Three-pion correlations for studying partial
coherence in nuclear collisions
E. Ikonen
Metrology Research Institute, Aalto University
and
Centre for Metrology and Accreditation (MIKES)
Espoo, Finland
Contents
I. SOURCE MODELS FOR PARTICLES AND PHOTONS
Partial coherence in nuclear collisions?
II. PARTICLE CORRELATIONS
Three-particle correlations
Multiple coherent components
III. PHOTON CORRELATIONS IN OPTICS
Coherent (free-electron laser)
Incoherent (chaotic)
IV. CONCLUSIONS
Source current models for particles and photons
Particles:
coherent
chaotic
M. Gyulassy, S. K. Kauffmann, and L. W. Wilson, Phys.
Rev. C 20, 2267 (1979)
=> two-pion correlations of partially coherent source
U. Heinz and Q. H. Zhang, Phys. Rev. C 56, 426 (1997)
=> three-pion correlations of partially coherent source
(heavy ion collisions)
Source current models for particles and photons
Particles:
coherent
M. Gyulassy, S. K. Kauffmann, and L. W. Wilson, Phys.
Rev. C 20, 2267 (1979)
=> two-pion correlations of partially coherent source
chaotic
U. Heinz and Q. H. Zhang, Phys. Rev. C 56, 426 (1997)
=> three-pion correlations of partially coherent source
(heavy ion collisions)
multiple
coherent
components
chaotic
Photons:
R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella,
and C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994)
=> analysis of free-electron laser (FEL)
Source current models for particles and photons
Particles:
coherent
M. Gyulassy, S. K. Kauffmann, and L. W. Wilson, Phys.
Rev. C 20, 2267 (1979)
=> two-pion correlations of partially coherent source
chaotic
U. Heinz and Q. H. Zhang, Phys. Rev. C 56, 426 (1997)
=> three-pion correlations of partially coherent source
(heavy ion collisions)
multiple
coherent
components
chaotic
Photons:
R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella,
and C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994)
=> analysis of free-electron laser (FEL)
number of co-operating electrons in XFEL
insertion device
(collision of bunch of electrons with magnetic
field of an undulator)
E. Ikonen, J. Opt. Soc. Am. B 21, 1403 (2004)
=> analysis of x-ray free-electron laser (XFEL)
Partial coherence in Au+Au collisions?
central
collisions
central
collisions
J. Adams et al., Phys. Rev. Lett. 91,
262301 (2003).
non-central
collisions
non-central
collisions
Partial coherence in Au+Au collisions?
central
collisions
central
collisions
J. Adams et al., Phys. Rev. Lett. 91,
262301 (2003).
non-central
collisions
non-central
collisions
r3/2 < 1 indicates partially coherent source (especially for non-central collisions)
Challenges in extrapolation to zero momentum
Conventional analysis method
U. Heinz and A. Sugarbaker, Phys. Rev. C
70, 054908 (2004)
Challenges in extrapolation to zero momentum
Conventional analysis method
Proposed analysis method
(more realistic source model
could produce larger deviation
at low momentum difference)
U. Heinz and A. Sugarbaker, Phys. Rev. C
70, 054908 (2004)
Contents
I. SOURCE MODELS FOR PARTICLES AND PHOTONS
Partial coherence in nuclear collisions?
II. PARTICLE CORRELATIONS
Three-particle correlations
Multiple coherent components
III. PHOTON CORRELATIONS IN OPTICS
Coherent (free-electron laser)
Incoherent (chaotic)
IV. CONCLUSIONS
Three-particle correlations
Zero-momentum-difference
intercept R2(p, p) is affected by
- long-lived resonances
- particle misidentification
- experimental binning effect
 these effects are cancelled in
the normalized three-particle
correlation function
r3 = R3(p, p, p) / [R2(p, p)]3/2
where R3(p, p, p) is the zeromomentum-difference intercept
of genuine three-particle
correlations
Three-particle correlations
Zero-momentum-difference
intercept R2(p, p) is affected by
- long-lived resonances
- particle misidentification
- experimental binning effect
 these effects are cancelled in
the normalized three-particle
correlation function
r3 = R3(p, p, p) / [R2(p, p)]3/2
where R3(p, p, p) is the zeromomentum-difference intercept
of genuine three-particle
correlations
R3(p, p, p)
H. Bøggild et al., Phys. Lett.
B455, 77 (1999).
fully incoherent
fully coherent
Au+Au collisions
Normalized three-particle
correlator r3/2 eliminates
experimental difficulties in
source coherence studies
central
collisions
non-central
collisions
r3 = R3(p, p, p)/[R2(p, p)]3/2
r3/2 < 1 indicates partially
coherent source (especially
for non-central collisions)
central
collisions
J. Adams et al., Phys. Rev. Lett. 91,
262301 (2003).
non-central
collisions
Contents
I. SOURCE MODELS FOR PARTICLES AND PHOTONS
Partial coherence in nuclear collisions?
II. PARTICLE CORRELATIONS
Three-particle correlations
Multiple coherent components
III. PHOTON CORRELATIONS IN OPTICS
Coherent (free-electron laser)
Incoherent (chaotic)
IV. CONCLUSIONS
Examples of ”macroscopic coherence”
milk drop
bullet through apple
forward
splash
backward splash
From the HCP2009 talk by Axel Drees (Stony Brook University)
Theory: E. Ikonen, PRC 78, 051901 (2008)
multiple coherent components + chaotic component
Theory: E. Ikonen, PRC 78, 051901 (2008)
multiple coherent components + chaotic component
Theory: E. Ikonen, PRC 78, 051901 (2008)
multiple coherent components + chaotic component
Data and models for S+Pb and Au+Au collisions
Relation between r3/2 and
R2(p, p) for different numbers N
of coherent source components
and related experimental data
from S+Pb (Boggild et al) and
Au+Au (Adams et al) collisions.
central
non-central
Data and models for S+Pb and Au+Au collisions
Relation between r3/2 and
R2(p, p) for different numbers N
of coherent source components
and related experimental data
from S+Pb (Boggild et al) and
Au+Au (Adams et al) collisions.
The result with a single
coherent component,
used in the analysis by Adams
et al, is shown by the curve
labeled N = 1.
Tentatively, experimental data
from S+Pb and Au+Au
collisions seem to be in
agreement with the curve
N = 2 (or N = 3).
central
non-central
Contents
I. SOURCE MODELS FOR PARTICLES AND PHOTONS
Partial coherence in nuclear collisions?
II. PARTICLE CORRELATIONS
Three-particle correlations
Multiple coherent components
III. PHOTON CORRELATIONS IN OPTICS
Coherent (free-electron laser)
Incoherent (chaotic)
IV. CONCLUSIONS
Pulsed photon correlations in XFEL
multiple
coherent
components
distance in undulator
Simulation of free-electron laser operation
R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and
C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994).
Simulation of free-electron laser operation
electron
bunch
length
electron cooperation
length
R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, and
C. Pellegrini, Phys. Rev. Lett. 73, 70 (1994).
Experimental FEL results
Collision of bunch of electrons with the
sinusoidal magnetic field of undulator
T. Shintake et al., Nature Photon. 2, 555 (2008)
Experimental FEL results
Collision of bunch of electrons with the
sinusoidal magnetic field of undulator
A single-shot spectrum (blue solid curve)
and averaged spectrum over 100 shots
(red solid curve)
T. Shintake et al., Nature Photon. 2, 555 (2008)
Incoherent (chaotic) photon spectra
Collision of bunch of electrons with the magnetic field of wiggler
P. Catravas et al., Phys. Rev. Lett. 82, 5261 (1999)
Si 1 1photon
1 beam splitter
Incoherent
correlations (x rays)
APD1
from monochromator
Si beam splitter
dy moving
slit
APD2
Si 1 1photon
1 beam splitter
Incoherent
correlations (x rays)
APD1
from monochromator
Si beam splitter
dy moving
APD2
slit
SPring-8, Japan
Si 1 1photon
1 beam splitter
Incoherent
correlations (x rays)
APD1
from monochromator
Si beam splitter
dy moving
APD2
slit
C2/CB - 1
Excess coincidences C2/CB - 1
E. Ikonen et al.,
Phys. Rev. A 74, 013816 (2006)
SPring-8, Japan
Photon and particle correlations
C2/CB - 1
Zero-momentum-difference
intercept R2(p, p)
E. Ikonen et al.,
Phys. Rev. A 74, 013816 (2006)
Photon and particle correlations
C2/CB - 1
Zero-momentum-difference
intercept R2(p, p)
H. Boggild et al., Phys. Lett B
349, 386 (1995)
E. Ikonen et al.,
Phys. Rev. A 74, 013816 (2006)
Photon and particle correlations
HBT 1956
(light from Hg lamp
and star Sirius)
C2/CB - 1
Zero-momentum-difference
intercept R2(p, p)
H. Boggild et al., Phys. Lett B
349, 386 (1995)
E. Ikonen et al.,
Phys. Rev. A 74, 013816 (2006)
Conclusions
• A model of a fully incoherent contribution, combined
with a single coherent component (N = 1), is used in
conventional heavy-ion collision analyses
Conclusions
• A model of a fully incoherent contribution, combined
with a single coherent component (N = 1), is used in
conventional heavy-ion collision analyses
• Another possibility is to have multiple coherent
components (N > 1), combined with fully incoherent
contribution (as used with free-electron lasers)
Conclusions
• A model of a fully incoherent contribution, combined
with a single coherent component (N = 1), is used in
conventional heavy-ion collision analyses
• Another possibility is to have multiple coherent
components (N > 1), combined with fully incoherent
contribution (as used with free-electron lasers)
• Tentatively, experimental data from S+Pb and Au+Au
collisions support the concept of multiple coherent
components
Conclusions
• A model of a fully incoherent contribution, combined
with a single coherent component (N = 1), is used in
conventional heavy-ion collision analyses
• Another possibility is to have multiple coherent
components (N > 1), combined with fully incoherent
contribution (as used with free-electron lasers)
• Tentatively, experimental data from S+Pb and Au+Au
collisions support the concept of multiple coherent
components
• Three-pion correlation data from new experiments
could give more information on the collision process