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There is a growing interest in reconstructing the density matrix of photoelectron wavepackets, in particular in complex systems where decoherence can be introduced either by a partial measurement of the system or through coupling with a stochastic environment. To this end, several methods to reconstruct the density matrix, quantum state tomography protocols, have been developed and tested on photoelectrons ejected from noble gases following absorption of extreme ultraviolet (XUV) photons from attosecond pulses. It remains a challenge to obtain model-free, single scan protocols that can reconstruct the density matrix with high fidelities. Current methods require extensive measurements or involve complex fitting of the signal. Efficient single-scan reconstructions would be of great help to increase the number of systems that can be studied. We propose a new and more efficient protocol that is able to reconstruct the continuous variable density matrix of a photoelectron in a single time delay scan. It is based on measuring the coherences of a photoelectron created by absorption of an XUV pulse using a broadband infrared (IR) probe that is scanned in time and a narrowband IR reference that is temporally fixed to the XUV pulse. We illustrate its performance for a Fano resonance in He as well as mixed states in Ar arising from spin-orbit splitting. We show that the protocol results in excellent fidelities and near-perfect estimation of the purity., Comment: 23 pages, 13 figures, 1 table

A photoelectron, emitted due to the absorption of light quanta as described by the photoelectric effect, is often characterized experimentally by a classical quantity, its momentum. However, since the photoelectron is a quantum object, its rigorous characterization requires the reconstruction of the complete quantum state, the photoelectron's density matrix. Here, we use quantum state tomography to fully characterize photoelectrons emitted from helium and argon atoms upon absorption of ultrashort, extreme ultraviolet light pulses. While in helium we measure a pure photoelectronic state, in argon, spin-orbit interaction induces entanglement between the ion and the photoelectron, leading to a reduced purity of the photoelectron state. Our work shows how state tomography gives new insights into the fundamental quantum aspects of light-induced electronic processes in matter, bridging the fields of photoelectron spectroscopy and quantum information, and offering new spectroscopic possibilities for quantum technology.

Non-Hermitian Hamiltonians and Lindblad operators are some of the most important generators of dynamics for describing quantum systems interacting with different kinds of environments. The first type differs from conservative evolution by an anti-Hermitian term that causes particle decay, while the second type differs by a dissipation operator in Lindblad form that allows energy exchange with a bath. However, although under some conditions the two types of maps can be used to describe the same observable, they form a disjoint set. In this work, we propose a generalized generator of dynamics of the form $L_\text{mixed}(z,\rho_S) = -i[H,\rho_S] + \sum_i \left(\frac{\Gamma_{c,i}}{z+\Gamma_{c,i}}F_i\rho_S F_i^{\dagger} -\frac{1}{2} \{F_i^{\dagger} F_i,\rho_S \}_+\right)$ that depends on a general energy $z$, and has a tunable parameter $\Gamma_c$ that determines the degree of particle density lost. It has as its limits non-Hermitian ($\Gamma_c \to 0$) and Lindbladian dynamics ($\Gamma_c \to \infty$). The intermediate regime evolves density matrices such that $0 \leq \text{Tr} (\rho_S) \leq 1$. We derive our generator with the help of an ancillary continuum manifold acting as a sink for particle density. The evolution describes a system that can exchange both particle density and energy with its environment. We illustrate its features for a two level system and a five $M$ level system with a coherent population trapping point., Comment: 15 pages, 7 figures, appendices with detailed derivation. Expanded text and examples

In polaritons, the properties of matter are modified by mixing the molecular transitions with light modes inside a cavity. Resultant hybrid light-matter states exhibit energy level shifts, are delocalized over many molecular units and have a different excited-state potential energy landscape which leads to modified exciton dynamics. Previously, non-Hermitian Hamiltonians have been derived to describe the excited states of molecules coupled to surface plasmons (i.e. plexcitons), and these operators have been successfully used in the description of linear and third order optical response. In this article, we rigorously derive non-Hermitian Hamiltonians in the response function formalism of nonlinear spectroscopy by means of Feshbach operators, and apply them to explore spectroscopic signatures of plexcitons. In particular we analyze the optical response below and above the exceptional point that arises for matching transition energies for plasmon and molecular components, and study their decomposition using double-sided Feynman diagrams. We find a clear distinction between interference and Rabi splitting in linear spectroscopy, and a qualitative change in the symmetry of the lineshape of the nonlinear signal when crossing the exceptional. This change corresponds to one in the symmetry of the eigenvalues of the Hamiltonian. Our work presents an approach for simulating the optical response of sublevels within an electronic system, and opens new applications of nonlinear spectroscopy to examine the different regimes of the spectrum of non-Hermitian Hamiltonians., Comment: 35 pages, 10 figures