Wave packet interferometry and quantum state reconstruction by acousto-optic phase modulation

Studies of wave packet dynamics often involve phase-selective measurements of coherent optical signals generated from sequences of ultrashort laser pulses. In wave packet interferometry (WPI), the separation between the temporal envelopes of the pulses must be precisely monitored or maintained. Here we introduce a new (and easy to implement) experimental scheme for phase-selective measurements that combines acousto-optic phase modulation with ultrashort laser excitation to produce an intensity-modulated fluorescence signal. Synchronous detection, with respect to an appropriately constructed reference, allows the signal to be simultaneously measured at two phases differing by 90 degrees. Our method effectively decouples the relative temporal phase from the pulse envelopes of a collinear train of optical pulse pairs. We thus achieve a robust and high signal-to-noise scheme for WPI applications, such as quantum state reconstruction and electronic spectroscopy. The validity of the method is demonstrated, and state reconstruction is performed, on a model quantum system--atomic Rb vapor. Moreover, we show that our measurements recover the correct separation between the absorptive and dispersive contributions to the system susceptibility.     

Implementation of quantum gate operations in molecules with weak laser fields

We numerically propose a way to perform quantum computations by combining an ensemble of molecular states and weak laser pulses. A logical input state is expressed as a superposition state (a wave packet) of molecular states, which is initially prepared by a designed femtosecond laser pulse. The free propagation of the wave packet for a specified time interval leads to the specified change in the relative phases among the molecular basis states, which corresponds to a computational result. The computational results are retrieved by means of quantum interferometry. Numerical tests are implemented in the vibrational states of the B state of I2 employing controlled-NOT gate, and 2 and 3 qubits Fourier transforms. All the steps involved in the computational scheme, i.e., the initial preparation, gate operation, and detection steps, are achieved with extremely high precision.     

Phase control over decaying molecular states in intense laser pulses

A time-dependent approach to study phase control over molecular photoabsorption, provided by intense laser pulses, is elaborate. The method allows for the decay linewidth of molecular states and frequency bandwidth of the controlling laser field, and can be applied in weak and strong laser fields where the perturbation theory is invalid. It is shown that a frequency mismatch between the fundamental laser wave and its third harmonic can destroy control. For the example of the one-photon versus three-photon control a simple picture of interference from two monochromatic absorption pathways is not enough to explain phase control and one needs to consider a nonlinear temporal interference of multiquantum transitions. In the perturbation-theory limit an elegant generalization of the famous Shapiro-Hepburn-Brumer equation for the one-photon versus three-photon control is derived. Various numerical calculations illustrate the dependence of phase control on molecular linewidth, fundamental laser wavelength, pulse duration, and peak intensity. It is obtained, that the one-photon versus three-photon control is productive if the molecular state populations, individually produced by each laser wave, have beats of approximately the same frequency. The calculations demonstrate that an enough intense optical pulse can suppress molecular decay and may be used in order to keep stable the state population of a decaying molecule for a long time. The available experimental results for the one-photon versus three-photon control over simple and large polyatomic molecules are analyzed and recommendations for the experimental improvement of control are formulated.     

Quantum control of a molecular system in an intense field via the selective population of dressed states

We theoretically investigate the physical mechanism of quantum control on a K(2) molecule with an ultrafast strong laser pulse by solving the time-dependent Schr?dinger equation exactly using a wave packet approach. The structures of the triple splitting in the 3-photon ionization spectra of a K(2) molecule are presented to analyze the information of a selective population of dressed states. In this work, it is found that the tunability of the dressed states energies is achieved by regulating the laser intensity and the high selectivity of the dressed state population is attained by altering the envelope and wavelength of the intense laser pulse.     

Laser-induced alignment and anti-alignment of rotationally excited molecules

We numerically investigate the post-pulse alignment of rotationally excited diatomic molecules upon nonresonant interaction with a linearly polarized laser pulse. In addition to the simulations, we develop a simple model which qualitatively describes the shape and amplitude of post-pulse alignment induced by a laser pulse of moderate power density. In our treatment we take into account that molecules in rotationally excited states can interact with a laser pulse not only by absorbing energy but also by stimulated emission. The extent to which these processes are present in the interaction depends, on the one hand, on the directionality of the molecular angular momentum (given by the M quantum number), and on the other hand on the ratio of transition frequencies and pulse duration (determined by the J number). A rotational wave packet created by a strong pulse from an initially pure state contains a broad range of rotational levels, over which the character of the interaction can change from non-adiabatic to adiabatic. Depending on the laser pulse duration and amplitude, the transition from the non-adiabatic to the adiabatic limit proceeds through a region with dominant rotational heating, or alignment, for short pulses and a large region with rotational cooling, and correspondingly preferred anti-alignment, for longer pulses.     

Three‐peak Autler‐Townes splitting in the photoelectron spectrum of Li2 molecules caused by femtosecond laser pulses

Three‐peak Autler‐Townes (A‐T) splitting in the resonant multiphoton ionization photoelectron spectrum for a rotating Li₂ molecular system in femtosecond pulse laser fields is studied by using two‐dimension time‐dependent quantum wave packet method. The A‐T splitting results from rapid Rabi oscillation caused by intense femtosecond laser pulses. Because of the effects of molecular rotation and alignment, the Rabi oscillation in the population distribution will be damped in a certain degree. The three‐peak A‐T splitting can only be observed for a strongly aligned molecule with rapid Rabi oscillation. The three‐peak A‐T splitting dynamics can be affected by intensity, duration, temporal profile of laser pulse, and initial molecular rotational temperature. The conditions to observe the A‐T splitting are discussed in detail. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Nonlinear wave-packet interferometry and molecular state reconstruction in a vibrating and rotating diatomic molecule

We formulate two-color nonlinear wave-packet interferometry (WPI) for application to a diatomic molecule in the gas phase and show that this form of heterodyne-detected multidimensional electronic spectroscopy will permit the reconstruction of photoinduced rovibrational wave packets from experimental data. Using two phase-locked pulse pairs, each resonant with a different electronic transition, nonlinear WPI detects the quadrilinear interference contributions to the population of an excited electronic state. Combining measurements taken with different phase-locking angles isolates various quadrilinear interference terms. One such term gives the complex overlap between a propagated one-pulse target wave packet and a variable three-pulse reference wave packet. The two-dimensional interferogram in the time domain specifies the complex-valued overlap of the given target state with a collection of variable reference states. An inversion procedure based on singular-value decomposition enables reconstruction of the target wave packet from the interferogram without prior detailed characterization of the nuclear Hamiltonian under which the target propagates. With numerically calculated nonlinear WPI signals subject to Gaussian noise, we demonstrate the reconstruction of a rovibrational wave packet launched from the A state and propagated in the E state of Li2.     

Ultrafast photofragmentation dynamics of molecular iodine driven with timed XUV and near-infrared light pulses

Photofragmentation dynamics of molecular iodine was studied as a response to the joint illumination with femtosecond 800 nm near-infrared and 13 nm extreme ultraviolet (XUV) pulses delivered by the free-electron laser facility FLASH. The interaction of the molecular target with two light pulses of different wavelengths but comparable pulse energy elucidates a complex intertwined electronic and nuclear dynamics. To follow distinct pathways out of a multitude of reaction channels, the recoil of created ionic fragments is analyzed. The delayed XUV pulse provides a way of following molecular photodissociation of I(2) with a characteristic time-constant of (55 ± 10) fs after the laser-induced formation of antibonding states. A preceding XUV pulse, on the other hand, preferably creates a 4d(-1) inner-shell vacancy followed by the fast Auger cascade with a revealed characteristic time constant τ(A2)=(23±11) fs for the second Auger decay transition. Some fraction of molecular cationic states undergoes subsequent Coulomb explosion, and the evolution of the launched molecular wave packet on the repulsive Coulomb potential was accessed by the laser-induced postionization. A further unexpected photofragmentation channel, which relies on the collective action of XUV and laser fields, is attributed to a laser-promoted charge transfer transition in the exploding molecule.     

Laser-operated chiral molecular switch: quantum simulations for the controlled transformation between achiral and chiral atropisomers

We report quantum dynamical simulations for the laser controlled isomerization of 1-(2-cis-fluoroethenyl)-2-fluorobenzene based on one-dimensional electronic ground and excited state potentials obtained from (TD)DFT calculations. 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports two chiral and one achiral atropisomers, the latter being the most stable isomer at room temperature. Using a linearly polarized IR laser pulse the molecule is excited to an internal rotation around its chiral axis, i.e. around the C-C single bond between phenyl ring and ethenyl group, changing the molecular chirality. A second linearly polarized laser pulse stops the torsion to prepare the desired enantiomeric form of the molecule. This laser control allows the selective switching between the achiral and either the left- or right-handed form of the molecule. Once the chirality is "switched on" linearly polarized UV laser pulses allow the selective change of the chirality using the electronic excited state as intermediate state.     

Accuracy of gates in a quantum computer based on vibrational eigenstates

A model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical time-propagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.     

强阿秒XUV激走脉冲下H2^＋分子光电子能谱角分布非对称性

利用2D平面模型,求解了描述定向H2^＋分子和阿秒XUV脉冲相互作用的薛定谔方程,并求得光电子的角度分布．在计算模型中,采用基态1sσg和第一激发态2pσu的等比例混合态作为初始态,而激光脉冲的光子能量大于电离势,强度为10^14 W/cm^2． 计算结果表明,光电子角分布的非对称性和脉冲的宽度密切相关．这种非对称性实际上是由于初始态的基态和激发态的相干振荡而导致的．当使用长脉冲时,这种相干振荡的周期效应就会被平均而消失,从而产生的光电子能谱会呈对称角分布．     

The operations of quantum logic gates with pure and mixed initial states

The implementations of quantum logic gates realized by the rovibrational states of a C(12)O(16) molecule in the X((1)Σ(+)) electronic ground state are investigated. Optimal laser fields are obtained by using the modified multitarget optimal theory (MTOCT) which combines the maxima of the cost functional and the fidelity for state and quantum process. The projection operator technique together with modified MTOCT is used to get optimal laser fields. If initial states of the quantum gate are pure states, states at target time approach well to ideal target states. However, if the initial states are mixed states, the target states do not approach well to ideal ones. The process fidelity is introduced to investigate the reliability of the quantum gate operation driven by the optimal laser field. We found that the quantum gates operate reliably whether the initial states are pure or mixed.     

Design of infrared laser pulses for the deexcitation of highly excited homonuclear diatomic molecules

We explore the possibility of using shaped infrared laser pulses to deexcite a homonuclear diatomic molecule from its highest vibrational state down to its ground vibrational state. The motivation for this study arises from the need to deexcite alkali metal dimers in a similar way so as to stabilize molecular Bose-Einstein condensates. We demonstrate that for the case of the H(2) molecule, where it is possible to evaluate all the necessary high accuracy ab initio data on the interaction of the molecule with an electric field, we are able to successfully design a sequence of infrared laser pulses to accomplish the desired deexcitation process in a highly efficient manner.     

Correlated electron dynamics: how aromaticity can be controlled

In this Article, we show that the aromaticity of a molecule can be turned off by controlling the electron dynamics. We present a controlled switching from the aromatic ground state of benzene to two different nonaromatic states, using a laser pulse. The propagation of the molecular wave function is carried out with the time-dependent configuration interaction method. The laser pulse for switching between the ground and excited states is optimized using optimal control theory. Bond orders and Mulliken charges serve as an aromaticity criterion. The nonaromatic target states exhibit localized bonds and partial charges on the carbon atoms; these localized electrons circulate on an attosecond time scale in the ring system.     

Distinguishing between relaxation pathways by combining dissociative ionization pump probe spectroscopy and ab initio calculations: a case study of cytosine

We present a general method for tracking molecular relaxation along different pathways from an excited state down to the ground state. We follow the excited state dynamics of cytosine pumped near the S(0)-S(1) resonance using ultrafast laser pulses in the deep ultraviolet and probed with strong field near infrared pulses which ionize and dissociate the molecules. The fragment ions are detected via time of flight mass spectroscopy as a function of pump probe delay and probe pulse intensity. Our measurements reveal that different molecular fragments show different timescales, indicating that there are multiple relaxation pathways down to the ground state. We interpret our measurements with the help of ab initio electronic structure calculations of both the neutral molecule and the molecular cation for different conformations en route to relaxation back down to the ground state. Our measurements and calculations show passage through two seams of conical intersections between ground and excited states and demonstrate the ability of dissociative ionization pump probe measurements in conjunction with ab initio electronic structure calculations to track molecular relaxation through multiple pathways.     

Control of Li2 wave packet dynamics by modification of the quantum mechanical amplitude of a single state

Sequences of pulses with different spectra are used to control rotational wave packet dynamics in Li(2) by exploiting quantum interference phenomena. Wave packet superpositions are excited in a two-step resonant Raman process by two different pulses. Interferences between individual states shared by both wave packets can be used to enhance or destroy specific components of a superposition by varying the time delay between the pulses and/or the relative phase within the pulses. Elimination of selected quantum beats is achieved by greater than 94% for each case. A simple, yet effective, method for generating different color phase-locked pairs of laser pulses in a liquid-crystal pulse shaper setup without the need for interferometric stabilization schemes is described. The ability to manipulate single states of a superposition is an important advancement for intuitive control schemes and provides a potential new approach for initialization schemes in the field of quantum information.     

Femtosecond time-resolved molecular multiphoton ionization and fragmentation of Na2: experiment and quantum mechanical calculations

We present a comparison between experimental and theoretical results for pump/probe multiphoton ionizing transitions of the sodium dimer, initiated by femtosecond laser pulses. It is shown that the motion of vibrational wave packets in two electronic states is probed simultaneously and their dynamics is reflected in the total Na ₂ ⁺ ion signal which is recorded as a function of the time delay between pump and probe pulse. The time dependent quantum calculations demonstrate that two ionization pathways leading to the same final states of the molecular ion exist: one gives an oscillating contribution to the ion signal, the other yields a constant background. From additional measurements of the Na⁺-transient photofragmentation spectrum it is deduced that another ionization process leading to different final ionic states exists. The process includes the excitation of a doubly excited bound Rydberg state. This conclusion is supported by the theoretical simulation.     

Isotope selective photoionization of NaK by optimal control: theory and experiment

We present a joint theoretical and experimental study of the maximization of the isotopomer ratio (23)Na(39)K(23)Na(41)K using tailored phase-only as well as amplitude and phase modulated femtosecond laser fields obtained in the framework of optimal control theory and closed loop learning (CLL) technique. A good agreement between theoretically and experimentally optimized pulse shapes is achieved which allows to assign the optimized processes directly to the pulse shapes obtained by the experimental isotopomer selective CLL approach. By analyzing the dynamics induced by the optimized pulses we show that the mechanism involving the dephasing of the wave packets between the isotopomers (23)Na (39)K and (23)Na (41)K on the first excited state is responsible for high isotope selective ionization. Amplitude and phase modulated pulses, moreover, allow to establish the connection between the spectral components of the pulse and corresponding occupied vibronic states. It will be also shown that the leading features of the theoretically shaped pulses are independent from the initial conditions. Since the underlying processes can be assigned to the individual features of the shaped pulses, we show that optimal control can be used as a tool for analysis.     

Effect of diatomic molecular properties on binary laser pulse optimizations of quantum gate operations

The importance of the ro-vibrational state energies on the ability to produce high fidelity binary shaped laser pulses for quantum logic gates is investigated. The single frequency 2-qubit ACNOT(1) and double frequency 2-qubit NOT(2) quantum gates are used as test cases to examine this behaviour. A range of diatomics is sampled. The laser pulses are optimized using a genetic algorithm for binary (two amplitude and two phase parameter) variation on a discretized frequency spectrum. The resulting trends in the fidelities were attributed to the intrinsic molecular properties and not the choice of method: a discretized frequency spectrum with genetic algorithm optimization. This is verified by using other common laser pulse optimization methods (including iterative optimal control theory), which result in the same qualitative trends in fidelity. The results differ from other studies that used vibrational state energies only. Moreover, appropriate choice of diatomic (relative ro-vibrational state arrangement) is critical for producing high fidelity optimized quantum logic gates. It is also suggested that global phase alignment imposes a significant restriction on obtaining high fidelity regions within the parameter search space. Overall, this indicates a complexity in the ability to provide appropriate binary laser pulse control of diatomics for molecular quantum computing.     

The influence of ultrafast laser pulses on electron transfer in molecular wires studied by a non-Markovian density-matrix approach

New features of molecular wires can be observed when they are irradiated by laser fields. These effects can be achieved by periodically oscillating fields but also by short laser pulses. The theoretical foundation used for these investigations is a density-matrix formalism where the full system is partitioned into a relevant part and a thermal fermionic bath. The derivation of a quantum master equation, either based on a time-convolutionless or time-convolution projection-operator approach, incorporates the interaction with time-dependent laser fields nonperturbatively and is valid at low temperatures for weak system-bath coupling. From the population dynamics the electrical current through the molecular wire is determined. This theory including further extensions is used for the determination of electron transport through molecular wires. As examples, we show computations of coherent destruction of tunneling in asymmetric periodically driven quantum systems, alternating currents and the suppression of the directed current by using a short laser pulse.