arXiv subjects

Sven Ahrens

Publications and source records attributed to Sven Ahrens.

At least 19 recordsLinked to original sources

arXiv2026

Strong coupling of virtual negative states in the Kapitza-Dirac effect

Negative states are an intrinsic property of relativistic quantum theory and related to anti-particles in the context of the Dirac sea concept. We show that negative states can dominantly contribute to the diffraction amplitude in the quantum dynamics of the two-photon Kapitza-Dirac effect. We draw our conclusion by investigating solutions from time-dependent perturbation theory, where the perturbative solutions are in match with numeric solutions of the relativistic quantum system and also with the numeric and analytic solutions from the relativistic equations of motion of a classical point-like electron in an external standing wave light field. While our numeric solutions assume a strong laser field, the analytic solutions indicate that negative state coupling remains dominant for arbitrary low field amplitudes, where in the single-photon case (Compton scattering) negative state coupling can be mathematically associated with the interaction of a virtual electron-positron pair in the context of a quantized theory in old-fashioned perturbation theory.

quant-ph↗

arXiv2025

Gravitational photon echo

The generation, controls, and storage of the gravitationally induced photon echo using the 8.4 eV Thorium-229 nuclear clock transition on Earth are theoretically investigated. With its exceptionally narrow linewidth of approximately 1 mHz and high quality factor in the order of $10^{19}$, the Thorium-229 clock transition allows for the potential detection of gravitational-redshift effects at millimeter-scale altitude variations. Moreover, the 1740-second half lifetime of the Thorium-229 isomeric state allows for the slow movement of the system within its coherence time. Along this line, we explore the generation, controls, and storage of photon echo arising from a rotation induced inversion of the gravitational frequency shift in a single target or in multiple equally spaced samples. Our approach lays the foundation for the controllable gravitational quantum optics on Earth.

quant-ph↗

arXiv2024

Perturbative solution approach for computing the two-photon Kapitza-Dirac effect in a Gaussian beam standing light wave

Theoretical spin properties of the Kapitza-Dirac effect beyond the plane-wave description are not known in detail. We develop a method for computing electron diffraction of the two-photon Kapitza-Dirac effect in a two-dimensional Gaussian beam standing light wave within a relativistic formulation. The solutions are computed on the basis of time-dependent perturbation theory, where a momentum space formulation with the use of a Fourier transformation of the external potential allows for the solving the perturbative time-integrals. An iteration over each possible quantum state combination leads to a quadratic scaling of our method with respect to spacial grid resolution, where time-stepping does not occur in the numeric implementation. The position- and momentum space grids are adapted to the two-photon interaction geometry at low resolution, for which our study only finds partial convergence of the simulated diffraction pattern. Further, the method has the advantage of having an easy implementable parallelization layout.

quant-ph↗

arXiv2023

Two-dimensional simulation of the spin-flip in the Kapitza-Dirac effect

Many calculations in strong field quantum field theory are carried out by using a simple field geometry, often neglecting the spacial field envelope. In this article, we simulate the electron diffraction quantum dynamics of the Kapitza-Dirac effect in a Gaussian beam standing light wave. The two-dimensional simulation is computed in a relativistic framework, by solving the Dirac equation with the fast Fourier transform split operator method. Except the numerical propagation method, our results are obtained without applying approximations and demonstrate that a spin-flip in the Kapitza-Dirac effect is possible. We further discuss properties, such as the validity of a plane wave approach for the theoretical description, the influence of the longitudinal polarization component due to laser beam focusing and higher order diffraction peaks in Kapitza-Dirac scattering.

quant-ph↗

arXiv2023

Parameter space investigation for spin-dependent electron diffraction in the Kapitza-Dirac effect

We demonstrate that spin-dependent electron diffraction is possible for a smooth range of transverse electron momenta in a two-photon Bragg scattering scenario of the Kapitza-Dirac effect. Our analysis is rendered possible by introducing a generalized specification for quantifying spin-dependent diffraction, yielding an optimization problem which is solved by making use of a Newton gradient iteration scheme. With this procedure, we investigate the spin-dependent effect for different transverse electron momenta and different laser polarizations of the standing light wave Kapitza-Dirac scattering. The possibility for using arbitrarily low transverse electron momenta, when setting up a spin-dependent Kapitza-Dirac experiment allows longer interaction times of the electron with the laser and therefore enables less constraining parameters for an implementation of the effect.

quant-ph↗

arXiv2023

Gravitationally sensitive structured x-ray optics using nuclear resonances

Einstein's general theory of relativity not only revolutionized human understanding of the universe, but also brought many gravitational applications in large scale, such as gravitational-wave astronomy, gravitational lensing, and the operation of the global positioning system. However, it still remains a challenge to implement applications for gravitational effects at small spacial extensions on Earth. Here, we investigate a structured waveguide system that allows for the control of an x-ray profile at altitude separations of millimeters and even shorter using the nuclear resonant scattering of x rays. Our present results suggest a potential compact scheme for turning the Earth's gravity into a practical application of x-ray optics.

physics.optics↗

arXiv2022

Beam focus and longitudinal polarization influence on spin dynamics in the Kapitza-Dirac effect

We theoretically investigate the influence of a longitudinal laser polarization component from beam focusing on spin dynamics in Kapitza-Dirac scattering by solving the relativistic Dirac equation with time-dependent perturbation theory. The transverse spacial dependence of the longitudinal beam polarization component is accounted for, by approximating a Gaussian beam with plane-wave components. We find that corrections from a longitudinal laser beam polarization component approximately scale with the second power of the diffraction angle $ε$, from which we conclude that a related influence from beam focusing can be made negligibly small for sufficiently low beam foci.

physics.optics↗

arXiv2020

Spin-dependent two-photon Bragg scattering in the Kapitza-Dirac effect

We present the possibility of spin-dependent Kapitza-Dirac scattering based on a two-photon interaction only. The interaction scheme is inspired from a Compton scattering process, for which we explicitly show the mathematical correspondence to the spin-dynamics of an electron diffraction process in a standing light wave. The spin effect has the advantage that it already appears in a Bragg scattering setup with arbitrary low field amplitudes, for which we have estimated the diffraction count rate in a realistic experimental setup at available X-ray free-electron laser facilities.

quant-ph↗

arXiv2017

Spin in Compton scattering with pronounced polarization dynamics

We theoretically investigate a scattering configuration in Compton scattering, in which the orientation of the electron spin is reversed and simultaneously, the photon polarization changes from linear polarization into circular polarization. The intrinsic angular momentum of electron and photon are computed along the coincident propagation direction of the incoming and outgoing photon. We find that this intrinsic angular momentum is not conserved in the considered scattering process. We also discuss the generation of entanglement for the considered scattering setup and present an angle dependent investigation of the corresponding differential cross section, Stokes parameters and spin expectation.

quant-ph↗

arXiv2017

Electron spin filter and polarizer in a standing light wave

We demonstrate the theoretical feasibility of spin-dependent diffraction and spin-polarization of an electron in two counter-propagating, circularly polarized laser beams. The spin-dynamics appears in a two-photon process of the Kapitza-Dirac effect in the Bragg regime. We show the spin-dependence of the diffraction process by comparison of the time-evolution of a spin-up and spin-down electron in a relativistic quantum simulation. We further discuss the spin properties of the scattering by studying an analytically approximated solution of the time-evolution matrix. A classification scheme in terms of unitary or non-unitary propagation matrices is used for establishing a generalized and spin-independent description of the spin properties in the diffraction process.

quant-ph↗

arXiv2015

Simulation of Zitterbewegung by modelling the Dirac equation in Metamaterials

We develop a dynamic description of an effective Dirac theory in metamaterials, in which the wavefunction is modeled by the corresponding electric and magnetic field in the metamaterial. This electro-magnetic field can be probed in the experimental setup, which means that the wavefunction of the effective theory is directly accessible by measurement. Our model is based on a plane wave expansion, which ravels the identification of Dirac spinors with single-frequency excitations of the electro-magnetic field in the metamaterial. The characteristic Zitterbewegung is shown to emerge in simulations of the effective theory and we verify this signature with an analytic solution.

quant-ph↗

arXiv2015

Spin dynamics in relativistic light-matter interaction

Various spin effects are expected to become observable in light-matter interaction at relativistic intensities. Relativistic quantum mechanics equipped with a suitable relativistic spin operator forms the theoretical foundation for describing these effects. Various proposals for relativistic spin operators have been offered by different authors, which are presented in a unified way. As a result of the operators' mathematical properties only the Foldy-Wouthuysen operator and the Pryce operator qualify as possible proper relativistic spin operators. The ground states of highly charged hydrogen-like ions can be utilized to identify a legitimate relativistic spin operator experimentally. Subsequently, the Foldy-Wothuysen spin operator is employed to study electron-spin precession in high-intensity standing light waves with elliptical polarization. For a correct theoretical description of the predicted electron-spin precession relativistic effects due to the spin angular momentum of the electromagnetic wave has to be taken into account even in the limit of low intensities.

quant-ph↗

arXiv2014

Gravitational and Relativistic Deflection of X-Ray Superradiance

Exploring Einstein's theories of relativity in quantum systems, for example by using atomic clocks at high speeds can deepen our knowledge in physics. However, many challenges still remain on finding novel methods for detecting effects of gravity and of special relativity and their roles in light-matter interaction. Here we introduce a scheme of x-ray quantum optics that allows for a millimeter scale investigation of the relativistic redshift by directly probing a fixed nuclear crystal in Earth's gravitational field with x-rays. Alternatively, a compact rotating crystal can be used to force interacting x-rays to experience inhomogeneous clock tick rates in a crystal. We find that an association of gravitational or special-relativistic time dilation with quantum interference will be manifested by deflections of x-ray photons. Our protocol suggests a new and feasible tabletop solution for probing effects of gravity and special relativity in the quantum world.

quant-ph↗

arXiv2014

Electron-spin dynamics in elliptically polarized light waves

We investigate the coupling of the spin angular momentum of light beams with elliptical polarization to the spin degree of freedom of free electrons. It is shown that this coupling, which is of similar origin as the well-known spin-orbit coupling, can lead to spin precession. The spin-precession frequency is proportional to the product of the laser-field's intensity and its spin density. The electron-spin dynamics is analyzed by employing exact numerical methods as well as time-dependent perturbation theory based on the fully relativistic Dirac equation and on the nonrelativistic Pauli equation that is amended by a relativistic correction that accounts for the light's spin density.

quant-ph↗

arXiv2014

Electron-spin dynamics induced by photon spins

Strong rotating magnetic fields may cause a precession of the electron's spin around the rotation axis of the magnetic field. The superposition of two counterpropagating laser beams with circular polarization and opposite helicity features such a rotating magnetic field component but also carries spin. The laser's spin density, that can be expressed in terms of the lase's electromagnetic fields and potentials, couples to the electron's spin via a relativistic correction to the Pauli equation. We show that the quantum mechanical interaction of the electron's spin with the laser's rotating magnetic field and with the laser's spin density counteract each other in such a way that a net spin rotation remains with a precession frequency that is much smaller than the frequency one would expect from the rotating magnetic field alone. In particular, the frequency scales differently with the laser's electric field strength depending on if relativistic corrections are taken into account or not. Thus, the relativistic coupling of the electron's spin to the laser's spin density changes the dynamics not only quantitatively but also qualitatively as compared to the nonrelativistic theory. The electron's spin dynamics is a genuine quantum mechanical relativistic effect.

quant-ph↗

arXiv2014

Relativistic spin operators in various electromagnetic environments

Different operators have been suggested in the literature to describe the electron's spin degree of freedom within the relativistic Dirac theory. We compare concrete predictions of the various proposed relativistic spin operators in different physical situations. In particular, we investigate the so-called Pauli, Foldy-Wouthuysen, Czachor, Frenkel, Chakrabarti, Pryce, and Fradkin-Good spin operators. We demonstrate that when a quantum system interacts with electromagnetic potentials the various spin operators predict different expectation values. This is explicitly illustrated for the scattering dynamics at a potential step and in a standing laser field and also for energy eigenstates of hydrogenic ions. Therefore, one may distinguish between the proposed relativistic spin operators experimentally.

quant-ph↗

arXiv2014

What is the relativistic spin operator?

Although the spin is regarded as a fundamental property of the electron, there is no universally accepted spin operator within the framework of relativistic quantum mechanics. We investigate the properties of different proposals for a relativistic spin perator. It is shown that most candidates are lacking essential features of proper angular momentum operators, leading to spurious Zitterbewegung (quivering motion) or violating the angular momentum algebra. Only the Foldy-Wouthuysen operator and the Pryce operator qualify as proper relativistic spin operators. We demonstrate that ground states of highly charged hydrogen-like ions can be utilized to identify a legitimate relativistic spin operator experimentally.

quant-ph↗

arXiv2013

Kapitza-Dirac effect in the relativistic regime

A relativistic description of the Kapitza-Dirac effect in the so-called Bragg regime with two and three interacting photons is presented by investigating both numerical and perturbative solutions of the Dirac equation in momentum space. We demonstrate that spin-flips can be observed in the two-photon and the three-photon Kapitza-Dirac effect for certain parameters. During the interaction with the laser field the electron's spin is rotated, and we give explicit expressions for the rotation axis and the rotation angle. The off-resonant Kapitza-Dirac effect, that is, when the Bragg condition is not exactly fulfilled, is described by a generalized Rabi theory. We also analyze the in-field quantum dynamics as obtained from the numerical solution of the Dirac equation.

physics.atom-ph↗