Markus Kowalewski

Monotonic convergent optimal control theory with strict limitations on the spectrum of optimized laser fields.

X iv :0 80 1. 39 35 v1 [ qu an tph ] 2 5 Ja n 20 08 Montoni onvergent optimal ontrol theory to modulate bandwidth limited laser pulses in linear and non-linear opti al pro esses Caroline Gollub, Markus Kowalewski and Regina de Vivie-Riedle Department of Chemistry, Ludwig-Maximilians-Universität Mün hen, D-81377 Mün hen, Germany (Dated: 2008-01-24) We present a modi ed optimal ontrol s heme based on the Krotov method, whi h allows for stri t limitations on the spe trum of the optimized laser elds, without losing monotoni onvergen e of the algorithm. The method guarantees a lose link to learning loop ontrol experiments and is demonstrated for the hallenging ontrol of non-resonant Raman transitions, whi h are used to implement a set of global quantum gates for mole ular vibrational qubits. PACS numbers: 33.80.Wz, 03.67.Lx, 02.30.Yy With the progress of laser pulse shaping and learning loop te hniques [1℄ quantum ontrol experiments (OCE) be ame a forefront tool for the ontrol and de iphering of mole ular quantum pro esses [2, 3, 4, 5℄. Optimal ontrol theory (OCT) [6, 7℄ as the theoreti al ounterpart is a powerful method for the predi tion of pulse stru tures as initial guess and guidan e for OCE. With OCT, insight into the quantum pathways of these pro esses is dire tly available. The numerous appli ations of optimal ontrol range from the ontrol of hemi al rea tions in gas and ondensed phase [8, 9℄ to the ontrol in nanostru tures [10, 11℄ and to quantum opti al problems like quantum information pro essing [12, 13, 14, 15℄ or the preparation of old mole ules [16, 17℄. One fundamental di eren e between OCE and OCT is the spe tral bandwidth of the laser eld inherently present in the experiment but in prin iple unlimited in the original theoreti al formulation. The general omparability of experimental and theoreti al results may be ompli ated, sin e the theoreti al answer for the optimal pulse an always span a wide bandwidth with quantum pathways out of experimental rea h. Several suggestions have been made dealing with this hallenge [18, 19, 20℄, however, at the ost of monotoni onvergen e or general appli ability [21℄. We present a modi ed OCT approa h based on the Krotov method [22℄ that treats time and frequen y domain equally while providing monotoni onvergen e. The method o ers an elegant possibility to study OCEs theoreti ally by expli itly in luding as a onstraint the ru ial experimental feature of the spe tral bandwidth. As an ultimate test we demonstrate the new tool by the implementation of stimulated non-resonant Raman quantum gates for vibrational qubits. The idea of mole ular vibrational quantum omputing [12℄ has rst been introdu ed for IR-a tive modes. Ultrashort, spe ially shaped laser pulses a t as global quantum gate operations. Di erent types of quantum gates and quantum algorithms have been demonstrated theoreti ally for IR transitions [12, 23, 24, 25, 26℄ and STIRAP proesses [27, 28℄. Experimentally, mole ular quantum gates have been realized in the visible regime [29, 30℄ and latest IR shaping experiments [31, 32℄ open the route for the realization of vibrational qubits in the IR [33℄. Stimulated non-resonant Raman quantum gates will provide new exibilities, like the hoi e of laser wavelengths. Their theoreti al implementation an be regarded as a great hallenge for the new OCT s heme sin e it omprises a non-resonant, two-photon, twoolor pro ess. The multi-target optimal ontrol fun tional [12℄ for the mole ular non-resonant Raman intera tion in ludes two laser elds ǫl(t) with l = 1, 2 (Eq. 1). The orresponding Raman Hamiltonian is given by VR = − 12ǫ1(t) α̂ ǫ2(t), with the mole ular polarizability α̂.

Catching Conical Intersections in the Act: Monitoring Transient Electronic Coherences by Attosecond Stimulated X-Ray Raman Signals

Conical intersections (CIs) dominate the pathways and outcomes of virtually all photophysical and photochemical molecular processes. Despite extensive experimental and theoretical effort, CIs have not been directly observed yet and the experimental evidence is being inferred from fast reaction rates and some vibrational signatures. We show that short x-ray (rather than optical) pulses can directly detect the passage through a CI with the adequate temporal and spectral sensitivity. The technique is based on a coherent Raman process that employs a composite femtosecond or attosecond x-ray pulse to detect the electronic coherences (rather than populations) that are generated as the system passes through the CI.

Cavity Femtochemistry: Manipulating Nonadiabatic Dynamics at Avoided Crossings.

Molecular potential energy surfaces can be actively manipulated by light. This is usually done by strong classical laser light but was recently demonstrated for the quantum field in an optical cavity. The photonic vacuum state of a localized cavity mode can be strongly mixed with the molecular degrees of freedom to create hybrid field-matter states known as polaritons. We simulate the avoided crossing of sodium iodide in a cavity by incorporating the quantized cavity field into the nuclear wave packet dynamics calculation. The quantized field is represented on a numerical grid in quadrature space, thus avoiding the limitations set by the rotating wave approximation (RWA) when the field is expanded in Fock space. This approach allows the investigation of cavity couplings in the vicinity of naturally occurring avoided crossings and conical intersections, which is too expensive in the fock space expansion when the RWA does not apply. Numerical results show how the branching ratio between the covalent and ionic dissociation channels can be strongly manipulated by the optical cavity.

Optimal control theory – closing the gap between theory and experiment

Optimal control theory and optimal control experiments are state-of-the-art tools to control quantum systems. Both methods have been demonstrated successfully for numerous applications in molecular physics, chemistry and biology. Modulated light pulses could be realized, driving these various control processes. Next to the control efficiency, a key issue is the understanding of the control mechanism. An obvious way is to seek support from theory. However, the underlying search strategies in theory and experiment towards the optimal laser field differ. While the optimal control theory operates in the time domain, optimal control experiments optimize the laser fields in the frequency domain. This also implies that both search procedures experience a different bias and follow different pathways on the search landscape. In this perspective we review our recent developments in optimal control theory and their applications. Especially, we focus on approaches, which close the gap between theory and experiment. To this extent we followed two ways. One uses sophisticated optimization algorithms, which enhance the capabilities of optimal control experiments. The other is to extend and modify the optimal control theory formalism in order to mimic the experimental conditions.

Non-adiabatic dynamics of molecules in optical cavities.

Strong coupling of molecules to the vacuum field of micro cavities can modify the potential energy surfaces thereby opening new photophysical and photochemical reaction pathways. While the influence of laser fields is usually described in terms of classical field, coupling to the vacuum state of a cavity has to be described in terms of dressed photon-matter states (polaritons) which require quantized fields. We present a derivation of the non-adiabatic couplings for single molecules in the strong coupling regime suitable for the calculation of the dressed state dynamics. The formalism allows to use quantities readily accessible from quantum chemistry codes like the adiabatic potential energy surfaces and dipole moments to carry out wave packet simulations in the dressed basis. The implications for photochemistry are demonstrated for a set of model systems representing typical situations found in molecules.

Nucleophilic substitution dynamics: comparing wave packet calculations with experiment.

The reactive collision of chloride anions and methyl iodide molecules forming iodide anions and methyl chloride is a typical example of a concerted bimolecular nucleophilic substitution (SN2) reaction. We present wave packet dynamics calculations to investigate quantum effects in the collinear gas phase reaction. A new type of reduced coordinate system is introduced to allow for an efficient solution of the time-dependent Schrödinger equation on an ab initio potential energy surface. The reduced coordinates were designed to study the direct rebound mechanism under the Walden inversion. Especially the suppressed direct rebound mechanism at low collision energies, the quantum effects of the initial state preparation and the influence of the CH3 inversion mode are addressed. The internal energy distributions of the molecular product are evaluated from the wave packet calculations and compared to experimental results obtained with crossed-beam velocity map ion imaging. The observed reactivity is discussed in light of a dynamical barrier, a concept that is illustrated by the wave packet dynamics.

Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime

Crossings of electronic potential energy surfaces in nuclear configuration space, known as conical intersections, determine the rates and outcomes of a large class of photochemical molecular processes. Much theoretical progress has been made in computing strongly coupled electronic and nuclear motions at different levels, but how to incorporate them in different spectroscopic signals and the approximations involved are less established. This will be the focus of the present review. We survey a wide range of time-resolved spectroscopic techniques which span from the infrared to the X-ray regimes and can be used for probing the nonadiabatic dynamics in the vicinity of conical intersections. Transient electronic and vibrational probes and their theoretical signal calculations are classified by their information content. This includes transient vibrational spectroscopic methods (transient infrared and femtosecond off-resonant stimulated Raman), resonant electronic probes (transient absorption and photoelectron spectroscopy), and novel stimulated X-ray Raman techniques. Along with the precise definition of what to calculate for predicting the various signals, we outline a toolbox of protocols for their simulation.

Monitoring Nonadiabatic Electron-Nuclear Dynamics in Molecules by Attosecond Streaking of Photoelectrons

Streaking of photoelectrons has long been used for the temporal characterization of attosecond extreme ultraviolet pulses. When the time-resolved photoelectrons originate from a coherent superposition of electronic states, they carry additional phase information, which can be retrieved by the streaking technique. In this contribution we extend the streaking formalism to include coupled electron and nuclear dynamics in molecules as well as initial coherences. We demonstrate how streaked photoelectrons offer a novel tool for monitoring nonadiabatic dynamics as it occurs in the vicinity of conical intersections and avoided crossings. Streaking can provide high time resolution direct signatures of electronic coherences, which affect many primary photochemical and biological events.

Electron Dynamics and Its Control in Molecules: From Diatomics to Larger Molecular Systems

Electrons and their dynamics are involved in bond breaking and formation; thus, the idea to steer chemical reactions by localization of electronic wavepackets seems natural. The formation of a localized electronic wavepacket requires the superposition of two or more appropriate electronic states through, e.g., an external electric field. The guiding of such an electronic wavepacket is only possible within the coherence time of the system. In theoretical studies, we elucidate the role of electron wavepacket motion for the control of molecular processes. We analyze three examples of electron wavepacket-driven processes with direct connection to already performed or ongoing experiments. From these examples, we extract the system requirements defining the time window for intramolecular electronic coherence and efficient control. With this knowledge, we derived an appropriate molecular configuration in a photoreaction of a polyatomic molecule where a control by guiding electronic wavepackets is possible. For such a photoreaction, we designed a new control scheme with the carrier envelope phase as a control parameter that works at high efficiency.

Manipulating molecules with quantum light

It was first realized by Purcell (1) that the spontaneous emission rate of a quantum system can be enhanced or suppressed by placing it in a resonant radiofrequency cavity. Spontaneous emission as it was first theoretically described by Einstein (2) is not a pure property of matter. It is described by matter coupled to quantized radiation field modes, which can be manipulated in an artificial structure such as a cavity. Cavity quantum electrodynamics (QED) is used to describe such effects that intimately depend on the fact that light is made of photons. Cavity QED has been extensively studied in atoms and the experimental proof was awarded with the Nobel Prize in 2012 (3). It has been applied to cooling of single atoms and for the detection of single atoms and creating and studying states with few photons and few atoms (4). In more recent developments these ideas have been extended to manipulate electronic states (5) and vibrations in molecules (6, 7). In PNAS, Flick et al. (8) introduce recent theoretical developments for the application of cavity QED to molecules and suggest possible novel applications to photochemistry. These include nonadiabatic dynamics of molecules in cavities, the modification of molecular properties, and the integration of QED with density functional theory. A quantized electromagnetic field mode can be described as a harmonic oscillator whose coordinate is the electric field displacement (Fig. 1 A ). The zero point energy translates into a nonvanishing field intensity ⟨ e 2 ⟩ in the ground state | 0 ⟩ (vacuum fluctuations). The electric vacuum field increases for a small cavity volume e c = ℏ ω c V ϵ 0 , [1] Fig. 1. ( A ) Illustration of the standing wave cavity mode and the resulting field quantization (Fock states). ( B ) Combined matter-field states (dressed states, | ± , n ⟩ … [↵][1]1To whom correspondence should be addressed. Email: smukamel{at}uci.edu. [1]: #xref-corresp-1-1