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We have developed a microwave spectrometer for a measurement of the 2 S 1 / 2 - 2 P 1 / 2 Lamb shift of antihydrogen atoms towards the determination of the antiproton charge radius. The spectrometer consists of two consecutive apparatuses, of which the first apparatus, Hyperfine Selector (HFS), filters out 2 S 1 / 2 (F = 1) hyperfine states and pre-selects the 2 S 1 / 2 (F = 0) state, and the second apparatus, MicroWave Scanner (MWS), sweeps the frequency around the target transition to obtain the spectrum. We optimized the geometry of the apparatuses by evaluating the S-parameter that represents the ratio of the reflected microwave signal over the input, utilizing microwave simulations based on the finite element method. The HFS was designed to obtain a resonant property at 1.1 GHz for an efficient removal of the 2 S 1 / 2 (F = 1) hyperfine states, and the MWS was designed to realize weak frequency-dependency in the signal reflection. Also, the spatial distributions of microwave electric field were simulated. We report the design of the spectrometer and discuss an expected precision of the first measurement. [ABSTRACT FROM AUTHOR]

The Lamb shift of a quantum emitter in close proximity to a plasmonic nanostructure can be three or more orders of magnitude larger than that in the free space and is ultra-sensitive to the emitter position and polarization. We demonstrate that this large Lamb shift can be sensitively observed from the scattering or absorption spectrum dip shift of the coupled system when the plasmonic nanoparticle or tip scans the emitter. Using these observations, we propose a scanning optical scattering imaging method based on the plasmonic-enhanced Lamb shift with achieves sub-nanometer resolution. Our method is based on the scattering or absorption spectrum of the plasmon-emitter coupling system, which is free of the fluorescence quenching problem and easier to implement in a plasmon-emitter coupling system. In addition, our scheme works even if the quantum emitter is slightly below the dielectric surface, which can bring about broader applications, such as detecting atoms and molecules or quantum dots above or under a surface. [ABSTRACT FROM AUTHOR]

The Lamb shift, one of the most fundamental interactions in atomic physics, arises from the interaction of H atoms with the electromagnetic fluctuations of the quantum vacuum. The energy shift has been computed in a variety of ways. The energy shift, as Feynman, Power, and Milonni demonstrated, equals the change in the vacuum energy in the volume containing the H atoms due to the change in the index of refraction arising from the presence of the H atoms. Using this result and a group theoretical calculation of the contribution to the Lamb shift from each frequency of the vacuum fluctuations, in this paper we obtain an expression for the region of the vacuum energy for each frequency ω around the H atom due to the Lamb shift. This same field plays an essential role in the van der Waals force. We show the ground state atom is surrounded by a region of positive vacuum energy that extends well beyond the atom for low frequencies. This region can be described as a steady state cloud of vacuum fluctuations. For energies E = ℏ ω less than 1 eV, where ℏ is the reduced Planck constant and ω is frequency, the radius of the positive energy region is shown to be approximately 14.4/E Å. For a vacuum fluctuation of wavelength, λ , the radius is (α / 2 π) λ , where α is the fine-structure constant. Thus, for long wavelengths, the region has macroscopic dimensions. The energy–time uncertainty relation predicts a maximum possible radius that is larger than the radius based on the radiative shift calculations by a factor of 1 / 4 α . [ABSTRACT FROM AUTHOR]

In an atom, the interaction of a bound electron with the vacuum fluctuations of the electromagnetic field leads to complex shifts in the energy levels of the electron, with the real part of the shift corresponding to a shift in the energy level and the imaginary part to the width of the energy level. The most celebrated radiative shift is the Lamb shift between the 2 s 1 / 2 and the 2 p 1 / 2 levels of the hydrogen atom. The measurement of this shift in 1947 by Willis Lamb Jr. proved that the prediction by Dirac theory that the energy levels were degenerate was incorrect. Hans Bethe's non-relativistic calculation of the shift using second-order perturbation theory demonstrated the renormalization process required to deal with the divergences plaguing the existing theories and led to the understanding that it was essential for theory to include interactions with the zero-point quantum vacuum field. This was the birth of modern quantum electrodynamics (QED). Numerous calculations of the Lamb shift followed including relativistic and covariant calculations, all of which contain a nonrelativistic contribution equal to that computed by Bethe. The semi-quantitative models for the radiative shift of Welton and Power, which were developed in an effort to demonstrate physical mechanisms by which vacuum fluctuations lead to the shift, are also considered here. This paper describes a calculation of the shift using a group theoretical approach which gives the shift as an integral over frequency of a function, which is called the "spectral density of the shift." The energy shift computed by group theory is equivalent to that derived by Bethe yet, unlike in other calculations of the non-relativistic radiative shift, no sum over a complete set of states is required. The spectral density, which is obtained by a relatively simple computation, reveals how different frequencies of vacuum fluctuations contribute to the total energy shift. The analysis shows, for example, that half the radiative shift for the ground state 1S level in H comes from virtual photon energies below 9700 eV, and that the expressions of Power and Welton have the correct high-frequency behavior, but not the correct low-frequency behavior, although they do give approximately the correct value for the total shift. [ABSTRACT FROM AUTHOR]

Controlling the light emitted by individual molecules is instrumental to a number of advanced nanotechnologies ranging from super-resolution bioimaging and molecular sensing to quantum nanophotonics. Molecular emission can be tailored by modifying the local photonic environment, for example, by precisely placing a single molecule inside a plasmonic nanocavity with the help of DNA origami. Here, using this scalable approach, we show that commercial fluorophores may experience giant Purcell factors and Lamb shifts, reaching values on par with those recently reported in scanning tip experiments. Engineering of plasmonic modes enables cavity-mediated fluorescence far detuned from the zero-phonon-line (ZPL)─at detunings that are up to 2 orders of magnitude larger than the fluorescence line width of the bare emitter and reach into the near-infrared. Our results point toward a regime where the emission line width can become dominated by the excited-state lifetime, as required for indistinguishable photon emission, bearing relevance to the development of nanoscale, ultrafast quantum light sources and to the quest toward single-molecule cavity QED. In the future, this approach may also allow the design of efficient quantum emitters at infrared wavelengths, where standard organic sources have a reduced performance.

Laser spectroscopy of muonic atoms has been recently used to probe properties of light nuclei with unprecedented precision. We introduce nuclear effects in hydrogen-like atoms, nucleon structure quantities (form factors, structure functions, polarizabilities), and their effects in the Lamb shift and hyperfine splitting (HFS) of muonic hydrogen (μH). Updated theory predictions for the Lamb shift and HFS in μH are presented. We review the challenges of the ongoing effort to measure the ground-state HFS in μH and its impact on our understanding of the nucleon spin structure. To narrow down this search, we present a novel theory prediction obtained by scaling the measured HFS in hydrogen while leveraging radiative corrections. We also summarize recent developments in the spectroscopy of simple atomic and molecular systems and emphasize how they allow for precise determinations of fundamental constants, bound-state QED tests, and New Physics searches. [ABSTRACT FROM AUTHOR]

The recent progress in direct active cooling of the quantum‐electric degrees of freedom in engineered circuits, or quantum‐circuit refrigeration is reviewed. In 2017, the discovery of a quantum‐circuit refrigerator (QCR) based on photon‐assisted tunneling of quasiparticles through normal‐metal–insulator–superconductor junctions inspired a series of experimental studies demonstrating the following main properties: i) the direct‐current (dc) bias voltage of the junction can change the QCR‐induced damping rate of a superconducting microwave resonator by orders of magnitude and give rise to nontrivial Lamb shifts, ii) the damping rate can be controlled in nanosecond time scales, and ii) the dc bias can be replaced by a microwave excitation, the amplitude of which controls the induced damping rate. Theoretically, it is predicted that state‐of‐the‐art superconducting resonators and qubits can be reset with an infidelity lower than 10−4 in tens of nanoseconds using experimentally feasible parameters. A QCR‐equipped resonator has also been demonstrated as an incoherent photon source with an output temperature above 1 K yet operating at millikelvin. This source has been used to calibrate cryogenic amplification chains. In the future, the QCR may be experimentally used to quickly reset superconducting qubits, and hence assist in the great challenge of building a practical quantum computer. [ABSTRACT FROM AUTHOR]

Radiation is a process common to classical and quantum systems with very different effects in each regime. In a quantum system, the interaction of a bound electron with its own radiation field leads to complex shifts in the energy levels of the electron, with the real part of the shift corresponding to a shift in the energy level and the imaginary part to the width of the energy level. The most celebrated radiative shift is the Lamb shift between the 2 s 1 / 2 and the 2 p 1 / 2 levels of the hydrogen atom. The measurement of this shift in 1947 by Willis Lamb Jr. proved that the prediction by Dirac theory that the energy levels were degenerate was incorrect. Hans Bethe’s calculation of the shift showed how to deal with the divergences plaguing the existing theories and led to the understanding that interactions with the zero-point vacuum field, the lowest energy state of the quantized electromagnetic field, have measurable effects, not just resetting the zero of energy. This understanding led to the development of modern quantum electrodynamics (QED). This historical pedagogic paper explores the history of Bethe’s calculation and its significance. It explores radiative effects in classical and quantum systems from different perspectives, with the emphasis on understanding the fundamental physical phenomena. Illustrations are drawn from systems with central forces, the H atom, and the three-dimensional harmonic oscillator. A first-order QED calculation of the complex radiative shift for a spinless electron is explored using the equations of motion and the m a s s 2 operator, describing the fundamental phenomena involved, and relating the results to Feynman diagrams.

Ensembles of two-level systems interacting with a single-mode electromagnetic field are increasingly being used for the development of quantum information processors and mesoscopic quantum devices. These systems are characterized by a set of energy-level hybridizations, split by Lamb shifts, that occur when the ensemble and field mode interact coherently with high cooperativity. For high dimensions simulating system dynamics while including the complete set of Lamb shifts is generally intractable. We present a compact description of Lamb shift statistics and behavior across all collective angular momentum and excitation subspaces of the ensemble without resorting to overly restrictive approximations of the state space. We also calculate the averaged effective Lamb shift weighted over the degeneracies of these subspaces to connect our results to experiments. [ABSTRACT FROM AUTHOR]

The first 6 ionization potentials (IPs) of the uranium atom have been calculated using multireference configuration interaction (MRCI+Q) with extrapolations to the complete basis set limit using new all-electron correlation consistent basis sets. The latter was carried out with the third-order Douglas-Kroll-Hess Hamiltonian. Correlation down through the 5s5p5d electrons has been taken into account, as well as contributions to the IPs due to the Lamb shift. Spin-orbit coupling contributions calculated at the 4-component Kramers restricted configuration interaction level, as well as the Gaunt term computed at the Dirac-Hartree-Fock level, were added to the best scalar relativistic results. The final ionization potentials are expected to be accurate to at least 5 kcal/mol (0.2 eV) and thus more reliable than the current experimental values of IP3 through IP6. [ABSTRACT FROM AUTHOR]

The spectral and spatial dependence of the resonant Lamb shift of an exciton inside a photonic vacuum field landscape is considered to predict an optical dipole potential generated via virtual photons quantum fluctuations. This trapping potential can be exploited for exciton self‐positioning in electric field hotspots at the nanoscale in view of quantum electrodynamics effects. By non Hermitian decomposition of the electromagnetic Green tensor in terms of quasi normal modes, the resonant part of the Lamb shift is expressed as Fano profile strictly interlinked to the Purcell enhancement of the exciton radiative lifetime. This approach explains how to tailor the depth of the vacuum photonic potential in several possible scenarios. [ABSTRACT FROM AUTHOR]

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs. [ABSTRACT FROM AUTHOR]

The underlying structure and mechanisms of the fundamental hydrogen atom are not clear in current models; they are still found to be incomplete (Linnyk et al. [8]). For example, in heavy-ion collisions, “The photons provide a critical test for the theoretical model and in conclusion (Linnyk et al. [8]): the standard dynamical models – constructed to reproduce the ’hadronic world’ – fail to explain the photon experimental data.“ This ‘comments study’ builds upon a recent article in the Results in Physics journal entitled: ‘Mechanisms explaining Coulomb’s electric force & Lorentz’s magnetic force from a classical perspective’ (Correnti, 2018 [1]). For example, we use the electric force mechanism and the attending electron structure derived in the linked article (Correnti, 2018 [1]) to develop the atomic hydrogen structure. The H2 molecule and hydrogen gas structures then become accessible in this study and (Correnti, 2012 [2]).

We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line. Similar to the atomic cases, RDDI comes from exchange of virtual photons of the continuous modes, and causes the so-called collective Lamb shift (CLS). To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incident and reflected waves, even though it is considered to be decoupled from the field, it results in large energy splitting in the spectral profile of a resonant qubit located at an antinode. This directly implies the interplay of virtual photon processes and explicitly signals the CLS. We further derive a master equation to describe the system, which can take into account mismatch of participating qubits and dephasing effects. Our calculation also demonstrates the superradiant and subradiant nature of the atomic states, and how the CLS scales when more qubits are involved. [ABSTRACT FROM AUTHOR]