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We theoretically study an impulsively excited quantum bouncer (QB) - a particle bouncing off a surface in the presence of gravity. A pair of time-delayed pulsed excitations is shown to induce a wave-packet echo effect - a partial rephasing of the QB wave function appearing at twice the delay between pulses. In addition, an appropriately chosen observable [here, the population of the ground gravitational quantum state (GQS)] recorded as a function of the delay is shown to contain the transition frequencies between the GQSs, their populations, and partial phase information about the wave packet quantum amplitudes. The wave-packet echo effect is a promising candidate method for precision studies of GQSs of ultra-cold neutrons, atoms, and anti-atoms confined in closed gravitational traps., Comment: 7 pages, 6 figures

Quantum Kerr-nonlinear oscillator is a paradigmatic model in cavity and circuit quantum electrodynamics, and quantum optomechanics. We theoretically study the echo phenomenon in a single impulsively excited ("kicked") Kerr-nonlinear oscillator. We reveal two types of echoes, "quantum" and "classical" ones, emerging on the long and short time-scales, respectively. The mechanisms of the echoes are discussed, and their sensitivity to dissipation is considered. These echoes may be useful for studying decoherence processes in a number of systems related to quantum information processing., Comment: 12 pages, 9 figures

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 Schr\"{o}dinger equation. Our approach formulates the inverse problem as a target vector estimation problem and uses Bayesian surrogate models of the Schr\"{o}dinger 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 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 reduce 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 SO$_2$ and chiral 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 to within 1% accuracy. 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., Comment: 34 pages, 5 figures, and 5 tables

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. The underlying classical orientation mechanism common for all these fields is discussed, and its operation is demonstrated for a range of chiral molecules of various complexity: hydrogen thioperoxide (${\rm HSOH}$), propylene oxide (${\rm CH_{3}CHCH_{2}O}$) and ethyl oxirane (${\rm CH_{3}CH_{2}CHCH_{2}O}$). The presented results demonstrate generality, versatility and robustness of this optical method for manipulating molecular enantiomers in the gas phase.

We study interaction of generic asymmetric molecules with a pair of strong time-delayed short laser pulses with crossed linear polarizations. We show that such an excitation not only provides unidirectional rotation of the most polarizable molecular axis, but also induces a directed torque along this axis, which results in the transient orientation of the molecules. The asymmetric molecules are chiral in nature and different molecular enantiomers experience the orienting action in opposite directions causing out-of-phase oscillation of their dipole moments. The resulting microwave radiation was recently suggested to be used for analysis/discrimination of chiral molecular mixtures. We reveal the mechanism behind this laser induced orientation effect, show that it is classical in nature, and envision further applications of light with skewed polarization., Comment: 8 pages, 5 figures

We present what is probably the simplest classical system featuring the echo phenomenon - a collection of randomly oriented free rotors with dispersed rotational velocities. Following excitation by a pair of time-delayed impulsive kicks, the mean orientation/alignment of the ensemble exhibits multiple echoes and fractional echoes. We elucidate the mechanism of the echo formation by kick-induced filamentation of phase space, and provide the first experimental demonstration of classical alignment echoes in a thermal gas of CO_2 molecules excited by a pair of femtosecond laser pulses.

We study the dynamics of paramagnetic molecular superrotors in an external magnetic field. Optical centrifuge is used to create dense ensembles of oxygen molecules in ultra-high rotational states. It is shown for the first time, that the gas of rotating molecules becomes optically birefringent in the presence of magnetic field. The discovered effect of "magneto-rotational birefringence" indicates 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 propose three implementations of the Gauss sum factorization schemes discussed in part I of this series: (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 one-photon 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 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., Comment: 22 pages, 7 figures

We use the periodicity properties of generalized Gauss sums to factor numbers. Moreover, we derive rules for finding the factors and illustrate this factorization scheme for various examples. This algorithm relies solely on interference and scales exponentially., Comment: 21 pages, 8 figures

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$., Comment: 5 pages, 4 figures

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 trains with a large number of pulses separated on the time scale much shorter than the rotational revival (a few hundred femtosecond), enabling the use of conventional pulse shapers., Comment: 5 pages, 5 figures

The effects of laser-induced prealignment on the deflection of paramagnetic molecules by inhomogeneous static magnetic field are studied. Depending on the relevant Hund's coupling case of the molecule, two different effects were identified: either suppression of the deflection by laser pulses (Hund's coupling case (a) molecules, such as ClO), or a dramatic reconstruction of the broad distribution of the scattering angles into several narrow peaks (for Hund's 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 provide a theory of the deflection of polar and non-polar rotating molecules by inhomogeneous static electric field. Rainbow-like features in the angular distribution of the scattered molecules are analyzed in detail. Furthermore, we demonstrate that one may efficiently control the deflection process with the help of short and strong femtosecond laser pulses. In particular the deflection process may by turned-off by a proper excitation, and the angular dispersion of the deflected molecules can be substantially reduced. We study the problem both classically and quantum mechanically, taking into account the effects of strong deflecting field on the molecular rotations. In both treatments we arrive at the same conclusions. The suggested control scheme paves the way for many applications involving molecular focusing, guiding, and trapping by inhomogeneous fields.

We consider deflection of polarizable molecules by inhomogeneous optical fields, and analyze the role of molecular orientation and rotation in the scattering process. It is shown that molecular rotation induces spectacular rainbow-like features in the distribution of the scattering angle. Moreover, 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. We provide quantum and classical treatment of the deflection process. The effects of strong deflecting field on the scattering of rotating molecules are considered by the means of the adiabatic invariants formalism. This new control scheme opens new ways for many applications involving molecular focusing, guiding and trapping by optical and static fields.

We consider deflection of polarizable molecules by inhomogeneous optical fields, and analyze the role of molecular orientation and rotation in the scattering process. It is shown that molecular rotation induces spectacular rainbow-like features in the distribution of the scattering angle. Moreover, by pre-shaping 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., Comment: 4 pages, 4 figures

We consider laser alignment of ortho and para spin isomers of water molecules by using strong and short off-resonance laser pulses. A single pulse is found to create a distinct transient alignment and antialignment of the isomeric species. We suggest selective alignment of one isomeric species (leaving the other species randomly aligned) by a pair of two laser pulses., Comment: 6 pages, 4 figures, 3 tables

Single-shot time resolved Coherent Anti-Stokes Raman Scattering (CARS) is presented as a viable method for fast measurements of molecular spectra. The method is based on the short spatial extension of femtosecond pulses and maps time delays between pulses onto the region of intersection between broad beams. The image of the emitted CARS signal contains full temporal information on the field-free molecular dynamics, from which spectral information is extracted. The method is demonstrated on liquid samples of CHBr3 and CHCl3 and the Raman spectrum of the low-lying vibrational states of these molecules is measured.

We explore the role of laser induced anti-alignment in enhancing molecular orientation. A field-free enhanced orientation via anti-alignment scheme is presented, which combines a linearly polarized femtosecond laser pulse with a half-cycle pulse. The laser pulse induces transient anti-alignment in the plane orthogonal to the field polarization, while the half-cycle pulse leads to the orientation. We identify two qualitatively different enhancement mechanisms depending on the pulse order, and optimize their effects using classical and quantum models both at zero and non-zero temperature.

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. Operation of the focusing setup is considered as a nonlinear spatial squeezing of atoms 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 non-adiabatic and spontaneous emission effects limit the achievable minimal size of the deposited structures., Comment: 10 pages including 11 figures in Revtex

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 indication for distinct transient angular distributions of different isotopic species, paving the way to novel time-resolved analytic techniques, as well as to robust methods for isotope separation. When two pulses are used, enhancement or reduction of the degree of rotational excitation and of the corresponding molecular alignment is observed, depending on the delay between pulses. We implement the double pulse excitation scheme in a binary isotopic mixture, enhancing the rotational excitation of one isotopic component while almost totally reducing the rotational excitation of the other., Comment: 9 pages, 4 figures

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

We study the focusing of atoms by multiple layers of standing light waves in the context of atom lithography. In particular, atomic localization by a double-layer light mask is examined using the optimal squeezing approach. Operation of the focusing setup is analyzed both in the paraxial approximation and in the regime of nonlinear spatial squeezing for the thin-thin as well as thin-thick atom lens combinations. It is shown that the optimized double light mask may considerably reduce the imaging problems, improve the quality of focusing and enhance the contrast ratio of the deposited structures., Comment: 7 pages including 8 figures in Revtex

We present a detailed theory of spectacular semiclassical catastrophes happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett. {\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems are analyzed. It is shown that the wave function of the rotor develops a {\em cusp} at a certain delay after a kick, which results in a sharply focused rotational wave packet. The {\em cusp} is followed by a fold-type catastrophe manifested in the {\em rainbow}-like moving angular singularities. In the three-dimensional case, the rainbows are accompanied by additional singular features similar to {\em glory} structures known in wave optics. These catastrophes in the time-dependent angular wave function are well described by the appropriate tools of the quasiclassical wave mechanics, i.e. by Airy and Bessel approximations and Pearcey's functions. A scenario of "accumulative squeezing" is also presented in which a specially designed train of short kicks produces an unlimited narrowing of the rotor angular distribution. This scenario is relevant for the molecular alignment by short laser pulses, and also for atom lithography schemes in which cold atoms are focused by an optical standing wave., Comment: 22 pages, 12 postscript figures, 2 jpeg figures

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., Comment: Latex, 9 pages, 10 figures, submitted to PRA

Semiclassical catastrophes in the dynamics of a quantum rotor (molecule) driven by a strong time-varying field are considered. We show that for strong enough fields, a sharp peak in the rotor angular distribution can be achieved via time-domain focusing phenomenon, followed by the formation of angular rainbows and glory-like angular structures. Several scenarios leading to the enhanced angular squeezing are proposed that use specially designed and optimized sequences of pulses. The predicted effects can be observed in many processes, ranging from molecular alignment (orientation) by laser fields to heavy-ion collisions, and the squeezing of cold atoms in a pulsed optical lattice., Comment: 8 pages, Latex, 8 figures, based on the talk given at the Eighth Rochester Conference on Coherence and Quantum Optics (June 13-16, 2001). To appear in the proceedings of CQO8 (Plenum, 2002)