We investigate experimentally the effect of quantum resonance in the rotational excitation of the simplest quantum rotor - a diatomic molecule. By using the techniques of high-resolution femtosecond pulse shaping and rotational state-resolved detection, we measure directly the amount of energy absorbed by molecules interacting with a periodic train of laser pulses, and study its dependence on the train period. We show that the energy transfer is significantly enhanced at quantum resonance, and use this effect for demonstrating selective rotational excitation of two nitrogen isotopologues, $ ^{14}N_2$ and $ ^{15}N_2$. Moreover, by tuning the period of the pulse train in the vicinity of a fractional quantum resonance, we achieve spin-selective rotational excitation of para- and ortho-isomers of $ ^{15}N_2$.
The amplitude and probability of quantum transitions are represented as a path integrals in energy state space of the investigated multi-level quantum system. Using this approach we consider rotational dynamics of nitrogen molecules $^{14}N_{2}$ and $^{15}N_{2}$ which interact with a sequence of ultrashort laser pulses. Our computer simulations indicate the complex dependency of the high rotation states excitation probability upon ultrashort laser pulses sequence periods. We observe pronounced resonances, which correspond to the results of some experiments.
The two-photon transition $5S-5P-5D$ in rubidium vapor is investigated by detecting the fluorescence from the $6P_{3/2}$ state when the atomic system is excited by the combined action of a cw diode laser and a train of ultrashort pulses. The cw-laser plays a role as a velocity-selective filter and allows for a spectroscopy over a large spectral range including the $5D_{3/2}$ and $5D_{5/2}$ states. For a counterpropagating beam configuration, the response of each atomic velocity group is well characterized within the Doppler profile, and the excited hyperfine levels are clearly resolved. The co…
Strong ultrashort laser pulses give rise to prompt molecular alignment followed by full, half and quarter quantum revivals of the rotational wave packets. In Four Wave Mixing (FWM) experiments, we make use of the long succession of repetitive alignment revivals to demonstrate isotope-selective alignment and time-resolved discrimination between different isotopic species. For two isotopes with a commensurate ratio of their moments of inertia, we observe constructive and destructive interferences of the FWM signals originating from different isotopes. Such destructive interference serves as an i…
We demonstrate that the current laser technology used for field-free molecular alignment via a cascade of Raman rotational transitions allows for observing long-discussed non-linear 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 localisation in the angular momentum. Based on these findings, we suggest a novel approach to tunable selective rotational excitation and alignment in a molecular mixture, using trains of short laser pulses. We demonstrate the efficiency of t…
Trains of ultrashort laser pulses separated by the time of rotational revival (typically, tens of picoseconds) have been exploited for creating ensembles of aligned molecules. In this work we introduce a chiral pulse train - a sequence of linearly polarized pulses with the polarization direction rotating from pulse to pulse by a controllable angle. The chirality of such a train, expressed through the period and direction of its polarization rotation, is used as a new control parameter for achieving selectivity and directionality of laser-induced rotational excitation. The method employs chiral…
An efficient technique to produce a periodic sequence of ultrashort pulses of recoilless gamma-radiation via its transmission through the optically thick vibrating resonant absorber was demonstrated recently [Nature, 508, 80 (2014)]. In this work we extend the theoretical analysis to the case of a set of multiple absorbers. We consider an analytical model describing the control of spectral content of a frequency modulated gamma-radiation by selective correction of amplitudes and initial phases of some spectral components, using, respectively, the resonant absorption or dispersion of nuclei. On…
We obtained a simple theoretical unified parameter for the characterization of rotational population propagation of diatomic molecules in a periodic train of resonant optical pulses. The parameter comprises the peak intensity and interval between the pulses, and the level energies of the initial and final rotational states of the molecule. Using the unified parameter, we can predict the upper and lower boundaries of probability localization on the rotational level network, including the effect of centrifugal distortion. The unified parameter was tentatively derived from an analytical expressio…
In recent years it became possible to align molecules in free space using ultrashort laser pulses. Here we explore two schemes for controlling molecule-surface scattering process, which are based on the laser-induced molecular alignment. In the first scheme, a single ultrashort non-resonant 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 counter-clockwise). In the second scheme, two properly delayed laser pulses ar…
Following excitation by a strong ultra-short laser pulse, molecules develop coordinated rotational motion, exhibiting transient alignment along the direction of the laser electric field, followed by periodic full and fractional revivals that depend on the molecular rotational constants. In mixtures, the different species undergo similar rotational dynamics, all starting together but evolving differently with each demonstrating its own periodic revival cycles. For a bimolecular mixture of linear molecules, at predetermined times, one species may attain a maximally aligned state while the other …
Microwave three-wave mixing allows for enantiomer-selective excitation of randomly oriented chiral molecules into rotational states with different energy. The random orientation of molecules is reflected in the degeneracy of the rotational spectrum with respect to the orientational quantum number $M$ and reduces, if not accounted for, enantiomer-selectivity. Here, we show how to design pulse sequences with maximal enantiomer-selectivity from an analysis of the $M$-dependence of the Rabi frequencies associated with rotational transitions induced by resonant microwave drives. We compare differen…
The rotational echo response of molecules is found to strongly depend on the delay between the two ultrashort laser pulses, as opposed to two-level systems. We study this dependence experimentally and theoretically and show that by judicious control of the 2nd pulse intensity, 'rotational echo spectroscopy' in a multi-level molecular system becomes possible.
We experimentally demonstrate coherent control of a quantum system, whose dynamics is chaotic in the classical limit. Interaction of diatomic molecules with a periodic sequence of ultrashort laser pulses leads to the dynamical localization of the molecular angular momentum, a characteristic feature of the chaotic quantum kicked rotor. By changing the phases of the rotational states in the initially prepared coherent wave packet, we control the rotational distribution of the final localized state and its total energy. We demonstrate the anticipated sensitivity of control to the exact parameters…
Detecting the internal state of polar molecules is a substantial challenge when standard techniques such as resonance-enhanced multi photon ionization (REMPI) or laser-induced fluorescense (LIF) do not work. As this is the case for most polyatomic molecule species, we here investigate an alternative based on state selective removal of molecules from an electrically trapped ensemble. Specifically, we deplete molecules by driving rotational and/or vibrational transitions to untrapped states. Fully resolving the rotational state with this method can be a considerable challenge as the frequency di…
We consider the dynamics of a quantum directional reference frame undergoing repeated interactions. We first describe how a precise sequence of measurement outcomes affects the reference frame, looking at both the case that the measurement record is averaged over and the case wherein it is retained. We find, in particular, that there is interesting dynamics in the latter situation which cannot be revealed by considering the averaged case. We then consider in detail how a sequence of rotationally invariant unitary interactions affects the reference frame, a situation which leads to quite differ…
State-selective enantiomeric excess is realized using microwave-driven coherent population transfer. The method selectively promotes either R or S molecules to a higher rotational state by phase-controlled microwave pulses that drive electric-dipole allowed rotational transitions. We demonstrate the enantiomer-specific state transfer method using enantiopure samples of 1,2-propanediol. This method of state-specific enantiomeric enrichment can be applied to a large class of asymmetric, chiral molecules that can be vaporized and cooled to the point where rotationally resolved spectroscopy is pos…
We present an analysis of two experimental approaches to controlling the directionality of molecular rotation with ultrashort laser pulses. The two methods are based on the molecular interaction with either a pair of pulses (a "double kick" scheme) or a longer pulse sequence (a "chiral pulse train" scheme). In both cases, rotational control is achieved by varying the polarization of and the time delay between the consecutive laser pulses. Using the technique of polarization sensitive resonance-enhanced multi-photon ionization, we show that both methods produce significant rotational directiona…
We experimentally study a system of quantum kicked rotors - an ensemble of diatomic molecules exposed to a periodic sequence of ultrashort laser pulses. In the regime, where the underlying classical dynamics is chaotic, we investigate the quantum phenomenon of dynamical localization by means of state-resolved coherent Raman spectroscopy. We examine the dependence of the exponentially localized angular momentum distribution and of the total rotational energy on the time period between the pulses and their amplitude. The former parameter is shown to provide control over the localization center, …
In creating a large-scale quantum information processor, the ability to construct control pulses for implementing an arbitrary quantum circuit in a scalable manner is an important requirement. For liquid-state nuclear magnetic resonance (NMR) quantum computing, a circuit is generally realized through a sequence of selective soft pulses, in which various control imperfections exist and are to be corrected. In this work, we present a comprehensive analysis of the errors arisen in a selective pulse network by using the zeroth and first order average Hamiltonian theory. Effective correction rules …
We experimentally study the optical- and terahertz- induced rotational dynamics of asymmetric molecules in the gas phase. Terahertz and optical fields are identified as two distinct control handles over asymmetric molecules, as they couple to the rotational degrees of freedom via the molecular- dipole and polarizability selectively. The distinction between those two rotational handles is highlighted by different types of quantum revivals observed in long duration (>100ps) field-free rotational evolution. The experimental results are in excellent agreement with Random Phase Wave Function simula…
We present a rigorous study of vibrational relaxation in p-H2 + p-H2 collisions at cold and ultracold temperatures and identify an efficient mechanism of ro-vibrational energy transfer. If the colliding molecules are in different rotational and vibrational levels, the internal energy may be transferred between the molecules through an extremely state-selective process involving simultaneous conservation of internal energy and total rotational angular momentum. The same transition in collisions of distinguishable molecules corresponds to the rotational energy transfer from one vibrational state…
We introduce a new scheme for controlling the sense of molecular rotation. By varying the polarization and the delay between two ultrashort laser pulses, we induce unidirectional molecular rotation, thereby forcing the molecules to rotate clockwise/counterclockwise under field-free conditions. We show that unidirectionally rotating molecules are confined to the plane defined by the two polarization vectors of the pulses, which leads to a permanent anisotropy in the molecular angular distribution. The latter may be useful for controlling collisional cross-sections and optical and kinetic proces…
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 (~ 10%) degree of enantioselective orientation can be achieved at zero and at five kelvin 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…
We provide a detailed theoretical analysis of molecular rotational excitation by a chiral pulse train -- a sequence of linearly polarised pulses with the polarisation direction rotating from pulse to pulse by a controllable angle. Molecular rotation with a preferential rotational sense (clockwise or counter-clockwise) can be excited by this scheme. We show that the directionality of the rotation is caused by quantum interference of different excitation pathways. The chiral pulse train is capable of selective excitation of molecular isotopologues and nuclear spin isomers in a mixture. We demons…
Three-wave mixing spectroscopy of chiral molecules, which exist in left-handed and right-handed conformations, allows for enantio-selective population transfer despite random orientation of the molecules. This is based on constructive interference of the three-photon pathways for one enantiomer and destructive one for the other. We prove here that three mutually orthogonal polarization directions are required to this end. Two different dynamical regimes exist to realize enantio-selective population transfer, and we show that they correspond to different phase conditions in the three-wave mixin…
With a microwave-regime cyclic three-state configuration, an enantiomer-selective state transfer~(ESST) is carried out through the two-path interference between a direct one-photon coupling and an effective two-photon coupling. The $π$-phase difference in the one-photon process between two enantiomers makes the interference constructive for one enantiomer but destructive for the other. Therefore only one enantiomer is excited into a higher rotational state while the other remains in the ground state. The scheme is of flexibility in the pulse waveforms and the time order of two paths. We simula…
Quantum calculations are reported for the stereodynamic control of the H + D$_{2}\longleftrightarrow$ D + HD chemical reaction in the energy range of 1-50 K. Stereodynamic control is achieved by a formalism similar to that reported by Perreault et al. [Nature Chem. 10, 561 (2018)] in recent experimental works in which the alignment of the molecular bond axis relative to the incident relative velocity is controlled by selective preparations of the molecule in a specific or superposition of magnetic projection quantum numbers of the initial molecular rotational level. The approach presented here…
Using a quantum wave packet simulation including the nuclear and electronic degrees of freedom, we investigate the femtosecond and picosecond energy- and angle-resolved photoelectron spectra of the E($^1Σ_g^+$) electronic state of Li$_2$. We find that the angular distributions of the emitted photoelectrons depend strongly on the pulse duration in the regime of ultrashort laser pulses. This effect is illustrated by the extraction of a time-dependent asymmetry parameter whose variation with pulse duration can be explained by an incoherent average over different ion rotational quantum numbers. We…
We prove complete controllability for rotational states of an asymmetric top molecule belonging to degenerate values of the orientational quantum number M. Based on this insight, we construct a pulse sequence that energetically separates population initially distributed over degenerate M-states, as a precursor for orientational purification. Introducing the concept of enantio-selective controllability, we determine the conditions for complete enantiomer-specific population transfer in chiral molecules and construct pulse sequences realizing this transfer for population initially distributed ov…
Ultrashort laser pulses are widely used for transient field-free molecular orientation -- a phenomenon important in chemical reaction dynamics, ultrafast molecular imaging, high harmonics generation, and attosecond science. However, significant molecular orientation usually requires rotationally cold molecules, like in rarified molecular beams, because chaotic thermal motion is detrimental to the orientation process. Here we propose to use the mechanism of the echo phenomenon previously observed in hadron accelerators, free-electron lasers, and laser-excited molecules to overcome the destructi…
We present theoretical and experimental progress towards a new approach for the precision spectroscopy, coherent manipulation and state-to-state chemistry of single isolated molecular ions in the gas phase. Our method consists of a molecular beam for creating packets of rotationally cold neutrals from which a single molecule is state-selectively ionized and trapped inside a radiofrequency ion trap. In addition to the molecular ion, a single co-trapped atomic ion is used to cool the molecular external degrees of freedom to the ground state of the trap and to detect the molecular state using sta…
A new method for highly selective remote sensing of atmospheric trace polar molecular gases is described. Based on infrared/terahertz double resonance spectroscopic techniques, the molecule- specific coincidence between the lines of a CO2 laser and rotational-vibrational molecular absorption transitions provide two dimensions of recognition specificity: infrared coincidence frequency and the corresponding terahertz frequency whose absorption strength is modulated by the laser. Atmospheric pressure broadening expands the molecular recognition "specificity matrix" by simultaneously relaxing the …
