Twiss Interferometry Research Articles

Ultrafast partial measurement of fourth-order coherence by HBT interferometry of upconversion-based autocorrelation

We introduce, analyze, and experimentally demonstrate a compact semiconductor-based scheme for a femtosecond-scale partial fourth-order coherence g((4)) measurements. The scheme is based on a start-stop photon-counting Hanbury Brown and Twiss (HBT) interferometry of an upconversion-based Michelson-interferometer autocorrelation. The experimental realization employs second-harmonic generation in a semiconductor quantum-well structure, which may be further integrated with the HBT setup as a miniature photonic circuit, allowing compact characterization devices for photon-pair statistics in quantum photonics and quantum information processing.

Interferometry Signatures for QCD First-Order Phase Transition in High Energy Heavy Ion Collisions

Using the technique of quantum transport of the interfering pair we examine the Hanbury–Brown–Twiss (HBT) interferometry signatures for the particle-emitting sources of pions and kaons produced in heavy ion collisions at 10–30 AGeV. The evolution of the sources is described by relativistic hydrodynamics with the first-order phase transition from quark-gluon plasma (QGP) to hadronic matter. We use quantum probability amplitudes in a path-integral formalism to calculate the two-particle correlation functions, where the effects of particle decay and multiple scattering are taken into consideration. Our model-calculated results indicate that both the HBT radii of pions and kaons increase with the system initial energy density. The HBT lifetimes of the pion and kaon sources increase significantly when the initial energy density is tuned to the phase boundary between the QGP and mixed phase. This increase of HBT lifetimes will likely appear in heavy ion collisions with an incident energy between 10–30 AGeV.

Understanding the optical potential in Hanbury-Brown–Twiss interferometry

The validity of using a pion optical potential to incorporate the effects of final state interactions on Hanbury-Brown--Twiss interferometry is investigated. We find that, if the optical potential is real, the standard formalism is modified as previously described in the literature. However, if the optical potential is complex, a new term involving pion emission from eliminated states must be included. The size of such effects in previous work by Cramer and Miller is assessed.

Hanbury-Brown–Twiss interferometry with quantum transport of the interfering pair

In the late stage of the evolution of a pion system in high-energy heavy-ion collisions when pions undergo multiple scatterings, the quantum transport of the interfering pair of identical pions plays an important role in determining the characteristics of the Hanbury-Brown-Twiss (HBT) interference. We study the quantum transport of the interfering pair using the path-integral method, in which the evolution of the bulk matter is described by relativistic hydrodynamics while the paths of the two interfering pions by test particles following the fluid positions and velocity fields. We investigate in addition the effects of secondary pion sources from particle decays, for nuclear collisions at AGS and RHIC energies. We find that quantum transport of the interfering pair leads to HBT radii close to those for the chemical freeze-out configuration. Particle decays however lead to HBT radii greater than those for the chemical freeze-out configuration. As a consequence, the combined effects give rise to HBT radii between those extracted from the chemical freeze-out configuration and the thermal freeze-out configuration. Proper quantum treatments of the interfering pairs in HBT calculations at the pion multiple scattering stage are important for our understanding of the characteristics of HBT interferometry in heavy-ion collisions.

SINGLE-EVENT HANBURY-BROWN–TWISS INTERFEROMETRY

Large spatial density fluctuations in high energy heavy-ion collisions can come from many sources: initial transverse density fluctuations, non-central collisions, phase transitions, surface tension, and fragmentations. The common presence of some of these sources in high energy heavy-ion collisions suggests that large scale density fluctuations may often occur. The detection of large density fluctuations by single-event Hanbury-Brown–Twiss interferometry in heavy-ion collisions will provide useful information on density fluctuations and the dynamics of heavy-ion collisions.

Chaoticity parameter λ in Hanbury-Brown–Twiss interferometry

In Hanbury-Brown--Twiss interferometry measurements using identical bosons, the chaoticity parameter \ensuremath{\lambda} has been introduced phenomenologically to represent the momentum correlation function at zero relative momentum. It is useful to study an exactly solvable problem in which the \ensuremath{\lambda} parameter and its dependence on the coherence properties of the boson system can be worked out in great detail. We are therefore motivated to study the state of a gas of noninteracting identical bosons at various temperatures held together in a harmonic oscillator potential that arises either externally or from bosons' own mean fields. We determine the degree of Bose-Einstein condensation and its momentum correlation function as a function of the attributes of the boson environment. The parameter \ensuremath{\lambda} can then be evaluated from the momentum correlation function. We find that the $\ensuremath{\lambda}(p,T)$ parameter is a sensitive function of both the average pair momentum $p$ and the temperature $T$, and the occurrence of $\ensuremath{\lambda}=1$ is not a consistent measure of the absence of a coherent condensate fraction. In particular, for large values of $p$, the \ensuremath{\lambda} parameter attains the value of unity even for significantly coherent systems with large condensate fractions. We find that if a pion system maintains a static equilibrium within its mean field, and if it contains a root-mean-squared radius, a pion number, and a temperature typical of those in high-energy heavy-ion collisions, then it will contain a large fraction of the Bose-Einstein pion condensate.

PION ELLIPTIC FLOW AND HBT INTERFEROMETRY IN A GRANULAR QUARK-GLUON PLASMA DROPLET MODEL

We use a model of quark-gluon plasma granular droplets that evolve hydrodynamically to investigate pion elliptic flow and Hanbury–Brown–Twiss interferometry. We find that the data of pion transverse momentum spectra, elliptic flows, and HBT radii in [Formula: see text] Au + Au collisions at RHIC can be described well by an expanding source of granular droplets with an anisotropic velocity distribution.

Analysis of pion elliptic flow and Hanbury-Brown–Twiss interferometry in a granular quark-gluon plasma droplet model

In many simulations of high-energy heavy-ion collisions on an event-by-event analysis, it is known that the initial energy density distribution in the transverse plane is highly fluctuating. Subsequent longitudinal expansion will lead to many longitudinal tubes of quark-gluon plasma which have tendencies to break up into many spherical droplets because of sausage instabilities. We are therefore motivated to use a model of quark-gluon plasma granular droplets that evolve hydrodynamically to investigate pion elliptic flows and Hanbury-Brown-Twiss interferometry. We find that the data of pion transverse momentum spectra, elliptic flows, and HBT radii in \sqrt{s_{NN}}=200 GeV Au + Au collisions at RHIC can be described well by an expanding source of granular droplets with an anisotropic velocity distribution.

Hanbury Brown–Twiss interferometry for fractional and integer Mott phases

The theoretical framework of Hanbury Brown–Twiss interferometry (HBTI) is used to study integer and fractionally filled Mott insulator (MI) phases in period-2 optical superlattices. In contrast to the quasimomentum distribution, this second order interferometry pattern exhibits high contrast fringes in the insulating phases. Our detailed study of HBTI suggests that this interference pattern signals the various superfluid–insulator transitions and therefore can be used as a practical method to determine the phase diagram of the system. We find that in the presence of a confining potential the insulating phases become robust as they exist for a finite range of atom numbers. Furthermore, we show that in the trapped case, the HBTI interferogram signals the formation of the MI domains and probes the shell structure of the system.

HANBURY-BROWN–TWISS INTERFEROMETRY WITH IDENTICAL BOSONS IN RELATIVISTIC HEAVY ION COLLISIONS: COMPARISONS WITH HADRONIC SCATTERING MODELS

Identical boson Hanbury-Brown–Twiss interferometry as applied to relativistic heavy-ion collisions is reviewed. Emphasis is placed on the use of hadronic scattering models to interpret the physical significance of experimental results. Interferometric studies with center-of-mass energies from <1 GeV/nucleon up to 5500 GeV/nucleon are considered.

Hanbury Brown—Twiss interferometry

Hanbury Brown—Twiss interferometry

HBT: a (mostly) experimental overview**This review is based on a talk presented at Quark Matter 2004, the 17th International Conference on Ultra-Relativistic Nucleus–Nucleus Collisions, held at Oakland, CA, on 11–17 January 2004.

A review of the field of Hanbury Brown–Twiss interferometry in relativistic heavy-ion collisions is presented. The ‘HBT puzzle’ is explored in detail, emphasizing recent theoretical attempts to understand the persisting puzzle. Recent experimental results on azimuthally sensitive HBT and HBT of direct photons are presented, together with some surprises in the comparison of HBT results from p+p and Au+Au collisions at RHIC.

Azimuthally sensitive correlations in nucleus-nucleus collisions

We define a set of model-independent observables which generally characterize the azimuthal dependence of two-particle correlations in nucleus-nucleus collisions. We explain how they can be analyzed, and show to what extent such analyses are model dependent. We discuss specific applications to the anisotropic flow of decaying particles, azimuthally sensitive Hanbury-Brown Twiss interferometry, and correlations between particles at large transverse momentum. A quantitative prediction is made for jet quenching with respect to the reaction plane.

Correlations and fluctuations, a summary of Quark Matter 2002

Results for correlations and fluctuations presented at Quark Matter 2002 are summarized. These results include Hanbury-Brown Twiss interferometry of a wide variety of species, large scale fluctuations and correlations in p t and multiplicity, and charge fluctuations and charge balance functions.

Hanbury Brown–Twiss interferometry of direct photons in heavy ion collisions

We explore the possibility of measurements of Hanbury Brown–Twiss correlations in gg channels in the high multiplicity environment of heavy ion collisions. We consider all possible sources of photon-photon correlations and show that one can separate correlations of photons produced directly in the hot zone and residual correlations of decay photons: the former contribute to the region of small invariant relative momentum qinv&50 MeV, while the latter contribute to larger relative momentum and, negligibly, to the small qinv region. We make predictions of the photon correlation functions at SPS and RHIC energies.

In-medium baryon interactions and hypernuclear structure

We introduce a microscopic and relativistic theory describing free scattering and finite nuclei for the octet baryons in a consistent quantum field theoretical framework based on Dirac–Brueckner theory and nuclear mean field. In a first quantitative approach, yet still heuristic for dealing with the Λ hyperon, the quality of the description of finite (hyper)nuclei based on free meson exchange potentials is competitive with those from purely phenomenological relativistic mean-field calculations. In contrast to the latter our approach has the advantage of having a microscopic link to free interactions and complete control of which classes of diagrams are included. As a complementary way for determining hyperon–hyperon and hyperon–nucleon interactions the use of Hanbury–Brown–Twiss interferometry is discussed.

Measuring the space-time extent of nuclear collisions using interferometry

Hanbury-Brown and Twiss (HBT) interferometry is used to study the space-time evolution of nuclear collisions at CERN energies. Pairs of identified pions, kaons and protons are studied by NA44 for a variety of collisions systems ranging from p-Pb to PbPb. The pion and kaon correlation data from the 1994 and 1995 Pb runs are compared to published data. The systematic increase in radius parameter with system size is continued in the Pb data sample. Model comparision stress the importance of scattering in the evolution of the collision.

Physics of Coulomb corrections in Hanbury-Brown Twiss interferometry in ultrarelativistic heavy ion collisions

We discuss the elementary physics of the final state Coulomb interactions in Hanbury-Brown Twiss interferometry, showing — with explicit comparison to E877 data for π + π − and π ± p — that the Coulomb corrections in the pair correlation function can be well understood in terms of simple classical physics. We connect the classical picture with descriptions in terms of Coulomb wave functions, and investigate the influence of the “central” Coulomb potential on the pair correlation function.

Transverse momentum dependence of Hanbury-Brown-Twiss correlation radii.

The transverse momentum dependence of Hanbury-Brown--Twiss (HBT) interferometry radii for two-body correlation functions provides experimental access to the collective dynamics in heavy-ion collisions. We present an analytical approximation scheme for these HBT radii which combines the recently derived model-independent expressions with an approximate determination of the saddle point of the emission function. The method is illustrated for a longitudinally boost-invariant hydrodynamical model of a heavy-ion collision with freezeout on a sharp hypersurface. The analytical approximation converges rapidly to the width of the numerically computed correlation function and reproduces correctly its exact transverse momentum dependence. However, higher order corrections within our approximation scheme are essential, and the previously published leading order results with simple ${\mathit{m}}_{\mathrm{\ensuremath{\perp}}}$ scaling behavior are quantitatively and qualitatively unreliable. \textcopyright{} 1996 The American Physical Society.

HBT correlators - current formalism vs. Wigner function formulation

We clarify the relationship between the current formalism developed by Gyulassy, Kaufmann and Wilson and the Wigner function formulation suggested by Pratt for the 2-particle correlator in Hanbury-Brown Twiss interferometry. When applied to a hydrodynamical description of the source with a sharp freeze-out hypersurface, our results remove a slight error in the prescription given by Makhlin and Sinyukov which has led to confusion in the literature.