Multichannel Quantum Defect Theory with a Frame Transformation for Ultracold Atom-Molecule Collisions in Magnetic Fields.

We extend the powerful formalism of multichannel quantum defect theory combined with a frame transformation to ultracold atom-molecule collisions in magnetic fields. By solving the coupled-channel equations with hyperfine and Zeeman interactions omitted at short range, the extended theory enables a drastically simplified description of the intricate quantum dynamics of ultracold molecular collisions in terms of a small number of short-range parameters. We apply the formalism to ultracold Mg+NH collisions in a magnetic field, achieving a 10^{4}-fold reduction in computational effort.

Interference is in the eye of the beholder: Application to the coherent control of collisional processes.

Interference is widely regarded as a foundational attribute of quantum mechanics. However, for a given experimental arrangement, interference can either contribute or not contribute to the outcome depending upon the basis in which it is measured. This observation is both foundational and particularly relevant to coherent control of molecular processes, an approach based upon quantum interference. Here, we address this issue and its relevance to controlling molecular processes via the "coherent control scattering (CCS) matrix," a formalism that allows for an analysis of modifications in an interference structure resulting from a change of basis. This analysis reveals that the change in the interference structure can be attributed to the non-commutativity of the transformation matrix with the CCS matrix and the non-orthogonality of the transformation. Additionally, minimal interference is shown to be associated with the CCS eigenbasis and that the Fourier transform of the eigenvectors of the CCS matrix provides the maximal interference and hence the best coherent control. The change of controllability through a change of basis is illustrated with an example of 85Rb+ 85Rb scattering. In addition, the developed formalism is applied to explain recent experimental results on He + D2 inelastic scattering demonstrating the presence or absence of interference depending on the basis.

Complete Quantum Coherent Control of Ultracold Molecular Collisions.

We show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics that is free from the limitations of commonly used methods that rely on external electromagnetic fields. By varying the relative populations and phases of initial coherent superpositions of degenerate molecular states, we demonstrate complete coherent control over integral scattering cross sections in the ultracold s-wave regime of both the initial and final collision channels. The proposed control methodology is applied to ultracold O_{2}+O_{2} collisions, showing extensive control over s-wave spin-exchange cross sections and product branching ratios over many orders of magnitude.

Computational approaches to efficient generation of the stationary state for incoherent light excitation.

Light harvesting processes are often computationally studied from a time-dependent viewpoint, in line with ultrafast coherent spectroscopy experiments. Yet, natural processes take place in the presence of incoherent light, which induces a stationary state. Such stationary states can be described using the eigenbasis of the molecular Hamiltonian, but for realistic systems, a full diagonalization is prohibitively expensive. We propose three efficient computational approaches to obtain the stationary state that circumvents system Hamiltonian diagonalization. The connection between the incoherent perturbations, decoherence, and Kraus operators is established.

Multi-objective optimization for retinal photoisomerization models with respect to experimental observables.

The fitting of physical models is often done only using a single target observable. However, when multiple targets are considered, the fitting procedure becomes cumbersome, there being no easy way to quantify the robustness of the model for all different observables. Here, we illustrate that one can jointly search for the best model for each desired observable through multi-objective optimization. To do so, we construct the Pareto front to study if there exists a set of parameters of the model that can jointly describe multiple, or all, observables. To alleviate the computational cost, the predicted error for each targeted objective is approximated with a Gaussian process model as it is commonly done in the Bayesian optimization framework. We applied this methodology to improve three different models used in the simulation of stationary state cis-trans photoisomerization of retinal in rhodopsin, a significant biophysical process. Optimization was done with respect to different experimental measurements, including emission spectra, peak absorption frequencies for the cis and trans conformers, and energy storage. Advantages and disadvantages of previously proposed models are exposed.

Pulsed two-photon coherent control of channelrhodopsin-2 photocurrent in live brain cells.

Channelrhodopsin-2 (ChR2) is an ion channel activated by the absorption of light. A recent experiment demonstrated that the current emanating from neurons in live brain cells expressing ChR2 can be controlled using two-photon phase control. Here, we propose an experimentally testable coherent control mechanism for this phenomenon. Significantly, we describe how femtosecond, quantum coherent processes arising from weak-field ultrafast excitation are responsible for the reported control of the millisecond classical dynamics of the neuronal current.

LH1-RC light-harvesting photocycle under realistic light-matter conditions.

Quantum master equations are used to simulate the photocycle of the light-harvesting complex 1 (LH1) and the associated reaction center (RC) in purple bacteria excited with natural incoherent light. The influence of the radiation and protein environments and the full photocycle of the complexes, including the charge separation and RC recovery processes, are taken into account. Particular emphasis is placed on the steady state excitation energy transfer rate between the LH1 and the RC and the steady state dependence on the light intensity. The transfer rate is shown to scale linearly with light intensity near the value in the natural habitat and at higher light intensities is found to be bounded by the rate-determining step of the photocycle, the RC recovery rate. Transient (e.g., pulsed laser induced) dynamics, however, shows rates higher than the steady state value and continues to scale linearly with the intensity. The results show a correlation between the transfer rate and the manner in which the donor state is prepared. In addition, the transition from the transient to the steady state results can be understood as a cascade of ever slower rate-determining steps and quasi-stationary states inherent in multi-scale sequential processes. This type of transition of rates is relevant in most light-induced biological machinery.

Energy transfer under natural incoherent light: Effects of asymmetry on efficiency.

The non-equilibrium stationary coherences that form in donor-acceptor systems are investigated to determine their relationship to the efficiency of energy transfer to a neighboring reaction center. It is found that the effects of asymmetry in the dimer are generally detrimental to the transfer of energy. Four types of systems are examined, arising from combinations of localized trapping, delocalized (Forster) trapping, eigenstate dephasing, and site basis dephasing. In the cases of site basis dephasing, the interplay between the energy gap of the excited dimer states and the environment is shown to give rise to a turnover effect in the efficiency under weak dimer coupling conditions. Furthermore, the nature of the coherences and associated flux is interpreted in terms of pathway interference effects. In addition, regardless of the cases considered, the ratio of the real part and the imaginary part of the coherences in the energy-eigenbasis tends to a constant value in the steady state limit.

Multiple time scale open systems: Reaction rates and quantum coherence in model retinal photoisomerization under incoherent excitation.

Many important open quantum systems, such as light harvesting systems irradiated with natural incoherent light, present challenging computational problems. Specifically, such systems are characterized by multiple time scales over many orders of magnitude. We describe and apply an efficient approach to determine rates and dynamics in such systems. As an example, we present a theoretical and computational analysis of retinal isomerization under incoherent solar excitation using a minimal retinal model. Solar- and bath-induced Fano coherences are shown to have a small but non-negligible effect on the reaction dynamics, and the effect of Fano coherences on the reaction rate is shown to depend strongly upon the form and strength of the system-bath coupling. Using the isomerization probability to obtain the time-dependent cellular hyperpolarization, we show that the effect of coherence on hyperpolarization dynamics is small compared to the effect of natural variations in the solar intensity.

Light-induced processes in nature: Coherences in the establishment of the nonequilibrium steady state in model retinal isomerization.

Dynamics and coherences in retinal isomerization are investigated in a standard two-mode two-state model irradiated by natural incoherent light using the Markovian partial-secular Bloch-Redfield formalism. The two-mode two-state model is a minimal model of retinal that considers vibronic states on a ground and excited electronic manifold coupled to two continuous Ohmic harmonic baths. All light-induced coherent oscillations are shown to disappear as the turn-on time becomes realistically slow. Rather, an interplay between incoherent-light induced coherences and environmentally induced coherences is exposed as the system approaches a nonequilibrium steady state. The dynamics of the system reveal stable steady state coherences under realistic conditions, producing a small but robust transient enhancement of quantum yield.

An efficient spectral method for numerical time-dependent perturbation theory.

We develop the Fourier-Laplace Inversion of the Perturbation Theory (FLIPT), a novel numerically exact "black box" method to compute perturbative expansions of the density matrix with rigorous convergence conditions. Specifically, the FLIPT method is extremely well-suited to simulate multiphoton pulsed laser experiments with complex pulse shapes. The n-dimensional frequency integrals of the nth order perturbative expansion are evaluated numerically using tensor products. The N-point discretized integrals are computed in O(N2) operations, a significant improvement over the O(Nn) scaling of standard quadrature methods.

Influence of non-Markovian dynamics in equilibrium uncertainty-relations.

Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that in quantum mechanics, these deviations originate from the uncertainty principle and are supported by the non-Markovian character of the dynamics. Specifically, it is shown that the lower bound of the dispersion of the total energy of the system, imposed by the uncertainty principle, is dominated by the bath power spectrum; therefore, quantum mechanics inhibits the system thermal-equilibrium-state from being described by the canonical Boltzmann's distribution. We show for a wide class of systems, systems interacting via central forces with pairwise-self-interacting environments; this general observation is in sharp contrast to the classical case, for which the thermal equilibrium distribution, irrespective of the interaction strength, is exactly characterized by the canonical Boltzmann distribution; therefore, no dependence on the bath power spectrum is present. We define an effective coupling to the environment that depends on all energy scales in the system and reservoir interaction. Sample computations in regimes predicted by this effective coupling are demonstrated. For example, for the case of strong effective coupling, deviations from standard thermodynamics are present and for the case of weak effective coupling, quantum features such as stationary entanglement are possible at high temperatures.

Coherent Control of Penning and Associative Ionization: Insights from Symmetries.

Coherent control of reactive atomic and molecular collision processes remains elusive experimentally due to quantum interference-based requirements. Here, with insights from symmetry conditions, a viable method for controlling Penning and associative ionization in atomic collisions is proposed. Computational applications to He^{*}(^{3}S)-Li(^{2}S) and Ne^{*}(^{3}P_{2})-Ar(^{1}S_{0}) show extensive control over the ionization processes under experimentally feasible conditions.

Quantumness in light harvesting is determined by vibrational dynamics.

We demonstrate for the multi-level spin-boson (MLSB) Hamiltonian, typically used to describe biological light-harvesting, that the distinction between quantum and classical dynamics is determined entirely by the thermal environment. In particular, any MLSB model featuring classical interactions with a classical bath is exactly equivalent in its absorption and energy transfer dynamics to a classical model involving coupled harmonic oscillators. This result holds in the linear response regime for both pulsed and incoherent excitation. In the biological context, this finding highlights the centrality of vibrational dynamics in determining the "quantumness" of photosynthetic light-harvesting, particularly in the creation of the photosynthetic energy funnel where excitation energy concentrates near the reaction center via a series of downhill energy transfer events. These findings support the idea that this energy funnel is exclusively quantum-mechanical in origin, although it need not rely on entanglement.

Classical coherent two-dimensional vibrational spectroscopy.

Two-dimensional (2D) ultrafast spectroscopy is a powerful tool for studying the electronic and vibrational structures of complex systems. Unfortunately, the physical interpretation of these experiments is obscured by conceptual problems in classical response theory, i.e., the divergence of classical nonlinear response functions. We demonstrate that these difficulties are avoided by modeling classical 2D experiments nonperturbatively, illustrating that nonlinear spectroscopy and nonlinear response are not synonymous. Numerical simulations allow a direct comparison between classical and quantum 2D spectra for simple, weakly anharmonic systems relevant to vibrational spectroscopy. We find that nonperturbative classical theory-although differing in quantitative details-accurately captures the key qualitative features of the quantum 2D spectrum, including the separation of the signal into wavevector-selected pathways, formation of cross peaks between coupled vibrational modes, and coherent beating in the signal as a function of waiting time (so-called "quantum beats"). These results are discussed in terms of a simple analytical model which captures the key physical features of classical 2D spectroscopy and provides a link between classical and quantum descriptions. One interesting conclusion from this comparison is that the "coherence" observed in ultrafast spectroscopy may (at least in vibrational experiments) be understood as a purely classical phenomenon, without reference to quantum mechanics.

An efficient approach to the quantum dynamics and rates of processes induced by natural incoherent light.

In many important cases, the rate of excitation of a system embedded in an environment is significantly smaller than the internal system relaxation rates. An important example is that of light-induced processes under natural conditions, in which the system is excited by weak, incoherent (e.g., solar) radiation. Simulating the dynamics on the time scale of the excitation source can thus be computationally intractable. Here we describe a method for obtaining the dynamics of quantum systems without directly solving the master equation. We present an algorithm for the numerical implementation of this method and, as an example, use it to reconstruct the internal conversion dynamics of pyrazine excited by sunlight. Significantly, this approach also allows us to assess the role of quantum coherence on biological time scales, which is a topic of ongoing interest.

Non-equilibrium stationary coherences in photosynthetic energy transfer under weak-field incoherent illumination.

We present a theoretical study of the quantum dynamics of energy transfer in a model photosynthetic dimer excited by incoherent light and show that the interplay between incoherent pumping and phonon-induced relaxation, dephasing, and trapping leads to the emergence of non-equilibrium stationary states characterized by substantial stationary coherences in the energy basis. We obtain analytic expressions for these coherences in the limits of rapid dephasing of electronic excitations and of small excitonic coupling between the chromophores. The stationary coherences are maximized in the regime where the excitonic coupling is small compared to the trapping rate. We further show that the non-equilibrium coherences anti-correlate with the energy transfer efficiency in the regime of localized coupling to the reaction center and that no correlation exists under delocalized (Förster) trapping conditions.

Interfering resonance as an underlying mechanism in the adaptive feedback control of radiationless transitions: Retinal isomerization.

Control of molecular processes via adaptive feedback often yields highly structured laser pulses that have eluded physical explanation. By contrast, coherent control approaches propose physically transparent mechanisms but are not readily visible in experimental results. Here, an analysis of a condensed phase adaptive feedback control experiment on retinal isomerization shows that it manifests a quantum interference based coherent control mechanism: control via interfering resonances. The result promises deep insight into the physical basis for the adaptive feedback control of a broad class of bound state processes.

Laser-induced molecular alignment in the presence of chaotic rotational dynamics.

Coherent control of chaotic molecular systems, using laser-assisted alignment of sulphur dioxide (SO2) molecules in the presence of a static electric field as an example, is considered. Conditions for which the classical version of this system is chaotic are established, and the quantum and classical analogs are shown to be in very good correspondence. It is found that the chaos present in the classical system does not impede the alignment, neither in the classical nor in the quantum system. Using the results of numerical calculations, we suggest that laser-assisted alignment is stable against rotational chaos for all asymmetric top molecules.

Spin-Orbit Interactions and Quantum Spin Dynamics in Cold Ion-Atom Collisions.

We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb^{+}-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-order spin-orbit (SO) interaction as the dominant source of hyperfine relaxation in cold Yb^{+}-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb^{+} immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than is predicted by the Langevin capture theory and display a weak T^{-0.3} temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb^{+}-Li should be used to minimize hyperfine relaxation and decoherence of trapped ions in ultracold atomic gases.