Higher Fock States Research Articles

Quantum emulation of the transient dynamics in the multistate Landau-Zener model

Quantum simulation is one of the most promising near term applications of quantum computing. Especially, systems with a large Hilbert space are hard to solve for classical computers and thus ideal targets for a simulation with quantum hardware. In this work, we study experimentally the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. The underlying Hamiltonian is emulated by superconducting quantum circuit, where a tunable transmon qubit is coupled to a bosonic mode ensemble comprising four lumped element microwave resonators. We investigate the model for different initial states: Due to our circuit design, we are not limited to merely exciting the qubit, but can also pump the harmonic modes via a dedicated drive line. Here, the nature of the transient dynamics depends on the average photon number in the excited resonator. The greater effective coupling strength between qubit and higher Fock states results in a quasi-adiabatic transition, where coherent quantum oscillations are suppressed without the introduction of additional loss channels. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.

Production of excited heavy quarkonia in e+e−→γ*/Z0→|(QQ¯)[n]⟩+γ at super Z factory

Within the nonrelativistic quantum chromodynamics framework, we make a comprehensive study of the exclusive production of excited charmonium and bottomonium in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\gamma}}^{*}/{Z}^{0}\ensuremath{\rightarrow}|(Q\overline{Q})[n]⟩+\ensuremath{\gamma}$ ($Q=c$ or $b$ quarks) at a future $Z$ factory, where the [$n$] represents the color-singlet $n{^{1}S}_{0}$, $n{^{3}S}_{1}$, $n{^{1}P}_{0}$, and $n{^{3}P}_{J}$ ($n=1$, 2, 3, 4; $J=0$, 1, 2) Fock states. The ``improved trace technology'' is adopted to derive the analytic expressions at the amplitude level, which is useful for calculating the complicated $nP$-wave channels. Total cross sections, differential distributions, and uncertainties are discussed in system. According to our study, production rates of heavy quarkonia of high excited Fock states are considerable at a future $Z$ factory. The cross sections of charmonium for $2S$-, $3S$-, $4S$-, $1P$-, $2P$-, $3P$-, and $4P$-wave states are about 53.5%, 30.4%, 23.7%, 13.7%, 6.8%, 9.2%, and 9.2% of that of the $1S$ state, respectively. And cross sections of bottomonium for $2S$-, $3S$-, $4S$-, $1P$-, $2P$-, $3P$-, and $4P$-wave states are about 39.3%, 12.3%, 14.3%, 7.1%, 3.1%, 2.7%, and 3.1% of that of the $1S$ state, respectively. The main uncertainties come from the radial wave functions at the origin and their derivatives at the origin under different potential models. Then, this super $Z$ factory should be a good platform to study the properties of the high excited charmonium and bottomonium states.

Sequential phonon measurements of atomic motion

The motion of trapped atoms plays an essential role in quantum mechanical sensing, simulations and computing. Small disturbances of atomic vibrations are still challenging to be sensitively detected. It requires a reliable coupling between individual phonons and internal electronic levels that light can readout. As available information in a few electronic levels about the phonons is limited, the coupling needs to be sequentially repeated to further harvest the remaining information. We analyze such phonon measurements on the simplest example of the force and heating sensing using motional Fock states. We prove that two sequential measurements are sufficient to reach sensitivity to force and heating for realistic Fock states and saturate the quantum Fisher information for a small amount of force or heating. It is achieved by the conventionally available Jaynes–Cummings coupling. The achieved sensitivities are found to be better than those obtained from classical states. Further enhancements are expectable when the higher Fock state generation is improved. The result opens additional applications of sequential phonon measurements of atomic motion. This measurement scheme can also be directly applied to other bosonic systems including cavity QED and circuit QED.

Light-cone distribution amplitudes of the nucleon and \u2206 baryon

We investigate the light-cone wave functions and leading-twist distribution amplitudes for the nucleon and ∆ baryon within the framework of the chiral quark-soliton model. The baryon wave function consists of the valence quark and vacuum wave functions. The vacuum wave functions generate all possible higher Fock states by expanding them. We find that it is essential to consider the five-quark component and relativistic corrections to evaluate the distribution amplitudes of the nucleon and ∆ isobar. Having taken into account them, we derive the distribution amplitudes. The results are in good agreement with the lattice data.

Experimental Fock-state bunching capability of non-ideal single-photon states

Advanced quantum technologies, as well as fundamental tests of quantum physics, crucially require the interference of multiple single photons in linear-optics circuits. This interference can result in the bunching of photons into higher Fock states, leading to a complex bosonic behavior. These challenging tasks timely require to develop collective criteria to benchmark many independent initial resources. Here we determine whether n independent imperfect single photons can ultimately bunch into the Fock state | n ⟩ . We thereby introduce an experimental Fock-state bunching capability for single-photon sources, which uses phase-space interference for extreme bunching events as a quantifier. In contrast to autocorrelation functions, this operational approach takes into account not only residual multi-photon components but also a vacuum admixture and the dispersion of individual photon statistics. We apply this approach to high-purity single photons generated from an optical parametric oscillator and show that they can lead to a Fock-state capability of at least 14. Our work demonstrates a novel collective benchmark for single-photon sources and their use in subsequent stringent applications.

Double parton correlations in mesons within AdS/QCD soft-wall models: a first comparison with lattice data

Double parton distribution functions (dPDFs), entering the double parton scattering (DPS) cross section, are unknown fundamental quantities encoding new interesting properties of hadrons. Here, the pion dPDFs are investigated within different holographic QCD quark models in order to access their basic features. Results of the calculations obtained within the AdS/QCD soft-wall approach, have been compared with predictions of lattice QCD evaluations of the pion two-current correlation functions. The present analysis confirms that double parton correlations, affecting dPDFs, are very important and not direct accessible from generalised parton distribution functions and electromagnetic form factors. The comparison between lattice data and quark model calculations unveils the relevance of the contributions of high partonic Fock states in the pion. Nevertheless, by using a complete general procedure, results of lattice QCD have been used, for the first time, to estimate the mean value of the so called sigma _{eff}, a relevant experimental observable for DPS processes. In addition, the results of the first calculations of the rho meson dPDFs are discussed in order to make predictions.

Excited heavy quarkonium production in Higgs boson decays

The rare decay channels of Higgs boson to heavy quarkonium offer vital opportunities to explore the coupling of Higgs to heavy quarks. We study the semi-exclusive decay channels of Higgs boson to heavy quarkonia, i.e., $H^0\to |(Q\bar{Q^{\prime}})[n]\rangle+\bar{Q}Q^{\prime}$ ($Q^{(\prime)}=c~\text{or}~b$ quark) within the NRQCD framework. In addition to the lower-level Fock states $|(Q\bar{Q'})[1S]\rangle$ continent, contributions of high excited states $|(Q\bar{Q'})[2S]\rangle$, $|(Q\bar{Q'})[3S]\rangle$, $|(Q\bar{Q'})[4S]\rangle$, $|(Q\bar{Q'})[1P]\rangle$, $|(Q\bar{Q'})[2P]\rangle$, $|(Q\bar{Q'})[3P]\rangle$ and $|(Q\bar{Q'})[4P]\rangle$ are also studied. According to our study, the contributions of high excited Fock states should be considered seriously. Differential distributions of total decay width with respect to invariant-mass and angles, as well as uncertainties caused by non-perturbative hadronic non-perturbative matrix elements are discussed. If all excited heavy quarkonium states decay to the ground spin-singlet state through electromagnetic or hadronic interactions, we obtain the decay widths for $|(Q\bar{Q'})\rangle$ quarkonium production through $H^0$ semi-exclusive decays: $25.10^{+11.6\%}_{-51.6\%}$ keV for $|(b\bar{c})[n]\rangle$ meson, $3.23^{+0\%}_{-62.2\%}$ keV for $|(c\bar{c})[n]\rangle$ and $2.36^{+0\%}_{-57.1\%}$ keV for $|(b\bar{b})[n]\rangle$, where uncertainties are caused by adopting different non-perturbative potential models. At future high energy LHC ($\sqrt{s}=27$ TeV), numerical results show that sizable amounts of events for those high excited states can be produced, which implies that one could also consider exploring the coupling properties of Higgs to heavy quarks in these high excited states channels, especially for the charmonium and bottomonium.

Magnon heralding in cavity optomagnonics

In the emerging field of cavity optomagnonics, photons are coupled coherently to magnons in solid-state systems. These new systems are promising for implementing hybrid quantum technologies. Being able to prepare Fock states in such platforms is an essential step towards the implementation of quantum information schemes. We propose a magnon-heralding protocol to generate a magnon Fock state by detecting an optical cavity photon. Due to the peculiarities of the optomagnonic coupling, the protocol involves two distinct cavity photon modes. Solving the quantum Langevin equations of the coupled system, we show that the temporal scale of the heralding is governed by the magnon-photon cooperativity and derive the requirements for generating high fidelity magnon Fock states. We show that the nonclassical character of the heralded state, which is imprinted in the autocorrelation of an optical "read" mode, is only limited by the magnon lifetime for small enough temperatures. We address the detrimental effects of nonvacuum initial states, showing that high fidelity Fock states can be achieved by actively cooling the system prior to the protocol.

Relativistic Studies of Few-Body Systems Using the Bethe–Salpeter Approach

The Bethe–Salpeter equation is one of the most appropriate tools in quantum field theory for the treatment of bound state systems. We review two problems in this approach: (i) the influence of the cross-ladder (non-planar) interaction kernel with color degrees of freedom in two-boson systems; and (ii) the higher Fock-state contributions to the three-boson bound state. Some new calculations have been performed to illustrate the previous topics.

Determination of electric dipole transitions in heavy quarkonia using potential non-relativistic QCD

The electric dipole transitions with J = 0, 1, 2 and are computed using the weak-coupling version of a low-energy effective field theory named potential non-relativistic QCD (pNRQCD). In order to improve convergence and thus give firm predictions for the studied reactions, the full static potential is incorporated into the leading order Hamiltonian; moreover, we must handle properly renormalon effects and re-summation of large logarithms. The precision we reach is , where kγ is the photon energy, m is the mass of the heavy quark and v its velocity. Our analysis separates those relativistic contributions that account for the electromagnetic interaction terms in the pNRQCD Lagrangian which are v2 suppressed and those that account for wave function corrections of relative order v2. Among the last ones, corrections from 1/m and 1/m2 potentials are computed, but not those coming from higher Fock states since they demand non-perturbative input and are or suppressed, at least, in the strict weak coupling regime. These proceedings are based on the forthcoming publication [1].

Quantum non-Gaussian multiphoton light

We propose an experimental method of recognizing quantum non-Gaussian multiphoton states. This is a native quantum property of Fock states, the fundamental quantum states with a constant number of particles. Our method allows experimental development and characterization of higher Fock states of light, reaching even beyond the current technical limits of their generation. We experimentally demonstrate that it is capable of distinguishing realistic quantum non-Gaussian light with the mean number of photons up to five despite detection efficiency of 50%. We also provide evidence that our method can help to distinguish the number of single-photon emitters based only on their collective emission.

Generalized parton distributions: confining potential effects within AdS/QCD

Generalized parton distributions are investigated within a holographic approach where the string modes in the fifth dimension describe the nucleon in a bottom–up or AdS/QCD framework. The aim is to bring the AdS/QCD results in the realm of phenomenology in order to extract consequences and previsions. Two main aspects are studied: (i) the role of the confining potential needed for breaking conformal invariance and introducing confinement (both: classic soft-wall and recent infra-red potentials are investigated); (ii) the extension of the predicted GPDs to the entire range of off-forward kinematics by means of double distributions. Higher Fock states are included describing the nucleon as a superposition of three valence quarks and quark–antiquark pairs and gluons.

Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region

We present a comprehensive analysis of the spacelike nucleon electromagnetic form factors and their flavor decomposition within the framework of light-front holographic QCD. We show that the inclusion of the higher Fock components $\ket {qqqq\bar{q}}$ has a significant effect on the spin-flip elastic Pauli form factor and almost zero effect on the spin-conserving Dirac form factor. We present light-front holographic QCD results for the proton and neutron form factors at any momentum transfer range, including asymptotic predictions, and show that our results agree with the available experimental data with high accuracy. In order to correctly describe the Pauli form factor we need an admixture of a five quark state of about 30$\%$ in the proton and about 40$\%$ in the neutron. We also extract the nucleon charge and magnetic radii and perform a flavor decomposition of the nucleon electromagnetic form factors. The free parameters needed to describe the experimental nucleon form factors are very few: two parameters for the probabilities of higher Fock states for the spin-flip form factor and a phenomenological parameter $r$, required to account for possible SU(6) spin-flavor symmetry breaking effects in the neutron, whereas the Pauli form factors are normalized to the experimental values of the anomalous magnetic moments. The covariant spin structure for the Dirac and Pauli nucleon form factors prescribed by AdS$_5$ semiclassical gravity incorporates the correct twist scaling behavior from hard scattering and also leads to vector dominance at low energy.

Deterministic synthesis of mechanical NOON states in ultrastrong optomechanics

We propose a protocol for the deterministic preparation of entangled NOON mechanical states. The system is constituted by two identical, optically coupled optomechanical systems. The protocol consists of two steps. In the first, one of the two optical resonators is excited by a resonant external $\ensuremath{\pi}$-like Gaussian optical pulse. When the optical excitation coherently partly transfers to the second cavity, the second step starts. It consists of sending simultaneously two additional $\ensuremath{\pi}$-like Gaussian optical pulses, one at each optical resonator, with specific frequencies. In the optomechanical ultrastrong coupling regime, when the coupling strength becomes a significant fraction of the mechanical frequency, we show that NOON mechanical states with quite high Fock states can be deterministically obtained. The operating range of this protocol is carefully analyzed. Calculations have been carried out taking into account the presence of decoherence, thermal noise, and imperfect cooling.

χ cJ → e + e − decays revisited

We present a calculation of the width for $\chi_{cJ}\rightarrow e^{+}e^{-}$ decay. The amplitude of the process is computed within the NRQCD framework. The leading-order contribution is described by two terms associated with the two different integration domains in the electromagnetic loop describing two-photon annihilation of the heavy quark-antiquark pair. The corresponding operators are defined in the framework of NRQCD. The matrix element of one of these operators describes a configuration with an ultrasoft photon and can be associated with the higher Fock state of the heavy meson. In order to compute this contribution we use the heavy hadron chiral perturbation theory. We obtain that this contribution is numerically dominant. The obtained estimates for the decay widths of the $\chi_{c1}$ and $\chi_{c2}$ states are $0.09$ eV and $0.06$ eV, respectively.

Generalized Parton Distributions for Nucleon in the Impact Parameter Space

We investigate the generalized parton distributions (GPDs) for the proton and neutron in both momentum and position space in the soft-wall approach of anti-de Sitter/QCD model. The soft-wall model is based upon an action which incorporates confinement through the presence of a background dilaton field and the contribution of higher Fock states are holographically incorporated via studying the dynamics of 5D fermion fields of different scaling dimension. Our results are comparable with the other phenomenological models of the nucleon GPDs.

Nucleon Properties in AdS/QCD models with several Fock States

We discuss a holographic soft-wall model that consider several Fock states in nucleon description. In our approach nucleon structure is a superposition of a three-valence quark state with high Fock states including an adjustable number of partons (quarks, antiquarks and gluons). With a minimal number of free parameters (dilaton scale parameter, mixing parameters of partial contributions of Fock states, coupling constants in the effective Lagrangian) we achieve a reasonable agreement with data.

Transverse-momentum-dependent wave functions with Glauber gluons inB→ππ,ρρdecays

We investigate the Glauber-gluon effect on the $B \to \pi \pi$ and $\rho \rho$ decays, which is introduced via a convolution of a universal Glauber phase factor with transverse-momentum-dependent(TMD) meson wave functions in the $k_T$ factorization theorem. For an appropriate parametrization of the Glauber phase, it is observed that a TMD wave function for the pion ($\rho$ meson) with a weak (strong) falloff in parton transverse momentum $k_T$ leads to significant (moderate) modification of the $B^0 \to \pi^0 \pi^0$ ($B^0 \to \rho^0 \rho^0$) branching ratio: the former (latter) is enhanced (reduced) by about a factor of 2 (15\%). This observation is consistent with the dual role of the pion as a massless Nambu-Goldstone boson and as a $q \bar q$ bound state, which requires a tighter spatial distribution of its leading Fock state relative to higher Fock states. The agreement between the theoretical predictions and the data for all the $B \to \pi \pi$ and $\rho^0 \rho^0$ branching ratios is then improved simultaneously, and it is possible to resolve the $B \to \pi \pi$ puzzle.

Nucleon Structure Including High Fock States in AdS/QCD Models

We discuss a holographic soft-wall model that consider several Fock states in nucleon description. In our approach nucleon structure is a superposition of a three-valence quark state with high Fock states including an adjustable number of partons (quarks, antiquarks and gluons). With a minimal number of free parameters (dilaton scale parameter, mixing parameters of partial contributions of Fock states, coupling constants in the effective Lagrangian) we achieve a reasonable agreement with data.

Generalized parton distributions in the soft-wall model of AdS/QCD

We present a numerical analysis of helicity independent nucleon generalized parton distributions (GPDs) using the known formalism based on inclusion of higher Fock states in the soft-wall approach of the anti-de Sitter/QCD model. We calculate the momentum space GPDs by matching the electromagnetic form factors in the AdS model to the sum rules in QCD. We investigate their Mellin moments, transverse impact parameter GPDs, transverse mean square radius, and transverse width. We further extend this work to investigate the charge and anomalous magnetization densities for both unpolarized and transversely polarized nucleons. A comparison of results on density functions with phenomenological parametrization is also presented.