The evolution of Bose-Einstein condensates is amply described by the time-dependent Gross-Pitaevskii mean-field theory which assumes all bosons to reside in a single time-dependent one-particle state throughout the propagation process. In this work, we go beyond mean field and develop an essentially exact many-body theory for the propagation of the time-dependent Schrödinger equation of $N$ interacting identical bosons. In our theory, the time-dependent many-boson wave function is written as a sum of permanents assembled from orthogonal one-particle functions, or orbitals, where both the expansion coefficients and the permanents (orbitals) themselves are time-dependent and fully determined according to a standard time-dependent variational principle. By employing either the usual Lagrangian formulation or the Dirac-Frenkel variational principle we arrive at two sets of coupled equations of motion, one for the orbitals and one for the expansion coefficients. The first set comprises of first-order differential equations in time and nonlinear integrodifferential equations in position space, whereas the second set consists of first-order differential equations with time-dependent coefficients. We call our theory multiconfigurational time-dependent Hartree for bosons, or $\text{MCTDHB}\left(M\right)$, where $M$ specifies the number of time-dependent orbitals used to construct the permanents. Numerical implementation of the theory is reported and illustrative numerical examples of many-body dynamics of trapped Bose-Einstein condensates are provided and discussed. The convergence of the method with a growing number $M$ of orbitals is demonstrated in a specific example of four interacting bosons in a double well.

The first- and second-order correlation functions of trapped interacting Bose-Einstein condensates are investigated numerically on a many-body level from first principles. Correlations in real space and momentum space are treated. The coherence properties are analyzed. The results are obtained by solving the many-body Schrödinger equation. It is shown in an example how many-body effects can be induced by the trap geometry. A generic fragmentation scenario of a condensate is considered. The correlation functions are discussed along a pathway from a single condensate to a fragmented condensate. It is shown that strong correlations can arise from the geometry of the trap, even at weak interaction strengths. The natural orbitals and natural geminals of the system are obtained and discussed. It is shown how the fragmentation of the condensate can be understood in terms of its natural geminals. The many-body results are compared to those of mean-field theory. The best solution within mean-field theory is obtained. The limits in which mean-field theories are valid are determined. In these limits the behavior of the correlation functions is explained within an analytical model.

We show that the successful and formally exact multiconfigurational time-dependent Hartree method (MCTDH) takes on a unified and compact form when specified for systems of identical particles (MCTDHF for fermions MCTDHB for bosons). In particular the equations of motion for the orbitals depend explicitly and solely on the reduced one- and two-body density matrices of the system’s many-particle wave function. We point out that this appealing representation of the equations of motion opens up further possibilities for approximate propagation schemes.

The ionization of an atom by a high-frequency intense laser pulse, where the energy of a single photon is sufficient to ionize the system, is investigated from first principles. It is shown that as a consequence of an ac Stark effect in the continuum, the energy of the photoelectron follows the envelope of the laser pulse. This is demonstrated to result in strong dynamic interference of the photoelectrons of the same kinetic energy emitted at different times. Numerically exact computations on the hydrogen atom demonstrate that the dynamic interference spectacularly modifies the photoionization process and is prominently manifested in the photoelectron spectrum by the appearance of a distinct multipeak pattern. The general theory is well approximated by explicit analytical expressions that allow for a transparent understanding of the discovered phenomena and for making predictions on the dependence of the measured spectrum on the pulse.

In classical laser fields with frequencies resonant with the electronic excitation in molecules it is by now known that conical intersections are induced by the field and are called light-induced conical intersections (LICI). As optical cavities have become accessible, the question arises whether their quantized modes can also lead to the appearance of LICIs. A theoretical framework is formulated for the investigation of LICIs of diatomic molecules in such quantum light. The eigenvalue spectrum of the dressed states in the cavity is studied with particular emphasis on the investigation of absorption spectra, i.e., transitions between these dressed states, measured by employing a weak probe pulse. The theory is exemplified for the sodium dimer molecule. The dependence of the spectra on the light-matter coupling strength in the cavity and on the frequency of the cavity mode are studied in detail. The computations demonstrate strong non-adiabatic effects caused by the appearing LICI.