Dynamics of an atomic electron and its electromagnetic field in a cavity (original) (raw)
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Analytical and numerical analysis of the atom–field dynamics in non-stationary cavity QED
Journal of Physics B: Atomic, Molecular and Optical Physics, 2011
We study analytically and numerically the dynamics of the quantum non-stationary system composed of a two-level atom interacting with a single mode cavity field whose frequency is rapidly modulated in time (with a small amplitude). We identify modulation laws resulting in qualitatively different dynamical regimes and we present analytical solutions in some simple cases. In particular, we analyse minutely the influence of the field-atom coupling on the photon generation from vacuum via the dynamical Casimir effect.
Quantum magneto-electrodynamics of electrons embedded in a photon cavity
2012
We investigate the coupling between a quantized electromagnetic field in a cavity resonator and a Coulomb interacting electronic system in a nanostructure in an external magnetic field. Effects caused by the geometry of the electronic system and the polarization of the electromagnetic field are explicitly taken into account. Our numerical results demonstrate that the two-level system approximation and the Jaynes-Cummings model remain valid in the weak electron-photon coupling regime, while the quadratic vector potential in the diamagnetic part of the charge current leads to significant correction to the energy spectrum in the strong coupling regime. Furthermore, we find that a coupling to a strong cavity photon mode polarizes the charge distribution of the system requiring a large basis of single-electron eigenstates to be included in the model.
Schrödinger Theory of Electrons in Electromagnetic Fields: New Perspectives
Computation
The Schrödinger theory of electrons in an external electromagnetic field is described from the new perspective of the individual electron. The perspective is arrived at via the time-dependent "Quantal Newtonian" law (or differential virial theorem). (The time-independent law, a special case, provides a similar description of stationary-state theory). These laws are in terms of "classical" fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. The laws reveal the following physics: (a) in addition to the external field, each electron experiences an internal field whose components are representative of a specific property of the system such as the correlations due to the Pauli exclusion principle and Coulomb repulsion, the electron density, kinetic effects, and an internal magnetic field component. The response of the electron is described by the current density field; (b) the scalar potential energy of an electron is the work done in a conservative field. It is thus path-independent. The conservative field is the sum of the internal and Lorentz fields. Hence, the potential is inherently related to the properties of the system, and its constituent property-related components known. As the sources of the fields are functionals of the wave function, so are the respective fields, and, therefore, the scalar potential is a known functional of the wave function; (c) as such, the system Hamiltonian is a known functional of the wave function. This reveals the intrinsic self-consistent nature of the Schrödinger equation, thereby providing a path for the determination of the exact wave functions and energies of the system; (d) with the Schrödinger equation written in self-consistent form, the Hamiltonian now admits via the Lorentz field a new term that explicitly involves the external magnetic field. The new understandings are explicated for the stationary state case by application to two quantum dots in a magnetostatic field, one in a ground state and the other in an excited state. For the time-dependent case, the evolution of the same states of the quantum dots in both a magnetostatic and a time-dependent electric field is described. In each case, the satisfaction of the corresponding "Quantal Newtonian" law is demonstrated.
Coupling of electrons to the electromagnetic field in a localized basis
Physical Review B, 2008
A simple formula is obtained for coupling electrons in a complex system to the electromagnetic field. It includes the effect of intra-atomic excitations and nuclear motion, and can be applied in, e.g., first-principles-based simulations of the coupled dynamics of electrons and nuclei in materials and molecules responding to ultrashort laser pulses. Some additional aspects of nonadiabatic dynamical simulations are also discussed, including the potential of "reduced Ehrenfest" simulations for treating problems where standard Ehrenfest simulations will fail.
Shaking' of an atom in a non-stationary cavity
Physics Letters A, 2000
We consider an atom interacting with a quantized electromagnetic field inside a cavity with variable parameters. The atom in the ground state located in the initially empty cavity can be excited by variation of cavity parameters. We have discovered two mechanisms of atomic excitation. The first arises due to the interaction of the atom with the non-stationary electromagnetic field created by modulation of cavity parameters. If the characteristic time of variation of cavity parameters is of the order of the atomic transition time, the processes of photon creation and atomic excitation are going on simultaneously and hence excitation of the atom cannot be reduced to trivial absorption of the photons produced by the dynamical Casimir effect. The second mechanism is "shaking" of the atom due to fast modulation of its ground state Lamb shift which takes place as a result of fast variation of cavity parameters. The last mechanism has no connection with the vacuum dynamical Casimir effect. Moreover, it opens a new channel of photon creation in the non-stationary cavity. Nevertheless, the process of photon creation is altered by the presence of the atom in the cavity, even if one disregards the existence of the new channel. In particular, it removes the restriction for creation of only even number of photons and also changes the expectation value for the number of created photons. Our consideration is based on a simple model of a two-level atom interacting with a single mode of the cavity field. Qualitatively our results are valid for a real atom in a physical cavity.
Pramana, 2017
In this paper, the model describing a double five-level atom interacting with a single mode electromagnetic cavity field in the (off) non-resonate case is studied. We obtained the constants of motion for the considered model. Also, the state vector of the wave function is given by using the Schrödinger equation when the atom is initially prepared in its excited state. The dynamical evolutions for the collapse revivals, the antibunching of photons and the field squeezing phenomena are investigated when the field is considered in a coherent state. The influence of detuning parameters on these phenomena is investigated. We noticed that the atom-field properties are influenced by changing the detuning parameters. The investigation of these aspects by numerical simulations is carried out using the Quantum Toolbox in Python (QuTip).
Dynamics of Two Atoms Coupled to a Cavity Field
Modern Physics Letters B, 2003
We investigate the interaction of two two-level atoms with a single mode cavity field. One of the atoms is exactly at resonance with the field, while the other is well far from resonance and hence is treated in the dispersive limit. We find that the presence of the non-resonant atom produces a shift in the Rabi frequency of the resonant atom, as if it was detuned from the field. We focus on the discussion of the evolution of the state purity of each atom.
Dynamics of a three-level atom interacting with a bimodal field in a resonant cavity
We have discussed the time evolution along with the nonclassicality phenomena of a system containing a vee-type three-level atom interacting with a bimodal electromagnetic field. A general expression for the atomic inversion is presented. It is found that the model undergoes Rabi oscillation. The total noise of the output state is measured.
The Vacuum Electromagnetic Fields and the Schrödinger Equation
Foundations of Physics, 2007
Several authors have used the Heisenberg picture to show that the atomic transitions, the stability of the ground state and the positionmomentum commutation relation [x, p] = i , can only be explained by introducing radiation reaction and vacuum electromagnetic fluctuation forces. Here we consider the simple case of a nonrelativistic charged harmonic oscillator, in one dimension, to investigate how to take into account the radiation reaction and vacuum fluctuation forces within the Schrödinger picture. We consider the effects of both classical zero-point and thermal electromagnetic vacuum fields. We show that the zero-point electromagnetic fluctuations are dynamically related to the momentum operator p = −i ∂/∂x used in the Schrödinger picture. Consequently, the introduction of the zero-point electromagnetic fields in the vector potential A x (t) used in the Schrödinger equation, generates "double counting", as was shown recently by A.J. Faria et al. (Physics Letters A 305 (2002) 322). We explain, in details, how to avoid the "double counting" by introducing only the radiation reaction and the thermal electromagnetic fields into the Schrödinger equation.