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.Comment: 17 pages, 4 figures, 1 table and Supplemental Material

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

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

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

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.Comment: minor correction

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

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.Comment: 11 pages, 9 figure

Investigation of the Kapitza-Dirac effect in the relativistic regime

Quantum mechanical diffraction is of particular interest, because it contradicts our everyday life experience. This theoretical work considers the diffraction of electrons at standing waves of light, referred to as the Kapitza-Dirac effect. The work focuses on a special version of a Kapitza-Dirac effect in which the electron interacts with three photons. The particular property of this 3-photon Kapitza-Dirac effect is, that the electron spin is rotated. This work considers different relativistic and non-relativistic quantum mechanical wave equations which are described in momentum space. On one hand, the quantum dynamics of the diffracted electrons is solved numerically in momentum space and the properties of the 3-photon Kapitza-Dirac effect are investigated in detail. On the other hand, the quantum dynamics is solved via time-dependent perturbation theory and is compared with the numerical results. In contrast to the originally proposed Kapitza-Dirac effect with two interacting photons, the number of absorbed and emitted photons by the electron is not equal for the 3-photon Kapitza-Dirac effect. Therefore, the diffraction process only appears for relativistic electron momenta in laser propagation direction. Furthermore, a very high field strength of the laser beam is required for driving the Kapitza- Dirac effect with a measurable diffraction probability. The electron spin is rotated along the axis of the magnetic field of the laser beam, when it undergoes the diffraction process. The rotation angle of the spin rotation depends on the electron momentum component in laser polarization direction. Therefore, the probability for flipping the electron spin can be tuned by choosing the electron momentum in the direction of the laser polarization. An experimental investigation may by established by utilizing future X-ray laser facilities