89 research outputs found

### Pair-eigenstates and mutual alignment of coupled molecular rotors in a magnetic field

We examine the rotational states of a pair of polar $^2\Sigma$ molecules
subject to a uniform magnetic field. The electric dipole-dipole interaction
between the molecules creates entangled pair-eigenstates of two types. In one
type, the Zeeman interaction between the inherently paramagnetic molecules and
the magnetic field destroys the entanglement of the pair-eigenstates, whereas
in the other type it does not. The pair-eigenstates exhibit numerous
intersections, which become avoided for pair-eigenstates comprised of
individual states that meet the selection rules $\Delta J_{i}=0,\pm 1$, $\Delta
N_{i}=0,\pm 2$, and $\Delta M_{i}=0,\pm 1$ imposed by the electric
dipole-dipole operator. Here $J_{i}$, $N_{i}$ and $M_{i}$ are the total,
rotational and projection angular momentum quantum numbers of molecules $i=1,2$
in the absence of the electric dipole-dipole interaction. We evaluate the
mutual alignment of the pair-eigenstates and find it to be independent of the
magnetic field, except for states that undergo avoided crossings, in which case
the alignment of the interacting states is interchanged at the magnetic field
corresponding to the crossing point. We present an analytic model which
provides ready estimates of the pairwise alignment cosine that characterises
the mutual alignment of the coupled rotors.Comment: 29 Pages, 11 figures, submitted to PCC

### 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.Comment: 4 pages, 1 figur

### 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.Comment: 9 pages, 9 figures, 4 table

### Supersymmetry and eigensurface topology of the planar quantum pendulum

We make use of supersymmetric quantum mechanics (SUSY QM) to find three sets
of conditions under which the problem of a planar quantum pendulum becomes
analytically solvable. The analytic forms of the pendulum's eigenfuntions make
it possible to find analytic expressions for observables of interest, such as
the expectation values of the angular momentum squared and of the orientation
and alignment cosines as well as of the eigenenergy. Furthermore, we find that
the topology of the intersections of the pendulum's eigenenergy surfaces can be
characterized by a single integer index whose values correspond to the sets of
conditions under which the analytic solutions to the quantum pendulum problem
exist

### Supersymmetry and eigensurface topology of the spherical quantum pendulum

We undertook a mutually complementary analytic and computational study of the
full-fledged spherical (3D) quantum rotor subject to combined orienting and
aligning interactions characterized, respectively, by dimensionless parameters
$\eta$ and $\zeta$. By making use of supersymmetric quantum mechanics (SUSY
QM), we found two sets of conditions under which the problem of a spherical
quantum pendulum becomes analytically solvable. These conditions coincide with
the loci $\zeta=\frac{\eta^2}{4k^2}$ of the intersections of the eigenenergy
surfaces spanned by the $\eta$ and $\zeta$ parameters. The integer topological
index $k$ is independent of the eigenstate and thus of the projection quantum
number $m$. These findings have repercussions for rotational spectra and
dynamics of molecules subject to combined permanent and induced dipole
interactions.Comment: arXiv admin note: text overlap with arXiv:1404.224

### Topology of surfaces for molecular Stark energy, alignment and orientation generated by combined permanent and induced electric dipole interactions

We show that combined permanent and induced electric dipole interactions of
polar and polarizable molecules with collinear electric fields lead to a sui
generis topology of the corresponding Stark energy surfaces and of other
observables - such as alignment and orientation cosines - in the plane spanned
by the permanent and induced dipole interaction parameters. We find that the
loci of the intersections of the surfaces can be traced analytically and that
the eigenstates as well as the number of their intersections can be
characterized by a single integer index. The value of the index, distinctive
for a particular ratio of the interaction parameters, brings out a close
kinship with the eigenproperties obtained previously for a class of Stark
states via the apparatus of supersymmetric quantum mechanics.Comment: 22 pages, including 2 tables and 8 figure

### 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.Comment: 22 pages, 1 table, 7 figure

### Directional properties of polar paramagnetic molecules subject to congruent electric, magnetic and optical fields

We show that congruent electric, magnetic and non-resonant optical fields
acting concurrently on a polar paramagnetic (and polarisable) molecule offer
possibilities to both amplify and control the directionality of the ensuing
molecular states that surpass those available in double-field combinations or
in single fields alone. At the core of these triple-field effects is the
lifting of the degeneracy of the projection quantum number $M$ by the magnetic
field superimposed on the optical field and a subsequent coupling of the
members of the "doubled" (for states with $M \neq 0$) tunneling doublets due to
the optical field by even a weak electrostatic field.Comment: 25 pages, 25 figures. Submitted to New Journal of Physic

### 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.Comment: slightly corrected version, 4 pages, 1 figure, 3 table

### Directional States of Symmetric-Top Molecules Produced by Combined Static and Radiative Electric Fields

We show that combined electrostatic and radiative fields can greatly amplify
the directional properties, such as axis orientation and alignment, of
symmetric top molecules. In our computational study, we consider all four
symmetry combinations of the prolate and oblate inertia and polarizability
tensors, as well as the collinear and perpendicular (or tilted) geometries of
the two fields. In, respectively, the collinear or perpendicular fields, the
oblate or prolate polarizability interaction due to the radiative field forces
the permanent dipole into alignment with the static field. Two mechanisms are
found to be responsible for the amplification of the molecules' orientation,
which ensues once the static field is turned on: (a) permanent-dipole coupling
of the opposite-parity tunneling doublets created by the oblate polarizability
interaction in collinear static and radiative fields; (b) hybridization of the
opposite parity states via the polarizability interaction and their coupling by
the permanent dipole interaction to the collinear or perpendicular static
field. In perpendicular fields, the oblate polarizability interaction, along
with the loss of cylindrical symmetry, is found to preclude the wrong-way
orientation, causing all states to become high-field seeking with respect to
the static field. The adiabatic labels of the states in the tilted fields
depend on the adiabatic path taken through the parameter space comprised of the
permanent and induced-dipole interaction parameters and the tilt angle between
the two field vectors

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