Hanbury Brown-Twiss Correlations Research Articles

Entropy per Rapidity in Pb-Pb Central Collisions using Thermal and Artificial Neural Network (ANN) Models at LHC Energies

The entropy per rapidity produced in central Pb-Pb ultra-relativistic nuclear collisions at LHC energies is calculated using experimentally identified particle spectra and source radii estimated from Hanbury Brown-Twiss (HBT) correlations for particles π, k, p, Λ, Ω, and and π, k, p, Λ, and at and TeV, respectively. An artificial neural network (ANN) simulation model is used to estimate the entropy per rapidity at the considered energies. The simulation results are compared with equivalent experimental data, and a good agreement is achieved. A mathematical equation describing the experimental data is obtained. Extrapolation of the transverse momentum spectra at is required to calculate ; thus, we use two different fitting functions, the Tsallis distribution and hadron resonance gas (HRG) model. The success of the ANN model in describing the experimental measurements leads to the prediction of several spectra values for the mentioned particles, which may lead to further predictions in the absence of experiments.

Investigating Effect of Coherent Emission Length on Pion Interferometry in High-Energy Collisions Using a Multiphase Transport Model

We study the two-pion Hanbury Brown–Twiss correlation functions for a partially coherent source constructed with the emission points and momenta of the identical pions generated by a multiphase transport model. A coherent emission length is introduced, the effects of which on the two-pion interferometry results in central Au-Au collisions at sNN=200 GeV, central Pb-Pb collisions at sNN=2.76 TeV, and p-p collisions at s=13 TeV are investigated. It is found that the effect of coherent emission length reduces the two-pion correlation functions in the nucleus–nucleus collisions, leading to an average decrease of chaoticity parameter by approximately 15% in the high transverse momentum range. However, the influence of coherent emission length on the two-pion correlation functions in the p-p collisions is small, while the effect of coherent emission length on the chaoticity parameter is almost independent of the transverse momentum of pion pair in the p-p collisions.

Time- and frequency-domain two-particle correlations of a driven dissipative Bose-Hubbard model

We investigate theoretically the time- and frequency-domain two-particle correlations of a driven-dissipative Bose-Hubbard model at and near a dissipative phase transition (DPT). We compute the Hanbury Brown--Twiss (HBT)-type two-particle temporal correlation function ${g}^{2}(\ensuremath{\tau})$ which, as a function of time delay $\ensuremath{\tau}$, exhibits oscillations with frequencies determined by the imaginary part of the Liouvillian gap. As the gap closes near a transition point, the oscillations at that point die down. For parameters slightly away from the transition point, the HBT correlations show oscillations from superbunching to antibunching regimes. We show that the Fourier transform of HBT correlations into the frequency domain provide information about DPT and Liouvillian dynamics. We numerically solve the many-body Lindblad master equation and calculate the Wigner distribution of the system in the steady state to ascertain the DPT. Below a certain drive strength, the Fourier transform shows a two-peak structure, while above that strength it exhibits either a Lorentzian-like single-peak structure or a structure with two dips. The width of the single-peak structure is minimal at the phase-transition point and the peak of this structure always lies at zero frequency. The positions of the two symmetrical peaks in case of a two-peak structure are given by the imaginary parts of the Liouvillian gap while their half width at half maximum is given by the real part of the gap. The positions and widths of the two dips are also related to low-lying eigenvalues of the Liouvillian operator. We discuss quantum statistical properties of the model in terms of the HBT correlation function and its Fourier transform.

CSHINE for studies of HBT correlation in heavy ion reactions

The compact spectrometer for heavy ion experiment (CSHINE) is under construction for the study of isospin chronology via the Hanbury Brown–Twiss (HBT) particle correlation function and the nuclear equation of state of asymmetrical nuclear matter. The CSHINE consists of silicon strip detector (SSD) telescopes and large-area parallel-plate avalanche counters, which measure the light charged particles and fission fragments, respectively. In phase I, two SSD telescopes were used to observe 30 MeV/u $$^{40}$$ Ar + $$^{197}$$ Au reactions. The results presented here demonstrate that hydrogen and helium were observed with high isotopic resolution, and the HBT correlation functions of light charged particles could be constructed from the obtained data.

Coulomb and strong interactions in the final state of Hanbury-Brown–Twiss correlations for Lévy-type source functions

We present detailed calculations about the expected shape of two-pion Bose-Einstein [or Hanbury-Brown--Twiss (HBT)] correlations in high energy heavy ion collisions that include a realistic treatment of final state Coulomb interaction as well as strong interactions (dominated by $s$-wave scattering). We assume L\'evy type source functions, a generalization that goes beyond the Gaussian approximation. Various recent experimental results found the use of such source types necessary to properly describe the shape of the measured correlation functions. We find that strong interaction effects for like-sign pions are small, but their consideration may become important in future precision measurements, especially if one considers source parameters beyond the Gaussian HBT radii. Precise experimental determination of these source parameters (such as L\'evy stability exponent, correlation strength, etc.) may then benefit from the inclusion of the treatment of strong interaction not just for heavier particles (e.g., protons, $\mathrm{\ensuremath{\Lambda}}\mathrm{s}$) but also in case of two-pion measurements.

Probing the evolution of heavy-ion collisions using direct photon interferometry

We investigate the measurement of Hanbury Brown-Twiss (HBT) photon correlations as an experimental tool to discriminate different sources of photon enhancement, which are proposed to simultaneously reproduce the direct photon yield and the azimuthal anisotropy measured in nuclear collisions at RHIC and the LHC. To showcase this, we consider two different scenarios in which we enhance the yields from standard hydrodynamical simulations. In the first, additional photons are produced from the early pre-equilibrium stage computed from the \textit{bottom-up} thermalization scenario. In the second, the thermal rates are enhanced close to the pseudo-critical temperature $T_c\approx 155\,\text{MeV}$ using a phenomenological ansatz. We compute the correlators for relative momenta $q_o, \,q_s$ and $q_l$ for different transverse pair momenta, $K_\perp$, and find that the longitudinal correlation is the most sensitive to different photon sources. Our results also demonstrate that including anisotropic pre-equilibrium rates enhances non-Gaussianities in the correlators, which can be quantified using the kurtosis of the correlators. Finally, we study the feasibility of measuring a direct photon HBT signal in the upcoming high-luminosity LHC runs. Considering only statistical uncertainties, we find that with the projected $\sim 10^{10}$ heavy ion events a measurement of the HBT correlations for $K_\perp<1\, \text{GeV}$ is statistically significant.

Clustering structure effect on Hanbury-Brown–Twiss correlation in $$^{12}\hbox {C} {+^{197}}\hbox {Au}$$ collisions at 200 GeV

Through $$^{12}\hbox {C} {+^{197}}\hbox {Au}$$ collisions at $$\sqrt{s_{NN}} = 200\,\hbox {GeV}$$ using a multiphase transport (AMPT) model, the azimuthal angle dependences of the Hanbury Brown–Twiss (HBT) radii relative to the second- and third-order participant plane from $$\pi $$–$$\pi $$ correlations are discussed. Three initial geometric configurations of $$^{12}\hbox {C}$$, namely three-$$\alpha $$-cluster triangle, three-$$\alpha $$-cluster chain and Woods–Saxon distribution of nucleons, are taken into account, and their effects on the correlations are investigated. The ratio of the third- to the second-order HBT radii $$R_{o(s),3}^2/R_{o(s),2}^2$$ is shown to be a clear probe for three configurations. In addition, this work presents the hadronic rescattering time evolution of the azimuthally dependent HBT radii. From the present study, one can learn that the HBT correlation from identical particles at freeze-out is able to provide the information of different initial configurations as collective flow proposed before.

Hanbury Brown-Twiss Correlations for a Driven Superatom.

Hanbury Brown-Twiss interference and stimulated emission, two fundamental processes in atomic physics, have been studied in a wide range of applications in science and technology. We study interference effects that occur when a weak probe is sent through a gas of two-level atoms that are prepared in a singly excited collective (Dicke or "superatom") state and for atoms prepared in a factorized state. We measure the time-integrated second-order correlation function g^{(2)} of the output field as a function of the delay τ between the input probe field and radiation emitted by the atoms and find that, for the Dicke state, g^{(2)} is twice as large for τ=0 as it is for γ_{e}τ≫1 (γ_{e} is an excited state decay rate), while for the product state, this ratio is equal to 3/2. The results agree with those of a theoretical model in which any effects related to stimulated emission are totally neglected-the coincidence counts measured in our experiment arise from Hanbury Brown-Twiss interference between the input field and the field radiated by the atoms.

Normalized multi-pion Hanbury–Brown–Twiss correlation functions of pion-emitting sources with Bose–Einstein condensation

Recently, the ALICE collaboration analyzed the three- and four-pion Hanbury–Brown–Twiss (HBT) correlations in Pb–Pb collisions at the Large Hadron Collider. The measured suppressions of three- and four-pion correlations may originate from a substantial coherence of the particle-emitting sources. In this work we investigate the normalized three- and four-pion HBT correlation functions for evolving pion gas (EPG) sources with Bose–Einstein condensation. We find that the intercepts of the normalized correlation functions at zero relative momentum are sensitive to source condensation and particle momentum. The normalized correlation functions in low average-momentum regions of three and four pions decrease with decreasing temperature and increasing particle number of the source, indicating a dependence of the normalized correlation functions on source condensation. However, this dependence becomes weak in an intermediate average-momentum region because particles with high momenta are likely emitted from excited states incoherently in the EPG model, even if the source has a considerable condensation fraction. For a wide momentum range, the normalized correlation functions for low source temperatures are enhanced at larger relative momenta because of a rapid increase of two-pion chaoticity parameter with increasing particle momentum. We hope the significant enhancement of the normalized four-pion correlation function at high relative momentum will be identified through future analyses of experimental data.

Generalized Hanbury Brown–Twiss effect and Stokes scintillations in the focal plane of a lens

We explore the recently introduced concept of a generalized Hanbury Brown--Twiss (HBT) effect as applied to the focal plane of a lens that is used to focus a random electromagnetic beam. We find that the strength of the HBT correlation can be increased by the lens. Furthermore, the associated Stokes scintillations of the focused field display a surprisingly complicated spatial behavior. We illustrate, using the sum rules for scintillations and correlations, how focused fields can be tuned for different applications.

Stimulated emission of relic gravitons and their super-Poissonian statistics

The degree of second-order coherence of the relic gravitons produced from the vacuum is super-Poissonian and larger than in the case of a chaotic source characterized by a Bose–Einstein distribution. If the initial state does not minimize the tensor Hamiltonian and has a dispersion smaller than its averaged multiplicity, the overall statistics is by definition sub-Poissonian. Depending on the nature of the sub-Poissonian initial state, the final degree of second-order coherence of the quanta produced by stimulated emission may diminish (possibly even below the characteristic value of a chaotic source) but it always remains larger than one (i.e. super-Poissonian). When the initial statistics is Poissonian (like in the case of a coherent state or for a mixed state weighted by a Poisson distribution) the degree of second-order coherence of the produced gravitons is still super-Poissonian. Even though the quantum origin of the relic gravitons inside the Hubble radius can be effectively disambiguated by looking at the corresponding Hanbury Brown–Twiss correlations, the final distributions caused by different initial states maintain their super-Poissonian character which cannot be altered.

Quantum coherence of relic gravitons and Hanbury Brown-Twiss interferometry

The coherence of the relic gravitons is investigated within a quantum mechanical perspective. After introducing the notion and the properties of the generalized Glauber correlators valid in the tensor case, the degrees of first- and second-order coherence are evaluated both inside and beyond the effective horizon. The inclusive approach (encompassing the polarizations of the gravitons) is contrasted with the exclusive approximation where the total intensity is calculated either from a single polarization or even from a single mode of the field. While the relic gravitons reentering the effective horizon after the end of a quasi-de Sitter stage of expansion are first-order coherent, the Hanbury Brown-Twiss correlations always exhibit a super-Poissonian statistics with different quantitative features that depend on the properties of their initial states and on the average over the tensor polarizations.

Hanbury-Brown–Twiss correlation functions and radii from event-by-event hydrodynamics

Hanbury-Brown--Twiss correlation functions and radii from event-by-event hydrodynamics (HoTCoffeeh) is a new computational tool which determines Hanbury-Brown--Twiss (HBT) charged-pion (${\ensuremath{\pi}}^{+}$) correlation functions and radii for event-by-event hydrodynamics with fluctuating initial conditions in terms of Cooper--Frye integrals, including resonance-decay contributions. In this paper, we review the basic formalism for computing the HBT correlation functions and radii with resonance-decay contributions included and discuss our implementation of this formalism in the form of HoTCoffeeh. This tool may easily be integrated with other numerical packages [see, e.g., [Comput. Phys. Commun. 199, 61 (2016)]] for the purpose of simulating the evolution of heavy-ion collisions and thereby extracting predictions for heavy-ion observables.

Hanbury Brown–Twiss correlations and multi-mode dynamics in quenched, inhomogeneous density spinor Bose–Einstein condensates

We have studied the effects of multiple, competing spatial modes that are excited by a quantum quench of an antiferromagnetic spinor Bose–Einstein condensate. We observed Hanbury Brown–Twiss correlations and associated super-Poissonian noise in the mode populations. The decay of these correlations was consistent with experimentally observed spin domain patterns. Data were compared with a real-space Bogoliubov theory as well as numerical solution of the coupled Gross–Pitaevskii equations that were seeded by quantum noise via the truncated Wigner approximation. The spatial modes that were both observed experimentally and deduced theoretically are intimately connected to the inhomogeneous density profile of the condensate. Unique features were observed not present in a homogeneous system, including unstable modes located near the center of the cloud, where the dynamics were initiated.

Bose enhancement, the Liouville effective action, and the high multiplicity tail in p−A collisions

In the framework of dense-dilute CGC approach we study fluctuations in the multiplicity of produced particles in p-A collisions. We show that the leading effect that drives the fluctuations is the Bose enhancement of gluons in the proton wave function. We explicitly calculate the moment generating function that resums the effects of Bose enhancement. We show that it can be understood in terms of the Liouville effective action for the composite field which is identified with the fluctuating density, or saturation momentum of the proton. The resulting probability distribution turns out to be very close to the gamma-distribution. We also calculate the first correction to this distribution which is due to pairwise Hanbury Brown-Twiss correlations of produced gluons.

Analyses of multi-pion Hanbury Brown–Twiss correlations for the pion-emitting sources with Bose–Einstein condensation

We calculate the three- and four-particle correlations of identical pions in an evolving pion gas (EPG) model with Bose–Einstein condensation. The multi-pion correlation functions in the EPG model are analyzed in different momentum intervals and compared with the experimental data for Pb–Pb collisions at . It is found that the multi-pion correlation functions and cumulant correlation functions are sensitive to the condensation fraction of the EPG sources in the low average transverse-momentum intervals of the three and four pions. The model results of the multi-pion correlations are consistent with the experimental data in a considerable degree, which gives a source condensation fraction between 16% and 47%.

Squeezed relic photons beyond the horizon

Owing to the analogy with the ordinary photons in the visible range of the electromagnetic spectrum, the Glauber theory is generalized to address the quantum coherence of the gauge field fluctuations parametrically amplified during an inflationary stage of expansion. The first and second degrees of quantum coherence of relic photons are then computed beyond the effective horizon defined by the evolution of the susceptibility. In the zero-delay limit the Hanbury Brown-Twiss correlations exhibit a super-Poissonian statistics which is however different from the conventional results of the single-mode approximation customarily employed, in quantum optics, to classify the coherence properties of visible light. While in the case of large-scale curvature perturbations the degrees of quantum coherence coincide with the naive expectation of the single-mode approximation, the net degree of second-order coherence computed for the relic photons diminishes thanks to the effect of the polarizations. We suggest that the Hanbury Brown-twiss correlations are probably the only tool to assess the quantum or classical origin of the large-scale magnetic fluctuations and of the corresponding curvature perturbations.

Effects of hadronic mean-field potentials on Hanbury-Brown–Twiss correlations in relativistic heavy-ion collisions

With the parameters fitted by the particle multiplicity, the energy density at chemical freeze-out, and the charged particle elliptic flow, we have studied the effects of the hadronic mean-field potentials on the Hanbury-Brown and Twiss (HBT) correlation in relativistic heavy-ion collisions based on a multiphase transport model. The hadronic mean-field potentials are found to delay the emission time of the system and lead to large HBT radii extracted from the correlation function. Effects on the energy dependence of ${R}_{o}^{2}\ensuremath{-}{R}_{s}^{2}$ and ${R}_{o}/{R}_{s}$ as well as the eccentricity of the emission source are discussed. The HBT correlations can also be useful in understanding the mean-field potentials of protons, kaons, and antiprotons as well as baryon-antibaryon annihilations.

A classical optical approach to the ‘non-local Pancharatnam-like phases’ in Hanbury-Brown–Twiss correlations

We examine a recent proposal to show the presence of nonlocal Pancharatnam type geometric phases in a quantum mechanical treatment of intensity interferometry measurements upon inclusion of polarizing elements in the setup. It is shown that a completely classical statistical treatment of such effects is adequate for practical purposes. Further we show that the phase angles that appear in the correlations, while at first sight appearing to resemble Pancharatnam phases in their mathematical structure, cannot actually be interpreted in that manner. We also describe a simpler Mach–Zehnder type setup where similar effects can be observed without use of the paraxial approximation.

Hanbury–Brown–Twiss measurements at large rapidity separations, or can we measure the proton radius in p-A collisions?

We point out that current calculations of inclusive two-particle correlations in p-A collisions based on the Color Glass Condensate approach exhibit a contribution from Hanbury–Brown–Twiss correlations. These HBT correlations are quite distinct from the standard ones, in that they are apparent for particles widely separated in rapidity. The transverse size of the emitter which is reflected in these correlations is the gluonic size of the proton. This raises an interesting possibility of measuring the proton size directly by the HBT effect of particle pairs produced in p-A collisions.