A formulation of quantum electrodynamics is given that applies to atoms in a strong laser field by perturbation theory in a non-relativistic regime. Dipole approximation is assumed. The dual Dyson series, here discussed by referring it to the Birkhoff theorem for singularly perturbed linear differential equations, can be applied and a perturbation series obtained transforming the Hamiltonian by a Pauli-Fierz transformation. But, if just few photons are present high-order harmonics cannot be generated. So, it is proven that odd high-order harmonics only appear when the laser field is intense and one can substitute the creation and annihilation operators by the square root of the mean number of photons taken to be huge, the field retaining its coherency property as observed experimentally for harmonics. In this case, the Hamiltonian for perturbation theory comes to the Kramers-Henneberger form. The theory has a dipolar contribution when the free-electron quiver motion amplitude is larger than the atomic radius. For a Coulomb potential one has that the outer electron is periodically kicked, and so a prove is given that the same should happen to Rydberg atoms in intense microwave fields. The distribution representing the kicking has a Fourier series with just odd terms. Using a modified Rayleigh-Schrödinger perturbation theory, it is shown that under the same condition of validity of the quiver motion amplitude to atomic radius ratio, the atomic wave function is only slightly modified by the laser field due to the way the energy levels rearrange themselves. This gives a prove of stabilization in the limit of laser frequency going to infinity. Then, perturbation theory can be applied when the Keldysh parameter becomes smaller with respect to the shifted distance between the energy levels of the atom.
Quantum electrodynamics in a laser is formulated, in which the electron-laser interaction is exactly considered, while the interaction of an electron and a single photon is considered by perturbation. The formulation is applied to the electron-laser collisions. The effect of coherence between photons in the laser is therefore fully considered in these collisions. The possibility of $γ-$ray laser generation by use of this kind of collision is discussed.
We find the quantum power emitted and distribution in $3+1$-dimensions of relativistic acceleration radiation using a single perfectly reflecting mirror via Lorentz invariance demonstrating close analogies to point charge radiation in classical electrodynamics.
A laser-atom interaction simulator derived from quantum electrodynamics (LASED) is presented, which has been developed in the python programming language. LASED allows a user to calculate the time evolution of a laser-excited atomic system. The model allows for any laser polarization, a Gaussian laser beam profile, a rotation of the reference frame chosen to define the states, and an averaging over the Doppler profile of an atomic beam. Examples of simulations using LASED are presented for excitation of calcium from the 4$^1S_0$ state to the 4$^1P_1$ state, for excitation from the helium 3$^1D…
The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels of these equations include one-photon exchange interactions. The equations have the expected Schroedinger non-relativistic limit. Application to some exotic few lepton systems is discussed briefly.
In a recent paper [arXiv:1502.06856] the authors studied numerically the hydrogen ground state in stochastic electrodynamics (SED) within the the non-relativistic approximation. In quantum theory the leading non-relativistic corrections to the ground state energy dominate the Lamb shift related to the photon cloud that should cause the quantum-like behaviour of SED. The present work takes these corrections into account in the numerical modelling. It is found that they have little effect; the self-ionisation that occurs without them remains present. It is speculated that the point-charge approx…
A relativistic density-functional theory based on a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electron-positron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrained-search formalism, a Kohn-Sham scheme is formulated in a quite similar way to non-relativistic density-functi…
Electrodynamical processes induced in complex systems like semiconductors by strong electromagnetic fields, have traditionally/conventionally been described using semi-classical approaches. Although these approaches, allowed the investigation of ultrafast dynamics in solids culminating in multi-petahertz electronics, they do not provide any access in the quantum optical nature of the interaction as they treat the driving-field classically and unaffected by the interaction. Here, using a full quantum-optical approach, we demonstrate that the sub-cycle electronic response in a strongly driven se…
Energy equipartition is appropriate only for nonrelativistic classical mechanics, but has only limited relevance for a relativistic theory such as classical electrodynamics. In this article, we discuss harmonic-oscillator thermal equilibrium from three different perspectives. First, we contrast the thermal equilibrium of nonrelativistic mechanical oscillators (where point collisions are allowed and frequency is irrelevant) with the equilibrium of relativistic radiation modes (where frequency is crucial). The Rayleigh-Jeans law appears from applying a dipole-radiation approximation to impose th…
The ability to achieve ultra-strong coupling between light and matter promises to bring about new means to control material properties, new concepts for manipulating light at the atomic scale, and fundamentally new insights into quantum electrodynamics (QED). Thus, there is a need to develop quantitative theories of QED phenomena in complex electronic and photonic systems. In this Letter, we develop a variational theory of general non-relativistic QED systems of coupled light and matter. Essential to our ansatz is the notion of an effective photonic vacuum whose modes are different than the mo…
A semi-relativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that relativistic effects induced by a super-intense laser field can, to a surprisingly large extent, be accounted for by the Schr{ö}dinger equation, provided that we replace the rest mass in the propagation gauge Hamiltonian by the corresponding time-dependent field-dressed mass. The validity of the semi-relativistic approach is tested numerically on a hydrogen atom exposed to an intense XUV laser pulse strong enough to accelerate the electron t…
We develop a relativistic Coulomb-corrected strong field approximation (SFA) for the investigation of spin effects at above-threshold ionization in relativistically strong laser fields with highly charged hydrogen-like ions. The Coulomb-corrected SFA is based on the relativistic eikonal-Volkov wave function describing the ionized electron laser-driven continuum dynamics disturbed by the Coulomb field of the ionic core. The SFA in different partitions of the total Hamiltonian is considered. The formalism is applied for direct ionization of a hydrogen-like system in a strong linearly polarized l…
The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interactio…
High-order harmonic generation (HHG) by hydrogenlike atoms/ions in the uniform periodic electric field, formed by the two linearly polarized counterpropagating laser beams of relativistic intensities, is studied. The relativistic quantum theory of HHG in such fields, at which the impeding factor of relativistic magnetic drift of a strong wave can be eliminated, is presented arising from the Dirac equation. Specifically, a scheme of HHG in underdense plasma with the copropagating ultraintense laser and fast ion beams is proposed.
The availability of efficient photon sources with specific properties is important for quantum-technological applications. However, the realization of such photon sources is often challenging and hence alternative perspectives that suggest new means to enhance desired properties while suppressing detrimental processes are valuable. In this work we highlight that ab-initio simulations of coupled light-matter systems can provide such new avenues. We show for a simple model of a quantum ring that by treating light and matter on equal footing we can create and enhance novel pathways for down-conve…
The recent experimental observation of spinor self-ordering of ultracold atoms in optical resonators has set the stage for the exploration of emergent magnetic orders in quantum-gas--cavity systems. Based on this platform, we introduce a generic scheme for the implementation of long-range quantum spin Hamiltonians composed of various types of couplings, including Heisenberg and Dzyaloshinskii-Moriya interactions. Our model is comprised of an effective two-component Bose-Einstein condensate, driven by two classical pump lasers and coupled to a single dynamic mode of a linear cavity in a double …
The ideas behind the nonlocal classical statistical field theory model for the quantized Klein-Gordon field introduced in Morgan(2001, quant-ph/0106141) are extended to accommodate quantum electrodynamics. The anticommutation rules for the quantized Dirac spinor field are given a classical interpretation as a relativistically covariant modification of the minimal coupling interaction between the classical electromagnetic field and a classical Dirac spinor field.
The dynamics of cold trapped ions in a high-finesse resonator results from the interplay between the long-range Coulomb repulsion and the cavity-induced interactions. The latter are due to multiple scatterings of laser photons inside the cavity and become relevant when the laser pump is sufficiently strong to overcome photon decay. We study the stationary states of ions coupled with a mode of a standing-wave cavity as a function of the cavity and laser parameters, when the typical length scales of the two self-organizing processes, Coulomb crystallization and photon-mediated interactions, are …
In the present note new effects concerned the dynamics of a charged spin-1/2 particle in a strong monochromatic plane wave background are discussed beyond the conventional dipole approximation. Namely using the semiclassical approach in the semi-relativistic regime it is shown that the magnetic forces associated with the laser field have been retained and alter the spin evolution appreciably.
Spectroscopic signatures associated with symmetric Lorentzian and asymmetric Fano line shapes are ubiquitous. Distinct features of Fano resonances in contrast with conventional symmetric resonances have found several applications in photonics such as optical switching, sensing, lasing, and nonlinear and slow-light devices. Therefore, it is important to have control over the generation of these resonances. In this work, we show through ab initio simulations of coupled light-matter systems that Fano interference phenomena can be realized in a multimode photonic environment by strong coupling to …
Light-Matter Response in Non-Relativistic Quantum Electrodynamics: Quantum Modifications of Maxwell's Equations
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）
