arXiv subjects

Per K. Rekdal

Publications and source records attributed to Per K. Rekdal.

9 recordsLinked to original sources

arXiv2026

Fractional Angular Momentum and Quasi-Probability Densities for Angular Degrees of Freedom

In the present update work we consider properly defined two-parameter quasi-probability densities that, e.g., can be used as witness for quantum behaviour for a class of pure states as expressed in terms of a self-adjoint observable angular position and the corresponding angular momentum operator L. It is shown that negative values of the corresponding quasi-probability densities may reveal the quantum nature of superpositions of angular momentum eigenstates with a fractional mean value of L but in an ambiguous manner. For a suitable choice of parameters these quasi-probability densities are positive and are in accordance with Borns rule in quantum mechanics. It is also shown that experimental data of the uncertainties for the angular position and L observables can be sufficient to reveal some unique quantum-mechanical features of such states without necessarily making use of quasi-probability densities.

quant-ph↗

arXiv2023

On Quantum States for angular Position and Angular Momentum of Light

In the present paper we construct a properly defined quantum state expressed in terms of elliptic Jacobi theta functions for the self-adjoint observables angular position $θ$ and the corresponding angular momentum operator $L = -id/dθ$. The quantum uncertainties $Δθ$ and $ΔL$ for the state are well-defined and are, e.g., shown to give a lower value of the uncertainty product $ΔθΔL$ than the minimal uncertainty states of Ref.\cite{Padgett_2004}. The mean value $< L >$ of the state is not required to be an integer. In the case of any half-integer mean value $< L >$ the state constructed exhibits a remarkable critical behavior with upper and lower bounds $Δθ< \sqrt{π^2/3 -2}$ and $ΔL > 1/2$.

quant-ph↗

arXiv2019

Causality in Quantum Field Theory with Classical Sources - Quantum Electrodynamics

In an exact quantum-mechanical framework, we show that expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge, and in the presence of classical sources, automatically lead to causal and retarded electro-magnetic field strengths. The classical $\hbar$-independent Maxwell's equations naturally emerge from this fundamental quantum-mechanical approach in terms of expectation values of quantum fields, and are therefore also consistent with the special theory of relativity. The fundamental difference between interference phenomena due to the linear nature of the classical Maxwell theory as, e.g., in classical optics, and interference effects of quantum states is clarified. The framework outlined also provides for a simple approach to, e.g., spontaneous photon emission and/or absorption processes as well as to the classical Vavilov-Cherenkov radiation. The inherent and necessary quantum fluctuations, limiting a precise space-time knowledge of expectation values of the quantum fields considered, are, finally, recalled.

quant-ph↗

arXiv2018

Quantum Field Theory with Classical Sources - Linearized Quantum Gravity

In a previous work and in terms of an exact quantum-mechanical framework, $\hbar$-independent causal and retarded expectation values of the second-quantized electro-magnetic fields in the Coulomb gauge were derived in the presence of a conserved classical electric current. The classical $\hbar$-independent Maxwell's equations then naturally emerged. In the present work, we extend these considerations to linear gravitational quantum deviations around a flat Minkowski space-time in a Coulomb-like gauge. The emergence of the classical causal and properly retarded linearized classical theory of general relativity with a conserved classical energy-momentum tensor is then outlined. The quantum-mechanical framework also provides for a simple approach to classical quadrupole gravitational radiation of Einstein and microscopic spontaneous graviton emission and/or absorption processes.

gr-qc↗

arXiv2012

Memory Effects in Spontaneous Emission Processes

We consider a quantum-mechanical analysis of spontaneous emission in terms of an effective two-level system with a vacuum decay rate $Γ_0$ and transition angular frequency $ω_A$. Our analysis is in principle exact, even though presented as a numerical solution of the time-evolution including memory effects. The results so obtained are confronted with previous discussions in the literature. In terms of the {\it dimensionless} lifetime $τ= tΓ_0$ of spontaneous emission, we obtain deviations from exponential decay of the form ${\cal O} (1/τ)$ for the decay amplitude as well as the previously obtained asymptotic behaviors of the form ${\cal O} (1/τ^2)$ or ${\cal O} (1/τ\ln^2τ)$ for $τ\gg 1 $. The actual asymptotic behavior depends on the adopted regularization procedure as well as on the physical parameters at hand. We show that for any reasonable range of $τ$ and for a sufficiently large value of the required angular frequency cut-off $ω_c$ of the electro-magnetic fluctuations, i.e. $ω_c \gg ω_A$, one obtains either a ${\cal O} (1/τ)$ or a ${\cal O} (1/τ^2)$ dependence. In the presence of physical boundaries, which can change the decay rate with many orders of magnitude, the conclusions remains the same after a suitable rescaling of parameters.

quant-ph↗

arXiv2006

Decay Processes in the Presence of Thin Superconducting Films

In a recent paper [Phys. Rev. Lett. 97, 070401 (2006)] the transition rate of magnetic spin-flip of a neutral two-level atom trapped in the vicinity of a thick superconducting body was studied. In the present paper we will extend these considerations to a situation with an atom at various distances from a dielectric film. Rates for the corresponding electric dipole-flip transition will also be considered. The rates for these atomic flip transitions can be reduced or enhanced, and in some situations they can even be completely suppressed. For a superconducting film or a thin film of a perfect conducting material various analytical expressions are derived that reveals the dependence of the physical parameters at hand.

quant-ph↗

arXiv2006

Collective Two-Atom Effects and Trapping States in the Micromaser

We investigate signals of trapping states in the micromaser system in terms of the average number of cavity photons as well as a suitably defined correlation length of atoms leaving the cavity. In the description of collective two-atom effects we allow the mean number of pump atoms inside the cavity during the characteristic atomic cavity transit time to be as large as of order one. The master equation we consider, which describes the micromaser including collective two-atom effects, still exhibits trapping states for even for a mean number of atoms inside the cavity close to one. We, however, argue more importantly that the trapping states are more pronounced in terms of the correlation length as compared to the average number of cavity photons, i.e. we suggest that trapping states can be more clearly revealed experimentally in terms of the atom correlation length. For axion detection in the micromaser this observable may therefore be an essential ingredient.

quant-ph↗

arXiv2003

On the Preparation of Pure States in Resonant Microcavities

We consider the time evolution of the radiation field (R) and a two-level atom (A) in a resonant microcavity in terms of the Jaynes-Cummings model with an initial general pure quantum state for the radiation field. It is then shown, using the Cauchy-Schwarz inequality and also a Poisson resummation technique, that {\it perfect} coherence of the atom can in general never be achieved. The atom and the radiation field are, however, to a good approximation in a pure state $|ψ>_A\otimes|ψ>_R$ in the middle of what has been traditionally called the ``collapse region'', independent of the initial state of the atoms, provided that the initial pure state of the radiation field has a photon number probability distribution which is sufficiently peaked and phase differences that do not vary significantly around this peak. An approximative analytic expression for the quantity $\Tr[ρ^2_{A}(t)]$, where $ρ_{A}(t)$ is the reduced density matrix for the atom, is derived. We also show that under quite general circumstances an initial entangled pure state will be disentangled to the pure state $|ψ>_{A\otimes R}$.

quant-ph↗

arXiv2000

Macroscopic Interference Effects in Resonant Cavities

We investigate the possibility of interference effects induced by macroscopic quantum-mechanical superpositions of almost othogonal coherent states - a Schroedinger cats state - in a resonant microcavity. Despite the fact that a single atom, used as a probe of the cat state, on the average only change the mean number of photons by one unit, we show that this single atom can change the system drastically. Interference between the initial and almost orthogonal macroscopic quantum states of the radiation field can now take place. Dissipation under current experimental conditions is taken into account and it is found that this does not necessarily change the intereference effects dramatically.

quant-ph↗