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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

We propose a continuous variable quantum state tomography protocol of electrons which result from the ionization of atoms or molecules by the absorption of extreme ultraviolet light pulses. Our protocol is benchmarked against a direct calculation of the quantum state of photoelectrons ejected from helium and argon in the vicinity of a Fano resonance. In the latter case, we furthermore distill ion-photoelectron entanglement due to spin-orbit splitting. This opens new routes towards the investigation of quantum coherence and entanglement properties on the ultrafast timescale.

In recent years, the manipulation of Fano resonances in the time domain has unlocked deep insights into a broad spectrum of systems' coherent dynamics. Here, inelastic scattering of light with coherent acoustic phonons is harnessed to achieve complex Fano resonances. The sudden change of phonon momentum during reflection leads to a transition from anti-Stokes to Stokes light scattering, producing two different resonances that interfere in the measurement process. We highlight the conditions necessary to achieve such interference, revealing an underlying symmetry between photons and phonons, and verify the theory experimentally. Then, we demonstrate the possibility to characterize energy and coherence losses at rough interfaces, thus providing a mechanism for nondestructive testing of interface quality. Our results describe numerous unexplained observations in ultrafast acoustics and can be generalized to the scattering of light with any waves.

Adiabatic elimination methods allow the reduction of the space dimension needed to describe systems dynamics which exhibits separation of time scale. For open quantum system, it consists in eliminating the fast part assuming it has almost instantaneously reached its steady-state and obtaining an approximation of the evolution of the slow part. These methods can be applied to eliminate a linear subspace within the system Hilbert space, or alternatively to eliminate a fast subsystems in a bipartite quantum system. In this work, we extend an adiabatic elimination method used for removing fast degrees of freedom within a open quantum system (Phys. Rev. A 2020, 101,042102) to eliminate a subsystem from an open bipartite quantum system. As an illustration, we apply our technique to a dispersively coupled two-qubit system and in the case of the open Rabi model., Comment: 11 pages, 2 figures

Molecular aggregates on plasmonic nanoparticles have emerged as attractive systems for the studies of cavity quantum electrodynamics. They are highly tunable, scalable, easy to synthesize and offer sub-wavelength confinement, all while giving access to the ultrastrong light-matter coupling regime at room temperature and promising a plethora of applications. However, the complexity of both the molecular aggregate and plasmonic nanoparticle introduces many more processes affecting the excitation and its relaxation, than are present in atom-cavity systems. Here, we follow the complex relaxation pathways of the photoexcitation of such hybrid systems and conclude that while the metal is responsible for destroying the coherence of the excitation, the molecular aggregate significantly participates in dissipating the energy. We rely on two-dimensional electronic spectroscopy in a combined theory-experiment approach, which allows us to ascribe the different timescales of relaxation to processes inside the molecules or the metal nanoparticle. We show that the dynamics beyond a few femtoseconds has to be cast in the language of hot electron distributions and excitons instead of the accepted lower and upper polariton branches, and furthermore set the framework for delving deeper into the photophysics of excitations that could be used in hot electron transfer, for example to drive photocatalytic reactions., Comment: revised simulations and interpretation

Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform the construction of effective operators in frequency space, and using the final value theorem or alternatively the Keldysh theorem, we provide a correction for the trace of the density matrix which takes into account the non trace-preserving character of the evolution. We illustrate our results with two different systems, ones where the eliminated fast subspace is constituted by a continuous set of states and ones with discrete states. Furthermore, we show that the two models converge for very large dissipation and at coherent population trapping points. Our results also provide an intuitive picture of the correction to the trace of the density matrix as a detailed balance equation., Comment: 12 pages, 9 figures, improved literature review

Fano interferences in nanostructures are influenced by dissipation effects as well as many-body interactions. Two dimensional coherent spectroscopies have just begun to be applied to these systems where the spectroscopic signatures of a discrete-continuum structure are not known. In this article we calculate the excited-state absorption contribution for different models of higher-lying excited states. We find that the characteristic asymmetry of one-dimensional spectroscopies is recovered from the many-body contributions, and that the higher-lying excited manifolds have distorted lineshapes that are not anticipated from discrete-level Hamiltonians. We show that the SE cannot have contributions from a flat continuum of states. This work completes the Ground-State Bleach and Stimulated Emission signals that were calculated previously (Phys. Rev. B. 2016, 94, 205137). The model reproduces the observations reported for molecules on surfaces probed by 2DIR., Comment: 10 pages, 8 figures

Dark states are eigenstates or steady-states of a system that are decoupled from the radiation. Their use, along with associated techniques such as Stimulated Raman Adiabatic Passage, has extended from atomic physics where it is an essential cooling mechanism, to more recent versions in condensed phase where it can increase the coherence times of qubits. These states are often discussed in the context of unitary evolution and found with elegant methods exploiting symmetries, or via the Bruce-Shore transformation. However, the link with dissipative systems is not always transparent, and distinctions between classes of CPT are not always clear. We present a detailed overview of the arguments to find stationary dark states in dissipative systems, and examine their dependence on the Hamiltonian parameters, their multiplicity and purity. We find a class of dark states that depends not only on the detunings of the lasers but also on their relative intensities. We illustrate the criteria with the more complex physical system of the hyperfine transitions of $^{87}$Rb and show how a knowledge of the dark state manifold can inform the preparation of pure states., Comment: additional examples

Fano models - consisting of a Hamiltonian with discrete-continuous spectrum - are one of the basic toy models in spectroscopy. They have been succesfull in explaining the lineshape of experiments in atomic physics and condensed matter. These models however have largely been out of the scope of dissipative dynamics, with ony a handful of works considering the effect of a thermal bath. Yet in nanostructures and condensed matter systems, dissipation strongly modulates the dynamics. In this article, we present an overview of the theoretical works dealing with Fano interferences coupled to a thermal bath and compare them to the scattering formalism. We provide the solution to any discrete-continuous Hamiltonian structure within the wideband approximation coupled to a Markovian bath. In doing so, we update the toy models that have been available for unitary evolution since the 1960s. We find that the Fano lineshape is preserved as long as we allow a rescaling of the parameters, and an additional Lorentzian contribution that reflects the destruction of the interference by dephasings. We discuss the pertinence of each approach - dissipative and unitary - to different experimental setups: scattering, transport and spectroscopy of dissipative systems. We finish by discussing the current limitations of the theories due to the wideband approximation and the memory effects of the bath., Comment: Expanded bibliography, minor typos corrected

The Fano lineshape arises from the interference of two excitation pathways to reach a continuum. Its generality has resulted in a tremendous success in explaining the lineshapes of many one-dimensional spectroscopies - absorption, emission, scattering, conductance, photofragmentation - applied to very varied systems - atoms, molecules, semiconductors and metals. Unravelling a spectroscopy into a second dimension reveals the relationship between states in addition to decongesting the spectra. Femtosecond-resolved two-dimensional electronic spectroscopy (2DES) is a four-wave mixing technique that measures the time-evolution of the populations, and coherences of excited states. It has been applied extensively to the dynamics of photosynthetic units, and more recently to materials with extended band-structures. In this letter, we solve the full time-dependent third-order response, measured in 2DES, of a Fano model and give the new system parameters that become accessible.

We obtain an explicit solution for the stationary state populations of a dissipative Fano model, where a discrete excited state is coupled to a continumm set of states; both excited set of states are reachable by photo-excitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the continuum states population as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a $4\times 4$ matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic induced-transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter., Comment: appendix added, corrected some typos

The scattering amplitude from a set of discrete states coupled to a continuum became known as the Fano profile, characteristic for its asymmetric lineshape and originally investigated in the context of photoionization. The generality of the model, and the proliferation of engineered nanostructures with confined states gives immense success to the Fano lineshape, which is invoked whenever an asymmetric lineshape is encountered. However, many of these systems do not conform to the initial model worked out by Fano in that i) they are subject to dissipative processes and ii) the observables are not entirely analogous to the ones measured in the original photoionization experiments. In this letter, we work out the full optical response of a Fano model with dissipation. We find that the exact result for absorption, Raman, Rayleigh and fluorescence emission is a modified Fano profile where the typical lineshape has an additional Lorentzian contribution. Expressions to extract model parameters from a set of relevant observables are given., Comment: corrected typos

A minimal model is exactly solved for electron spin transport on a helix. Electron transport is assumed to be supported by well oriented $p_z$ type orbitals on base molecules forming a staircase of definite chirality. In a tight binding interpretation, the SOC opens up an effective $\pi_z-\pi_z$ coupling via interbase $p_{x,y}-p_z$ hopping, introducing spin coupled transport. The resulting continuum model spectrum shows two Kramers doublet transport channels with a gap proportional to the SOC. Each doubly degenerate channel satisfies time reversal symmetry, nevertheless, a bias chooses a transport direction and thus selects for spin orientation. The model predicts which spin orientation is selected depending on chirality and bias, changes in spin preference as a function of input Fermi level and scattering suppression protected by the SO gap. We compute the spin current with a definite helicity and find it to be proportional to the torsion of the chiral structure and the non-adiabatic Aharonov- Anandan phase. To describe room temperature transport we assume that the total transmission is the result of a product of coherent steps limited by the coherence length.