
MeV
•Catching of antiprotons within a 3 Tesla
magnetic field, UHV, 4 Kelvin, e- cooling
Trapping
keV
Cooling
eV
•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
•Cooling antiprotons down to 100 mK
•105 antiprotons ready for
Antihydrogen production
• Sympathetic cooling with
laser cooled Os- ions
U. Warring et al., PRL 102 (2009) 043001
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A E g I S 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
Antiprotons
Positrons
The vertical displacement (gravity fall) will be
measured on the last (sensitive) plane of the
deflectometer
Such measurement would represent the first direct determination of the gravitational effect on antimatter
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Antihydrogen detector
How do we know that this works?
Intermediate level: need to know that we are producint Antihydrogen!
Ps converter
e+ Bunch
 1cm
Ps*
Antiprotons
Antihydrogen monitor
Antiproton
Catching
Zone (3 T)

Antihydrogen
Formation
Zone (1 T)
511 keV
Silicon micro
strips
Deflectometer
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
CsI
crystals


511 keV

The Athena Anti-hydrogen detector
GOAL
Vertex from tracking of charged particles
Identification of 511 keV gammas
Time and space coincidence of tracks + gammas
192 CsI (pure)
Crystals
DESIGN
Compact (radial thickness ~ 3 cm, length ~ 25
cm)
Large solid angle (~ 80 %)
High granularity
Operation at T ~ 140 K, B = 3 Tesla
2 Layers of Si strips (r,f) and pads (z)
Time Resolution ~ 5 ms (CsI decay time ~ 1 ms)
C. Regenfus, NIM A 501, 65 (2003).
Space Resolution ~ 4 mm (Vertex reconstruction  )
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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
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Atoms (1/ms-1)
- 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
no acceleration
acceleration
Horizontal velocity (m/s)
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)
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Gravity Measurement
Seems easy:
H
h
L
AEgIS realistic numbers:
- horizontal flight path L ~ 1 m
vertical deflection ~ 30 μm
- horizontal velocity vz ~ 500 m/s
• 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
h 30 m m

 3103
h
1 cm
Downward shift by 30 μm
DISPLACEMENT DUE TO GRAVITY HARD TO MEASURE THIS WAY
Varenna - July 2009
Let us collimate!
Position
sensitive
detector
cm
h
30 m m

 0.3
h
100 m m
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
L1
L2
Let us collimate!
cm
If L1 = L2 the new paths add up to the previous information on the 3rd plane
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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
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
L
py 
h
dg
h
 d g
dg p
tg 
L
h
dg p
h
 d g2
p
L dB  d g2
L dB  10 m m
So, it is a classical device if dg>> 10 μm
Varenna - July 2009
g-measurement position sensitive
detector
g-measurement position Sensitive Detector (gSD)
MEASURING THE ANNIHILATION POINT WITH GREAT PRECISION IS ESSENTIAL
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
➠ silicon μ-strip detector
- 8000 silicon strips
- 20 cm long
- 25 μm pitch
- 300 μm thick
corresponding to
20x20 cm2 area,
300 μm thick silicon slab
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
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...
8000 strips
25 μm wide
...
20 cm
20 cm
DETECTOR SIMULATION
moiré
deflectometer
M o i r é deflectometer
3
4
5
(x/a)
annihilation hit position on the final detector
(in a units)
beam horizontal velocity
-2
solid
slit
-3
slit
0.25
0.5
0.75
1
x/a
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-5
-4
Fringe
shift !
0
grating slits shadow
fringe shift
annihilation hit position on the final
detector
(in a units, modulo grating period a)
counts (a.u.)
2
vz = 600 m/s
vz = 250 m/s
1
Z
Grating transparency = 30%
(total transmission 9%)
0
Suppose:
- L = 40 cm
- grating period a = 80 μm
- grating size = 20 cm (2500 slits)
- gravity
-1
X
counts (a.u.)
]a
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
Varenna - July 2009
 
gT 2
 T   0  2
a
2
The accuracy of the g measurement
Systematic error on <T2>: about 0.5 % error in the mean axial position of the beam
T2/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)
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M o i r é deflectometer
counts (a.u.)
Out beam is not monochromatic
(T varies quite a lot)
fringe shift of the shadow image
v
T = time of flight = [tSTARK - tDET]
(L~ 1 m, v ~ 500 m/s ➠T ~ 2 ms)
Binning antihydrogens with mean velocity of 600-550-500-450400-350-300-250-200 m/s,
and plotting δ as a function of
➠
counts (a.u.)
➠
δ (a.u.)
m/s
T2
g comes from the fit
ms2
time of flight T (s)
Varenna - July 2009
Now, before moving on to more serious problems, we would
like to thank the organizers for this pleasant time here
Varenna - July 2009
Positronium Laser Excitation
to Rydberg Levels in Magnetic Field
(an intriguing topic of atomic physics)
2
1

me
-
Se

mp

Sp
+
F. Castelli and M.G. Giammarchi
Varenna - July 2009

B
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
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Ps energy levels for n = 1,2:
tests on quantum electrodynamics
para-Ps
(singlet states S=0)

ortho-Ps
(triplet states S=1)
Ghz

short living state
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)
1.1 · 10-4 eV
8.5 · 10-4 eV
(203,4 Ghz)
long living state
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Fine structure: spin-orbit,
hyperfine, relativistic interactions,
and weak magnetic fields
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))
continuum
high n
~1.69 eV
~730 nm
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
5.10 eV
243 nm
n=2
n=1
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Ps in magnetic field B ~ 1 T : theory
Ps at rest



Hˆ  Hˆ C  Hˆ F  Hˆ Z  Hˆ dia
two particles with
Coulomb interaction
(4n2 degeneration)
En ,...
fine structure
 1/n3 (negligible
for n ≥ 2)
Zeeman

with velocity v

 Hˆ MS
diamagnetic
(or quadratic
Zeeman)
motional Stark
13.6 eV
 
 EF  EZ  Edia  EMS
2
2n
quantum numbers n,l,m,s…?
Varenna - July 2009
(1) linear Zeeman effect
a) 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)
max EZ  4 mB B  2.4  104 eV
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)
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(1) linear Zeeman effect
a) 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)
max EZ  4 mB B  2.4  104 eV
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
max Edia  B 2 , n 4
Edia  EZ
(R.H. Garstang, Rep. Prog. Phys. 40, 105 (1977))
Varenna - July 2009
for n  30 (for Ps)
(3) Moving Ps: motional Stark effect
transformation of e.m. fields in Ps rest frame
(up to first order in vPs / c)
laboratory frame
z
x

B
v

E0
Ps rest frame
 

 B '  B  B zˆ


 

E '  vPs  B  v B xˆ  E

vPs
z
y
x
Varenna - July 2009

B'
 
E '  E
y
(3) Moving Ps: motional Stark effect
transformation of e.m. fields in Ps rest frame
(up to first order in vPs / c)
laboratory frame
z
x

B
 

 B '  B  B zˆ


 

E '  vPs  B  v B xˆ  E

vPs

E0
v
Ps rest frame
y

E
induced electric field
acting on moving Ps
z
x

B'
 
E '  E
y
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!
Varenna - July 2009
Hˆ MS
 
  e r  Ε
with the transverse electric field:
 Stark effect



E  vPs  B
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
EMS


 3 e aPs n (n  1) | E |
Varenna - July 2009
aPs  2a0 
Hˆ MS
 
  e r  Ε
with the transverse electric field:
 Stark effect



E  vPs  B
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
EMS


 3 e aPs n (n  1) | E |
aPs  2a0 
Ps : the lightest atom
motional Stark effect is largerly the dominant contribution
to sublevel splitting energy for Rydberg Ps
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assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)

v  k BT / mPs  2.75  104 m/s
Varenna - July 2009
comparison with H
vH  1 / 30 v  103 m/s
assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)

v  k BT / mPs  2.75  104 m/s

E  275 V/cm  ionization of Rydberg red states n > 27
 Minimum electric field for Rydberg ionization
e
1 


Eion 
2
4 
(Gallagher, Rep. Prog. Phys. 51, 143 (1988)
4


a
9
n
0 Ps


Varenna - July 2009
comparison with H
vH  1 / 30 v  103 m/s
E  10 V/cm
(ionization for n > 87)
assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)

v  k BT / mPs  2.75  104 m/s

E  275 V/cm  ionization of Rydberg red states n > 27
 Minimum electric field for Rydberg ionization
e
1 


Eion 
2
4 
(Gallagher, Rep. Prog. Phys. 51, 143 (1988)
4


a
9
n
0 Ps


 EMS  EZ , Edia
comparison with H
vH  1 / 30 v  103 m/s
E  10 V/cm
(ionization for n > 87)
EZ  E MS , Edia
for n > 6
for n < 40
Edia  E MS  En
for n > 46
Varenna - July 2009
assuming Ps thermal velocity at the reference temperature 100 K and B =1T (AEGIS proposal)

v  k BT / mPs  2.75  104 m/s

E  275 V/cm  ionization of Rydberg red states n > 27
comparison with H atoms
vH  1 / 30 v  103 m/s
E  10 V/cm
(ionization for n > 87)
 Minimum electric field for Rydberg ionization

e
1 l,m

 mixing interleaving of n-manifolds
Eion 
2
4 
(Gallagher, Rep. Prog. Phys. 51, 143 (1988)
4


a
9
n
0 Ps


 EMS  EZ , Edia
n 1
E n1
for n > 6
E n
n
n 1
EZ  E MS , Edia
for n < 40
Edia  E MS  En
for n > 46 n2 sublevels

EMS
13.6 eV
 En 
n3
Energy difference between
neighboring unperturbed n-levels
for n > 18
motional Stark electric field strength
interleaving of different
n-sublevel manifolds!
Varenna - July 2009
moving Rydberg Ps in magnetic field:
max. energy splitting contributes and sublevel structure
E n
energy difference
between adjacent n
E Z
Zeeman energy,
only for spins
energy,
E dia diamagnetic
axial symmetry
E MS
motional Stark energy,
no symmetry
Varenna - July 2009
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
Rydberg laser excitation of Ps
continuum
high n
~0.75 eV
~1650 nm
n=3
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
6.05 eV
205 nm
n=1
continuum
high n
~1.69 eV
~730 nm
5.10 eV
243 nm
n=2
n=1
Varenna - July 2009
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 

 (   0 ) 2 
NPs ( )
1
 gD ( ) 
exp 

2
NPs
 
 

total Ps atoms


v
c
  0 1   ;
resonant frequency
of Ps with velocity v
(first order in v/c)

0

2 kB T
m c2
g ( )
FWHM  2  ln 2
0
Varenna - July 2009

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)
Varenna - July 2009
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)
basic characteristics of laser pulses:
time length L of some ns,
Gaussian spectral profiles FWHM = L
coherence time ( phase coherence) tcoh
t coh 

2
laser pulse intensity profile
1
0.8
c L
0.6
L
0.4
(Fourier analysis)
0.2
5
5
10
15
ns
laser pulse phase
4
3
2
1
5
Varenna - July 2009
5
10
15
ns
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)
basic characteristics of laser pulses:
time length L of some ns,
Gaussian spectral profiles FWHM = L
coherence time ( phase coherence) tcoh
t coh 

2
laser pulse intensity profile
1
0.8
c L
0.6
0.4
(Fourier analysis)
0.2
5
with large bandwidth,
tcoh << L
L
5
10
15
ns
laser pulse phase
 incoherent excitation
4
3
(rapidly varying laser pulse phase)
2
1
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
5
5
10
15
ns
Modeling incoherent excitations
Theory of incoherent excitation
from level a to level b: definition
of a cross-section

ab ( ) 
lineshape function
(normalized to 1)
number of photons absorbed
photon flux
(B.W.Shore,The theory of coherent
excitations, Wiley (1990))
Varenna - July 2009
 g ( )
Einstein B coefficient
for absorption

Bab ( )
c
Modeling incoherent excitations
Theory of incoherent excitation
from level a to level b: definition
of a cross-section


ab ( ) 
lineshape function
(normalized to 1)
number of photons absorbed
photon flux
Excitation probability for unit time:
with spectral radiation intensity I ( )

 g ( )
Wab  
E L
Einstein B coefficient
for absorption

Bab ( )
c
d
I ( )
 ab ( )

and bandwidth EL

Saturation fluence:
total pulse energy for unit target area;
with a FSAT pulse  43% of atoms in excited state;
FSAT defined from rate equations
(max excitation 50% when laser fluence  )
(B.W.Shore,The theory of coherent
excitations, Wiley (1990))
Varenna - July 2009
FSAT (a  b)
Modeling Ps excitation to Rydberg levels:
determination of fluence, energy and bandwidth for laser pulses
comparison of broadening of optical transitions lineshapes, for both excitation paths
(reference B field = 1T, reference temperature = 100 K)
Doppler:
D  FW HM 2 / 2c
motional Stark
MS  EMS 2 / hc
1) transitions 1  2 and 2  high n
2) transitions 1  3 and 3  high n
 (nm) D (nm) MS (nm)
 (nm) D (nm) MS (nm)
12
243
0.054
0.85·10-3
13
205
0.045
1.8·10-3
2  n >15
730
0.16
> 0.9
3  n >15
1650
0.36
> 4.0
Varenna - July 2009
Modeling Ps excitation to Rydberg levels:
determination of fluence, energy and bandwidth for laser pulses
comparison of broadening of optical transitions lineshapes, for both excitation paths
(reference B field = 1T, reference temperature = 100 K)
Doppler:
D  FW HM 2 / 2c
motional Stark
MS  EMS 2 / hc
1) transitions 1  2 and 2  high n
2) transitions 1  3 and 3  high n
 (nm) D (nm) MS (nm)
 (nm) D (nm) MS (nm)
12
243
0.053
0.85·10-3
13
205
0.044
1.8·10-3
2  n >16
730
0.16
> 0.9
3  n >16
1650
0.36
> 4.0

dominant contribution to lineshape:
low n excitation  Doppler
high n excitation  motional Stark
Varenna - July 2009
Fluence and energy of laser pulses : low n excitations 1  2,3
Absorption cross section (Doppler lineshape):
Einstein coeff.
 | d |2
B12,3 ( ) 
;
 0 2
 ( )  gD ( )
 
d   n1m | e r   | 100

B ( )
c
(n  2,3)
matrix element of electric dipole allowed
transition ( polarization vector)
Saturation fluence,
c2
with laser bandwidth
FSAT 
B ( )
= Doppler linewidth D
2 3 D
ln 2 2
As expected FSAT proportional to D
Varenna - July 2009
Fluence and energy of laser pulses : high n excitations 2,3  n
line broadenings for transition to Rydberg states (from n = 3)
(n+1,n : energy diff. in nm between adjacent n levels)
AEGIS useful range of Rydberg
n-levels is in a region of dominant
motional Stark lineshape
ionization limit

useful range

 strong mixing of of n-manifolds and
n2 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
  ( ) 
Varenna - July 2009
density of energy sublevels
per unit angular frequency
Generalization of the theory of incoherent excitation
cross section
excitation probability

 n ( )   ( )
BMS ( )
c
Wn (t )  
E L
BMS() = absorption Einstein coeff.
for excitation of a single sublevel
d
I ( , t )
 n ( )

EL = laser energy bandwidth
( Doppler bandwidth, not critical)
Varenna - July 2009
Generalization of the theory of incoherent excitation
cross section
excitation probability

 n ( )   ( )
BMS ( )
c
Wn (t )  
E L
BMS() = absorption Einstein coeff.
for excitation of a single sublevel
number of sub-states
of a n-manifold
d
I ( , t )
 n ( )

EL = laser energy bandwidth
( Doppler bandwidth, not critical)
number of interleaved
unperturbed n levels
under MS energy width
n2 EMS / En

5
 ( ) 
 n
EMS / 
13.6 eV
angular frequency
MS width
Varenna - July 2009
An expression for () in the
full mixed range n > 17
independent from
Ps velocity and B !
from definition of Einstein coeff 
 n   clm  nlm
 
BMS ()   n | e r   | 31m
2
unknown normalized wavefunction of a mixed single sublevel
l ,m
assuming full l,m mixing:
clm 
1
n
BMS ( ) 
 
1

|
e
r
  | 31m
nlm'
2
n
and using electric
dipole selection rules
2
 BMS ( ) 
1
B3n ( )
2
n
(with sum on final quantum numbers l = 0, 2)
Varenna - July 2009
from definition of Einstein coeff 
 n   clm  nlm
 
BMS ()   n | e r   | 31m
2
unknown normalized wavefunction of a mixed single sublevel
l ,m
assuming full l,m mixing:
clm 
1
n
BMS ( ) 
 
1

|
e
r
  | 31m
nlm'
2
n
and using electric
dipole selection rules
2
 BMS ( ) 
1
B3n ( )
2
n
(with sum on final quantum numbers l = 0, 2)
Scaling of BMS coefficient and excitation probability
Rydberg state wave
functions scale as n-3/2
sublevel density
() scale as n5


BMS ( ) 
1
n5
Wn (t )  BMS 
Wn is independent from n,
Ps velocity and B !
Varenna - July 2009
from definition of Einstein coeff 
 n   clm  nlm
 
BMS ()   n | e r   | 31m
2
unknown normalized wavefunction of a mixed single sublevel
l ,m
assuming full l,m mixing:
clm 
1
n
BMS ( ) 
 
1

|
e
r
  | 31m
nlm'
2
n
2
and using electric
dipole selection rules
 BMS ( ) 
1
B3n ( )
2
n
(with sum on final quantum numbers l = 0, 2)
Scaling of BMS coefficient and excitation probability
Rydberg state wave
functions scale as n-3/2
sublevel density
() scale as n5


BMS ( ) 
1
n5
Wn (t )  BMS 
Wn is independent from n,
Ps velocity and B !
Varenna - July 2009
E L
En
EMS
Stark effect strength
Finally: saturation fluence of laser pulses, excitations 2,3  n
(F.Castelli et al, PRA 78, 052512 (2008))
in full mixed range
(note the independence from laser bandwidth)
FSAT (2,3  n) 
c
 13.6 eV
3
B2,3n ( )  n
an example of Rydberg excitation
dependence on Ps temperature

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
Varenna - July 2009
Energy of laser pulses (reference case B = 1T, T = 100K)
r  0.28 cm
time length 5 ns, transverse Gaussian profile,
spot size FWHM = r = diameter of Ps cloud,
peak fluence = 4 FSAT (with a security factor)
Ps
1) transitions 1  2 and 2  high n

bandwidth
= D
pulse energy
12
243 nm
0.054 nm
4.4 mJ
2  n =25
730 nm
0.16 nm
1.5 mJ
2) transitions 1  3 and 3  high n

bandwidth
= D
pulse energy
13
205 nm
0.045 nm
32 mJ
3  n =25
1664 nm
0.36 nm
350 mJ
(see the poster of F.Villa for this laser R&D)
Varenna - July 2009
Energy of laser pulses (reference case B = 1T, T = 100K)
r  0.28 cm
time length 5 ns, transverse Gaussian profile,
spot size FWHM = r = diameter of Ps cloud,
peak fluence = 4 FSAT (with a security factor)
Ps
1) transitions 1  2 and 2  high n

bandwidth
= D
pulse energy
12
243 nm
0.054 nm
4.4 mJ
2  n =25
730 nm
0.16 nm
1.5 mJ
2) transitions 1  3 and 3  high n

bandwidth
= D
pulse energy
13
205 nm
0.045 nm
32 mJ
3  n =25
1664 nm
0.36 nm
350 mJ
(see the poster of F.Villa for this laser R&D)
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)
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
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
Varenna - July 2009
Plot of population dynamics in a
single realization of the process
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
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 ?
Varenna - July 2009
Collimation of the beam with a classical M o i r é deflectometer
new position-sensitive detector
(to detect antihydrogen
annihilation)
upgraded version
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 cm2
Pitch of grating 100 μm
Opening fraction 30%
Varenna - July 2009
Production point
Velocity distribution
Hitting the first plane
Getting out from first plane
Varenna - July 2009
Action of the second plane
g
no-g
Third plane
Varenna - July 2009
Gravity
No gravity
f 
2 y
dg
Varenna - July 2009
moiré
deflectometer
M o i r é deflectometer
5
(x/a)
annihilation hit position on the final detector
(in x/a units)
3
Suppose:
- L = 40 cm
- grating period a = 80 μm
- grating size = 20 cm (2500 slits)
- no gravity
4
X
solid
slit
-3
slit
0
0.25
0.5
0.75
Δo (calculated experimentally)
1
x/a
Varenna - July 2009
-5
-4
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
counts (a.u.)
grating slits shadow
1
-2
-1
counts (a.u.)
annihilation hit position on the final
detector
(in x/a units, modulo grating period a)
0
fringes
2
Z
Grating transparency = 30%
(total transmission 9%)
]a
moiré
deflectometer
M o i r é deflectometer
3
4
5
(x/a)
annihilation hit position on the final detector
(in a units)
beam horizontal velocity
-2
solid
slit
-3
slit
0.25
0.5
0.75
1
x/a
Varenna - July 2009
-5
-4
Fringe
shift !
0
grating slits shadow
fringe shift
annihilation hit position on the final
detector
(in a units, modulo grating period a)
counts (a.u.)
2
vz = 600 m/s
vz = 250 m/s
1
Z
Grating transparency = 30%
(total transmission 9%)
0
Suppose:
- L = 40 cm
- grating period a = 80 μm
- grating size = 20 cm (2500 slits)
- gravity
-1
X
counts (a.u.)
]a
M o i r é deflectometer
counts (a.u.)
Out beam is not monochromatic
(T varies quite a lot)
fringe shift of the shadow image
v
T = time of flight = [tSTARK - tDET]
(L~ 1 m, v ~ 500 m/s ➠T ~ 2 ms)
Binning antihydrogens with mean velocity of 600-550-500-450400-350-300-250-200 m/s,
and plotting δ as a function of
➠
counts (a.u.)
➠
δ (a.u.)
m/s
T2
g comes from the fit
ms2
time of flight T (s)
Varenna - July 2009