Lowest Order Quantum Research Articles

Once-in-a-lifetime encounter models for neutrino media: From coherent oscillations to flavor equilibration

Collective neutrino oscillations are typically studied using the lowest-order quantum kinetic equation, also known as the mean-field approximation. However, some recent quantum many-body simulations suggest that quantum entanglement among neutrinos may be important and may result in flavor equilibration of the neutrino gas. In this work, we develop new quantum models for neutrino gases in which any pair of neutrinos can interact at most once in their lifetimes. A key parameter of our models is γ=μΔz, where μ is the neutrino coupling strength, which is proportional to the neutrino density, and Δz is the duration over which a pair of neutrinos can interact each time. Our models reduce to the mean-field approach in the limit γ→0 and achieve flavor equilibration in time t≫(γμ)−1. These models demonstrate the emergence of coherent flavor oscillations from the particle perspective and may help elucidate the role of quantum entanglement in collective neutrino oscillations. Published by the American Physical Society 2024

Collective radiative interactions in the discrete truncated Wigner approximation

Interfaces of light and matter serve as a platform for exciting many-body physics and photonic quantum technologies. Due to the recent experimental realization of atomic arrays at sub-wavelength spacings, collective interaction effects such as superradiance have regained substantial interest. Their analytical and numerical treatment is however quite challenging. Here we develop a semiclassical approach to this problem that allows to describe the coherent and dissipative many-body dynamics of interacting spins while taking into account lowest-order quantum fluctuations. For this purpose we extend the discrete truncated Wigner approximation, originally developed for unitarily coupled spins, to include collective, dissipative spin processes by means of truncated correspondence rules. This maps the dynamics of the atomic ensemble onto a set of semiclassical, numerically inexpensive stochastic differential equations. We benchmark our method with exact results for the case of Dicke decay, which shows excellent agreement. For small arrays we compare to exact simulations, again showing good agreement at early times and at moderate to strong driving, and to a second order cumulant expansion. We conclude by studying the radiative properties of a spatially extended three-dimensional, coherently driven gas and compare the coherence of the emitted light to experimental results.

Dielectron production at midrapidity at low transverse momentum in peripheral and semi-peripheral Pb–Pb collisions at {sqrt{s}}_{textrm{NN}} = 5.02 TeV

The first measurement of the e+e− pair production at low lepton pair transverse momentum (pT,ee) and low invariant mass (mee) in non-central Pb–Pb collisions at {sqrt{s}}_{textrm{NN}} = 5.02 TeV at the LHC is presented. The dielectron production is studied with the ALICE detector at midrapidity (|ηe| < 0.8) as a function of invariant mass (0.4 ≤ mee< 2.7 GeV/c2) in the 50–70% and 70–90% centrality classes for pT,ee< 0.1 GeV/c, and as a function of pT,ee in three mee intervals in the most peripheral Pb–Pb collisions. Below a pT,ee of 0.1 GeV/c, a clear excess of e+e− pairs is found compared to the expectations from known hadronic sources and predictions of thermal radiation from the medium. The mee excess spectra are reproduced, within uncertainties, by different predictions of the photon–photon production of dielectrons, where the photons originate from the extremely strong electromagnetic fields generated by the highly Lorentz-contracted Pb nuclei. Lowest-order quantum electrodynamic (QED) calculations, as well as a model that takes into account the impact-parameter dependence of the average transverse momentum of the photons, also provide a good description of the pT,ee spectra. The measured sqrt{leftlangle {p}_{textrm{T},textrm{ee}}^2rightrangle } of the excess pT,ee spectrum in peripheral Pb–Pb collisions is found to be comparable to the values observed previously at RHIC in a similar phase-space region.

Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems

We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation (DTWA) based on Monte-Carlo sampling in a discrete phase space that improves the classical treatment by accounting for lowest-order quantum fluctuations. We provide a rigorous derivation of the DTWA by embedding it in a continuous phase space, thereby introducing a hybrid discrete-continuous truncated Wigner approximation (DCTWA). We derive a set of operator-differential mappings that yield an exact equation of motion (EOM) for the continuous SU(2) Wigner function of spins. The standard DTWA is then recovered by a systematic neglection of specific terms in this exact EOM. The hybrid approach permits us to determine the validity conditions and to gain detailed understanding of the quality of the approximation, paving the way for systematic improvements. Furthermore, we show that the continuous embedding allows for a straightforward extension of the method to open spin systems subject to dephasing, losses and incoherent drive, while preserving the key advantages of the discrete approach, such as a positive definite Wigner distribution of typical initial states. We derive exact stochastic differential equations for processes which cannot be described by the standard DTWA due to the presence of non-classical noise. We illustrate our approach by applying it to the dissipative dynamics of Rydberg excitation of one-dimensional arrays of laser-driven atoms and compare it to exact results for small systems.

Perturbation theory and thermal transport in mass-disordered alloys: Insights from Green's function methods

Lowest-order quantum perturbation theory (Fermi's golden rule) for phonon-disorder scattering has been used to predict thermal conductivities in several semiconducting alloys with surprising success given its underlying hypothesis of weak and dilute disorder. In this paper, we explain how this is possible by focusing on the case of maximally mass-disordered ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Sn}}_{x}$. We use a Chebyshev polynomials Green's function method, which allows a full treatment of disorder on very large systems (tens of millions of atoms) to probe individual phonon linewidths and frequency-resolved thermal transport. We demonstrate that the success of perturbation theory originates from the specific form of mass disorder terms in the phonon Green's function and from the interplay between anharmonic and disorder scattering.

Relativistic coupled-cluster calculation of hyperfine-structure constants of Th3+229 and evaluation of the electromagnetic nuclear moments of Th229

$^{229}$Th is a promising candidate for developing a nuclear optical clock and searching the new physics beyond the standard model. Accurate knowledge of the nuclear properties of $^{229}$Th is very important. In this work, we calculate hyperfine-structure constants for the first four states of $^{229}$Th$^{3+}$ using the relativistic coupled-cluster method based on the Gauss basis set. The no-pair Dirac-Coulomb-Breit Hamiltonian with the lowest-order quantum electrodynamics (QED) correction is the starting point, together with all linear and non-linear terms of single and double excitations are included in coupled-cluster calculation. With the measured value of the hyperfine-structure constants [Phys. Rev. Lett. 106. 223001(2011)], we get the magnetic dipole moment, $\mu=0.359(9)$, and the electric quadrupole moment, $Q=2.95(7)$, of the $^{229}$Th nucleus. Our magnetic dipole moment is perfectly consistent with the recommended values, $\mu=0.360(7)$, from the all-order calculation by Safronova \textit{et. al.}[Phys.Rev.A 88, 060501 (2013)], but our electric quadrupole moment is smaller than their recommended value, $Q=3.11(6)$, about 5\%. Our results show that the non-linear terms of single and double excitations, which were not included in the all-order calculation by Safronova \textit{et. al.}, are very crucial to produce a precise $Q$ value of $^{229}$Th. Additionally, we also present magnetic octupole hyperfine-structure constants and some important non-diagonal hyperfine transition matrix elements, which are required for further extracting the magnetic octupole moment $\Omega$ of $^{229}$Th nucleus.

Causality in Higher Order Process Theories

Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key features of quantum supermaps were captured through a general categorical framework, which led to a framework of higher order process theories (HOPT). The HOPT framework models lower and higher order transformations in a single unified theory, with its mathematical structure shown to coincide with the notion of a closed symmetric monoidal category. Here we provide an equivalent construction of the HOPT framework from four simple axioms of process-theoretic nature. We then use the HOPT framework to establish connections between foundational features such as causality, determinism and signalling, alongside exploring their interaction with the mathematical structure of *-autonomy.

S2 Rydberg spectrum of the boron atom

Benchmark variational calculations of the lowest ten Rydberg $^{2}S$ states of two stable isotopes of the boron atom $(^{10}\mathrm{B} \mathrm{and} ^{11}\mathrm{B})$ are reported. The nonrelativistic wave functions of this five-electron system are expanded in terms of 16 000 all-particle explicitly correlated Gaussians (ECGs). The ECG nonlinear exponential parameters are extensively optimized using a procedure that employs the analytic gradient of the energy with respect to these parameters. A finite nuclear mass value is used in the calculations and the motion of the nucleus is explicitly represented in the nonrelativistic Hamiltonian. The leading relativistic corrections to the energy levels are computed in the framework of the perturbation theory. The lowest-order quantum electrodynamics corrections are also estimated. The results obtained for the energy levels enable determination of interstate transition frequencies with accuracy that approaches the available experimental spectroscopic data.

Accurately simulating nine-dimensional phase space of relativistic particles in strong fields

Next-generation high-power laser systems that can be focused to ultra-high intensities exceeding 1023 W/cm2 are enabling new physics regimes and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In the presence of strong electromagnetic fields, the motion of charged particles and their spin is affected by radiation reaction (either the semi-classical or the quantum limit). Standard (PIC) codes usually use Boris or similar operator-splitting methods to advance the particles in standard phase space. These methods have been shown to require very small time steps in the strong-field regime in order to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a nine-dimensional (9D) particle phase space, i.e., (x,u,s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime (where both the spin and momentum evolution are affected by radiation reaction) are desired. We present a new particle pusher that works in 9D and 6D phase space (i.e., with and without spin) based on analytical rather than leapfrog solutions to the momentum and spin advance from the Lorentz force, together with the semi-classical form of radiation reaction in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. Analytical solutions for the position advance are also obtained, but these are not amenable to the staggering of space and time in standard PIC codes. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step duration for each particle as a function of the lab frame time step. Due to the analytical integration of particle trajectory and spin orbit, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. The time step required in a PIC code for accurately advancing the fields may provide additional constraints. We present single-particle simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 6D or 9D phase space for given laser fields. We have implemented the new pusher into the PIC code Osiris. Example simulations show that the proposed pusher provides improvement for a given time step. A discussion on the numerical efficiency of the proposed pusher is also provided.

Low-lying S2 states of the singly charged carbon ion

In this work, we report benchmark variational calculations of the five lowest doublet $S$-states of the ${\mathrm{C}}^{+}$ ion. The wave functions of this five-electron system are expanded in terms of 16 000 all-particle explicitly correlated Gaussians (ECGs) whose nonlinear variational parameters are subject to extensive optimization. The motion of the finite-mass nucleus is explicitly included in the Hamiltonian, while relativistic corrections to the energy levels are computed in the framework of the perturbation theory. Lowest-order quantum electrodynamics (QED) corrections are also estimated. The results obtained for the energy levels enable the determination of transition frequencies with the accuracy that approaches the available experimental data and may open up avenues for future determination of nuclear charge radii of carbon isotopes.

Conforming the measured lifetimes of the5d2D3/2,5/2states in Cs with theory

We find very good agreement between our theoretically evaluated lifetimes of the $5d \ ^2D_{3/2}$ and $5d \ ^2D_{5/2}$ states of Cs with the experimental values reported in [Phys. Rev. A {\bf 57}, 4204 (1998)], which were earlier evinced to be disagreeing with an earlier rigorous theoretical study [Phys. Rev. A {\bf 69}, 040501(R) (2004)] and with another precise measurement [Opt. Lett. {\bf 21}, 74 (1996)]. In this work, we have carried out calculations of the radiative transition matrix elements using many variants of relativistic many-body methods, mainly in the coupled-cluster theory framework, and analyze propagation of the electron correlation effects to elucidate their roles for accurate evaluations of the matrix elements. We also demonstrate contributions explicitly from the Dirac-Coulomb interactions, frequency independent Breit interaction and lower order quantum electrodynamics (QED) effects. Uncertainties to these matrix elements due to different possible sources of errors are estimated. By combining our calculated radiative matrix elements with the experimental values of the transition wavelengths, we obtain the transition probabilities due to both the allowed and lower order forbidden channels. Adding these quantities together, the lifetimes of the above two states are determined precisely and plausible reasons for the reported inconsistencies between the earlier theoretical calculations and the experimental results have been pointed out.

Relativistic energy-consistent pseudopotentials for superheavy elements 119 and 120 including quantum electrodynamic effects

Relativistic energy-consistent pseudopotentials for the superheavy elements with nuclear charges 119 and 120 replacing 92 electrons of a [Xe]4f(14)5d(10)5f(14) core were adjusted to relativistic multi-configuration Dirac-Coulomb-Breit finite nucleus all-electron reference data including lowest-order quantum electrodynamic effects, i.e., vacuum polarization and electron self-energy. The parameters were fitted by two-component multi-configuration Hartree-Fock calculations in the intermediate coupling scheme to the total valence energies of 131 to 140 relativistic states arising from 31 to 33 nonrelativistic configurations covering also anionic and highly ionized states, with mean absolute errors for the nonrelativistic configurations below 0.01 eV. Primitive basis sets for one- and two-component calculations with errors below 0.02 and 0.03 eV to the Hartree-Fock limit, respectively, as well as general contractions of these basis sets with double- to quadruple-zeta quality were obtained. Atomic highly correlated test calculations using the Fock-space coupled-cluster method yield for valence excitation energies and ionization potentials mean absolute errors of 26 cm(-1) and 59 cm(-1), respectively. Correlated and uncorrelated molecular test calculations show deficiencies below 0.005 Å for the bond lengths and 3 N m(-1) for the force constants.

Plasma equilibrium in a semiclassical plasma due to non-resonant wave particle interactions

A nonresonant perturbative approach has been utilized to probe the modification of the equilibrium plasma distribution function due to plasma interaction with externally launched high-frequency large-amplitude RF waves in the presence of quantum effects. The quantum distribution function from the complete Wigner equation has been obtained for a high-frequency wave with constant amplitude. For waves with weak spatial or temporal modulation, the equilibrium distribution function has been obtained by solving the Wigner equation as an initial or boundary-value problem and retaining only lowest-order quantum effects. In the dipole approximation, a higher order diffusion has been identified in addition to quantum modified ponderomotive and quasilinear diffusion effects. Additional terms of the Wigner equation give the impression of higher order diffusion effects in the system.

Accurate relativistic energy-consistent pseudopotentials for the superheavy elements 111 to 118 including quantum electrodynamic effects

Energy-consistent two-component semi-local pseudopotentials for the superheavy elements with atomic numbers 111-118 have been adjusted to fully relativistic multi-configuration Dirac-Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian, including perturbative corrections for the frequency-dependent Breit interaction in the Coulomb gauge and lowest-order quantum electrodynamic effects. The pseudopotential core includes 92 electrons corresponding to the configuration [Xe]4f(14)5d(10)5f(14). The parameters for the elements 111-118 were fitted by two-component multi-configuration Hartree-Fock calculations in the intermediate coupling scheme to the total energies of 267 up to 797 J levels arising from 31 up to 62 nonrelativistic configurations, including also anionic and highly ionized states, with mean absolute errors clearly below 0.02 eV for averages corresponding to nonrelativistic configurations. Primitive basis sets for one- and two-component pseudopotential calculations have been optimized for the ground and excited states and exhibit finite basis set errors with respect to the finite-difference Hartree-Fock limit below 0.01 and 0.02 eV, respectively. General contraction schemes have been applied to obtain valence basis sets of polarized valence double- to quadruple-zeta quality. Results of atomic test calculations in the intermediate coupling scheme at the Fock-space coupled-cluster level are in good agreement with those of corresponding fully relativistic all-electron calculations based on the Dirac-Coulomb-Breit Hamiltonian. The results demonstrate besides the well-known need of a relativistic treatment at the Dirac-Coulomb level also the necessity to include higher-order corrections for the superheavy elements.

Bound-state properties of four-body muonic quasiatoms

Total energies and various bound-state properties are determined for the ground states in all six four-body muonic ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ quasiatoms. These quasiatoms contain two nuclei of the hydrogen isotopes ${p}^{+},{d}^{+},{t}^{+}$, one negatively charged muon ${\ensuremath{\mu}}^{\ensuremath{-}}$, and one electron ${e}^{\ensuremath{-}}$. In general, each of the four-body muonic ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ quasiatoms, where $(a,b)=(p,d,t)$, can be considered as the regular one-electron (hydrogen) atom with the complex nucleus ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ that has a finite number of bound states. Furthermore, all properties of such quasinuclei ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ are determined from highly accurate computations performed for the three-body muonic ions ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ with the use of pure Coulomb interaction potentials between particles. It is shown that the bound-state spectra of such quasiatoms are similar to the spectrum of the regular hydrogen atom, but there are a few important differences. Such differences can be used in future experiments to improve the overall accuracy of current evaluations of various properties of hydrogenlike systems, including the lowest-order relativistic and quantum electrodynamics corrections to the total energies.

Gravitational Corrections to Non-Gauge Interactions

We compute the lowest order quantum gravitational corrections to Yukawa and ϕ 4 interactions.

Spin–orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals

Spin–orbit coupling of electrons with the crystal lattice plays a crucial role in materials without inversion symmetry, lifting spin degeneracy of the Bloch states and endowing the resulting nondegenerate bands with complex spin textures and topologically nontrivial wavefunctions. We present a detailed symmetry-based analysis of the spin–orbit coupling and the band degeneracies in noncentrosymmetric metals. We systematically derive the semiclassical equations of motion for fermionic quasiparticles near the Fermi surface, taking into account both the spin–orbit coupling and the Zeeman interaction with an applied magnetic field. Some of the lowest-order quantum corrections to the equations of motions can be expressed in terms of a fictitious “magnetic field” in the momentum space, which is related to the Berry curvature of the band wavefunctions. The band degeneracy points or lines serve as sources of a topologically nontrivial Berry curvature. We discuss the observable effects of the wavefunction topology, focusing, in particular, on the modifications to the Lifshitz–Onsager semiclassical quantization condition and the de Haas-van Alphen effect in noncentrosymmetric metals.

High-Precision Calculations of the Hyperfine Constants for the Low-Lying Excited 2S States of Be+

High-precision Hylleraas-type calculations of the hyperfine constants for the four lowest excited 3 (2)S, 4 (2)S, 5 (2)S, and 6 (2)S states of the (9)Be(+) ion are reported. Small adjustments to the hyperfine constants arising from effects that include the finite nuclear mass, the magnetization density distribution over the nucleus, the Breit-Rosenthal correction for finite nuclear size, and lowest-order relativistic and quantum electrodynamic corrections are considered. The final values obtained for the hyperfine constants for the n (2)S states were: -158.78, -62.43, -30.66, and -17.29 MHz for n = 3, 4, 5, and 6, respectively.

Quantum corrections for Boltzmann equation

We present the lowest order quantum correction to the semiclassical Boltzmann distribution function, and the equation satisfied by this correction is given. Our equation for the quantum correction is obtained from the conventional quantum Boltzmann equation by explicitly expressing the Planck constant in the gradient approximation, and the quantum Wigner distribution function is expanded in powers of Planck constant, too. The negative quantum correlation in the Wigner distribution function which is just the quantum correction terms is naturally singled out, thus obviating the need for the Husimi’s coarse grain averaging that is usually done to remove the negative quantum part of the Wigner distribution function. We also discuss the classical limit of quantum thermodynamic entropy in the above framework.

Spatial dynamics and spin squeezing in Bose-Einstein condensates

We develop a cumulant based formalism to deterministically calculate the lowest order quantum fluctuations of a two-component Bose-Einstein condensate. We use this to study spin squeezing induced by the atom-atom interaction nonlinearity. Our formalism naturally accounts for the multimode spatial description of the condensate, extending previous spin squeezing work which assumed a single spatial mode. We study spin squeezing in both the miscible and immiscible (phase separating) regimes for the scattering lengths. In the miscible regime, we find the squeezing parameter deviates very little from the single spatial mode approach, while in the phase separating regime, we find the squeezing is slightly reduced, though significant squeezing still occurs.