Publications

We present a comprehensive study of enantioselective orientation of chiral molecules excited by a pair of delayed cross-polarized femtosecond laser pulses. We show that by optimizing the pulses parameters, a significant degree (∼10%) of enantioselective orientation can be achieved at 0 and 5 K rotational temperatures. This study suggests a set of reasonable experimental conditions for inducing and measuring strong enantioselective orientation. The strong enantioselective orientation and the wide availability of the femtosecond laser systems required for the proposed experiments may open new avenues for discriminating and separating molecular enantiomers.

Rotational dynamics of D2 molecules inside helium nanodroplets is induced by a moderately intense femtosecond pump pulse and measured as a function of time by recording the yield of HeD+ ions, created through strong-field dissociative ionization with a delayed femtosecond probe pulse. The yield oscillates with a period of 185 fs, reflecting field-free rotational wave packet dynamics, and the oscillation persists for more than 500 periods. Within the experimental uncertainty, the rotational constant BHe of the in-droplet D2 molecule, determined by Fourier analysis, is the same as Bgas for an isolated D2 molecule. Our observations show that the D2 molecules inside helium nanodroplets essentially rotate as free D2 molecules.

Rotational dynamics of D2 molecules inside helium nanodroplets is induced by a moderately intense femtosecond (fs) pump pulse and measured as a function of time by recording the yield of HeD+ ions, created through strong-field dissociative ionization with a delayed fs probe pulse. The yield oscillates with a period of 185 fs, reflecting field-free rotational wave packet dynamics, and the oscillation persists for more than 500 periods. Within the experimental uncertainty, the rotational constant BHe of the in-droplet D2 molecule, determined by Fourier analysis, is the same as Bgas for an isolated D2 molecule. Our observations show that the D2 molecules inside helium nanodroplets essentially rotate as free D2 molecules.

We study the excitation of asymmetric-top (including chiral) molecules by two-color femtosecond laser pulses. In the cases of non-chiral asymmetric-top molecules excited by an orthogonally polarized two-color pulse, we demonstrate, classically and quantum mechanically, three-dimensional orientation. For chiral molecules, we show that the orientation induced by a cross-polarized two-color pulse is enantioselective along the laser propagation direction, namely, the two enantiomers are oriented in opposite directions. The classical and quantum simulations are in excellent agreement on the short time scale, whereas on the longer time scale, the enantioselective orientation exhibits quantum beats. These observations are qualitatively explained by analyzing the interaction potential between the two-color pulse and molecular (hyper-)polarizability. The prospects for using the enantioselective orientation for enantiomers' separation is discussed.

Impulsive orientation of symmetric-top molecules excited by two-color femtosecond pulses is considered. In addition to the well-known transient orientation appearing immediately after the pulse and then reemerging periodically due to quantum revivals, we report the phenomenon of field-free long-lasting orientation. Long-lasting means that the time averaged orientation remains non-zero until destroyed by other physical effects, e.g., intermolecular collisions. The effect is caused by the combined action of the field-polarizability and field-hyperpolarizability interactions. The dependence of degree of long-lasting orientation on temperature and pulse parameters is considered. The effect can be measured by means of second (or higher-order) harmonic generation, and may be used to control the deflection of molecules traveling through inhomogeneous electrostatic fields.

Chirality and chiral molecules are key elements in modern chemical and biochemical industries. Individual addressing and the eventual separation of chiral enantiomers have been and still are important elusive tasks in molecular physics and chemistry, and a variety of methods have been introduced over the years to achieve these goals. Here, we theoretically demonstrate that a pair of cross-polarized THz pulses interacting with chiral molecules through their permanent dipole moments induces in these molecules an enantioselective orientation. This orientation persists for a long time, exceeding the duration of the THz pulses by several orders of magnitude, and its dependency on temperature and pulses' parameters is investigated. This persistent orientation may enhance the deflection of the molecules in inhomogeneous electromagnetic fields, potentially leading to viable separation techniques.

We demonstrate an efficient algorithm for inverse problems in time-dependent quantum dynamics based on feedback loops between Hamiltonian parameters and the solutions of the Schrödinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schrödinger equation solutions to direct the optimization of feedback loops. For the surrogate models, we use Gaussian processes with vector outputs and composite kernels built by an iterative algorithm with the Bayesian information criterion (BIC) as a kernel selection metric. The outputs of the Gaussian processes are designed to model an observable simultaneously at different time instances. We show that the use of Gaussian processes with vector outputs and the BIC-directed kernel construction reduces the number of iterations in the feedback loops by, at least, a factor of 3. We also demonstrate an application of Bayesian optimization for inverse problems with noisy data. To demonstrate the algorithm, we consider the orientation and alignment of polyatomic molecules SO2 and propylene oxide (PPO) induced by strong laser pulses. We use simulated time evolutions of the orientation or alignment signals to determine the relevant components of the molecular polarizability tensors. We show that, for the five independent components of the polarizability tensor of PPO, this can be achieved with as few as 30 quantum dynamics calculations.

Short laser pulses are widely used for controlling molecular rotational degrees of freedom and inducing molecular alignment, orientation, unidirectional rotation, and other types of coherent rotational motion. To follow the ultrafast rotational dynamics in real time, several techniques for producing molecular movies have been proposed based on the Coulomb explosion of rotating molecules, or recovering molecular orientation from the angular distribution of high harmonics. The present work offers and demonstrates a novel nondestructive optical method for direct visualization and recording of movies of coherent rotational dynamics in a molecular gas. The technique is based on imaging the time-dependent polarization dynamics of a probe light propagating through a gas of coherently rotating molecules. The probe pulse continues through a radial polarizer, and is then recorded by a camera. The technique is illustrated by implementing it with two examples of time-resolved rotational dynamics: alignmentantialignment cycles in a molecular gas excited by a single linearly polarized laser pulse, and unidirectional molecular rotation induced by a pulse with twisted polarization. This method may open new avenues in studies on fast chemical transformation phenomena and ultrafast molecular dynamics caused by strong laser fields of various complexities.

Echoes occur in many physical systems, typically in inhomogeneously broadened ensembles of nonlinear objects. They are often used to eliminate the effects of dephasing caused by interactions with the environment as well as to enable the observation of proper, inherent object properties. Here, we report the experimental observation of quantum wave-packet echoes in a single, isolated molecule. The entire dephasing-rephasing cycle occurs without any inhomogeneous spread of molecular properties, or any interaction with the environment, and offers a way to probe the internal coherent dynamics of single molecules. In our experiments, we impulsively excite a vibrational wave packet in an anharmonic molecular potential and observe its oscillations and eventual dispersion with time. A second, delayed pulse gives rise to an echo-a partial recovery of the initial coherent oscillations. The vibrational dynamics of single molecules is visualized by a time-delayed probe pulse dissociating them, one at a time. Two mechanisms for the echo formation are discussed: a.c. Stark-induced molecular potential shaking and creation of a depletion-induced 'hole' in the nuclear spatial distribution. The single-molecule wave-packet echoes may lead to the development of new tools for probing ultrafast intramolecular processes in various molecules.Following an impulsive laser excitation of a single molecule, a dispersed vibrational wave-packet is partially rephased by a second pulse, and a wave-packet echo is observed. This wave-packet echo probes ultrafast intramolecular processes in the isolated molecule.

We report on the first experimental demonstration of enantioselective rotational control of chiral molecules with a laser field. In our experiments, two enantiomers of propylene oxide are brought to accelerated unidirectional rotation by means of an optical centrifuge. Using Coulomb explosion imaging, we show that the centrifuged molecules acquire preferential orientation perpendicular to the plane of rotation, and that the direction of this orientation depends on the relative handedness of the enantiomer and the rotating centrifuge field. The observed effect is in agreement with theoretical predictions and is reproduced in numerical simulations of the centrifuge excitation followed by Coulomb explosion of the centrifuged molecules. The demonstrated technique opens new avenues in optical enantioselective control of chiral molecules with a plethora of potential applications in differentiation, separation, and purification of chiral mixtures.

We explore a pure optical method for enantioselective orientation of chiral molecules by means of laser fields with twisted polarization. Several field implementations are considered, including a pair of delayed, cross-polarized laser pulses, an optical centrifuge, and polarization-shaped pulses. We show that these schemes lead to out-of-phase time-dependent dipole signals for different enantiomers, and we also predict a substantial permanent molecular orientation persisting long after the laser fields are over. The underlying classical orientation mechanism common to all of these fields is discussed, and its operation is demonstrated for a range of chiral molecules of various complexity: hydrogen thioperoxide (HSOH), propylene oxide (CH3CHCH2O), and ethyl oxirane (CH3CH2CHCH2O). The presented results demonstrate generality, versatility, and robustness of this optical method for manipulating molecular enantiomers in the gas phase.

In recent years, several femtosecond laser techniques have been developed that can make gas molecules rotate extremely fast, whereas the gas stays translationally cold. Herein we use molecular-dynamics simulations to investigate the collisional dynamics of gases of such molecules (superrotors). We found that the common route of superrotors to equilibrium is rather generic. It starts with a long-lasting gyroscopic stage, during which the molecules keep their fast rotation and the orientation of their angular momentum despite the many collisions they undergo. The inhibited rotational relaxation is characterized by a persistent anisotropy in the molecular angular distribution, manifested in long-lasting optical birefringence and in anisotropic diffusion of the gas. Later, the gyroscopic stage is abruptly terminated by a self-accelerating explosive rotational-translational energy exchange that generates sound and macroscopic vortices with a hot rotating core.

We study the dynamics of paramagnetic molecular superrotors in an external magnetic field. An optical centrifuge is used to create dense ensembles of oxygen molecules in ultrahigh rotational states. In is shown, for the first time, that the gas of rotating molecules becomes optically birefringent in the presence of a magnetic field. The discovered effect of "magneto-rotational birefringence" indicates the preferential alignment of molecular axes along the field direction. We provide an intuitive qualitative model, in which the influence of the applied magnetic field on the molecular orientation is mediated by the spin-rotation coupling. This model is supported by the direct imaging of the distribution of molecular axes, the demonstration of the magnetic reversal of the rotational Raman signal, and by numerical calculations.

We present a quantum localization phenomenon that exists in periodically kicked three-dimensional rotors, but is absent in the commonly studied two-dimensional ones: edge localization. We show that under the condition of a fractional quantum resonance there are states of the kicked rotor that are strongly localized near the edge of the angular momentum space at J=0. These states are analogs of surface states in crystalline solids, and they significantly affect resonant excitation of molecular rotation by laser pulse trains.

Nitrogen gas is rotationally excited by a train of eight impulsive kicks. The resulting population alignment evolution exhibits two phenomena explained by analogy to the famous condensed matter effects of dynamical localization and Bloch oscillations.

The paper explores the prospects of observing the phenomenon of dynamical Anderson localization via nonresonant Raman-type rotational excitation of molecules by periodic trains of short laser pulses. We define conditions for such an experiment and show that current femtosecond technology used for nonadiabatic laser alignment of linear molecules is sufficient for this task. Several observables which can serve as indicators for Anderson localization are suggested for measurement, and the influence of experimental limitations imposed by the laser intensity noise, finite pulse duration, limited number of pulses in a train, and thermal effects is analyzed.

We show that molecules kicked periodically by laser pulses currently used in molecular alignment experiments allow to observe effects of the periodically kicked quantum rotor in a real rotational system. Among these effects are Anderson localisation in angular momentum and the scaling of the quantum resonance. Based on this, we propose a new scheme for selective molecular rotational excitation.

We show that the current laser technology used for field-free molecular alignment via impulsive Raman rotational excitation allows for observing long-discussed nonlinear quantum phenomena in the dynamics of the periodically kicked rotor. This includes the scaling of the absorbed energy near the conditions of quantum resonance and Anderson-like localization in the angular momentum. Based on this, we show that periodic trains of short laser pulses provide an efficient tool for selective rotational excitation and alignment in a molecular mixture. We demonstrate the efficiency of this approach by applying it to a mixture of two nitrogen isotopologues (14N ₂ and 15N ₂), and show that strong selectivity is possible even at room temperature.

Recently, several femtosecond-laser techniques have demonstrated molecular excitation to high rotational states with a preferred sense of rotation. We consider collisional relaxation in a dense gas of such unidirectionally rotating molecules, and suggest that due to angular momentum conservation, collisions lead to the generation of macroscopic vortex gas flows. This argument is supported using the Direct Simulation MonteCarlo method, followed by a computational gas-dynamic analysis.

In recent years it has become possible to align molecules in free space using ultrashort laser pulses. Here we explore two schemes for controlling molecule-surface scattering processes and which are based on laser-induced molecular alignment. In the first scheme, a single ultrashort nonresonant laser pulse is applied to a molecular beam hitting the surface. This pulse modifies the angular distribution of the incident molecules and causes the scattered molecules to rotate with a preferred sense of rotation (clockwise or counterclockwise). In the second scheme, two properly delayed laser pulses are applied to a molecular beam composed of two chemically close molecular species (isotopes, or nuclear-spin isomers). As the result of the double-pulse excitation, these species are selectively scattered to different angles after the collision with the surface. These effects may provide new means for the analysis and separation of molecular mixtures.

The effects of laser-induced pre-alignment on the deflection of paramagnetic molecules by inhomogeneous static magnetic field are studied. Depending on the relevant Hunds coupling case of the molecule, two different effects were identified: either suppression of the deflection by laser pulses (Hunds coupling case (a) molecules, such as ClO), or a dramatic reconstruction of the broad distribution of the scattering angles into several narrow peaks (for Hunds coupling case (b) molecules, such as O₂ or NH). These findings are important for various applications using molecular guiding, focusing and trapping with the help of magnetic fields.

We propose three implementations of the Gauss sum factorization schemes discussed in part I of this series (Wölk et al 2011 New J. Phys. 13 103007): (i) A two-photon transition in a multi-level ladder system induced by a chirped laser pulse, (ii) A chirped one-photon transition in a two-level atom with a periodically modulated excited state and (iii) A linearly chirped onephoton transition driven by a sequence of ultrashort pulses. For each of these quantum systems, we show that the excitation probability amplitude is given by an appropriate Gauss sum. We provide rules on how to encode the number N to be factored in our system and how to identify the factors of N in the fluorescence signal of the excited state.

Several laser techniques have been suggested and demonstrated recently for preparing polarizable molecules in rapidly spinning states with a disk-like angular distribution. We consider motion of these spinning disks in inhomogeneous fields and show that the molecular trajectories may be precisely controlled by the tilt of the plane of the laser-induced rotation. The feasibility of the scheme is illustrated by optical deflection of linear molecules twirled by two delayed cross-polarized laser pulses. These results open new ways for many applications involving molecular focusing, guiding, and trapping and may be suitable for separating molecular mixtures by optical and static fields.

We study the optimal focusing of two-level atoms with a near-resonant standing wave light, using both classical and quantum treatments of the problem in the thin- and thick-lens regimes. It is found that the near-resonant standing wave focuses the atoms with a reduced background in comparison with far-detuned light fields. For some parameters, the quantum atomic distribution shows even better localization than the classical one. Spontaneous emission effects are included via the technique of quantum Monte Carlo wave function simulations. We investigate the extent to which nonadiabatic and spontaneous emission effects limit the achievable minimal size of the deposited structures.

We consider deflection of polarizable molecules by inhomogeneous optical fields, and analyze the role of molecular orientation and rotation in the scattering process. We show that by preshaping molecular angular distribution with the help of short and strong femtosecond laser pulses, one may efficiently control the scattering process, manipulate the average deflection angle and its distribution, and reduce substantially the angular dispersion of the deflected molecules. This opens new ways for many applications involving molecular focusing, guiding, and trapping by optical and static fields.

We present a new approach to nonresonant laser deceleration and cooling of atoms based on their interaction with a bistable optical cavity. The cooling mechanism presents a photonic version of Sisyphus cooling, in which the conservative motion of atoms is interrupted by sudden transitions between two stable states of the cavity mode. The mechanical energy is extracted due to the hysteretic nature of those transitions. The bistable character of the cavity may be achieved by an external feedback loop, or by means of nonlinear intracavity optical elements. In contrast to the conventional cavity cooling, in which atoms experience a viscoustype force, bistable cavity cooling imitates "dry friction" and stops atoms much faster. Based on this novel approach, we explore the prospects of using optical bistability for efficient radiation pressure cooling of micromechanical devices that are modeled as a Fabry-Perot resonator with one fixed and one oscillating mirror. In all cases, analytical results are presented, supported by realistic numerical examples.

By varying the polarization and delay between two ultrashort laser pulses, we control the plane, speed, and sense ofmolecular rotation. This control may be implemented to individual components within a molecular mixture.

We propose a generic approach to nonresonant laser cooling of atoms and molecules in a bistable optical cavity. The method exemplifies a photonic version of Sisyphus cooling, in which the matter-dressed cavity extracts energy from the particles and discharges it to the external field as a result of sudden transitions between two stable states.

We factor the number 157573 using an NMR implementation of Gauss sums. Although the current implementation is classical and scales exponentially, we believe that an extension to the quantum regime using entangled states is possible.

Double pulse excitation of fractional revivals of rotational wavepackets is demonstrated as an effective tool for spin-selective alignment in a multi-component mixture of molecular spin isomers.

We demonstrate single-pulse retrieval of coherent vibrational evolution of molecules by geometrical space-time mapping combined with non-linear signal imaging. The method is tested experimentally to yield spectrum of simple liquids.

We demonstrate single-pulse retrieval of coherent vibrational evolution of molecules by geometrical space-time mapping combined with non-linear signal imaging. The method is tested experimentally to yield spectrum of simple liquids.

Optical shaking with feedback is proposed as a new method for laser cooling of atoms and molecules to high phase-space density and without the loss of particles typical of evaporative cooling.

Selective alignment by femtosecond pulses of molecules in multi-component mixtures is shown to be a powerful tool for the detection, identification, and separation of chemically close species.

We demonstrate single shot retrieval of coherent molecular field-free evolution by geometric space-time mapping combined with non-linear signal imaging.

We show that field-free molecular orientation induced by a half-cycle pulse may be considerably enhanced by an additional laser pulse inducing molecular antialignment. Two qualitatively different enhancement mechanisms are identified, depending on the pulse order, and their effects are optimized with the help of quasiclassical as well as fully quantum models.

We propose a novel generic approach to laser cooling based on the nonresonant interactions of atoms and molecules with optical standing waves experiencing sudden phase jumps. The technique, termed "optical shaking," combines the elements of stochastic cooling and Sisyphus cooling. An optical signal that measures the instantaneous force applied by the standing wave on the ensemble of particles is used as feedback to determine the phase jumps. This guarantees a drift towards lower energies and higher phase-space density without the loss of particles typical of evaporative cooling.

The process of molecular alignment by using strong, ultrashort laser pulses is investigated. The analysis of the single-pulse alignment is analyzed in both classical and quantum-mechanical regimes. The effect of laser pulses having finite width is considered by assuming that the envelope of the laser pulses has a Gaussian shape. A multipulse excitation scheme leading to enhanced molecular alignment is suggested and conditions for femtosecond experiments of this kind is defined.

We study the process of squeezing of an ensemble of cold atoms in a pulsed optical lattice. The problem is treated both classically and quantum mechanically under various thermal conditions. We show that a dramatic compression of the atomic density near the minima of the optical potential can be achieved with a proper pulsing of the lattice. Several strategies leading to the enhanced atomic squeezing are suggested, compared, and optimized.

Generic features in the dynamics of a quantum rotor (molecule) drive by strong pulses are analyzed. In addition, a strategy is given for efficient squeezing of the rotor angular distribution by a sequence of pulses of moderate intensity.

We present an optimal control approach to the process of molecular isotope separation by exciting vibrational wave packets with femtosecond laser pulses. In the weak-field limit, we developed an optimization procedure for designing shaped laser pulses leading to the best selectivity in the two-photon ionization processes. Several control scenarios are identified, which mainly belong to two groups. The first takes advantage of the revival phenomenon, which allows one to find times at which excited wave packets of different isotopes are well localized and spatially separated in the intramolecular space. The second is based on isotopically selective quantum interference between several wave packets excited in the same molecular potential by a designed sequence of laser pulses. Simulations have been done for the isotopic mixture of ⁷⁹Br₂ and ⁸¹Br₂ molecules, which was used in the first experiments on wave-packet isotope separation.

Observing the fluctuations of femtosecond correlated fluorescence generated by pairs of pulses with randomized relative phase, fractional revivals (order 1/2 and 1/4) of vibrational wavepackets have been found in the B-state of molecular Iodine.

In traditional wave packet interferometry, time-resolved dynamics of a quantum wave packet in studied by exciting an additional delayed probe wave packet in the same system, and detecting the resulting interference signal. In recent COIN (Coherent Observation of Interference Noise) method, a pair of delayed, randomly phased pulses is used for excitation. The stability problem is solved by measuring the fluctuations about the average signal, instead of the interference signal itself.

The light scattering from a single resonant molecule, or nano-sized particle located near the tip of an apertureless scanning near-field microscope is studied, and different regimes of scattering are analyzed. The tip enhances the external field, and serves as an efficient transmission 'antenna' for the molecular dipole oscillations. The light scattering occurs via two channels: direct scattering from the tip, and tip-mediated molecular scattering. The total detected intensity of the scattered light shows interference of the channels, which we suggest to use for efficient near-field microscopy. At certain detunings from resonances the scanning signal experiences spatial narrowing similar to that one observed in two-photon microscopy, thus allowing for sub-nanometer resolution.

The problem of how to measure the wavefunction of a quantum system in amplitude and phase has attracted a lot of attention over the last few years. In this paper we analyze and further develop our method of Quantum State Holography for reconstructing quantum superposition states in molecules or atoms.

We introduce and demonstrate a general wave packet method for laser isotope separation. In this scheme, laser excited molecular (or atomic) wave packets of differing isotopes become spatially separated in the course of their long-time free evolution. In order to overcome the quantum spreading of wave packets, we make use of the phenomenon of revivals. We demonstrate experimentally, with mixed ⁷⁹Br₂/⁸¹Br₂ isotopes, that significant control over the isotope ratio can be achieved in a single shot.

We consider the focusing and deflection of a nonresonant atomic beam propagating through a spatially inhomogeneous quantized electromagnetic field. Different Fock states of the field deflect the atoms in different angles and focus them at different points. We find a regime in which individual foci corresponding to neighboring Fock states can be reoslved even for large average number of photons. In this sense this quantum lens for atomic waves leaves intact the discreteness of the photons even in the classical limit.

The discrete nature of photons is the central consequence of the quantization of the electromagnetic field. Intuitively, we associate this property with a field of small average photon number, although the discrete composition persists even in the classical limit, but how do we resolve in this case the individual photon states?