Digital Optimal Robust Control.

The lack of ability to determine and implement accurately quantum optimal control is a strong limitation to the development of quantum technologies. We propose a digital procedure based on a series of pulses where their amplitudes and (static) phases are designed from an optimal continuous-time protocol for given type and degree of robustness, determined from a geometric analysis. This digitalization combines the ease of implementation of composite pulses with the potential to achieve global optimality, i.e., to operate at the ultimate speed limit, even for a moderate number of control parameters. We demonstrate the protocol on IBM's quantum computers for a single qubit, obtaining a robust transfer with a series of Gaussian or square pulses in a time T=382 ns for a moderate amplitude. We find that the digital solution is practically as fast as the continuous one for square subpulses with the same peak amplitudes.

Optimal Pulse Design for Dissipative-Stimulated Raman Exact Passage.

Quantum control of lossy systems is known to be achieved by adiabatic passage via an approximate dark state relatively immune to loss, such as the emblematic example of stimulated Raman adiabatic passage (STIRAP) featuring a lossy excited state. By systematic optimal control study, via the Pontryagin maximum principle, we design alternative more efficient routes that, for a given admissible loss, feature an optimal transfer with respect to the cost defined as (i) the pulse energy (energy minimization) or (ii) the pulse duration (time minimization). The optimal controls feature remarkably simple sequences in the respective cases: (i) operating far from a dark state, of π-pulse type in the limit of low admissible loss, or (ii) close to the dark state with a counterintuitive pulse configuration sandwiched by sharp intuitive sequences, referred to as the intuitive/counterintuitive/intuitive (ICI) sequence. In the case of time optimization, the resulting stimulated Raman exact passage (STIREP) outperforms STIRAP in term of speed, accuracy, and robustness for low admissible loss.

Characterization of a Driven Two-Level Quantum System by Supervised Learning.

We investigate the extent to which a two-level quantum system subjected to an external time-dependent drive can be characterized by supervised learning. We apply this approach to the case of bang-bang control and the estimation of the offset and the final distance to a given target state. For any control protocol, the goal is to find the mapping between the offset and the distance. This mapping is interpolated using a neural network. The estimate is global in the sense that no a priori knowledge is required on the relation to be determined. Different neural network algorithms are tested on a series of data sets. We show that the mapping can be reproduced with very high precision in the direct case when the offset is known, while obstacles appear in the indirect case starting from the distance to the target. We point out the limits of the estimation procedure with respect to the properties of the mapping to be interpolated. We discuss the physical relevance of the different results.

Quantum Control by Few-Cycles Pulses: The Two-Level Problem.

We investigate the problem of population transfer in a two-states system driven by an external electromagnetic field featuring a few cycles, until the extreme limit of two or one cycle. Taking the physical constraint of zero-area total field into account, we determine strategies leading to ultrahigh-fidelity population transfer despite the failure of the rotating wave approximation. We specifically implement adiabatic passage based on adiabatic Floquet theory for a number of cycles as low as 2.5 cycles, finding and making the dynamics follow an adiabatic trajectory connecting the initial and targeted states. Nonadiabatic strategies with shaped or chirped pulses, extending the π-pulse regime to two- or single-cycle pulses, are also derived.

Optimal Robust Quantum Control by Inverse Geometric Optimization.

We develop an inverse geometric optimization technique that allows the derivation of optimal and robust exact solutions of low-dimension quantum control problems driven by external fields. We determine in the dynamical variable space optimal trajectories constrained to robust solutions by Euler-Lagrange optimization; the control fields are then derived from the obtained robust geodesics and the inverted dynamical equations. We apply this method, referred to as robust inverse optimization (RIO), to design optimal control fields producing a complete or half population transfer and a not quantum gate robust with respect to the pulse inhomogeneities. The method is versatile and can be applied to numerous quantum control problems, e.g., other gates, other types of imperfections, Raman processes, or dynamical decoupling of undesirable effects.

A generalized vibronic-coupling Hamiltonian for molecules without symmetry: Application to the photoisomerization of benzopyran.

We present a model for the lowest two potential energy surfaces (PESs) that describe the photoinduced ring-opening reaction of benzopyran taken as a model compound to study the photochromic ring-opening reaction of indolinobenzospiropyran and its evolution toward its open-chain analog. The PESs are expressed in terms of three effective rectilinear coordinates. One corresponds to the direction between the equilibrium geometry in the electronic ground state, referred to as the Franck-Condon geometry, and the minimum of conical intersection (CI), while the other two span the two-dimensional branching space at the CI. The model correctly reproduces the topography of the PESs. The ab initio calculations are performed with the extended multiconfiguration quasidegenerate perturbation theory at second order method. We demonstrate that accounting for electron dynamic correlation drastically changes the global energy landscape since some zwitterionic states become strongly stabilized. Quantum dynamics calculations using this PES model produce an absorption spectrum that matches the experimental one to a good accuracy.

Quantum dynamics of the photostability of pyrazine.

We investigate the radiationless decay of photoexcited pyrazine to its ground electronic state using multireference electronic structure and quantum dynamics calculations. We construct a quadratic vibronic coupling Hamiltonian, including the four lowest electronic states and ten vibrational modes, by fitting to more than 5000 ab initio points. We then use this model to simulate the non-adiabatic excited state dynamics of the molecule using the multi-configuration time-dependent Hartree method. On the basis of these calculations, we propose a new mechanism for this decay process involving a conical intersection between the Au(nπ*) state and the ground state. After excitation to the B2u(ππ*) state, the molecule decays to both the B3u(nπ*) and Au(nπ*) states on an ultrashort timescale of approximately 20 fs. The radiationless decay to the ground state then occurs from the Au(nπ*) state on a much longer timescale.

Chaotic spin-spin entanglement on a recursive lattice.

We propose an exactly solvable multisite interaction spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice for the rigorous studies of chaotic entanglement. By making use of the generalized star-triangle transformation, we map the initial model onto an effective Ising one on a Husimi lattice, which we solve then exactly by applying the recursive method. Expressing the entanglement of the Heisenberg spins, that we quantify by means of the concurrence, in terms of the magnetic quantities of the system, we demonstrate its bifurcation and chaotic behavior. Furthermore, we show that the underlying chaos may slightly enhance the amount of the entanglement and present on the phase diagram the transition lines from the uniform to periodic and from the periodic to chaotic regimes.

Comparing the electronic relaxation dynamics of aniline and d(7)-aniline following excitation at 272-238 nm.

Femtosecond time-resolved photoelectron spectroscopy experiments have been used to compare the electronic relaxation dynamics of aniline and d7-aniline following photoexcitation in the range 272-238 nm. Together with the results of recent theoretical investigations of the potential energy landscape [M. Sala, O. M. Kirkby, S. Guérin and H. H. Fielding, Phys. Chem. Chem. Phys., 2014, 16, 3122], these experiments allow us to resolve a number of unanswered questions surrounding the nonradiative relaxation mechanism. We find that tunnelling does not play a role in the electronic relaxation dynamics, which is surprising given that tunnelling plays an important role in the electronic relaxation of isoelectronic phenol and in pyrrole. We confirm the existence of two time constants associated with dynamics on the 1(1)πσ* surface that we attribute to relaxation through a conical intersection between the 1(1)πσ* and 1(1)ππ* states and motion on the 1(1)πσ* surface. We also present what we believe is the first report of an experimental signature of a 3-state conical intersection involving the 2(1)ππ*, 1(1)πσ* and 1(1)ππ* states.

Coherent destruction of tunneling in a six-dimensional model of NHD2: a computational study using the multi-configuration time-dependent Hartree method.

We investigate the phenomenon of coherent destruction of tunneling in a six-dimensional model of the NHD2 molecule. Two regimes are considered for the frequency of the laser field. A non-resonant regime where the frequency of the laser field is high with respect to the ground vibrational state tunneling splitting but smaller than the transition frequencies between the ground and excited vibrational states; and a quasi-resonant regime where the frequency of the laser field is close to the transition frequency between the ground and first excited vibrational states. In each case, we study the laser driven dynamics in the framework of the Floquet formalism and derive simple analytical formulas that explain the shape of the quasienergy curves associated with the two tunneling components of the ground vibrational state. This analysis allows us to obtain the parameters (frequency and amplitude) of the laser field that lead to the coherent destruction of tunneling. The multi-configuration time-dependent Hartree method is then used to solve the time-dependent Schrödinger equation for a six-dimensional model of the molecule in interaction with an adiabatically turned on monochromatic laser field, in order to confirm the results obtained from this analysis.

Full-dimensional control of the radiationless decay in pyrazine using the dynamic Stark effect.

We present a full quantum-mechanical study of the laser control of the radiationless decay between the B3u(nπ(*)) and B2u(ππ(*)) states of pyrazine using the dynamic Stark effect. In contrast to our previous study [Sala et al., J. Chem. Phys. 140, 194309 (2014)], where a four-dimensional model was used, all the 24 degrees of freedom are now included in order to test the robustness of the strategy of control. Using a vibronic coupling Hamiltonian model in a diabatic representation, the multi-layer version of the multi-configuration time-dependent Hartree method is exploited to propagate the corresponding wave packets. We still observe a trapping of the wavepacket on the B2u(ππ(*)) potential energy surface due to the Stark effect for a longer time than the "non-resonant field-free" B2u(ππ(*)) lifetime.

The role of the low-lying dark nπ* states in the photophysics of pyrazine: a quantum dynamics study.

The excited state dynamics of pyrazine has attracted considerable attention in the last three decades. It has long been recognized that after UV excitation, the dynamics of the molecule is impacted by strong non-adiabatic effects due to the existence of a conical intersection between the B2u(ππ*) and B3u(nπ*) electronic states. However, a recent study based on trajectory surface hopping dynamics simulations suggested the participation of the Au(nπ*) and B2g(nπ*) low-lying dark electronic states in the ultrafast radiationless decay of the molecule after excitation to the B2u(ππ*) state. The purpose of this work was to pursue the investigation of the role of the Au(nπ*) and B2g(nπ*) states in the photophysics of pyrazine. A linear vibronic coupling model hamiltonian including the four lowest excited electronic states and the sixteen most relevant vibrational degrees of freedom was constructed using high level XMCQDPT2 electronic structure calculations. Wavepacket propagations using the MCTDH method were then performed and used to simulate the absorption spectrum and the electronic state population dynamics of the system. Our results show that the Au(nπ*) state plays an important role in the photophysics of pyrazine.

Laser control of the radiationless decay in pyrazine using the dynamic Stark effect.

The laser control of the radiationless decay between the B(3u)(nπ*) and B(2u)(ππ*) states of pyrazine using the dynamic Stark effect has been investigated. A vibronic coupling model Hamiltonian in diabatic representation, including potential energy, transition dipole, and static polarizability surfaces as a function of the four most important vibrational modes of the molecule has been parametrized using multi-reference electronic structure calculations. The interaction of the molecule with a strong non-resonant laser pulse has been analyzed in terms of dressed potential energy surfaces. Because of the large polarizability difference between the vibronically coupled B(3u)(nπ*) and B(2u)(ππ*) states, the Stark effect induced by the non-resonant laser pulse shifts the conical intersection away from the Franck-Condon region. We have shown, by solving the time-dependent Schrödinger equation for the molecule interacting with a relatively weak pump pulse driving the electronic excitation from the ground state to the B(2u)(ππ*) state, and a strong non-resonant control pulse, that this control mechanism can be used to trap the wavepacket on the B(2u)(ππ*) potential energy surface for a much longer time than the natural B(2u)(ππ*) lifetime.

New insight into the potential energy landscape and relaxation pathways of photoexcited aniline from CASSCF and XMCQDPT2 electronic structure calculations.

There have been a number of recent experimental investigations of the nonadiabatic relaxation dynamics of aniline following excitation to the first three singlet excited states, 1(1)ππ*, 1(1)π3s/πσ* and 2(1)ππ*. Motivated by differences between the interpretations of experimental observations, we have employed CASSCF and XMCQDPT2 calculations to explore the potential energy landscape and relaxation pathways of photoexcited aniline. We find a new prefulvene-like MECI connecting the 1(1)ππ* state with the GS in which the carbon-atom carrying the amino group is distorted out-of-plane. This suggests that excitation above the 1(1)π3s/πσ* vertical excitation energy could be followed by electronic relaxation from the 1(1)ππ* state to the ground-electronic state through this MECI. We find a MECI connecting the 1(1)π3s/πσ* and 1(1)ππ* states close to the local minimum on 1(1)π3s/πσ* which suggests that photoexcitation to the 1(1)π3s/πσ* state could be followed by relaxation to the 1(1)ππ* state and to the dissociative component of the 1(1)π3s/πσ* state. We also find evidence for a new pathway from the 2(1)ππ* state to the ground electronic state that is likely to pass through a three-state conical intersection involving the 2(1)ππ*, 1(1)π3s/πσ* and 1(1)ππ* states.

Laser-induced enhancement of tunneling in NHD2.

We apply and explore techniques aiming at enhancing the tunneling by laser fields, originally developed for a one-dimensional model, to a complete six-dimensional vibrational model of the inversion motion in NHD(2). The computational study is performed with the multi-configuration time-dependent Hartree method. Assuming an ideal three-dimensional alignment we obtain a driven tunneling time twenty times smaller than the natural one, in rather good agreement with an oversimplified three-state model. In the case of one-dimensional alignment, a linearly polarized field leads to a poor enhancement of the tunneling probability, after averaging over the rotation about the alignment axis, whereas a circularly polarized field improves the rotationally averaged tunneling probability at the end of the pulse.

High-fidelity adiabatic passage by composite sequences of chirped pulses.

We present a method for optimization of the technique of adiabatic passage between two quantum states by composite sequences of frequency-chirped pulses with specific relative phases: composite adiabatic passage (CAP). By choosing the composite phases appropriately the nonadiabatic losses can be canceled to any desired order with sufficiently long sequences, regardless of the nonadiabatic coupling. The values of the composite phases are universal for they do not depend on the pulse shapes and the chirp. The accuracy of the CAP technique and its robustness against parameter variations make CAP suitable for high-fidelity quantum information processing.