Theory of Multiphoton Processes

In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the densityfunctional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

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“…In a next step, we transform the Hamiltonian into its lengthgauge form [85] by the unitary transformation…”

Section: Appendix A: Conventionsmentioning

confidence: 99%

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

et al. 2014

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“…(14), to which we limit our consideration. Different theoretical approaches can be used for a driven two-level system, which is described in the books and reviews [102][103][104][105][106][107]. The choice of the formalism depends on the formulation of a problem and on the parameters of the system, such as the bias offset ε 0 , driving amplitude A and frequency ω.…”

Section: Dynamical Behavior Of a Two-level Systemmentioning

confidence: 99%

Multiphoton transitions in Josephson-junction qubits (Review Article)

Shevchenko¹,

Omelyanchouk²,

Il’ichev³

2012

Low Temperature Physics

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Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator's state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices.We present recent results for the driven superconducting qubit -resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau-Zener-Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing. Contents

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“…2(a), given by eq. (24), and characterized by an average position z 0 , [2]. The probability density and the modulus of the wave-function (solid line) have a Gaussian distribution.…”

Section: Gaussian Wave-packets -Coherent Statesmentioning

confidence: 99%

“…The series then appears as a dominant peak accompanied by side bands shifted in energy by an integer multiple of the driving frequency ω. In the language of the scattering theory [18,23,24], these side bands can be seen as the scattering of the probe photon assisted by one or several photons of the drive. In any case, the Floquet formalism is well suited, since it contains this weak driving regime as a limiting case, as well as the strong driving regime needed to generate a non-dispersive wave-packet.…”

Section: Interaction Of a Non-dispersive Wave-packet With A Monochrommentioning

confidence: 99%

Non-dispersive wave packets in periodically driven quantum systems

2002

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With the exception of the harmonic oscillator, quantum wave packets usually spread as time evolves. This is due to the non-linear character of the classical equations of motion which makes the various components of the wave packet evolve at various frequencies. We show here that, using the non-linear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the non-linear resonance island. We discuss the general mechanism which produces the non-dispersive wave packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wave packets for a model one-dimensional as well as for realistic three-dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long lifetimes. The requirements for experiments aimed at observing such non-dispersive wave packets are also considered. The analysis is extended to situations in which the driving frequency is a multiple of the internal atomic frequency. Such a case allows us to discuss non-dispersive states composed of several, macroscopically separated wave packets communicating among themselves by tunneling. Similarly we briefly discuss other closely related phenomena in atomic and molecular physics as well as possible further extensions of the theory. (C) 2002 Elsevier Science B.V. All rights reserved

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Theory of Multiphoton Processes

Abstract: Theory of multiphoton processes.(Physics of atoms and molecules) Includes bibliographical references and index. I. Multiphoton processes. I. Title. II. Series.

Cited by 504 publications

References 0 publications

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Quantum-electrodynamical density-functional theory: Bridging quantum optics and electronic-structure theory

Multiphoton transitions in Josephson-junction qubits (Review Article)

Non-dispersive wave packets in periodically driven quantum systems

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