Measurements Of Correlation Function Research Articles

Measurement of the biphoton second-order correlation function with analog detectors.

An experimental scheme and data processing approaches are proposed for measuring by analog photo detectors the normalized second-order correlation function of the biphoton field generated under spontaneous parametric down-conversion. Obtained results are especially important for quantum SPDC-based technologies in the long-wave spectral ranges, where it is difficult to use the single-photon detector at least in one of the two biphoton channels. The methods of discrimination of analog detection samples are developed to eliminate the negative influence of the detection noises and get quantitatively true values of both the correlation function and the detector quantum efficiency. The methods are demonstrated depending on whether two single-photon avalanche photo detectors are used in both SPDC channels, or at least one single-photon detector is replaced by a photo-multiplier tube which cannot operate in the photon counting mode.

Wave Dark Matter

We review the physics and phenomenology of wave dark matter: a bosonic dark matter candidate lighter than about 30 eV. Such particles have a de Broglie wavelength exceeding the average interparticle separation in a galaxy like the Milky Way and are, thus, well described as a set of classical waves. We outline the particle physics motivations for such particles, including the quantum chromodynamics axion as well as ultralight axion-like particles such as fuzzy dark matter. The wave nature of the dark matter implies a rich phenomenology: ▪ Wave interference gives rise to order unity density fluctuations on de Broglie scale in halos. One manifestation is vortices where the density vanishes and around which the velocity circulates. There is one vortex ring per de Broglie volume on average. ▪ For sufficiently low masses, soliton condensation occurs at centers of halos. The soliton oscillates and undergoes random walks, which is another manifestation of wave interference. The halo and subhalo abundance is expected to be suppressed at small masses, but the precise prediction from numerical wave simulations remains to be determined. ▪ For ultralight ∼10−22 eV dark matter, the wave interference substructures can be probed by tidal streams or gravitational lensing. The signal can be distinguished from that due to subhalos by the dependence on stream orbital radius or image separation. ▪ Axion detection experiments are sensitive to interference substructures for wave dark matter that is moderately light. The stochastic nature of the waves affects the interpretation of experimental constraints and motivates the measurement of correlation functions. Current constraints and open questions, covering detection experiments and cosmological, galactic, and black hole observations, are discussed.

Higher-order spin-hole correlations around a localized charge impurity

Analysis of higher-order correlation functions has become a powerful tool for investigating interacting many-body systems in quantum simulators, such as quantum gas microscopes. Experimental measurements of mixed spin-charge correlation functions in the 2D Hubbard have been used to study equilibrium properties of magnetic polarons and to identify coherent and incoherent regimes of their dynamics. In this paper we consider theoretically an extension of this technique to systems which use a pinning potential to reduce the mobility of a single dopant in the Mott insulating regime of the 2D Hubbard model. We find that localization of the dopant has a dramatic effect on its magnetic dressing. The connected third-order spin correlations are weakened in the case of a mobile hole but strengthened near an immobile hole. In the case of the fifth-order correlation function, we find that its bare value has opposite signs in cases of the mobile and of fully pinned dopant, whereas the connected part is similar for both cases. We study suppression of higher-order correlators by thermal fluctuations and demonstrate that they can be observed up to temperatures comparable to the spin-exchange energy $J$. We discuss implications of our results for understanding the interplay of spin and charge in doped Mott insulators.

Study of used marine oils by the photon correlation spectroscopy method

In this paper, we investigate the possibility of using the method of photon correlation spectroscopy for diagnostics of marine engines based on used engine oil in order to improve efficiency and safety of operation of sea vessels. The study used the dynamic light scattering (DLS) method to measure correlation functions and then to obtain distributions of correlation times, diffusion coefficients and particle sizes. To invert the Laplace transform, a method based on standard deviation minimization and regularization (RILT) was used, modified to find the distribution of correlation times. It has been found that the distributions of the hydrodynamic radii of the particles for fresh and used oils differ significantly. By the nature of the distribution of large particles, it has been found that the level of aggregation or micelle formation of the polymer of the viscosity modifier decreases in waste oils. It is shown that the dynamic light scattering method makes it possible to obtain parameters suitable for analyzing the state of engine oil and for obtaining diagnostic data on the state of the engine for used oil.

Probing magnetic correlations with spin-echo modulated small angle neutron scattering (SEMSANS)

The first measurements of magnetic correlation functions are presented using time-of-flight Spin-echo modulated small angle neutron scattering (SEMSANS) on the Larmor instrument at the ISIS pulsed neutron source. The accessible length scale is beyond that of the conventional SANS. A simplified model is presented to calculate the expected correlation functions for various magnetisation fields applied to the sample. As an example, we present the experimental data of a soft iron sample at various configurations of magnetisation field.

Correcting correlation functions for redshift-dependent interloper contamination

ABSTRACT The construction of catalogues of a particular type of galaxy can be complicated by interlopers contaminating the sample. In spectroscopic galaxy surveys this can be due to the misclassification of an emission line; for example in the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX) low-redshift [O ii] emitters may make up a few per cent of the observed Ly α emitter (LAE) sample. The presence of contaminants affects the measured correlation functions and power spectra. Previous attempts to deal with this using the cross-correlation function have assumed sources at a fixed redshift, or not modelled evolution within the adopted redshift bins. However, in spectroscopic surveys like HETDEX, where the contamination fraction is likely to be redshift dependent, the observed clustering of misclassified sources will appear to evolve strongly due to projection effects, even if their true clustering does not. We present a practical method for accounting for the presence of contaminants with redshift-dependent contamination fractions and projected clustering. We show using mock catalogues that our method, unlike existing approaches, yields unbiased clustering measurements from the upcoming HETDEX survey in scenarios with redshift-dependent contamination fractions within the redshift bins used. We show our method returns autocorrelation functions with systematic biases much smaller than the statistical noise for samples with at least as high as 7 per cent contamination. We also present and test a method for fitting for the redshift-dependent interloper fraction using the LAE–[O ii] galaxy cross-correlation function, which gives less biased results than assuming a single interloper fraction for the whole sample.

Accelerated impurity solver for DMFT and its diagrammatic extensions

We present ComCTQMC, a GPU accelerated quantum impurity solver. It uses the continuous-time quantum Monte Carlo (CTQMC) algorithm wherein the partition function is expanded in terms of the hybridisation function (CT-HYB). ComCTQMC supports both partition and worm-space measurements, and it uses improved estimators and the reduced density matrix to improve observable measurements whenever possible. ComCTQMC efficiently measures all one and two-particle Green's functions, all static observables which commute with the local Hamiltonian, and the occupation of each impurity orbital. ComCTQMC can solve complex-valued impurities with crystal fields that are hybridized to both fermionic and bosonic baths. Most importantly, ComCTQMC utilizes graphical processing units (GPUs), if available, to dramatically accelerate the CTQMC algorithm when the Hilbert space is sufficiently large. We demonstrate acceleration by a factor of over 600 (100) in a simulation of δ-Pu at 600 K with (without) crystal fields. In easier problems, the GPU offers less impressive acceleration or even decelerates the CTQMC. Here we describe the theory, algorithms, and structure used by ComCTQMC in order to achieve this set of features and level of acceleration. Program summaryProgram Title: ComCTQMCCPC Library link to program files:https://doi.org/10.17632/x2gzgm8njh.1Licensing provisions: GPLv3Programming language: C++/CUDANature of problem: In dynamical mean-field theory (DMFT), the computational bottleneck is the repeated solution of a quantum impurity problem [1]. The continuous-time quantum Monte-Carlo (CTQMC) algorithm has emerged as one of the most efficient methods for solving multiorbital impurity problems at moderate-to-high temperatures [2]. However, the low-temperature regime remains inaccessible, particularly for f-shell systems, and the measurement of two-particle correlation functions on an impurity adds a substantial computational burden. The bottleneck of the CTQMC solver is itself the computation of the local trace which includes the multiplication of many moderate-to-large sized matrices. The efficient solution of the impurity, measurement of the two-particle correlation functions, and acceleration of the trace computation are therefore critical.Solution method: ComCTQMC uses the hybridisation expansion of the impurity action to explore partition space [3]. It uses the worm algorithm [4] to explore the union of the partition space with observables spaces, e.g., the two-particle correlation functions. It uses improved estimators to more accurately measure the one- and two-particle Green's functions [5]. Identical impurities are solved across all MPI ranks (for ideal weak scaling) and the trace computations of these impurities are distributed to and accelerated by GPUs (when available). The lazy-trace algorithm [6] is used to further reduce the burden of the local trace calculation.Additional comments including restrictions and unusual features: ComCTQMC solves nearly arbitrary impurities, including those with complex valued and time-dependent interactions. However, there are two restrictions: (1) The retarded part of the interaction is described by a set of bilinears (a paired creation and annihilation operator), and these bilinears must commute with the local Hamiltonian and have real quantum numbers; (2) If a local Green's function vanishes, then the corresponding hybridisation function also vanishes.

Detection of metallicity correlations in 100 nearby galaxies

ABSTRACT In this paper, we analyse the statistics of the 2D gas-phase oxygen abundance distributions of 100 nearby galaxies drawn from the Calar Alto Legacy Integral Field spectroscopy Area survey. After removing the large-scale radial metallicity gradient, we compute the two-point correlation functions of the resulting metallicity fluctuation maps. We detect correlations in the majority of our targets, which we show are significantly in excess of what is expected due to beam-smearing, and are robust against the choice of metallicity diagnostic. We show that the correlation functions are generally well-fit by the predictions of a simple model for stochastic metal injection coupled with diffusion, and from the model we show that, after accounting for the effects of both beam smearing and noise, the galaxies in our sample have characteristic correlation lengths of ∼1 kpc. Correlation lengths increase with both stellar mass and star formation rate, but show no significant variation with Hubble type, barredness, or merging state. We also find no evidence for a theoretically predicted relationship between gas velocity dispersion and correlation length, though this may be due to the small dynamic range in gas velocity dispersion across our sample. Our results suggest that measurements of 2D metallicity correlation functions can be a powerful tool for studying galaxy evolution.

Multi‐Spacecraft Measurement of Anisotropic Spatial Correlation Functions at Kinetic Range in the Magnetosheath Turbulence

AbstractWe investigate spatial correlation functions (SCFs) at kinetic range in the terrestrial magnetosheath because of wide angular distributions of the magnetic field fluctuations and the high Signal‐to‐Noise‐Ratio. We employ four‐point measurements of magnetic fluctuations from the Cluster and MMS concerning a spatiotemporally varying background magnetic field to constitute the two‐dimensional (2‐D) SCFs between ion and electron scales. It is found that two populations exist in the 2‐D SCFs, with the minority elongated along the perpendicular coordinate (S⊥) and the majority of population elongated along the coordinate parallel to average magnetic field (S||). This kind of phenomenon indicates that the distribution of magnetosheath turbulence in the wavenumber space is dominantly transverse to the background magnetic field, simultaneously partly along the field (i.e., k⊥ >> k||). In addition, we find that magnetosheath turbulence is the dominance of shear Alfvénic‐like fluctuations, and is quasi‐monofractal intermittent turbulence at kinetic range for both the Cluster case and the MMS case, indicating that strong spatially anisotropic fluctuations may be universal in the magnetosheath. Our observations pose new challenges to the theoretical modeling of turbulence and dissipation at kinetic range in the collisionless magnetized plasma.

Features of the ionosphere storm on December 21—24, 2016

The purpose of this work is to investigate the response of the F region and topside ionosphere to the moderate geomagnetic storm on December 21, 2016 (Kp max = 6). The subject of the study is the height–time variations in the parameters of the ionospheric plasma over Kharkiv. Experimental data were obtained using vertical sounding and incoherent scatter methods by the ionosonde and incoherent scatter radar. The presented results are based on the correlation analysis of the incoherent scattered signal. The ion and electron temperatures, as well as the ionospheric plasma velocity, were determined from a set of measured correlation functions of the incoherently scattered signal. The electron density was calculated using the following parameters measured for a number of ionospheric heights: power of the incoherent scatter signal, ion and electron temperatures, and the electron density at the ionospheric F2 layer peak, which is calculated from the critical frequency measured by the ionosonde. The moderate geomagnetic storm was accompanied by an ionospheric storm over Kharkiv with sign-variable phases (first positive and second negative). The peak increase in the electron density was 1.8 times and decrease was 3.4 times. The negative phase was accompanied by a slight rise of the F2 layer (by 20–28 km), which could be due to a decrease in the vertical component of the plasma velocity and an increase in the electron temperature by 600–800 K and ion temperature by 100–160 K. Effects of strong negative ionospheric disturbances were registered during the subsequent magnetospheric disturbance of December 22–24, 2016, with a decrease in electron density at the F2 layer peak up to 2.5–4.9 times. The effects of negative disturbances manifested themselves in the variations of temperatures of electrons and ions. In general, the moderate magnetic storm caused significant changes in the electron density in the ionospheric F2 layer peak, which were accompanied by heating of the ionospheric plasma as well as changes in variations of the vertical component of the ionospheric plasma velocity and the height of ionization during the main phase of the magnetic storm.

The PAU Survey: Intrinsic alignments and clustering of narrow-band photometric galaxies

We present the first measurements of the projected clustering and intrinsic alignments (IA) of galaxies observed by the Physics of the Accelerating Universe Survey (PAUS). With photometry in 40 narrow optical passbands (4500 Å–8500 Å), the quality of photometric redshift estimation is σz ∼ 0.01(1 + z) for galaxies in the 19 deg2 Canada-France-Hawaii Telescope Legacy Survey W3 field, allowing us to measure the projected 3D clustering and IA for flux-limited, faint galaxies (i < 22.5) out to z ∼ 0.8. To measure two-point statistics, we developed, and tested with mock photometric redshift samples, ‘cloned’ random galaxy catalogues which can reproduce data selection functions in 3D and account for photometric redshift errors. In our fiducial colour-split analysis, we made robust null detections of IA for blue galaxies and tentative detections of radial alignments for red galaxies (∼1 − 3σ), over scales of 0.1 − 18 h−1 Mpc. The galaxy clustering correlation functions in the PAUS samples are comparable to their counterparts in a spectroscopic population from the Galaxy and Mass Assembly survey, modulo the impact of photometric redshift uncertainty which tends to flatten the blue galaxy correlation function, whilst steepening that of red galaxies. We investigate the sensitivity of our correlation function measurements to choices in the random catalogue creation and the galaxy pair-binning along the line of sight, in preparation for an optimised analysis over the full PAUS area.

Clustering of CODEX clusters

Context. The clustering of galaxy clusters links the spatial nonuniformity of dark matter halos to the growth of the primordial spectrum of perturbations. The amplitude of the clustering signal is widely used to estimate the halo mass of astrophysical objects. The advent of cluster mass calibrations enables using clustering in cosmological studies. Aims. We analyze the autocorrelation function of a large contiguous sample of galaxy clusters, the Constrain Dark Energy with X-ray (CODEX) sample, in which we take particular care of cluster definition. These clusters were X-ray selected using the ROentgen SATellite All-Sky Survey and then identified as galaxy clusters using the code redMaPPer run on the photometry of the Sloan Digital Sky Survey. We develop methods for precisely accounting for the sample selection effects on the clustering and demonstrate their robustness using numerical simulations. Methods. Using the clean CODEX sample, which was obtained by applying a redshift-dependent richness selection, we computed the two-point autocorrelation function of galaxy clusters in the 0.1 < z < 0.3 and 0.3 < z < 0.5 redshift bins. We compared the bias in the measured correlation function with values obtained in numerical simulations using a similar cluster mass range. Results. By fitting a power law, we measured a correlation length r0 = 18.7 ± 1.1 and slope γ = 1.98 ± 0.14 for the correlation function in the full redshift range. By fixing the other cosmological parameters to their nine-year Wilkinson Microwave Anisotropy Probe values, we reproduced the observed shape of the correlation function under the following cosmological conditions: Ωm0 = 0.22−0.03+0.04 and S8 = σ8(Ωm0/0.3)0.5 = 0.85−0.08+0.10 with estimated additional systematic errors of σΩm0 = 0.02 and σS8 = 0.20. We illustrate the complementarity of clustering constraints by combining them with CODEX cosmological constraints based on the X-ray luminosity function, deriving Ωm0 = 0.25 ± 0.01 and σ8 = 0.81−0.02+0.01 with an estimated additional systematic error of σΩm0 = 0.07 and σσ8 = 0.04. The mass calibration and statistical quality of the mass tracers are the dominant source of uncertainty.

Vortices and waves in light dark matter

In a galactic halo like the Milky Way, bosonic dark matter particles lighter than about 100 eV have a de Broglie wavelength larger than the average inter-particle separation and are therefore well described as a set of classical waves. This applies to, for instance, the QCD axion as well as to lighter axion-like particles such as fuzzy dark matter. We show that the interference of waves inside a halo inevitably leads to vortices, locations where chance destructive interference takes the density to zero. The phase of the wavefunction has non-trivial winding around these points. This can be interpreted as a non-zero velocity circulation, so that vortices are sites where the fluid velocity has a non-vanishing curl. Using analytic arguments and numerical simulations, we study the properties of vortices and show they have a number of universal features: (1) In three spatial dimensions, the generic defects take the form of vortex rings. (2) On average there is about one vortex ring per de Broglie volume and (3) generically only single winding (± 1) vortices are found in a realistic halo. (4) The density near a vortex scales as r2 while the velocity goes as 1/r, where r is the distance to vortex. (5) A vortex segment moves at a velocity inversely proportional to its curvature scale so that smaller vortex rings move faster, allowing momentary motion exceeding escape velocity. We discuss observational/experimental signatures from vortices and, more broadly, wave interference. In the ultra-light regime, gravitational lensing by interference substructures leads to flux anomalies of 5–10 % in strongly lensed systems. For QCD axions, vortices lead to a diminished signal in some detection experiments but not in others. We advocate the measurement of correlation functions by axion detection experiments as a way to probe and capitalize on the expected interference substructures.

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.

The Subaru HSC Galaxy Clustering with Photometric Redshift. I. Dark Halo Masses versus Baryonic Properties of Galaxies at 0.3 ≤ z ≤ 1.4

Abstract We present the clustering properties of low-z (z ≤ 1.4) galaxies selected by the Hyper Suprime-Cam Subaru Strategic Program Wide layer over 145 deg2. The wide-field and multiwavelength observation yields 5,064,770 galaxies at 0.3 ≤ z ≤ 1.4 with photometric redshifts and physical properties. This enables the accurate measurement of angular correlation functions, and the subsequent halo occupation distribution (HOD) analysis allows us to identify the connection between baryonic and dark halo properties. The fraction of less-massive satellite galaxies at z ≲ 1 is found to be almost constant at ∼20%, but it gradually decreases beyond . However, the abundance of satellite galaxies at z > 1 is quite small even for less-massive galaxies due to the rarity of massive centrals at high-z. This decreasing trend is connected to the small satellite fraction of Lyman break galaxies at z > 3. The stellar-to-halo mass ratios at 0.3 ≤ z ≤ 1.4 are almost consistent with the predictions obtained using the latest empirical model; however, we identify small excesses from the theoretical model at the massive end. The pivot halo mass is found to be unchanged at at 0.3 ≤ z ≤ 1.4, and we systematically show that is a universal pivot halo mass up to z ∼ 5 that is derived using only the clustering/HOD analyses. Nevertheless, halo masses with peaked instantaneous baryon conversion efficiencies are much smaller than the pivot halo mass regardless of redshift, and the most efficient stellar-mass assembly is thought to be in progress in dark halos.

Charactering the photon statistics properties of a squeezed light with a modified-HBT interferometer

By replacing the two single-photon detectors in HBT experiment with a pair of homodyne detectors, a modified-HBT interferometer was constructed. We introduced the principle and procedure for the measurement of second-order correlation function g(2)(0) of light based on the modified-HBT interferometer. The subtraction of dark noise in the process was discussed in detail for the first time. By recording four permutations of the quadratures with the interferometer and then calculating the correlation, the measurement of second-order correlation function for displaced squeezed light was realized, hence the photon statistics properties were characterized. The behavior of g(2)(0) values was totally interpreted with a viewpoint of two-photon interference, which can provide a good physical image for understanding the photon statistics properties of the squeezed light. This technique based on homodyne detectors may provide another approach for the detection and characterization of nonclassical states in the fields of quantum communication processing and quantum metrology.

Clustering of LRGs in the DECaLS DR8 Footprint: Distance Constraints from Baryon Acoustic Oscillations Using Photometric Redshifts

Abstract A photometric redshift sample of luminous red galaxies (LRGs) obtained from the DECam Legacy Survey (DECaLS) is analyzed to probe cosmic distances by exploiting the wedge approach of the two-point correlation function. Although the cosmological information is highly contaminated by the uncertainties existing in the photometric redshifts from the galaxy map, an angular diameter distance can be probed at the perpendicular configuration in which the measured correlation function is minimally contaminated. An ensemble of wedged correlation functions selected up to a given threshold based on having the least contamination was studied in previous work (Sridhar & Song 2019) using simulations, and the extracted cosmological information was unbiased within this threshold. We apply the same methodology for analyzing the LRG sample from DECaLS, which will provide the optical imaging for targeting two-thirds of the Dark Energy Spectroscopic Instrument footprint and measure the angular diameter distances at z = 0.69 and z = 0.87 to be and with a fractional error of 4.77% and 6.09%, respectively. We obtain a value of H 0 = 66.58 ± 5.31 km s−1 Mpc−1, which supports the H 0 measured by all other baryon acoustic oscillation results and is consistent with the ΛCDM model.

The completed SDSS-IV extended baryon oscillation spectroscopic survey: growth rate of structure measurement from anisotropic clustering analysis in configuration space between redshift 0.6 and 1.1 for the emission-line galaxy sample

ABSTRACT We present the anisotropic clustering of emission-line galaxies (ELGs) from the Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16). Our sample is composed of 173 736 ELGs covering an area of 1170 deg2 over the redshift range 0.6 ≤ z ≤ 1.1. We use the convolution Lagrangian perturbation theory in addition to the Gaussian streaming redshift space distortions to model the Legendre multipoles of the anisotropic correlation function. We show that the eBOSS ELG correlation function measurement is affected by the contribution of a radial integral constraint that needs to be modelled to avoid biased results. To mitigate the effect from unknown angular systematics, we adopt a modified correlation function estimator that cancels out the angular modes from the clustering. At the effective redshift, zeff = 0.85, including statistical and systematical uncertainties, we measure the linear growth rate of structure fσ8(zeff) = 0.35 ± 0.10, the Hubble distance $D_ H(z_{\rm eff})/r_{\rm drag} = 19.1^{+1.9}_{-2.1}$, and the comoving angular diameter distance DM(zeff)/rdrag = 19.9 ± 1.0. These results are in agreement with the Fourier space analysis, leading to consensus values of: fσ8(zeff) = 0.315 ± 0.095, $D_H(z_{\rm eff})/r_{\rm drag} = 19.6^{+2.2}_{-2.1}$, and DM(zeff)/rdrag = 19.5 ± 1.0, consistent with ΛCDM model predictions with Planck parameters.

Entanglement characterization using quantum designs

We present in detail a statistical approach for the reference-frame-independent detection and characterization of multipartite entanglement based on moments of randomly measured correlation functions. We start by discussing how the corresponding moments can be evaluated with designs, linking methods from group and entanglement theory. Then, we illustrate the strengths of the presented framework with a focus on the multipartite scenario. We discuss a condition for characterizing genuine multipartite entanglement for three qubits, and we prove criteria that allow for a discrimination of W-type entanglement for an arbitrary number of qubits.

The completed SDSS-IV extended baryon oscillation spectroscopic survey: pairwise-inverse probability and angular correction for fibre collisions in clustering measurements

ABSTRACT The completed extended Baryon Oscillation Spectroscopic Survey (eBOSS) catalogues contain redshifts of 344 080 quasars at 0.8 < z < 2.2, 174 816 luminous red galaxies between 0.6 < z < 1.0, and 173 736 emission-line galaxies over 0.6 < z < 1.1 in order to constrain the expansion history of the Universe and the growth rate of structure through clustering measurements. Mechanical limitations of the fibre-fed spectrograph on the Sloan telescope prevent two fibres being placed closer than 62 arcsec in a single pass of the instrument. These ‘fibre collisions’ strongly correlate with the intrinsic clustering of targets and can bias measurements of the two-point correlation function resulting in a systematic error on the inferred values of the cosmological parameters. We combine the new techniques of pairwise-inverse probability and the angular upweighting (PIP+ANG) to correct the clustering measurements for the effect of fibre collisions. Using mock catalogues, we show that our corrections provide unbiased measurements, within data precision, of both the projected $\rm {\mathit{ w}_p}\left(\mathit{ r}_p\right)$ and the redshift-space multipole ξ(ℓ = 0, 2, 4)(s) correlation functions down to $0.1\, h^{-1}{\rm Mpc}$, regardless of the tracer type. We apply the corrections to the eBOSS DR16 catalogues. We find that, on scales $s\gtrsim 20\, h^{-1}{\rm Mpc}$ for ξℓ, as used to make baryon acoustic oscillation and large-scale redshift-space distortion measurements, approximate methods such as nearest-neighbour upweighting are sufficiently accurate given the statistical errors of the data. Using the PIP method, for the first time for a spectroscopic program of the Sloan Digital Sky Survey, we are able to successfully access the one-halo term in the clustering measurements down to $\sim 0.1\, h^{-1}{\rm Mpc}$ scales. Our results will therefore allow studies that use the small-scale clustering to strengthen the constraints on both cosmological parameters and the halo occupation distribution models.