Three-body Correlations Research Articles

Analysis of Local Structure of Mechanical and Thermal Rearrangements in Glasses with the Atomic Cluster Expansion.

We explore the structural signatures of excitations in amorphous materials with the atomic cluster expansion (ACE), a universal and complete linear basis of descriptors of the atomic environment. Body-orderd linear classifiers are constructed that distinguish between active and inactive particles in three different model glass formers, in which structural relaxation occurs either through spontaneous thermal activation or by simple shear. We find that in binary mixtures, maximum prediction accuracy is already achieved with very few two-body correlations, while a polymer glass requires both two- and three-body correlations. Trends are robust across both activation mechanisms.

Engineering impurity Bell states through coupling with a quantum bath

We theoretically demonstrate the feasibility of creating Bell states in multicomponent ultracold atomic gases by solely using the ability to control the interparticle interactions via Feshbach resonances. For this we consider two distinguishable impurities immersed in an atomic background cloud of a few bosons, with the entire system being confined in a one-dimensional harmonic trap. By analyzing the numerically obtained ground states we demonstrate that the two impurities can form spatially entangled bipolaron states due to mediated interactions from the bosonic bath. Our analysis is based on calculating the correlations between the two impurities in a two-mode basis, which is experimentally accessible by measuring the particle positions in the left or right sides of the trap. While interspecies interactions are crucial in order to create the strongly entangled impurity states, they can also inhibit correlations depending on the ordering of the impurities and three-body impurity-bath correlations. We show how these drawbacks can be mitigated by manipulating the properties of the bath, namely its size, mass, and intraspecies interactions, allowing one to create impurity Bell states over a wide range of impurity-impurity interactions. Published by the American Physical Society 2024

Collective Randomized Measurements in Quantum Information Processing.

The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce collective randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially separated two ensembles.

Precise Spectroscopy of the 3n and 3p Systems via the ^{3}H(t, ^{3}He)3n and ^{3}He(^{3}He, t)3p Reactions at Intermediate Energies.

To search for low-energy resonant structures in isospin T=3/2 three-body systems, we have performed the experiments ^{3}H(t,^{3}He)3n and ^{3}He(^{3}He,t)3p at intermediate energies. For the 3n experiment, we have newly developed a thick Ti-^{3}H target that has the largest tritium thickness among targets of this type ever made. The 3n experiment for the first time covered the momentum-transfer region as low as 15 MeV/c, which provides ideal conditions for producing fragile systems. However, in the excitation-energy spectra we obtained, we did not observe any distinct peak structures. This is in sharp contrast to tetraneutron spectra. The distributions of the 3n and 3p spectra are found to be similar, except for the displacement in energy due to Coulomb repulsion. Comparisons with theoretical calculations suggest that three-body correlations exist in the 3n and 3p systems, although not enough to produce a resonant peak.

Spatial distribution of reduced density of hard spheres near a hard-sphere dimer: Results from three-dimensional Ornstein–Zernike equations coupled with several different closures and from grand canonical Monte Carlo simulation

We calculated the spatial distribution function, which is the one-body reduced density distribution of solvent particles around a nonspherical solute, using the three-dimensional Ornstein–Zernike equations coupled with closures. The solvent was a hard-sphere fluid, and the contact dimer of the solvent particles was the nonspherical solute. Two traditional closures, the Percus–Yevick and hypernetted-chain approximations, and three closures with bridge functions (BFs) were examined. These spatial distribution functions were compared with the results obtained by grand canonical Monte Carlo (GCMC) simulations. Three closures with BFs, such as the modified hypernetted-chain (MHNC) closure using a bridge function proposed by Kinoshita, gave precise spatial distribution functions. These results were much more accurate than those obtained by the traditional closures. The deviations from the spatial distribution function obtained by the GCMC simulation appeared only near the concave surface of the solute dimer. However, the deviations were minor compared with those between the simulation and the predictions of the two traditional closures. By contrast, the three-body correlation functions for the closures with BFs were not more accurate than those obtained by the traditional closures.

Resonance triplet dynamics in the quenched unitary Bose gas

The quenched unitary Bose gas is a paradigmatic example of a strongly interacting out-of-equilibrium quantum system, whose dynamics become difficult to describe theoretically due to the growth of non-Gaussian quantum correlations. We develop a conserving many-body theory capable of capturing these effects, allowing us to model the postquench dynamics in the previously inaccessible time regime where the gas departs from the universal prethermal stage. Our results show that this departure is driven by the growth of strong lossless three-body correlations, rather than atomic losses, thus framing the heating of the gas in this regime as a fully coherent phenomenon. We uncover the specific few-body scattering processes that affect this heating and show that the expected connection between the two-body and three-body contacts and the tail of the momentum distribution is obscured following the prethermal stage, explaining the absence of this connection in experiments. Our general framework, which reframes the dynamics of unitary quantum systems in terms of explicit connections to microscopic physics, can be broadly applied to any quantum system containing strong few-body correlations. Published by the American Physical Society 2024

Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons

We study the impact of induced correlations and quasiparticle properties by immersing two distinguishable impurities in a harmonically trapped bosonic medium. It is found that when the impurities couple both either repulsively or attractively to their host, the latter mediates a two-body correlated behavior between them. In the reverse case, namely the impurities interact oppositely with the host, they feature anti-bunching. Monitoring the impurities relative distance and constructing an effective two-body model to be compared with the full many-body calculations, we are able to associate the induced (anti-) correlated behavior of the impurities with the presence of attractive (repulsive) induced interactions. Furthermore, we capture the formation of a bipolaron and a trimer state in the strongly attractive regime. The trimer refers to the correlated behavior of two impurities and a representative atom of the bosonic medium and it is characterized by an ellipsoidal shape of the three-body correlation function. Our results open the way for controlling polaron induced correlations and creating relevant bound states.

Can a coarse-grained water model capture the key physical features of the hydrophobic effect?

Coarse-grained (CG) molecular dynamics can be a powerful method for probing complex processes. However, most CG force fields use pairwise nonbonded interaction potentials sets, which can limit their ability to capture complex multi-body phenomena such as the hydrophobic effect. As the hydrophobic effect primarily manifests itself due to the nonpolar solute affecting the nearby hydrogen bonding network in water, capturing such effects using a simple one CG site or “bead” water model is a challenge. In this work, we systematically test the ability of CG one site water models for capturing critical features of the solvent environment around a hydrophobe as well as the potential of mean force (PMF) of neopentane association. We study two bottom-up models: a simple pairwise (SP) force-matched water model constructed using the multiscale coarse-graining method and the Bottom-Up Many-Body Projected Water (BUMPer) model, which has implicit three-body correlations. We also test the top-down monatomic (mW) and the Machine Learned mW (ML-mW) water models. The mW models perform well in capturing structural correlations but not the energetics of the PMF. BUMPer outperforms SP in capturing structural correlations and also gives an accurate PMF in contrast to the two mW models. Our study highlights the importance of including three-body interactions in CG water models, either explicitly or implicitly, while in general highlighting the applicability of bottom-up CG water models for studying hydrophobic effects in a quantitative fashion. This assertion comes with a caveat, however, regarding the accuracy of the enthalpy–entropy decomposition of the PMF of hydrophobe association.

Kinetic blockings in long-range interacting inhomogeneous systems.

Long-range interacting systems unavoidably relax through Poisson shot noise fluctuations generated by their finite number of particles, N. When driven by two-body correlations, i.e., 1/N effects, this long-term evolution is described by the inhomogeneous 1/N Balescu-Lenard equation. Yet, in one-dimensional systems with a monotonic frequency profile and only subject to 1:1 resonances, this kinetic equationexactly vanishes: this is a first-order full kinetic blocking. These systems' long-term evolution is then driven by three-body correlations, i.e., 1/N^{2} effects. In the limit of dynamically hot systems, this is described by the inhomogeneous 1/N^{2} Landau equation. We numerically investigate the long-term evolution of systems for which this second kinetic equationalso exactly vanishes: this a second-order bare kinetic blocking. We demonstrate that these systems relax through the "leaking" contributions of dressed three-body interactions that are neglected in the inhomogeneous 1/N^{2} Landau equation. Finally, we argue that these never-vanishing contributions prevent four-body correlations, i.e., 1/N^{3} effects, from ever being the main driver of relaxation.

Transcorrelated selected configuration interaction in a bi-orthonormal basis and with a cheap three-body correlation factor.

In this work, we develop a mathematical framework for a selected configuration interaction (SCI) algorithm within a bi-orthogonal basis for transcorrelated (TC) calculations. The bi-orthogonal basis used here serves as the equivalent of the standard Hartree-Fock (HF) orbitals. However, within the context of TC, it leads to distinct orbitals for the left and right vectors. Our findings indicate that the use of such a bi-orthogonal basis allows for a proper definition of the frozen core approximation. In contrast, the use of HF orbitals results in bad error cancellations for ionization potentials and atomization energies (AE). Compared to HF orbitals, the optimized bi-orthogonal basis significantly reduces the positive part of the second-order energy (PT2), thereby facilitating the use of standard extrapolation techniques of hermitian SCI. While we did not observe a significant improvement in the convergence of the SCI algorithm, this is largely due to the use in this work of a simple three-body correlation factor introduced in a recent study. This correlation factor, which depends only on atomic parameters, eliminates the need for re-optimization of the correlation factor for molecular systems, making its use straightforward and user-friendly. Despite the simplicity of this correlation factor, we were able to achieve accurate results on the AE of a series of 14 molecules on a triple-zeta basis. We also successfully broke a double bond until the full dissociation limit while maintaining the size consistency property. This work thus demonstrates the potential of the BiO-TC-SCI approach in handling complex molecular systems.

Nuclear three-body short-range correlations in coordinate space

Nuclear three-body short-range correlations in coordinate space

Biorthonormal Orbital Optimization with a Cheap Core-Electron-Free Three-Body Correlation Factor for Quantum Monte Carlo and Transcorrelation.

We introduce a novel three-body correlation factor that is designed to vanish in the core region around each nucleus and approach a universal two-body correlation factor for valence electrons. The transcorrelated Hamiltonian is used to optimize the orbitals of a single Slater determinant within a biorthonormal framework. The Slater-Jastrow wave function is optimized on a set of atomic and molecular systems containing both second-row elements and 3d transition metal elements. The optimization of the correlation factor and the orbitals, along with an increase in the basis set, results in a systematic lowering of the variational Monte Carlo energy for all systems tested. Importantly, the optimal parameters of the correlation factor obtained for atomic systems can be transferred to molecules. Additionally, the present correlation factor is computationally efficient and uses a mixed analytical-numerical integration scheme that reduces the costly numerical integration from to .

Nuclear short-range correlations and the zero-energy eigenstates of the Schrödinger equation

We present a systematic analysis of the nuclear two- and three-body short-range correlations and their relations to the zero-energy eigenstates of the Schr\"odinger equation. To this end we analyze the doublet and triplet coupled-cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state. Furthermore, we find that these coupled-cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator. These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear two-body short range correlations, and they might also be helpful for general coupled-cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.

Multi-Neutrino Entanglement and Correlations in Dense Neutrino Systems.

The time evolution of multi-neutrino entanglement and correlations are studied in two-flavor collective neutrino oscillations, relevant for dense neutrino environments, building upon previous works. Specifically, simulations performed of systems with up to 12 neutrinos using Quantinuum's H1-1 20 qubit trapped-ion quantum computer are used to compute n-tangles, and two- and three-body correlations, probing beyond mean-field descriptions. n-tangle rescalings are found to converge for large system sizes, signaling the presence of genuine multi-neutrino entanglement.

Emergent structural correlations in dense liquids.

The complete quantitative description of the structure of dense and supercooled liquids remains a notoriously difficult problem in statistical physics. Most studies to date focus solely on two-body structural correlations, and only a handful of papers have sought to consider additional three-body correlations. Here, we go beyond the state of the art by extracting many-body static structure factors from molecular dynamics simulations and by deriving accurate approximations up to the six-body structure factor via density functional theory. We find that supercooling manifestly increases four-body correlations, akin to the two- and three-body case. However, at small wave numbers, we observe that the four-point structure of a liquid drastically changes upon supercooling, both qualitatively and quantitatively, which is not the case in two-point structural correlations. This indicates that theories of the structure or dynamics of dense liquids should incorporate many-body correlations beyond the two-particle level to fully capture their intricate behavior.

Measuring nonlocal three-body spatial correlations with Rydberg trimers in ultracold quantum gases

We measure nonlocal third-order spatial correlations in nondegenerate ultracold gases of bosonic ($^{84}\mathrm{Sr}$) and spin-polarized fermionic ($^{87}\mathrm{Sr}$) strontium through studies of the formation rates for ultralong-range trimer Rydberg molecules. The trimer production rate is observed to be very sensitive to the effects of quantum statistics with a strong enhancement of up to a factor of 6 (3!), in the case of bosonic $^{84}\mathrm{Sr}$ due to bunching and a marked reduction for spin-polarized fermionic $^{87}\mathrm{Sr}$ due to antibunching. The experimental results are compared to theoretical predictions and good agreement is observed. The present approach opens the way to in situ studies of higher-order nonlocal spatial correlations in a wide array of ultracold atomic-gas systems.

On two-body and three-body spin correlations in leptonic toverline{t}Z production and anomalous couplings at the LHC

We study the anomalous toverline{t}Z couplings in the toverline{t}Z production in leptonic final state at the 13 TeV LHC. We use the polarizations of top quarks and Z boson, two-body and three-body spin correlations among the top quarks and Z boson, and the cross section to probe the anomalous couplings. We estimate one parameter and simultaneous limits on the couplings of the effective vertex as well as the effective operators for a set of luminosities 150 fb−1, 300 fb−1, 1000 fb−1, and 3000 fb−1. The polarizations and the spin correlations are found to be helpful on top of the cross section to better constrain the anomalous couplings.

Competition between pairing and tripling in one-dimensional fermions with coexistent s - and p -wave interactions

We theoretically investigate in-medium two- and three-body correlations in one-dimensional two-component Fermi gases with coexistent even-parity s-wave and odd-parity p-wave interactions. We find the solutions of the stable in-medium three-body cluster states such as Cooper triple by solving the corresponding in-medium variational equations. We further feature the phase diagram consisting of the s- and p-wave Cooper pairing phase, and Cooper tripling phase, in the plane of s- and p-wave pairing strengths. The Cooper tripling phase dominates over the pairing phases when both s- and p-wave interactions are moderately strong.

Method of difference-differential equations for some Bethe-ansatz-solvable models

In studies of one-dimensional Bethe ansatz solvable models, a Fredholm integral equation of the second kind with a difference kernel on a finite interval often appears. This equation does not generally admit a closed-form solution and hence its analysis is quite complicated. Here we study a family of such equations, concentrating on their moments. We find exact relations between the moments in the form of difference-differential equations. The latter results significantly advance the analysis, enabling one to practically determine all the moments from the explicit knowledge of the lowest one. As applications, several examples are considered. First, we study the moments of the quasimomentum distribution in the Lieb-Liniger model and find explicit analytical results. The latter moments determine several basic quantities, e.g., the $N$-body local correlation functions. We prove the equivalence between different expressions found in the literature for the three-body local correlation functions and find an exact result for the four-body local correlation function in terms of the moments of the quasimomentum distributions. We eventually find the analytical results for the three- and four-body correlation functions in the form of asymptotic series in the regimes of weak and strong interactions. Next, we study the exact form of the low-energy spectrum of a magnon (a polaron) excitation in the two-component Bose gas described by the Yang-Gaudin model. We find its explicit form, which depends on the moments of the quasimomentum distributions of the Lieb-Liniger model. Then, we address a seemingly unrelated problem of capacitance of a circular capacitor and express the exact result for the capacitance in the parametric form. In the most interesting case of short plate separations, the parametric form has a single logarithmic term. This should be contrasted with the explicit result that has a complicated structure of logarithms.

How to renormalize coupled cluster theory

Coupled cluster theory is an attractive tool to solve the quantum many-body problem because its singles and doubles (CCSD) approximation is computationally affordable and yields about 90% of the correlation energy. Capturing the remaining 10%, e.g., via including triples, is numerically expensive. Here, we assume that short-range three-body correlations dominate and---following Lepage (arXiv:nucl-th/9706029)---that their effects can be included within CCSD by renormalizing the three-body contact interaction. We renormalize this contact in $^{16}\mathrm{O}$ and obtain systematically improved CCSD results for $^{24}\mathrm{O}, ^{20--34}\mathrm{Ne}, ^{40,48}\mathrm{Ca}, ^{78}\mathrm{Ni}, ^{90}\mathrm{Zr}$, and $^{100}\mathrm{Sn}$.