QED Operator Research Articles

Two-mode squeezing operator in circuit QED

We theoretically investigate the implementation of the two-mode squeezing operator in circuit quantum electrodynamics. Inspired by a previous scheme for optical cavities [Phys. Rev. A $\textbf{73}$, 043803(2006)], we employ a superconducting qubit coupled to two nondegenerate quantum modes and use a driving field on the qubit to adequately control the resonator-qubit interaction. Based on the generation of two-mode squeezed vacuum states, firstly we analyze the validity of our model in the ideal situation and then we investigate the influence of the dissipation mechanisms on the generation of the two-mode squeezing operation, namely the qubit and resonator mode decays and qubit dephasing. We show that our scheme allows the generation of highly squeezed states even with the state-of-the-art parameters, leading to a theoretical prediction of more than 10 dB of two-mode squeezing. Furthermore, our protocol is able to squeeze an arbitrary initial state of the resonators, which makes our scheme attractive for future applications in continuous-variable quantum information processing and quantum metrology in the realm of circuit quantum electrodynamics.

QEDMOD: Fortran program for calculating the model Lamb-shift operator

We present Fortran package QEDMOD for computing the model QED operator hQED that can be used to account for the Lamb shift in accurate atomic-structure calculations. The package routines calculate the matrix elements of hQED with the user-specified one-electron wave functions. The operator can be used to calculate Lamb shift in many-electron atomic systems with a typical accuracy of few percent, either by evaluating the matrix element of hQED with the many-electron wave function, or by adding hQED to the Dirac–Coulomb–Breit Hamiltonian. New version program summaryProgram Title: QEDMODProgram Files doi:http://dx.doi.org/10.17632/ct869v4gxn.1Licensing provisions: Apache License 2.0.Programming language: Fortran 77.Journal reference of previous version: Computer Physics Communications 189 (2015) 175-181, http://dx.doi.org/10.1016/j.cpc.2014.12.002.Does the new version supersede the previous version?: Yes.Nature of problem: Fortran code for computation of the model QED operator that approximates the Lamb shift in many-electron atoms.Solution method: The method of solution is based on the algorithm developed in Ref. [1].Reasons for the new version: Extension of the region of applicability; fixing of minor bugs.Summary of revisions: Region of supported nuclear charges is extended to Z∈[3,120]; a problem that appeared for the extended nuclear model for several selected values of Z is fixed. [1]V. M. Shabaev, I. I. Tupitsyn, and V. A. Yerokhin, Model operator approach to the Lamb shift calculations in relativistic many-electron atoms, Phys. Rev. A 88, 012513 (2013).

Relativistic configuration-interaction calculations of the energy levels of the 1s22l and 1s2l2l′ states in lithiumlike ions: Carbon through chlorine

We present systematic calculations of energy levels of the $1s^22l$ and $1s2l2l'$ states of ions along the lithium isoelectronic sequence from carbon till chlorine. The calculations are performed by using the relativistic-configuration-interaction method adapted to the treatment of autoionizing core-excited states. The relativistic energies are supplemented with the QED energy shifts calculated within the model QED operator approach. A systematic estimation of the theoretical uncertainties is performed for every electronic state and every nuclear charge. The results are in agreement with existing high-precision theoretical and experimental data for the ground and first excited states. For the core-excited states, our theory is much more accurate than the presently available measurements.

Superspace unitary operator in QED with Dirac and complex scalar fields: Superfield approach

We exploit the strength of the superspace (SUSP) unitary operator to obtain the results of the application of the horizontality condition (HC) within the framework of the augmented version of the superfield formalism that is applied to the interacting systems of Abelian 1-form gauge theories where the U(1) Abelian 1-form gauge field couples to the Dirac and complex scalar fields in the physical four (3 + 1)-dimensions of spacetime. These interacting theories are generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the four -dimensional (4D) spacetime variables and a pair of Grassmannian variables. To derive the (anti-)BRST symmetries for the matter fields, we impose the gauge-invariant restrictions (GIRs) on the superfields defined on the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge out from our knowledge of the SUSP unitary operator and its Hermitian conjugate. The latter operator is derived without imposing any operation of Hermitian conjugation on the parameters and fields of our theory from outside. This is an interesting observation in our present investigation.

QEDMOD: Fortran program for calculating the model Lamb-shift operator

We present Fortran package QEDMOD for computing the model QED operator hQED that can be used to account for the Lamb shift in accurate atomic-structure calculations. The package routines calculate the matrix elements of hQED with the user-specified one-electron wave functions. The operator can be used to calculate Lamb shift in many-electron atomic systems with a typical accuracy of few percent, either by evaluating the matrix element of hQED with the many-electron wave function, or by adding hQED to the Dirac–Coulomb–Breit Hamiltonian. Program summaryProgram title: QEDMODCatalogue identifier: AEVE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVE_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 22861No. of bytes in distributed program, including test data, etc.: 347504Distribution format: tar.gzProgramming language: Fortran 77.Computer: PCs or higher performance computers.Operating system: Linux, Windows, MacOS.RAM: Kilobytes.Classification: 2.1.Nature of problem:Fortran code for computation of a model QED operator that approximates the Lamb shift in many-electron atoms.Solution method:The method of solution is based on the algorithm developed in Ref. [1].Running time:Seconds.

Relativistic configuration-interaction calculation ofKαtransition energies in berylliumlike iron

We perform relativistic configuration-interaction calculations of the energy levels of the low-lying and core-excited states of beryllium-like iron, Fe$^{22+}$. The results include the QED contributions calculated by two different methods, the model QED operator approach and the screening-potential approach. The uncertainties of theoretical energies are estimated systematically. The predicted wavelengths of the K\alpha transitions in beryllium-like iron improve previous theoretical results and compare favorably with the experimental data.

Model operator approach to the Lamb shift calculations in relativistic many-electron atoms

A model operator approach to calculations of the QED corrections to energy levels in relativistic many-electron atomic systems is developed. The model Lamb shift operator is represented by a sum of local and nonlocal potentials which are defined using the results of ab initio calculations of the diagonal and nondiagonal matrix elements of the one-loop QED operator with H-like wave functions. The model operator can be easily included in any calculations based on the Dirac-Coulomb-Breit Hamiltonian. The efficiency of the method is demonstrated by comparison of the model QED operator results for the Lamb shifts in many-electron atoms and ions with exact QED calculations.

Scalar vertex operator for bound-state QED in the Coulomb gauge

Adkins's result [Phys. Rev. D 34, 2489 (1986)] for the time component of the renormalized vertex operator in Coulomb-gauge QED is separated according to its tensor structure and some of the Feynman parameter integrals are carried out analytically, yielding a form suited for numerical bound-state QED calculations. This modified form is applied to the evaluation of the self-energy shift to the binding energy in hydrogenic ions of high nuclear charge.

Thermal operator and dispersion relation in QED at finite temperature and chemical potential

Combining the thermal operator representation with the dispersion relation in QED at finite temperature and chemical potential, we determine the complete retarded photon self-energy only from its absorptive part at zero temperature. As an application of this method, we show that, even for the case of a nonzero chemical potential, the temperature dependent part of the one loop retarded photon self-energy vanishes in $(1+1)$ dimensional massless QED.

Transport equation for the photon Wigner operator in noncommutative QED

We derive, in noncommutative QED, a gauge covariant quantum equation of motion for the photon Wigner operator. In the classical approximation, this reduces to a simple transport equation which describes the hard thermal effects in this theory. As an example of the effectiveness of this method we show that, to leading order, this equation generates in a direct way the Green amplitudes calculated perturbatively in quantum field theory at high temperature.

Polarized virtual photon structure functiong2γand twist-3 effects in QCD

We investigate the twist-3 effects in the polarized virtual photon structure. The structure functions $g_1^\gamma$ and $g_2^\gamma$ of polarized photon could be experimentally studied in the future polarized $ep$ or $e^+e^-$ colliders. The leading contributions to $g_1^\gamma$ are the twist-2 effects, while another structure function $g_2^\gamma$, which only exists for the virtual photon target, receives not only the twist-2 but also twist-3 contributions. We first show that the twist-3 effects actually exist in the box-diagram contributions and we extract the twist-3 part, which can also be reproduced by the pure QED operator product expansion. We then calculate the non-trivial lowest moment ($n=3$) of the twist-3 contribution to $g_2^\gamma$ in QCD. For large $N_c$ (the number of colors), the QCD analysis of the twist-3 effects in the flavor nonsinglet part of $g_2^\gamma$ becomes tractable and we can obtain its moments in a compact form for all $n$.

STRONG COUPLING QED BREAKS CHIRAL SYMMETRY

We show that the strong coupling limit of d-dimensional quantum electrodynamics with 2d/2[d/2] flavors of fermions can be mapped onto the s=1/2 quantum Heisenberg antiferromagnet in d–1 space dimensions. We use this mapping to prove that the strong coupling limit of QED breaks chiral symmetry. The staggered Néel order parameter of the antiferromagnet is the expectation value of a mass operator in QED and the spin-waves are pions. We speculate that the chiral symmetry breaking phase transition corresponds to a transition between the flux phase and the conventional Néel ordered phase of an antiferromagnetic t-J model.

On the spectrum of the staggered dirac operator at finite chemical potential

The spectrum of the staggered Dirac operator in two-dimensional QED is investigated at finite chemical potential. In the quenched model, it is shown that lattice artefacts cause a spurious scattering of eigenvalues. This scattering disappears when the lattice distance is taken to zero. In the unquenched model, a new approach is used to show that similar effects are absent.

The QED calculation of spin-orbit coupling resonances in electron storage rings

We present a quantum electrodynamics calculation of the spin polarization in a relativistic electron storage ring taking into account the emission of all synchrotron photons. We obtain an explicit formula for the resulting radiative polarization which exhibits a rich non-linear spin-orbit coupling resonance structure. To achieve our result we develop QED operator techniques which may be applicable in the calculation of transition amplitudes involving multiple photon emission for general two state systems.

Charged sectors and scattering states in quantum electrodynamics

Charge operator and charged sectors in four-dimensional QED are investigated, both within a local, covarian (indefinite metric), and within a positive metric formulation of QED. Assuming a few basic, physical principles-such as Gauss'law and a correspondence principle, etc.-we conclude that charge states determine non-Fock ( coherent state) representations of the algebra generated by the asymptotic, electromagnetic field, that Lorentz boosts do not leave the harged sectors invariant ( spontaneous breaking of boost symmetry), and that an unambiguous definition of the “mass” of the charged infraparticles is possible. This and other results represent first steps at extending the Haag-Ruelle scattering theory to charged infraparticles.