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Biomolecular light-harvesting antennas operate as nanoscale devices in a regime where the coherent interactions of individual light, matter and vibrational quanta are non-perturbatively strong. The complex behaviour arising from this could, if fully understood, be exploited for myriad energy applications. However, non-perturbative dynamics are computationally challenging to simulate, and experiments on biomaterials explore very limited regions of the non-perturbative 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 recent superconducting experiments of Poto{\v{c}}nik $\it{et}$ $\it{al.}$ (Nat. Com. 9, 904 (2018)) used to explore excitonic energy capture. By explicitly including the role of optical driving fields, non-perturbative dephasing noise and the full multi-excitation Hilbert space of a three-qubit quantum circuit, we predict the measureable 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 strong, non-additive action of the driving and optical fields.

Engineering and harnessing coherent excitonic transport in organic nanostructures has recently been suggested as a promising way towards improving man-made light harvesting materials. However, realising and testing the dissipative system-environment models underlying these proposals is presently very challenging in supramolecular materials. A promising alternative is to use simpler and highly tunable quantum simulators built from programmable qubits, as recently achieved in a superconducting circuit by Potocnik et al. In this article, we simulate the real-time dynamics of an exciton coupled to a quantum bath as it moves through a network based on the quantum circuit of Potocnik et al. Using the numerically exact hierarchical equations of motion to capture the open quantum system dynamics, we find that an ultrafast but completely incoherent relaxation from a high-lying bright exciton into a doublet of closely spaced dark excitons can spontaneously generate electronic coherences and oscillatory real-space motion across the network (quantum beats). Importantly, we show that this behaviour also survives when the environmental noise is classically stochastic (effectively high temperature), as in present experiments, and also leads to a novel, transient violation of detailed balance in the population relaxation. These predictions highlight the possibilities of designing matched electronic and spectral noise structures for robust coherence generation that does not require coherent excitation or cold environments.

Laser control of Open Quantum Systems (OQS) is a challenging issue as compared to its counterpart in isolated small size molecules, basically due to very large numbers of degrees of freedom to be accounted for. Such a control aims at appropriately optimizing decoherence processes of a central two-level system (a given vibrational mode, for instance) towards its environmental bath (including, for instance, all other normal modes). A variety of applications could potentially be envisioned, either to preserve the central system from decaying (long duration molecular alignment or orientation, qubit decoherence protection) or, to speed up the information flow towards the bath (efficient charge or proton transfers in long chain organic compounds). Achieving such controls require some quantitative measures of decoherence in relation with memory effects in the bath response, actually given by the degree of non-Markovianity. Characteristic decoherence rates of a Spin-Boson model are calculated using a Nakajima-Zwanzig type master equation with converged HEOM expansion for the memory kernel. It is shown that, by adequately tuning the two-level transition frequency through a controlled Stark shift produced by an external laser field, non-Markovianity can be enhanced in a continuous way leading to a first attempt towards the control of OQS.

Optimal control theory has been employed to populate separately two dark states of the acetylene polyad $N_s=1$, $N_r=5$ by indirect coupling via the ground state. Relevant level energies and transition dipole moments are extracted from the experimental literature. The optimal pulses are rather simple. The evolution of the populations is shown for the duration of the control process and also for the field free-evolution that follows the control. One of the dark states appears to be a potential target for realistic experimental investigation because the average population of the Rabi oscillation remains high and decoherence is expected to be weak., Comment: 28 pages, 5 figures

Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a $Cd^+$ ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schr\"odinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolution operator corresponding to the time-dependent Schr\"odinger equation of the simulated system. The corresponding matrix can be estimated by any numerical algorithm. The radio-frequency field able to drive this unitary transformation among the qubit states of the ion is obtained by multi-target optimal control theory. The ion is assumed to be cooled in the ground motional state and the preliminary step consists in initializing the qubits with the amplitudes of the initial simulated wave packet. The time evolution of the localization probability at the grids points is then obtained by successive applications of the gate and reading out the motional state population. The gate field is always identical for a given simulated potential, only the field preparing the initial wave packet has to be optimized for different simulations. We check the stability of the simulation against decoherence due to fluctuating electric fields in the trap electrodes by applying dissipative Lindblad dynamics., Comment: 31 pages, 8 figures. Revised version. New title, new figure and new references

We propose a new formulation of optimal and local control algorithms which enforces the constraint of time-integrated zero-area on the control field. The fulfillment of this requirement, crucial in many physical applications, is mathematically implemented by the introduction of a Lagrange multiplier aiming at penalizing the pulse area. This method allows to design a control field with an area as small as possible, while bringing the dynamical system close to the target state. We test the efficiency of this approach on two control purposes in molecular dynamics, namely, orientation and photodissociation., Comment: 11 pages, 2 figures

We illustrate some of the difficulties that may be encountered when computing photodissociation and radiative association cross sections from the same time-dependent approach based on wavepacket propagation. The total and partial photodissociation cross sections from the thirty-three vibrational levels of the b triplet {\Sigma}+ state of HeH+ towards the 9 other triplet {\Sigma}+ and 6 triplet {\Pi} n = 2, 3 higher-lying electronic states are calculated. The corresponding radiative association cross sections are extracted from the same calculations, and the photodissociation and radiative association rate constants are determined., Comment: 17 pages, 6 figures

We investigate the photodissociation of the metastable triplet state of HeH+ as well as its formation through the inverse process, radiative association. In models of astrophysical plasmas, HeH+ is assumed to be present only in the ground state, and the influence of the triplet state has not been explored. It may be formed by radiative association during collisions between a proton and metastable helium, which are present in significant concentrations in nebulae. The triplet state can also be formed by association of He+ and H, although this process is less likely to occur. We compute the cross sections and rate coefficients corresponding to the photodissociation of the triplet state by UV photons from a central star using a wave packet method. We show that the photodissociation cross sections depend strongly on the initial vibrational state and that the effects of excited electronic states and non-adiabatic couplings cannot be neglected. We then calculate the cross section and rate coefficient for the radiative association of HeH+ in the metastable triplet state.

The charge transfer in low energy (0.25 to 150 eV/amu) H($nl$) + He$^+(1s)$ collisions is investigated using a quasi-molecular approach for the $n=2,3$ as well as the first two $n=4$ singlet states. The diabatic potential energy curves of the HeH$^+$ molecular ion are obtained from the adiabatic potential energy curves and the non-adiabatic radial coupling matrix elements using a two-by-two diabatization method, and a time-dependent wave-packet approach is used to calculate the state-to-state cross sections. We find a strong dependence of the charge transfer cross section in the principal and orbital quantum numbers $n$ and $l$ of the initial or final state. We estimate the effect of the non-adiabatic rotational couplings, which is found to be important even at energies below 1 eV/amu. However, the effect is small on the total cross sections at energies below 10 eV/amu. We observe that to calculate charge transfer cross sections in a $n$ manifold, it is only necessary to include states with $n^{\prime}\leq n$, and we discuss the limitations of our approach as the number of states increases., Comment: 14 pages, 10 figures

We numerically study the implementation of a NOT gate by laser pulses in a model molecular system presenting two electronic surfaces coupled by non adiabatic interactions. The two states of the bit are the fundamental states of the cis-trans isomers of the molecule. The gate is classical in the sense that it involves a one-qubit flip so that the encoding of the outputs is based on population analysis which does not take the phases into account. This gate can also be viewed as a double photo-switch process with the property that the same electric field controls the two isomerizations. As an example, we consider one-dimensional cuts in a model of the retinal in rhodopsin already proposed in the literature. The laser pulses are computed by the Multi Target Optimal Control Theory with chirped pulses as trial fields. Very high fidelities are obtained. We also examine the stability of the control when the system is coupled to a bath of oscillators modelled by an Ohmic spectral density. The bath correlation time scale being smaller than the pulse duration the dynamics is carried out in the Markovian approximation., Comment: 29 pages, 7 figures

We present a complete analysis of the laser control of a model molecular system using both optimal control theory and adiabatic techniques. This molecule has a particular potential energy surface with a bifurcating region connecting three potential wells which allows a variety of processes such as isomerization, tunnelling or implementation of quantum gates on one or two qubits. The parameters of the model have been chosen so as to reproduce the main features of H3CO which is a molecule-benchmark for such dynamics. We show the feasibility of different processes and we investigate their robustness against variations of laser field. We discuss the conditions under which each method of control gives the best results. We also point out the relation between optimal control theory and local control., Comment: 41 pages, 14 figures