Excited-state dynamics of open quantum systems is analyzed by the hierarchical equations of motion (HEOM) or the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA) method when a discrete ab initio linear vibronic model is parameterized by continuous temperature-dependent spectral densities leading to crossed correlation functions, i.e., correlated fluctuations of the energy gap collective modes. We focus on a conical intersection involving two collective modes tuning the energy of each excited state, and we revisit the transformation of the initial correlated tuning baths to de-correlated shared baths in order to reduce the computational resources. While a completely frequency-dependent transformation poses problems for HEOM, we find that in some particular cases, an optimal approximate frequency-independent transformation may be derived. On the contrary, T-TEDOPA is very efficient and allows us to use this frequency-dependent transformation at the price of managing long-range couplings in the tensor chain. An illustrative application is shown by using the linear vibronic coupling model of a planar symmetrical (phenylethynyl)benzene dimer.

Excitation-energy transfer (EET) and relaxation in an optically excited building block of poly(phenylene ethynylene) (PPE) dendrimers are simulated using wavepackets with the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method and reduced-density matrices with the hierarchical equations of motion (HEOM) approach. The dynamics of the ultrafast electronic funneling between the first two excited electronic states in the asymmetrically meta-substituted PPE oligomer with two rings on one branch and three rings on the other side, with a shared ring in between, is treated with 93-dimensional ab initio vibronic-coupling Hamiltonian (VCH) models, either linear or with bilinear and quadratic terms. The linear VCH model is also used to calibrate an open quantum system that falls in a computationally demanding non-perturbative non-Markovian regime. The linear-response absorption and emission spectra are simulated with both the ML-MCTDH and HEOM methods. The latter is further used to explore the nonlinear regime toward two-dimensional spectroscopy. We illustrate how a minimal VCH model with the two main active bright states and the impulsive-pulse limit in third-order response theory may provide at lower cost polarization-sensitive time-resolved signals that monitor the early EET dynamics. We also confirm the essential role played by the high-frequency acetylenic and quinoidal vibrational modes.

In this study, we reexamine a recent optimal control simulation targeting the preparation of a superposition of two excited electronic states in the ultraviolet (UV) range in a complex molecular system. We revisit this control from the perspective of reinforcement learning, offering an efficient alternative to conventional quantum control methods. The two excited states are addressable by orthogonal polarizations and their superposition corresponds to a right or left localization of the electronic density. The pulse duration spans tens of femtoseconds to prevent excitation of higher excited bright states which leads to a strong perturbation by the nuclear motions. We modify an open source software by Giannelli et al. [L. Giannelli et al., Phys. Lett. A 434, 128054 (2022)] that implements reinforcement learning with Lindblad dynamics, to introduce non-Markovianity of the surrounding reservoir either by time-dependent rates, or more exactly, by using the hierarchical equations of motion with the QuTip-BoFiN package. This extension opens the way to wider applications for non-Markovian environments, in particular when the active system interacts with a highly structured noise.

In non-perturbative non-Markovian open quantum systems, reaching either low temperatures with the hierarchical equations of motion (HEOM) or high temperatures with the Thermalized Time Evolving Density Operator with Orthogonal Polynomials Algorithm (T-TEDOPA) formalism in Hilbert space remains challenging. We compare different ways of modeling the environment. Sampling the Fourier transform of the bath correlation function, also called temperature dependent spectral density, proves to be very effective. T-TEDOPA [Tamascelli et al., Phys. Rev. Lett. 123, 090402 (2019)] uses a linear chain of oscillators with positive and negative frequencies, while HEOM is based on the complex poles of an optimized rational decomposition of the temperature dependent spectral density [Xu et al., Phys. Rev. Lett. 129, 230601 (2022)]. Resorting to the poles of the temperature independent spectral density and of the Bose function separately is an alternative when the problem due to the huge number of Bose poles at low temperatures is circumvented. Two examples illustrate the effectiveness of the HEOM and T-TEDOPA approaches: a benchmark pure dephasing case and a two-bath model simulating the dynamics of excited electronic states coupled through a conical intersection. We show the efficiency of T-TEDOPA to simulate dynamics at a finite temperature by using either continuous spectral densities or only all the intramolecular oscillators of a linear vibronic model calibrated from ab initio data of a phenylene ethynylene dimer.

This work is a pedagogical survey about the hierarchical equations of motion and their implementation with the tensor-train format. These equations are a great standard in non-perturbative non-Markovian open quantum systems. They are exact for harmonic baths in the limit of relevant truncation of the hierarchy. We recall the link with the perturbative second order time convolution equations also known as the Bloch-Redfield equations. Some theoretical tools characterizing non-Markovian dynamics such as the non- Markovianity measures or the dynamical map are also briefly discussed in the context of HEOM simulations. The main points of the tensor-train expansion are illustrated in an example with a qubit interacting with a bath described by a Lorentzian spectral density. Finally, we give three illustrative applications in which the system-bath coupling operator is similar to that of the analytical treatment. The first example revisits a model in which population-to-coherence transfer via the bath creates a long-lasting coherence between two states. The second one is devoted to the computation of stationary absorption and emission spectra. We illustrate the link between the spectral density and the Stokes shift in situations with and without nonadiabatic interaction. Finally, we simulate an excitation transfer when the spectral density is discretized by undamped modes to illustrate a situation in which the TT formulation is more efficient than the standard one.

The ability to prepare a specific superposition of electronic excited states leading to a transitory symmetry breaking of the electronic density in complex systems remains a challenging concern. We investigate how an initial coherence can be controlled by laser fields. The selected molecular system is a symmetric dimer of phenylene ethynylene presenting different interesting properties: Two bright nearly degenerate excited states coupled through a conical intersection are addressable by orthogonal transition dipole moments and are well separated from neighboring states. Creating a superposed state with equal weights corresponds to a right or left electronic localization as in the double-well system followed by a transitory oscillation between the two wells. To ensure a spectral bandwidth typically smaller than 0.25 eV, the pulse duration is in the tens of femtoseconds range, so nuclear motion cannot be neglected. Optimal control theory (OCT) is applied with guess fields that effectively create the target coherence in the absence of dephasing due to the vibrational baths. We analyze the field reshaping proposed by the control and we further fit a sequence of pulses on the optimal field. The overall result is efficient and robust disymmetry control over reasonable timescales of few tens of femtoseconds, exceeding the pulse duration. The monotonically convergent algorithm is combined with the hierarchical equations of motion (HEOM) able to treat strongly coupled non-Markovian dynamics. We also check the implementation of the combined OCT-HEOM approach in the tensor-train representation with propagation using the time-dependent variational method.

The exquisite control of diluted atomic vapors that can be achieved using electromagnetic (em) fields triggered the overwhelming development of researches on ultracold (T<<1millikelvin) quantum gases through laser cooling and trapping, opening ways to amazing applications in quantum technologies. For a composite system like a molecule under such ultracold conditions, the additional control of the internal degrees of freedom has also been recently demonstrated [1] with cw visible, microwave, and radio radiation frequencies for electronic, rotational, and hyperfine transitions, respectively. Vibrational transitions could be addressed with THz transitions, as an attractive path for controlling the interatomic interactions and creating ultracold gases of a wide class of diatomic molecules in their absolute ground state. More specifically, THz radiation can induce a coupling between the bound level of a pair of trapped ultracold ground-state atoms and a loosely-bound vibrational level of the related molecular electronic ground state. This coupling, generated by the intrinsic permanent electric dipole moment of a heteronuclear atomic pair (RbSr in the present work), is related to a specific spectroscopic feature of the atomic pair dressed by the THz field, the Laser Assisted Self-Induced Feshbach Resonance (LASIFR) [2] . In analogy with magnetic Feshbach resonance, the scattering length can be controlled by tuning the THz radiation frequency around a LASIFR (see Fig (a)).

Funneling dynamics in conjugated dendrimers has raised great interest in the context of artificial light-harvesting processes. Photoinduced relaxation has been explored by time-resolved spectroscopy and simulations, mainly by semiclassical approaches or referring to open quantum systems methods, within the Redfield approximation. Here, we take the benefit of an ab initio investigation of a phenylacetylene trimer, and in the spirit of a divide-and-conquer approach, we focus on the early dynamics of the hierarchy of interactions. We build a simplified but realistic model by retaining only bright electronic states and selecting the vibrational domain expected to play the dominant role for timescales shorter than 500 fs. We specifically analyze the role of the in-plane high-frequency skeletal vibrational modes involving the triple bonds. Open quantum system non-adiabatic dynamics involving conical intersections is conducted by separating the electronic subsystem from the high-frequency tuning and coupling vibrational baths. This partition is implemented within a robust non-perturbative and non-Markovian method, here the hierarchical equations of motion. We will more precisely analyze the coherent preparation of donor states or of their superposition by short laser pulses with different polarizations. In particular, we extend the π-pulse strategy for the creation of a superposition to a V-type system. We study the relaxation induced by the high-frequency vibrational collective modes and the transitory dissymmetry, which results from the creation of a superposition of electronic donor states.

We have studied the formation of ultracold RbSr molecules with laser pulses. After discussing the advantages of the Mott insulator phase for the control with pulses, we present two classes of strategies. The first class involves two electronic states. Two extensions of stimulated Raman adiabatic passage (STIRAP) for multilevel transitions are used: alternating STIRAP (A-STIRAP) and straddle STIRAP (S-STIRAP). Both transfer dynamics are modeled and compared. The second class of strategies involves only the electronic ground state and uses infrared (IR) and terahertz (THz) pulses. The molecular bond is first created by the application of a THz chirped pulse or $\ensuremath{\pi}$-pulse. Subsequently, the molecules are transferred to their rovibrational ground level using IR pulses. For this last step, different optimized pulse sequences that were obtained through optimal control techniques have been studied. The relative merits of these strategies in terms of efficiency and robustness are discussed with respect to the experimental feasibility based on present laser technologies.

Biomolecular light-harvesting antennas operate as nanoscale devices in a regime where the coherent interactions of individual light, matter, and vibrational quanta are nonperturbatively strong. The complex behavior arising from this could, if fully understood, be exploited for myriad energy applications. However, nonperturbative dynamics are computationally challenging to simulate, and experiments on biomaterials explore very limited regions of the nonperturbative parameter space. So-called quantum simulators of light-harvesting models could provide a solution to this problem, and here we employ the hierarchical equations-of-motion technique to investigate the recent superconducting experiments of Potocnik et al. [A. Potocnik et al., Nat. Commun. 9, 904 (2018)] used to explore excitonic energy capture. By explicitly including the role of optical driving fields, nonperturbative dephasing noise, and the full multiexcitation Hilbert space of a three-qubit quantum circuit, we predict the measurable impact of these factors on transfer efficiency. By analysis of the eigenspectrum of the network, we uncover a structure of energy levels that allows the network to exploit optical "dark" states and excited-state absorption for energy transfer. We also confirm that time-resolvable coherent oscillations could be experimentally observed, even under the strong, nonadditive action of the driving and optical fields.

We propose a new kind of Feshbach Resonance (FR) : the Laser-Assisted Self-Induced Feshbach Resonance (LASIFR), applicable for all mixtures of ultracold atoms. The interspecies scattering length characterizing elastic collisions, a key property for many applications of ultracold quantum gases, can be controlled by a LASIFR through the laser intensity and the frequency. It can be also used for the formation of ultracold polar molecules.

N2 is a major constituent of Earth and planetary atmospheres. First, evidenced in 1952, the dissociative photoionization of molecular nitrogen, N2, plays an important role in the species abundance, out of equilibrium evolution, and chemical reactivity of diverse media including upper atmospheres (the so-called ionospheres) and plasma. Many scenarios were proposed for rationalizing the dissociative ionization mechanisms and exit channels, which are reviewed here, mainly involving the N2+(C2∑u+, v+) vibrational levels state-to-state dynamics on which we focus. We show, however, that previous studies are not comprehensive enough for fully shedding light on the complex undergoing processes. As a complementary global work, we used state-of-the-art quantum chemistry, time dependent and independent theoretical approaches associated to advanced experimental techniques to study the unimolecular decomposition of the N2+ ions forming the N+ + N products. In addition to the already suggested spin-orbit-induced predissociation of the cationic C2∑u+ state, we documented a new mechanism based on vibronic coupling and tunneling dissociation. Besides, the quantum processes highlighted here should be also in action in the dynamics of electronically excited larger molecular systems involved in physical and chemical phenomena in plasma and in various natural environments on Earth and beyond.

Targeted exciton transport is crucial for efficient light-harvesting, but its microscopic description in biological systems is complicated by strong environmental coupling, highly structured vibrational environments and non-Markovian open system dynamics. In this article we employ the non-perturbative hierarchical equations of motion (HEOM) technique to explore how structured environments and tuned electronic properties can lead to the generation of coherent motion across a directed transport network, i.e. one containing an energy gradient. By further exploiting the information contained in the auxiliary HEOM matrices, we also visualize the complete displacement distributions of the main reaction coordinate during the ultrafast relaxation, and show that highly non-Gaussian profiles emerge when the electronic dynamics become quasi-reversible and involve bath-induced delocalized states. These coherent dynamics are spontaneously generated by earlier incoherent relaxation events, and we also demonstrate the correlation between the environmental coordinates and a quantitative volume-based measure of non-Markovianity.

We investigate the possibility of extracting the probability distribution of the effective environmental tuning and coupling modes during the nonadiabatic relaxation through a conical intersection. Dynamics are dealt with an open quantum system master equation by partitioning a multistate electronic subsystem out of all the nuclear vibrators. This is an alternative to the more usual partition retaining the tuning and coupling modes of a conical intersection in the active subsystem coupled to a residual bath. The minimal partition of the electronic system generally leads to highly structured spectral densities for both vibrational baths and requires a strongly nonperturbative non-Markovian master equation, treated here by the hierarchical equations of motion (HEOMs). We extend-for a two-bath situation-the procedure proposed by Shi et al. [J. Chem. Phys. 140, 134106 (2014)], whereby the information contained in the auxiliary HEOM matrices is exploited in order to derive the nuclear dissipative wave packet, i.e., the statistical distribution of the displacement of the two tuning and coupling collective coordinates in each electronic state and the coherence. This allows us to visualize the distribution, all along the nonadiabatic decay. We explore a large parameter space for a symmetrical conical intersection model and a symmetrical initial Franck-Condon preparation. Some parameters could be controlled by external fields, while others are molecule dependent and could be designed by molecular engineering. We illustrate the relation between the strongly coupled electronic and bath dynamics together with a geometric measure of non-Markovianity.

We propose a new type of Feshbach resonance occurring when two different ultracold atoms in their ground state undergo an s-wave collision in the presence of a continuous-wave laser light. The atoms collide in the dissociation continuum of the molecular electronic ground state which is coupled by the light to a rovibrational level of the same electronic ground state: we name this a Laser-Assisted Self-Induced Feshbach Resonance (LASIFR). This mechanism, valid for all polar molecules, is analyzed on the example of ultracold 87Rb and 84Sr atoms, for which the laser frequency falls in the THz range. The control of the LASIFR with the laser frequency and intensity allows for a strong increase of the pair probability density at short distances, which tremendously increases the number of atoms pairs transfered toward the absolute ground state level by STImulated Rapid Adiabatic Passage (STIRAP). The LASIFR results in the observation of a standard Fano profile in the pump transition of the STIRAP process, and is also promising for the optical control of the interspecies scattering length without atom losses.

Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the two-level sub-system are taken as control objectives; namely, their revivals or exchange when switching off the field. We, in parallel, analyze how the optimal electric field consequently modifies the information back flow from the environment through different non-Markovian witnesses. Although the control field has a dipole interaction with the central sub-system only, its indirect influence on the bath collective mode dynamics is probed through HEOM auxiliary matrices, revealing a strong correlation between control and dissipation during a non-Markovian process. A heterojunction is taken as an illustrative example for modeling in a realistic way the two-level sub-system parameters and its spectral density function leading to a non-perturbative strong coupling regime with the bath. Although, due to strong system-bath couplings, control performances remain rather modest, the most important result is a noticeable increase of the non-Markovian bath response induced by the optimally driven processes.

A multidimensional quantum mechanical protocol is used to describe the photoinduced electron transfer and electronic coherence in plant cryptochromes without any semiempirical, e.g., experimentally obtained, parameters. Starting from a two-level spin-boson Hamiltonian we look at the effect that the initial photoinduced nuclear bath distribution has on an intermediate step of this biological electron transfer cascade for two idealized cases. The first assumes a slow equilibration of the nuclear bath with respect to the previous electron transfer step that leads to an ultrafast decay with little temperature dependence; while the second assumes a prior fast bath equilibration on the donor potential energy surface leading to a much slower decay, which contrarily displays a high temperature dependence and a better agreement with previous theoretical and experimental results. Beyond Marcus and semiclassical pictures these results unravel the strong impact that the presence or not of equilibrium initial conditions has on the electronic population and coherence dynamics at the quantum dynamics level in this and conceivably in other biological electron transfer cascades.