Interactions In Quantum Electrodynamics Research Articles

Strongly Interacting Photons in 2D Waveguide QED.

One-dimensional confinement in waveguide quantum electrodynamics (QED) plays a crucial role to enhance light-matter interactions and to induce a strong quantum nonlinear optical response. In two or higher-dimensional settings, this response is reduced since photons can be emitted within a larger phase space, opening the question whether strong photon-photon interaction can be still achieved. In this study, we positively answer this question for the case of a 2D square array of atoms coupled to the light confined into a two-dimensional waveguide. More specifically, we demonstrate the occurrence of long-lived two-photon repulsive and bound states with genuine 2D features. Furthermore, we observe signatures of these effects also in free-space atomic arrays in the form of weakly subradiant in-band scattering resonances. Our findings provide a paradigmatic signature of the presence of strong photon-photon interactions in 2D waveguide QED.

Anomaly in the electron orbital gyromagnetic factor: QED and radiative interactions

Using standard Quantum Electrodynamics (QED), we have calculated the anomaly in the electron orbital g-factor, which is in reasonable agreement with experimental data. For second-order corrections, the anomaly in the orbital g-factor is of the order α/3π, while for approximations to the same order, the well-known anomaly in the electron spin g-factor where α = 1/137 is the structure constant. Unlike the spin-g anomaly, the orbital-g anomaly is not intrinsic, but depends on the atomic state, and on Z, the atomic mass. Thus, the orbital anomaly is actually (α/3π)D, where D includes the effect of the magnetic field and/or the atomic properties. Hence, we have shown that radiative interactions, which are the sources of the spin-g anomaly, also produce an orbital anomaly. It is physically reasonable to expect that radiative interactions that modify many physical properties of electrons in electromagnetic fields will also modify the orbital magnetic moment of the electron.

Corrections to Hawking radiation from asteroid mass primordial black holes: Formalism of dissipative interactions in quantum electrodynamics

Primordial black holes (PBHs) within the mass range $10^{17} - 10^{22}$ g are a favorable candidate for describing the all of the dark matter content. Towards the lower end of this mass range, the Hawking temperature, $T_{\rm H}$, of these PBHs is $T_{\rm H} \gtrsim 100$ keV, allowing for the creation of electron -- positron pairs; thus making their Hawking radiation a useful constraint for most current and future MeV surveys. This motivates the need for realistic and rigorous accounts of the distribution and dynamics of emitted particles from Hawking radiation in order to properly model detected signals from high energy observations. This is the first in a series of papers to account for the $\mathcal{O}(\alpha)$ correction to the Hawking radiation spectrum. We begin by the usual canonical quantization of the photon and spinor (electron/positron) fields on the Schwarzschild geometry. Then we compute the correction to the rate of emission by standard time dependent perturbation theory from the interaction Hamiltonian. We conclude with the analytic expression for the dissipative correction, i.e. corrections due to the creation and annihilation of electron/positrons in the plasma.

Determination of the dipole polarizability of the alkali-metal negative ions

We present electric dipole polarizabilities ($\alpha_d$) of the alkali-metal negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation theory, random phase approximation and coupled-cluster (CC) theory. Roles of electron correlation effects and relativistic corrections are analyzed using the above many-body methods with size of the ions. We finally quote precise values of $\alpha_d$ of the above negative ions by estimating uncertainties to the CC results, and compare them with other calculations wherever available.

Waveguide quantum electrodynamics with superconducting artificial giant atoms.

Models of light-matter interactions in quantum electrodynamics typically invoke the dipole approximation1,2, in which atoms are treated as point-like objects when compared to the wavelength of the electromagnetic modes with which they interact. However, when the ratio between the size of the atom and the mode wavelength is increased, the dipole approximation no longer holds and the atom is referred to as a 'giant atom'2,3. So far, experimental studies with solid-state devices in the giant-atom regime have been limited to superconducting qubits that couple to short-wavelength surface acoustic waves4-10, probing the properties of the atom at only a single frequency. Here we use an alternative architecture that realizes a giant atom by coupling small atoms to a waveguide at multiple, but well separated, discrete locations. This system enables tunable atom-waveguide couplings with large on-off ratios3 and a coupling spectrum that can be engineered by the design of the device. We also demonstrate decoherence-free interactions between multiple giant atoms that are mediated by the quasi-continuous spectrum of modes in the waveguide-an effect that is not achievable using small atoms11. These features allow qubits in this architecture to switch between protected and emissive configurations in situ while retaining qubit-qubit interactions, opening up possibilities for high-fidelity quantum simulations and non-classical itinerant photon generation12,13.

NNLO QCD⊕QED corrections to Higgs production in bottom quark annihilation

We present next-to-next-to leading order (NNLO) quantum electrodynamics (QED) corrections to the production of the Higgs boson in bottom quark annihilation at the Large Hadron Collider (LHC) in the five flavor scheme. We have systematically included the NNLO corrections resulting from the interference of quantum chromodynamics (QCD) and QED interactions. We have investigated the infrared (IR) structure of the bottom quark form factor up to two loop level in QED and in QCD$\times$QED using K+G equation. We find that the IR poles in the form factor are controlled by the universal cusp, collinear and soft anomalous dimensions. In addition, we derive the QED as well as QCD$\times$QED contributions to soft distribution function as well as to the ultraviolet renormalization constant of the bottom Yukawa coupling up to second order in strong coupling and fine structure constant. Finally, we report our findings on the numerical impact of the NNLO results from QED and QCD$\times$QED at the LHC energies taking into account the dominant NNLO QCD corrections.

High-precision determination of Lorentz-symmetry-violating parameters in Ca+

We present high-precision calculations of local Lorentz invariance (LLI) violating parameters of the $3d{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{3/2;5/2}$ states in ${\mathrm{Ca}}^{+}$. We have employed three variants of the relativistic coupled-cluster (RCC) theory to determine these coefficients by gradually including electron correlation effects through the single, double, and triple excitation determinants from the Dirac-Hartree-Fock wave function. A precise estimate of the energy shift due to LLI violation depends on accurate evaluations of the expectation values of the square of the momentum operator ($\ensuremath{\langle}{p}^{2}\ensuremath{\rangle}$) and a second rank tensor ($\ensuremath{\langle}{T}_{0}^{(2)}\ensuremath{\rangle}$). It is found that the $\ensuremath{\langle}{T}_{0}^{(2)}\ensuremath{\rangle}$ values converge smoothly with the systematic inclusion of higher-order correlation effects in an expectation value evaluation approach, however, that is not the case for $\ensuremath{\langle}{p}^{2}\ensuremath{\rangle}$. Similar trends were also observed in the finite-field approach. To circumvent these problems, we determine $\ensuremath{\langle}{p}^{2}\ensuremath{\rangle}$ values very precisely by developing and applying an analytic gradient approach in the RCC framework. Corrections due to the Breit and quantum electrodynamics interactions are also estimated. Further, these calculations are validated by evaluating the energies and the quadrupole moments of the above states at different levels of approximations.

Local-Field Corrections as a Regularization Method for the Spin-Boson Model

The decoherence rate of a ‘central spin’ in a bosonic bath of magnetic fluctuations is computed using the spin-boson model. The magnetic fluctuations are treated in a fully quantum mechanical way by using the macroscopic quantum electrodynamics formalism and are expressed in terms of the classical electromagnetic Green’s function of the system. The resulting frequency integral formally diverges but it can be regularized by applying real-cavity, local-field corrections to the location of the ‘central spin’. This results in a cut-off function in terms of the magnetic permeability of the background material that leads to convergence at both high and low frequencies. This cut-off function appears naturally from the formalism and thus removes the need to rely on ad-hoc arguments to justify the form of the cut-off function. Furthermore, the magnetic permeability and the nature of interactions in quantum electrodynamics illuminate the connection between the two main models of ‘central spin’ decoherence, the spin-boson model and the spin-bath model, demonstrating how the two very different models are able to correctly model the same underlying physics.

Relativistic coupled-cluster analysis of parity nonconserving amplitudes and related properties of the 6s2 S1/2 − 5d2 D3/2; 5/2 transitions in 133Cs

ABSTRACTWe present the results of our calculations of the parity nonconserving electric dipole amplitudes(E1PNC) for the 6s2S1/2 − 5d2D3/2; 5/2 transitions of 133Cs employing a relativistic coupled-cluster (RCC) method. E1PNC values for the nuclear spin-independent and nuclear spin-dependent (NSD) parity non-conservation (PNC) effects for different hyperfine levels of the 6s2S1/2 − 5d2D3/2 transition and only due to the NSD PNC interaction Hamiltonian for all possible hyperfine levels of the 6s2S1/2 − 5d2D5/2 transition are given. We have also performed calculations of several properties that are relevant for assessing the reliability of the calculations of the amplitudes of the above-mentioned transitions. We highlight the importance of correlation effects by giving the results of both the Dirac–Fock and RCC contributions. Approximate contributions to these properties from the Breit and quantum electrodynamic interactions have also been evaluated. Plausible experimental schemes to measure these transition amplitudes by light shift techniques and interference involving induced Stark shifts are outlined.

Super-Coulombic atom\u2013atom interactions in hyperbolic media

Dipole–dipole interactions, which govern phenomena such as cooperative Lamb shifts, superradiant decay rates, Van der Waals forces and resonance energy transfer rates, are conventionally limited to the Coulombic near-field. Here we reveal a class of real-photon and virtual-photon long-range quantum electrodynamic interactions that have a singularity in media with hyperbolic dispersion. The singularity in the dipole–dipole coupling, referred to as a super-Coulombic interaction, is a result of an effective interaction distance that goes to zero in the ideal limit irrespective of the physical distance. We investigate the entire landscape of atom–atom interactions in hyperbolic media confirming the giant long-range enhancement. We also propose multiple experimental platforms to verify our predicted effect with phonon–polaritonic hexagonal boron nitride, plasmonic super-lattices and hyperbolic meta-surfaces as well. Our work paves the way for the control of cold atoms above hyperbolic meta-surfaces and the study of many-body physics with hyperbolic media.

Scrutinizing Al-like V10+51,Cr11+53,Mn12+55,Fe13+57,Co14+59,Ni15+61 , and Cu16+63 ions for atomic clocks with uncertainties below the 10−19 level

We investigate the transition between the fine structure levels of the ground state, $3p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{1/2}\ensuremath{\rightarrow}3p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$, of the highly charged Al-like $^{51}\mathrm{V}^{10+},\phantom{\rule{0.16em}{0ex}}^{53}\mathrm{Cr}^{11+},\phantom{\rule{0.16em}{0ex}}^{55}\mathrm{Mn}^{12+},\phantom{\rule{0.16em}{0ex}}^{57}\mathrm{Fe}^{13+},\phantom{\rule{0.16em}{0ex}}^{59}\mathrm{Co}^{14+},\phantom{\rule{0.16em}{0ex}}^{61}\mathrm{Ni}^{15+}$, and $^{63}\mathrm{Cu}^{16+}$ ions for frequency standards. To comprehend them as prospective atomic clocks, we determine their transition wavelengths, quality factors, and various plausible systematics during the measurements. Since most of these ions have nuclear spin $I=3/2$, uncertainties due to dominant quadrupole shifts can be evaded in the $F=0$ hyperfine level of the $3p{\phantom{\rule{0.16em}{0ex}}}^{2}{P}_{3/2}$ state. Other dominant systematics such as quadratic Stark and black-body radiation shifts have been evaluated precisely demonstrating the feasibility of achieving high accuracy, below ${10}^{\ensuremath{-}19}$ fractional uncertainty, atomic clocks using the above transitions. Moreover, relativistic sensitivity coefficients are determined to find out the aptness of these proposed clocks to investigate possible temporal variation of the fine structure constant. To carry out these analysis, a relativistic coupled-cluster method considering Dirac-Coulomb-Breit Hamiltonian along with lower-order quantum electrodynamics interactions is employed and many spectroscopic properties are evaluated. These properties are also of immense interest for astrophysical studies.

Development of a relativistic coupled-cluster method for one-electron detachment theory: Application to Mn ix, Fe x, Co xi, and Ni xii ions

We have developed one electron detachment theory from a closed-shell atomic configuration in the relativistic Fock-space coupled-cluster ansatz. Using this method, we determine sensitivity coefficients to the variation of the fine structure constant in the first three important low-lying transitions of the astrophysically interesting highly charged Mn IX, Fe X, Co XI and Ni XII ions. The potential of this method has been assessed by evaluating the detachment energies of the removed electrons and determining lifetimes of the atomic states in the above ions. To account the sensitivity of the higher order relativistic effects, we have used the four component wave functions of the Dirac-Coulomb-Breit Hamiltonian with the leading order quantum electrodynamics (QED) corrections. A systematic study has been carried out to highlight the importance of the Breit and QED interactions in the considered properties of the above ions.

Effects of adiabatic, relativistic, and quantum electrodynamics interactions on the pair potential and thermophysical properties of helium

The adiabatic, relativistic, and quantum electrodynamics (QED) contributions to the pair potential of helium were computed, fitted separately, and applied, together with the nonrelativistic Born-Oppenheimer (BO) potential, in calculations of thermophysical properties of helium and of the properties of the helium dimer. An analysis of the convergence patterns of the calculations with increasing basis set sizes allowed us to estimate the uncertainties of the total interaction energy to be below 50 ppm for interatomic separations R smaller than 4 bohrs and for the distance R = 5.6 bohrs. For other separations, the relative uncertainties are up to an order of magnitude larger (and obviously still larger near R = 4.8 bohrs where the potential crosses zero) and are dominated by the uncertainties of the nonrelativistic BO component. These estimates also include the contributions from the neglected relativistic and QED terms proportional to the fourth and higher powers of the fine-structure constant α. To obtain such high accuracy, it was necessary to employ explicitly correlated Gaussian expansions containing up to 2400 terms for smaller R (all R in the case of a QED component) and optimized orbital bases up to the cardinal number X = 7 for larger R. Near-exact asymptotic constants were used to describe the large-R behavior of all components. The fitted potential, exhibiting the minimum of -10.996 ± 0.004 K at R = 5.608 0 ± 0.000 1 bohr, was used to determine properties of the very weakly bound (4)He(2) dimer and thermophysical properties of gaseous helium. It is shown that the Casimir-Polder retardation effect, increasing the dimer size by about 2 Å relative to the nonrelativistic BO value, is almost completely accounted for by the inclusion of the Breit-interaction and the Araki-Sucher contributions to the potential, of the order α(2) and α(3), respectively. The remaining retardation effect, of the order of α(4) and higher, is practically negligible for the bound state, but is important for the thermophysical properties of helium. Such properties computed from our potential have uncertainties that are generally significantly smaller (sometimes by nearly two orders of magnitude) than those of the most accurate measurements and can be used to establish new metrology standards based on properties of low-density helium.

Nanodiamond induced high-Q resonances in defect-free photonic crystal slabs

We demonstrate that a high-Q photonic crystal cavity can be induced by the presence of a nanodiamond (ND) on the air-hole side wall in an otherwise defect-free photonic crystal. The ND itself acts as the perturbation, increasing the average refractive index, necessary to define the cavity; therefore self-aligned with the cavity. Such cavities are potentially useful for exploiting cavity quantum electro-dynamic interactions between fluorescent NDs and the cavity. A single ND can induce a cavity with Q~3 × 10(4) and two or more ND particles can induce a cavity with Q~1.5 × 10(5). We show numerically that perturbing the position and the size of the NDs has little effect on the cavity properties.

Testing QED and atomic-nuclear interactions with high-Z ions

Measurements of high-Z hydrogen-like ions have not yet been able to compete with the ultra-high precise test of quantum electrodynamics (QED) carried out using atomic hydrogen. However, recent advances in theory and experiment have enabled measurements involving high-Z lithium-like ions to test two-loop QED at a level similar to that achieved with atomic hydrogen. Tests of two-loop QED are limited in both cases by the uncertainties in the finite nuclear size, i.e. the uncertainties associated with the proton charge radius and the finite size of high-Z nuclei, respectively. Future experiments employing high-Z ions are described that might go beyond the present limitations. Measurements of the hyperfine splitting in highly charged ions cannot readily be described by theory, in part because of poor understanding of the finite nuclear magnetization radius. The discrepancy between measurements and theory leaves open the possibility of new physics not yet addressed by our current understanding of atomic–nuclear interactions.

Climbing the Jaynes–Cummings ladder and observing its nonlinearity in a cavity QED system

The field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has gained new momentum by recent reports of quantum optical experiments with solid-state semiconducting and superconducting systems. In cavity QED, the observation of the vacuum Rabi mode splitting is used to investigate the nature of matter-light interaction at a quantum-mechanical level. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED set-up, in which very strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high-quality on-chip microwave cavity. Circuit QED systems also provide a natural quantum interface between flying qubits (photons) and stationary qubits for applications in quantum information processing and communication.

Entangled photon–electron states and the number-phase minimum uncertainty states of the photon field

The exact analytic solutions of the energy eigenvalue equation of the system consisting of a free electron and one mode of the quantized radiation field are used for studying the physical meaning of a class of number-phase minimum uncertainty states. The states of the mode which minimize the uncertainty product of the photon number and the Suskind and Glogower (1964 Physics 1 49–61) cosine operator have been obtained by Jackiw (1968 J. Math. Phys. 9 339–46). However, these states have so far remained mere mathematical constructions without any physical significance. It is proved that the most fundamental interaction in quantum electrodynamics—namely the interaction of a free electron with a mode of the quantized radiation field—leads quite naturally to the generation of the mentioned minimum uncertainty states. It is shown that from the entangled photon–electron states developing from a highly excited number state, due to the interaction with a Gaussian electronic wave packet, the minimum-uncertainty states of Jackiw's type can be constructed. In the electron's coordinate representation, the physical meaning of the expansion coefficients of these states is the joint probability amplitudes of simultaneous detection of an electron and of a definite number of photons. The photon occupation probabilities in these states preserve their functional form as time elapses, but they depend on the location in space-time of the detected electron. An analysis of the entanglement entropies derived from the photon number distribution and from the electron's density operator is given.

Gauge principle for flows of an ideal fluid

A gauge principle is applied to flows of a compressible ideal fluid. First, a free-field Lagrangian is defined with a constraint condition of continuity equation. The Lagrangian is invariant with respect to global SO(3) gauge transformations as well as Galilei transformation. From the variational principle, we obtain the equation of motion for a potential flow. Next, in order to satisfy local SO(3) gauge invariance, we define a gauge field and a gauge-covariant derivative. Requiring the covariant derivative to be Galilei-invariant, it is found that the gauge field coincides with the vorticity and the covariant derivative is the material derivative for the velocity. Based on the gauge principle and the gauge-covariant derivative, the Euler's equation of motion is derived for a homentropic rotational flow. Noether's law associated with global SO(3) gauge invariance leads to the conservation of total angular momentum. This provides a gauge-theoretical ground for analogy between acoustic-wave and vortex interaction in fluid dynamics and the electron-wave and magnetic-field interaction in quantum electrodynamics.

Preparation of an arbitrary density matrix of a harmonic oscillator

Abstract We propose a deterministic method to generate an arbitrary (pure or mixed) density matrix of a harmonic oscillator. The general density matrices are achieved by manipulating quantum entanglement between the oscillator and an auxiliary oscillator. We discuss how our preparation scheme can be realized by cavity quantum electrodynamics interactions so that a general density matrix of a single-mode electromagnetic field can be created.

Preparation of an arbitrary density matrix of a harmonic oscillator

We propose a deterministic method to generate an arbitrary (pure or mixed) density matrix of a harmonic oscillator. The general density matrices are achieved by manipulating quantum entanglement between the oscillator and an auxiliary oscillator. We discuss how our preparation scheme can be realized by cavity quantum electrodynamics interactions so that a general density matrix of a single-mode electromagnetic field can be created.