The angular correlation of two Lyman-α photons generated by the linearly polarized single-photon absorption of H 2 (X 1 Σ g + ) followed by the neutral dissociation of the doubly excited Q 2 1 Π u (1) state has been theoretically investigated with the second-order correlation function in quantum optics. A strong angular correlation has been obtained even for the molecules randomly oriented in space, due to the complicated entanglement of two H(2p) atoms in the intermediate state. It has been revealed how the symmetry properties in the electronic state are transferred to the two-photon state and how they manifest themselves in the angular correlation function.
The angular correlation functions (ACFs) of a pair of Lyman-\ensuremath{\alpha} photons emitted from H fragments in the photodissociation of a hydrogen molecule are measured at a 33.66-eV incident photon energy and at hydrogen gas pressures of approximately 0.1 and 1 Pa. The ACFs are measured for both opposite and nonopposite arrangements of the two photon detectors. It turns out that the experimental ACFs involve neither the contribution of the reactions
H(n=2)+H2 nor the contribution of the cascade from
H(n \ensuremath{\geqslant} 3) to H(
2p) fragments. Thus the experimental ACFs are those for primary H(
2p) pairs following the photodissociation of
H2. The experimental ACFs are compared with (i) the theoretical ACF for entangled pairs of H(
2p) atoms, where the magnetic quantum number of each hydrogen atom is indefinite, and (ii) the theoretical ACF for H(
2p) pairs with definite magnetic quantum number of each hydrogen atom relative to the internuclear axis [the former entangled state of H(
2p) pairs is a sum of the latter pair states with definite magnetic quantum number]. In the theoretical ACF in (ii), the disentanglement in H(
2p) pairs during the dissociation is considered. The experimental ACFs show a similar tendency in angular dependence to the theoretical ACF for entangled H(
2p) pairs. However, there still remains a considerable difference in the variation magnitude between those experimental and theoretical ACFs. The experimental ACFs show the reverse tendency in angular dependence to the theoretical ACF for H(
2p) pairs with definite magnetic quantum number of each hydrogen atom relative to the internuclear axis. We thus conclude that the pair of H(
2p) atoms in the photodissociation of
H2 is unlikely to be in the definite states of magnetic quantum number of each hydrogen atom relative to the internuclear axis, i.e., unlikely to be in the components of the entangled state of H(
2p) pairs.
An analytical expression of the angular correlation function of a pair of Lyman-$\ensuremath{\alpha}$ photons in the photodissociation of a hydrogen molecule is derived theoretically in a manner based on both atomic and molecular physics and quantum optics. The angular correlation function turns out to be expressed in terms of cosine (sine) functions of four angular variables of detectors with five coefficients. The angular correlation function is expanded in terms of the spherical harmonics for investigating which terms are involved, and we discuss the reason why they are involved. Interesting features are revealed in the expansion. We then search for a special detector arrangement where the angular-dependent terms vanish in the angular correlation function expressed in terms of the spherical harmonics. It turns out that no such detector arrangement in fact exists, but there is a special pair of detector arrangements where the angular-dependent terms vanish in the summation of two values of the angular correlation function expressed in terms of the spherical harmonics. We refer to such a pair of detector arrangements as a magic pair.
The radiative recombination of a free electron into excited states of bare, high- Z ions and the subsequent photon decay are studied in the framework of the density matrix theory. Emphasis is placed, in particular, on the angular correlation between the recombination and the decay photons. The general expression for the photon–photon angular correlation function is derived, based on Dirac's equation as appropriate for high- Z ions. Computations for the dependence of the photon–photon correlation function on the nuclear charge and the projectile energies are carried out for the capture into the 2p 3/2 level and the subsequent Lyman -α 1 (2p 3/2 → 1s 1/2 ) radiation.
The dynamics and the cross sections associated with the excitation of a ground-state dipolar molecule to an excited state, by the simultaneous absorption of two photons, are discussed using the rotating wave approximation and time-dependent perturbation theory. The excitations of ten- and two-energy level representations of model dipolar molecules are used for illustrative purposes. The temporal development of the final state of the excitation process and the two-photon excitation cross sections are discussed as functions of laser intensity, laser–molecule interaction time and the two types of excitation mechanism (which are available for dipolar molecules, relative to the one mechanism for a non-polar molecule). The results are used to discuss the validity of perturbation theory treatments of the problem and various strategies for the enhancement of the intrinsically weak two-photon excitation process.
The two-photon decay of highly charged hydrogenlike ions is studied within the framework of second-order perturbation theory, based on Dirac's equation. Attention has been paid to the angle-angle correlations between the two emitted photons. In particular, the density matrix theory is applied in order to explore how these angle-angle correlations are affected by the alignment of the excited states of the ions. Detailed computations have been carried out for the $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition in hydrogenlike uranium
U91+ ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the
3d5∕2 state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.