arXiv subjects

Mikhail Lemeshko

Publications and source records attributed to Mikhail Lemeshko.

104 records · Page 6Linked to original sources

arXiv2011

Supersymmetric factorization yields exact solutions to the molecular Stark effect problem for "stretched" states

By invoking supersymmetry, we found a condition under which the Stark effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable. The exact solvability condition for the interaction parameters involved yields exact wavefunction for the "stretched" states, $|J=m,m>$, and for the $|1,1>$ state in the case of a purely induced-dipole interaction. The analytic expressions for the eigenenergy, the space-fixed dipole moment, the alignment cosine, and the expectation value of the angular momentum allow to readily reverse-engineer the problem of finding the values of the interaction parameters required for creating quantum states with preordained characteristics.

physics.chem-ph↗

arXiv2011

Controlling a diatomic shape resonance with non-resonant light

A (diatomic) shape resonance is a metastable state of a pair of colliding atoms quasi-bound by the centrifugal barrier imposed by the angular momentum involved in the collision. The temporary trapping of the atoms' scattering wavefunction corresponds to an enhanced atom pair density at low interatomic separations. This leads to larger overlap of the wavefunctions involved in a molecule formation process such as photoassociation, rendering the process more efficient. However, for an ensemble of atoms, the atom pair density will only be enhanced if the energy of the resonance comes close to the temperature of the atomic ensemble. Herein we explore the possibility of controlling the energy of a shape resonance by shifting it toward the temperature of atoms confined in a trap. The shifts are imparted by the interaction of non-resonant light with the anisotropic polarizability of the atom pair, which affects both the centrifugal barrier and the pair's rotational and vibrational levels. We find that at laser intensities of up to $5\times 10^{9}$ W/cm$^2$ the pair density is increased by one order of magnitude for $^{87}$Rb atoms at $100 μ$K and by two orders of magnitude for $^{88}$Sr atoms at $20 μ$K.

physics.atom-ph↗

arXiv2010

Multiple scattering of matter waves: an analytic model of the refractive index for atomic and molecular gases

We present an analytic model of the refractive index for matter waves propagating through atomic or molecular gases. The model, which combines a WKB treatment of the long range attraction with the Fraunhofer model treatment of the short range repulsion, furnishes a refractive index in compelling agreement with recent experiments of Jacquey et al. [Phys. Rev. Lett. 98, 240405 (2007)] on Li atom matter waves passing through dilute noble gases. We show that the diffractive contribution, which arises from scattering by a two dimensional "hard core" of the potential, is essential for obtaining a correct imaginary part of the refractive index.

physics.atom-ph↗

arXiv2010

Fine-tuning molecular energy levels by nonresonant laser pulses

We evaluate the shifts imparted to vibrational and rotational levels of a linear molecule by a nonresonant laser field at intensities of up to 10^12 W/cm^2. Both types of shift are found to be either positive or negative, depending on the initial rotational state acted upon by the field. An adiabatic field-molecule interaction imparts a rotational energy shift which is negative and exceeds the concomitant positive vibrational shift by a few orders of magnitude. The rovibrational states are thus pushed downward in such a field. A nonresonant pulsed laser field that interacts nonadiabatically with the molecule is found to impart rotational and vibrational shifts of the same order of magnitude. The nonadiabatic energy transfer occurs most readily at a pulse duration which amounts to about a tenth of the molecule's rotational period, and vanishes when the sudden regime is attained for shorter pulses. We applied our treatment to the much studied 87Rb_2 molecule in the last bound vibrational levels of its lowest singlet and triplet electronic states. Our calculations indicate that 15 ns and 1.5 ns laser pulses of an intensity in excess of 5x10^9 W/cm^2 are capable of dissociating the molecule due to the vibrational shift. Lesser shifts can be used to fine tune the rovibrational levels and thereby to affect collisional resonances by the nonresonant light. The energy shifts may be discernible spectroscopically, at a 10 MHz resolution.

physics.chem-ph↗

arXiv2010

When diffraction rules the stereodynamics of rotationally inelastic collisions

Following upon our recent work on vector correlations in the Ar-NO collisions [PCCP 12, 1038 (2010)], we compare model results with close-coupling calculations for a range of channels and collision energies for the He-NO system. The striking agreement between the model and exact polarization moments indicates that the stereodynamics of rotationally inelastic atom-molecule collisions at thermal energies is governed by diffraction of matter waves from a two-dimensional repulsive core of the atom-molecule potential. Furthermore, the model polarization moments characterizing the He-NO, He-O$_2$, He-OH, and He-CaH stereodynamics are found to coalesce into a single, distinctive pattern, which can serve as a "fingerprint" to identify diffraction-driven stereodynamics in future work.

physics.chem-ph↗

arXiv2009

An analytic model of the stereodynamics of rotationally inelastic molecular collisions

We develop an analytic model of vector correlations in rotationally inelastic atom-diatom collisions and test it against the much examined Ar--NO ($\mathbf X^2 Π$) system. Based on the Fraunhofer scattering of matter waves, the model furnishes complex scattering amplitudes needed to evaluate the polarization moments characterizing the quantum stereodynamics. The analytic polarization moments are found to be in an excellent agreement with experimental results and with close-coupling calculations available at thermal energies. The model reveals that the stereodynamics is governed by diffraction from the repulsive core of the Ar--NO potential, which can be characterized by a single Legendre moment.

physics.chem-ph↗

arXiv2009

Rotational structure of weakly bound molecular ions

Relying on the quantization rule of Raab and Friedrich [Phys. Rev. A (2009) in press], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecular ion. We also provide analytic estimates of the rotational constants of any such levels up to threshold for dissociation and obtain a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential.

physics.atom-ph↗

arXiv2009

A model analysis of rotationally inelastic Ar + H$_2$O scattering in an electric field

We develop an analytic model of thermal state-to-state rotationally inelastic collisions of asymmetric-top molecules with closed-shell atoms in electric fields, and apply it to the Ar--H$_2$O collision system. The predicted cross sections as well as the steric asymmetry of the collisions show at fields up to 150 kV/cm characteristic field-dependent features which can be experimentally tested. Particularly suitable candidates for such tests are the $0_{00} \to 2_{20}$ and $1_{01} \to 2_{21}$ channels, arising from the relaxation of the field-free selection rules due to the hybridization of $J$ states. Averaging over the $M'$ product channels is found to largely obliterate the orientation effects brought about by the field.

physics.chem-ph↗

arXiv2009

Rotational and rotationless states of weakly-bound molecules

By making use of the quantization rule of Raab and Friedrich [P. Raab and H. Friedrich, Phys. Rev. A 78, 022707 (2008)], we derive simple and accurate formulae for the number of rotational states supported by a weakly-bound vibrational level of a diatomic molecule and the rotational constants of any such levels up to the threshold, and provide a criterion for determining whether a given weakly-bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential and are applicable to halo molecules.

physics.atom-ph↗

arXiv2009

Probing weakly-bound molecules with nonresonant light

We show that weakly-bound molecules can be probed by "shaking" in a pulsed nonresonant laser field. The field introduces a centrifugal term which expels the highest vibrational level from the potential that binds it. Our numerical simulations applied to the Rb$_2$ and KRb Feshbach molecules indicate that shaking by feasible laser pulses can be used to accurately recover the square of the vibrational wavefunction and, by inversion, also the long-range part of the molecular potential.

physics.atom-ph↗

arXiv2009

Quantum Zeno Effect

We present the physics of the quantum Zeno effect, whose gist is often expressed by invoking the adage "a watched pot never boils". We review aspects of the theoretical and experimental work done on the effect since its inception in 1977, and mention some applications. We dedicate the article - with our very best wishes - to Rudolf Zahradnik at the occasion of his great jubilee. Perhaps Rudolf's lasting youthfulness and freshness are due to that he himself had been frequently observed throughout his life: until the political turn-around in 1989 by those who wished, by their surveillance, to prevent Rudolf from spoiling the youth by his personal culture and his passion for science and things beautiful and useful in general. This attempt had failed. Out of gratitude, the youth has infected Rudolf with its youthfulness. Chronically. Since 1989, Rudolf has been closely watched by the public at large. For the same traits of his as before, but with the opposite goal and for the benefit of all generations. We relish keeping him in sight ...

physics.pop-ph↗

arXiv2008

Collisions of paramagnetic molecules in magnetic fields: an analytic model based on Fraunhofer diffraction of matter waves

We investigate the effects of a magnetic field on the dynamics of rotationally inelastic collisions of open-shell molecules ($^2Σ$, $^3Σ$, and $^2Π$) with closed-shell atoms. Our treatment makes use of the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric [M. Lemeshko and B. Friedrich, J. Chem. Phys. \textbf{129}, 024301 (2008)] and radiative fields [M. Lemeshko and B. Friedrich, Int. J. Mass. Spec. in press (2008)]. A magnetic field aligns the molecule in the space-fixed frame and thereby alters the effective shape of the diffraction target. This significantly affects the differential and integral scattering cross sections. We exemplify our treatment by evaluating the magnetic-field-dependent scattering characteristics of the He -- CaH ($X ^2Σ^+$), He -- O$_2$ ($X ^3Σ^-$) and He -- OH ($X ^2Π_Ω$) systems at thermal collision energies. Since the cross sections can be obtained for different orientations of the magnetic field with respect to the relative velocity vector, the model also offers predictions about the frontal-versus-lateral steric asymmetry of the collisions. The steric asymmetry is found to be almost negligible for the He -- OH system, weak for the He -- CaH collisions, and strong for the He -- O$_2$. While odd $ΔM$ transitions dominate the He -- OH $(J=3/2,f \to J', e/f)$ integral cross sections in a magnetic field parallel to the relative velocity vector, even $ΔM$ transitions prevail in the case of the He -- CaH ($X ^2Σ^+$) and He -- O$_2$ ($X ^3Σ^-$) collision systems. For the latter system, the magnetic field opens inelastic channels that are closed in the absence of the field. These involve the transitions $N=1, J=0 \to N', J' $ with $J'=N'$.

physics.atom-ph↗

arXiv2008

An analytic model of rotationally inelastic collisions of polar molecules in electric fields

We present an analytic model of thermal state-to-state rotationally inelastic collisions of polar molecules in electric fields. The model is based on the Fraunhofer scattering of matter waves and requires Legendre moments characterizing the "shape" of the target in the body-fixed frame as its input. The electric field orients the target in the space-fixed frame and thereby effects a striking alteration of the dynamical observables: both the phase and amplitude of the oscillations in the partial differential cross sections undergo characteristic field-dependent changes that transgress into the partial integral cross sections. As the cross sections can be evaluated for a field applied parallel or perpendicular to the relative velocity, the model also offers predictions about steric asymmetry. We exemplify the field-dependent quantum collision dynamics with the behavior of the Ne-OCS($^{1}Σ$) and Ar-NO($^2Π$) systems. A comparison with the close-coupling calculations available for the latter system [Chem. Phys. Lett. \textbf{313}, 491 (1999)] demonstrates the model's ability to qualitatively explain the field dependence of all the scattering features observed.

physics.chem-ph↗

arXiv2008

The effect of a nonresonant radiative field on low-energy rotationally inelastic $\text{Na}^{+} + \text{N}_2$ collisions

We examine the effects of a linearly polarized nonresonant radiative field on the dynamics of rotationally inelastic $\text{Na}^{+} + \text{N}_2$ collisions at eV collision energies. Our treatment is based on the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric fields [arXiv:0804.3318v1]. The nonresonant radiative field changes the effective shape of the target molecule by aligning it in the space-fixed frame. This markedly alters the differential and integral scattering cross sections. As the cross sections can be evaluated for a polarization of the radiative field collinear or perpendicular to the relative velocity vector, the model also offers predictions about steric asymmetry of the collisions.

physics.chem-ph↗