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Roadmap for Achieving a BEC of Positronium
*
Edison Liang, Rice University
Motivation
Positronium (Ps) is the lightest, simplest, weakly interacting,
purely leptonic atom with many unique physical properties.
A Bose

Einstein condensate (BEC) of Ps, if achievable,
represents a new quantum regime of matter with many exotic
fundamental properties and potentially transformative
technological applications, from Doppler free spectroscopy,
tests of QED, to annihilation gamma

ray laser (GRASAR).
Recent advances in laser pair production demonstrate that
the high density of positrons needed to achieve a BEC of Ps
may soon be reachable in the laboratory.
*research supported by DOE DE

SC0001481
.
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Advantages of using laser

created positron beams
1.
Short

pulse (~ps).
2.
High current (≥ 10
21
e+/s)
3. High initial density (≥10
17
e+/cc)
4. Narrow beam size (~100 microns)
5. Moderate energies (MeV’s instead of GeV’s)
6. Energy efficiency (~ few % of laser energy
can be converted into positrons)
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Major Technical Challenges
1. Positron yield ≥ 10
13
per pulse
2. Positron density ≥ 10
18
/cc (=BEC critical density
at cryogenic temperatures)
3. Slow/Cool positrons from MeV’s to ~10eV in
short times (< ns)
4. Trap positrons with density ≥ 10
18
/cc in a
volume ~ mm x 0.1mm x0.1mm.
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Strategies to achieve High Positron Yield
1.
To optimize positron yield for a given laser
pulse energy, we propose to use hotter
incident electrons and thicker targets.
We need to explore the regime with
kT
ehot
> 10 MeV, and thickness ≥ 5 mm.
2. We need to revisit the use of double

sided
irradiation and longer pulses.
3. We need to optimize target shape to allow
more positrons to escape
.
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Strategies for Collimation and Cooling
1. Use axial B (> 10 MG) to collimate the pair jet
(r
gyro
= 2 micron
/B
7
). Such B can be created
using Helmholtz coils driven by long

pulse lasers.
2. Use intense IR lasers to cool hot electrons via
resonant Compton scattering. Since resonant
cross section >> Thomson cross section the
cooling efficiency is enhanced. Preliminary
estimates suggest <100 kJ of
>10
m laser
energy is sufficient to cool a region ~ 0.1mm
across. Such cooling may be achieved in < 1 ns.
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Strategy for Ps and BEC formation
1.
Once the positrons are cooled to ~10 eV they
can be dumped out electrostatically as a slow
beam and injected into a cryogenically cooled
porous silica matrix or aerogel Ps converter.
2. Formation and themalization rate of Ps need
to be modeled carefully to predict the number
and fraction of Ps that will condense into the
p
=0 state, and the rate of global BEC formation
3. Techniques for detecting and measuring the
BEC need to be developed.
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Strategy for making a GRASAR
1.
The stimulated annihilation cross

section of
pPs with only natural broadening is 10

20
cm

2
.
Hence a Ps column density of 10
21
cm

2
is
needed for gL=10 amplification. For a 1

m
wide column we need a total of 10
13
Ps.
2. To limit the loss of spontaneous annihilation,
we will start with a long narrow column of
oPs and flip the oPs into pPs with a 204 GHz
microwave pulse sweeping in only one direction.
3. Detail physics of the GRASAR must be modeled
carefully before experiments.
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References
1. Cassidy, D. & Mills, A. 2007, Phys. Stat. Solidi A 4
3419.
2. Chen, H. et al 2009 PRL 102, 105001.
3. Charlton, M. & Humberston, J. 2001
Positron
Physics
(Cambridge, UK).
4. Cowan, T. et al 1999, Laser Part. Beams 17, 773.
5. Liang, E. & Dermer, C. 1988, Opt. Comm. 65, 419.
6. Liang, E., Wilks, S. & Tabak, M.1998, PRL 81,4887.
7. Liang, E. 2002, AIP Conf. Proc. 611 p.369(AIP, NY)
8. Nakashima, K. & Takabe, H. 2002, Phys. of Plasmas
9, 1505.
9. Surko, C. & Greaves, R. 2004, Phys. of Plasmas 11,
2333.
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