Virtual Photon Exchange Research Articles

The Unified Theory of Resonance Energy Transfer According to Molecular Quantum Electrodynamics

An overview is given of the molecular quantum electrodynamical (QED) theory of resonance energy transfer (RET). In this quantized radiation field description, RET arises from the exchange of a single virtual photon between excited donor and unexcited acceptor species. Diagrammatic time-dependent perturbation theory is employed to calculate the transfer matrix element, from which the migration rate is obtained via the Fermi golden rule. Rate formulae for oriented and isotropic systems hold for all pair separation distances, R, beyond wave function overlap. The two well-known mechanisms associated with migration of energy, namely the R−6 radiationless transfer rate due to Förster and the R−2 radiative exchange, correspond to near- and far-zone asymptotes of the general result. Discriminatory pair transfer rates are also presented. The influence of an environment is accounted for by invoking the polariton, which mediates exchange and by introducing a complex refractive index to describe local field and screening effects. This macroscopic treatment is compared and contrasted with a microscopic analysis in which the role of a neutral, polarizable and passive third-particle in mediating transfer of energy is considered. Three possible coupling mechanisms arise, each requiring summation over 24 time-ordered diagrams at fourth-order of perturbation theory with the total rate being a sum of two- and various three-body terms.

Entanglement harvesting in double-layer graphene by vacuum fluctuations in a microcavity

The aim of this work is to study the entanglement harvesting between two graphene layers inside a planar microcavity. Applying time-dependent perturbation theory it is shown that nonclassical correlations between electrons in different layers are obtained through the exchange of virtual photons. Considering different initial states of the electrons and the vacuum state of the electromagnetic field, the negativity measure that quantifies the entanglement is computed through the photon propagator for time scales smaller than the light-crossing time of the double layer. The results are compared with those obtained for hydrogenic probes and pointlike Unruh-DeWitt detectors, showing that for different initial states, entangled X states and more general entangled reduced matrices are obtained, which enlarge the classification of bipartite quantum states.

Construction of two-qubit logical gates by transmon qubits in a three-dimensional cavity**Project supported by the National Basic Research and Development Program of China (Grant No. 2011CBA00304), the National Natural Science Foundation of China (Grant Nos. 60836001 and 61174084), and the Tsinghua University Initiative Scientific Research Program, China (Grant No. 20131089314).

We report the implementation of qubit–qubit coupling in a three-dimensional (3D) cavity, using the exchange of virtual photons, to realize logical operations. We measure single photon and multi-photon transitions in this qubit–qubit coupling system and obtain its energy avoided-crossing spectrum. With ac-Stark effect, fast control of the qubits is achieved to tune the effective coupling on and off and the state-swap gate is successfully constructed. Moreover, using two-photon transition between the ground state and doubly excited states, a kind of two-photon Rabi-like oscillation is observed. A quarter period of this oscillation corresponds to the logical gate , which is used for generating Bell states. and are the foundations of future preparation of two-qubit Bell states and realization of CNOT gate.

Spectroscopic Study of EUV and SXR Transitions of Ba XLVI

An extensive set of energy levels, inverse radiative rates, wave-function composition in LSJ and JJ coupling schemes for the lowest 162 fine structure levels along with transition wavelengths, oscillator strengths, line strengths and transition probabilities for electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2) EUV and SXR transitions from the ground state have been presented for Ba XLVI. For these calculations, the fully relativistic Multiconfiguration Dirac-Fock (MCDF) approach is employed. The QED corrections due to vacuum polarization and self-energy effects and Breit correction due to the exchange of virtual photons between two electrons are fully considered. To assess the authenticity and credibility of presented results, analogous calculations have also been performed by using a fully relativistic configuration interaction program (Flexible Atomic Code) based on self-consistent Dirac-Fock-Slater iteration method. Extreme Ultraviolet (EUV) and Soft X-ray (SXR) transitions are also identified. Comparison is also made with the available experimental and theoretical data. These accurate data are expected to be useful in fusion research and astrophysical investigations and applications.

Modified dipole-dipole interaction and dissipation in an atomic ensemble near surfaces

We study how the radiative properties of a dense ensemble of atoms can be modified when they are placed near or between metallic or dielectric surfaces. If the average separation between the atoms is comparable or smaller than the wavelength of the scattered photons, the coupling to the radiation field induces long-range coherent interactions based on the interatomic exchange of virtual photons. Moreover, the incoherent scattering of photons back to the electromagnetic field is known to be a many-body process, characterized by the appearance of superradiant and subradiant emission modes. By changing the radiation field properties, in this case by considering a layered medium where the atoms are near metallic or dielectric surfaces, these scattering properties can be dramatically modified. We perform a detailed study of these effects, with focus on experimentally relevant parameter regimes. We finish with a specific application in the context of quantum information storage, where the presence of a nearby surface is shown to increase the storage time of an atomic excitation that is transported across a one-dimensional chain.

Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

A method for calculating the electronic levels in the compact superheavy nuclear quasi-molecules, based on solving the two-center Dirac equation using the multipole expansion of two-center potential, is developed. For the internuclear distances up to $d\sim100$~fm such technique reveals a quite fast convergence and allows for computing the electronic levels in such systems with accuracy $\sim 10^{-6} $. The critical distances $R_{cr}$ between the nuclei for $1\sigma_g$ and $1\sigma_u$ electronic levels in the region $Z\simeq 87-100$ are calculated. By means of the same technique the shifts of electronic levels due to the effective interaction $\Delta U_{AMM}$ of the electron's magnetic anomaly with the Coulomb field of the closely spaced heavy nuclei are evaluated as a function of the internuclear distance and the charge of the nuclei, non-perturbatively both in $Z\alpha$ and (partially) in $\alpha/\pi$. It is shown, that the levels shifts near the lower continuum decrease with the enlarging size of the system of Coulomb sources both in the absolute units and in units of $Z^4 \alpha^5 / \pi n^3$. The last result is generalized to the whole self-energy contribution to the level shifts and so to the possible behavior of radiative part of QED-effects with virtual photon exchange near the lower continuum in the overcritical region.

Enhanced Electromagnetic Corrections to the Rare Decay B_{s,d}→μ^{+}μ^{-}.

We investigate electromagnetic corrections to the rare B-meson leptonic decay B_{s,d}→μ^{+}μ^{-} from scales below the bottom-quark mass m_{b}. Contrary to QCD effects, which are entirely contained in the B-meson decay constant, we find that virtual photon exchange can probe the B-meson structure, resulting in a "nonlocal annihilation" effect. We find that this effect gives rise to a dynamical enhancement by a power of m_{b}/Λ_{QCD} and by large logarithms. The impact of this novel effect on the branching ratio of B_{s,d}→μ^{+}μ^{-} is about 1%, of the order of the previously estimated nonparametric theoretical uncertainty, and four times the size of previous estimates of next-to-leading order QED effects due to residual scale dependence. We update the standard model (SM) prediction to B[over ¯](B_{s}→μ^{+}μ^{-})_{SM}=(3.57±0.17)×10^{-9}.

Dynamical screening of AMM and QED effects for large-Z hydrogen-like atoms

The effective interaction ΔU AMM of the anomalous magnetic moment (AMM) of an electron with the Coulomb field of an extended nucleus is analyzed. As soon as the q 2 dependence of the electron formfactor F 2(q 2)is taken into account from the beginning, the AMM is found to be dynamically screened at small distances of r ≪ 1/m. The ΔU AMM effects on the low-lying electronic levels of a superheavy extended nucleus with Zα > 1are analyzed using the nonperturbative approach. The growth rate of the ΔU AMM contribution with increasing Z is shown to be essentially nonmonotonic. At the same time, the energy shifts of electronic levels in the vicinity of the threshold of the lower continuum monotonically decrease in the region Z ≫Z cr,1s . The latter result is generalized to the whole self-energy contribution to energy shifts of electronic levels, thus also referring to the possible behavior of QED radiative effects with virtual-photon exchange, considered beyond the framework of the perturbative expansion in Zα.

Circuit QED with qutrits: Coupling three or more atoms via virtual-photon exchange

We present a model to describe a generic circuit QED system which consists of multiple artificial three-level atoms, namely qutrits, strongly coupled to a cavity mode. When the state transition of the atoms disobey the selection rules the process that does not conserve the number of excitations can happen determinatively. Therefore, we can realize coherent exchange interaction among three or more atoms mediated by the exchange of virtual photons. In addition, we generalize the one cavity mode mediated interactions to the multi-cavity situation, providing a method to entangle atoms located in different cavities. Using experimental feasible parameters, we investigate the dynamics of the model including three cyclic-transition three-level atoms, for which the two lowest-energy levels can be treated as qubits. Hence, we have found that two qubits can jointly exchange excitation with one qubit in a coherent and reversible way. In the whole process, the population in the third level of atoms is negligible and the cavity photon number is far smaller than 1. Our model provides a feasible scheme to couple multiple distant atoms together, which may find applications in quantum information processing.

Thermal Schwinger pair production at arbitrary coupling

We calculate the rate of thermal Schwinger pair production at arbitrary coupling in weak external fields. Our calculations are valid independently of many properties of the charged particles produced, in particular their spin and whether they are electric or magnetic. Using the worldline formalism, we calculate the logarithm of the rate to leading order in the weak external field and to all orders in virtual photon exchange, taking us beyond the perturbative expansion about the leading order, weak coupling result.

Perturbativity vs nonperturbativity in QED-effects for H-like atoms with Zα > 1

The behavior of levels near the threshold of the lower continuum in superheavy H-like atoms with [Formula: see text], caused by the interaction [Formula: see text] of the electron’s magnetic anomaly (AMM) dynamically screened at small distances [Formula: see text], with the Coulomb field of atomic nucleus is considered by taking into account the complete dependence of electron’s wave function (WF) on [Formula: see text]. It is shown that the calculation of the contribution caused by [Formula: see text] via both the quark structure and the whole nucleus, considered as a uniformly charged extended Coulomb source, leads to results, which coincide within the accepted precision of calculations. It is also shown that there appears some difference in results between perturbative and nonperturbative methods of accounting for the contribution from [Formula: see text] within the corresponding Dirac equation (DE) in favor of the latter. Moreover, the growth rate of the contribution from [Formula: see text] reaches its maximum at [Formula: see text], while by further increase of [Formula: see text] into the supercritical region [Formula: see text], the shift of levels caused by [Formula: see text] near the lower continuum decreases monotonically to zero. The last result is generalized to the whole self-energy contribution to the shift of levels and so to the possible behavior of radiative QED-effects with virtual photon exchange near the lower continuum.

Cooperative Lamb shift and superradiance in an optoelectronic device

When a single excitation is shared between a large number of two-level systems, a strong enhancement of the spontaneous emission appears. This phenomenon is known as superradiance. This enhanced rate can be accompanied by a shift of the emission frequency, the cooperative Lamb shift, issued from the exchange of virtual photons between the emitters. In this work we present a semiconductor optoelectronic device allowing the observation of these two phenomena at room temperature. We demonstrate experimentally and theoretically that plasma oscillations in spatially separated quantum wells interact through real and virtual photon exchange. This gives rise to a superradiant mode displaying a large cooperative Lamb shift.

Interatomic Coulombic Decay of HeNe dimers after ionization and excitation of He and Ne

We study the decay of a helium/neon dimer after ionization and simultaneous excitation of either the neon or the helium atom using Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS). We find that, depending on the decaying state, either direct Interatomic Coulombic Decay (ICD) (i.e. mediated by a virtual photon exchange), exchange ICD (mediated by electron exchange) or radiative charge transfer occurs. The corresponding channels are identified.

Long-range photon-mediated gate scheme between nuclear spin qubits in diamond

Defect centers in diamond are exceptional solid-state quantum systems that can have exceedingly long electron and nuclear spin coherence times. So far, single-qubit gates for the nitrogen nuclear spin, a two-qubit gate with a nitrogen-vacancy (NV) center electron spin, and entanglement between nearby nitrogen nuclear spins have been demonstrated. Here, we develop a scheme to implement a universal two-qubit gate between two distant nitrogen nuclear spins. Virtual excitation of an NV center that is embedded in an optical cavity can scatter a laser photon into the cavity mode; we show that this process depends on the nuclear spin state of the nitrogen atom. If two NV centers are simultaneously coupled to a common cavity mode and individually excited, virtual cavity photon exchange can mediate an effective interaction between the nuclear spin qubits, conditioned on the spin state of both nuclei, which implements a universal controlled-$\textit{Z}$ gate. We predict operation times below 100 nanoseconds, which is several orders of magnitude faster than the decoherence time of nuclear spin qubits in diamond.

Cavity-mediated coupling of mechanical oscillators limited by quantum back-action

A complex quantum system can be constructed by coupling simple quantum elements to one another. For example, trapped-ion or superconducting quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively quantum objects can be coupled by the exchange of real photons, particularly when driven within resonators that amplify interactions with a single electro-magnetic mode. However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised. Here, we realize phase-coherent interactions between two spatially separated, near-ground-state mechanical oscillators within a driven optical cavity. We observe also the noise imparted by the optical coupling, which results in correlated mechanical fluctuations of the two oscillators. Achieving the quantum backaction dominated regime opens the door to numerous applications of cavity optomechanics with a complex mechanical system. Our results thereby illustrate the potential, and also the challenge, of coupling quantum objects with light.

Long-range quantum gate via Rydberg states of atoms in a thermal microwave cavity

We propose an implementation of a universal quantum gate between pairs of spatially separated atoms in a microwave cavity at finite temperature. The gate results from reversible laser excitation of Rydberg states of atoms interacting with each other via exchange of virtual photons through a common cavity mode. Quantum interference of different transition paths between the two-atom ground and double-excited Rydberg states makes both the transition amplitude and resonance largely insensitive to the excitations in the microwave cavity "quantum bus" which can therefore be in any superposition or mixture of photon number states. Our scheme for attaining ultralong-range interactions and entanglement also applies to mesoscopic atomic ensembles in the Rydberg blockade regime and is scalable to many ensembles trapped within a centimeter sized microwave resonator.

Virtual photon exchange, intermolecular interactions and optical response functions

According to molecular quantum electrodynamics, coupling between material particles occurs due to an exchange of one or more virtual photons. In this work, the relationship between polarisability and hyperpolarisability tensors of atoms and molecules that feature in linear and nonlinear optical processes, and their analytically continued form in the complex frequency domain that appear in formulae describing fundamental inter-particle interactions, is studied. Examples involving a single virtual photon exchange, which are linearly proportional to electric dipole moments at each centre, include the electrostatic energy and the resonant transfer of excitation energy. The Casimir–Polder dispersion potential, and its discriminatory counterpart applicable to coupled chiral molecules, are used to illustrate response properties depending on the exchange of two virtual photons. Meanwhile, the energy shift between two hyperpolarisable species, a higher order discriminatory contribution to the dispersion potential, is employed to represent forces arising from the three virtual photon exchange. It is shown that for energy shifts that are quadratic or bilinear or cubic in the transition dipole moment, it is necessary to account for all two- and three-photon optical processes, such as absorption, emission and linear and nonlinear scattering of light in order to arrive at the correct form of the molecular response tensor.

Modified and controllable dispersion interaction in a one-dimensional waveguide geometry

Dispersion interactions such as the van der Waals interaction between atoms or molecules derive from quantum fluctuations of the electromagnetic field and can be understood as the exchange of virtual photons between the interacting partners. Any modification of the environment in which those photons propagate will thus invariably lead to an alteration of the van der Waals interaction. Here we show how the two-body dispersion interaction inside a cylindrical waveguide can be made to decay asymptotically exponentially, and how this effect sensitively depends on the material properties and the length scales of the problem, eventually leading to the possibility of controllable interactions. Further, we discuss the possibility to detect the retarded van der Waals interaction by resonant enhancement of the interaction between Rydberg atoms in the light of long-range potentials due to guided modes.

Nonlinear coupling between a nitrogen-vacancy-center ensemble and a superconducting qubit

By exchange of virtual microwave photon induced by a transmission line resonator, the nonlinear interaction between a nitrogen-vacancy-center ensemble (NVE) and a superconducting charge qubit is achieved in circuit quantum electrodynamics, where the nonlinear coupling results from the second order of the coupling between the magnetic field of the transmission line resonator and the charge qubit. In our case, the nonlinear coupling can be much enhanced by a factor of the total spin number in the NVE. As an application, we present a potentially practical scheme to realize the squeezing of the NVE using the nonlinear coupling, which is within reach of the currently available technology.

Quantum criticality of geometric phase in coupled optical cavity arrays under linear quench

The atoms trapped in microcavities and interacting through the exchange of virtual photons can be modeled as an anisotropic Heisenberg spin-1/2 lattice. We study the dynamics of the geometric phase of this system under the linear quenching process of laser field detuning, which shows XX criticality of the geometric phase and also gives the result of quantum criticality for different quenching rates.