arXiv subjects

Bretislav Friedrich

Publications and source records attributed to Bretislav Friedrich.

At least 37 records · Page 2Linked to original sources

arXiv2015

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.

physics.chem-ph↗

arXiv2015

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 $η$ and $ζ$. 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 $ζ=\frac{η^2}{4k^2}$ of the intersections of the eigenenergy surfaces spanned by the $η$ and $ζ$ 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.

quant-ph↗

arXiv2014

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.

physics.chem-ph↗

arXiv2013

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.

physics.chem-ph↗

arXiv2012

Implementation of Quantum Logic Gates Using Polar Molecules in Pendular States

We present a systematic approach to implementation of basic quantum logic gates operating on polar molecules in pendular states as qubits for a quantum computer. A static electric field prevents quenching of the dipole moments by rotation, thereby creating the pendular states; also, the field gradient enables distinguishing among qubit sites. Multi-Target Optimal Control Theory (MTOCT) is used as a means of optimizing the initial-to-target transition probability via a laser field. We give detailed calculations for the SrO molecule, a favorite candidate for proposed quantum computers. Our simulation results indicate that NOT, Hadamard and CNOT gates can be realized with high fidelity for such pendular qubit states.

quant-ph↗

arXiv2012

Making the best of mixed-field orientation of polar molecules: A recipe for achieving adiabatic dynamics in an electrostatic field combined with laser pulses

We have experimentally and theoretically investigated the mixed-field orientation of rotational-state-selected OCS molecules and we achieve strong degrees of alignment and orientation. The applied moderately intense nanosecond laser pulses are long enough to adiabatically align molecules. However, in combination with a weak dc electric field, the same laser pulses result in nonadiabatic dynamics in the mixed-field orientation. These observations are fully explained by calculations employing, both, adiabatic and non-adiabatic time-dependent models.

physics.chem-ph↗

arXiv2011

Otto Stern (1888-1969): The founding father of experimental atomic physics

We review the work and life of Otto Stern who developed the molecular beam technique and with its aid laid the foundations of experimental atomic physics. Among the key results of his research are: the experimental determination of the Maxwell-Boltzmann distribution of molecular velocities (1920), experimental demonstration of space quantization of angular momentum (1922), diffraction of matter waves comprised of atoms and molecules by crystals (1931) and the determination of the magnetic dipole moments of the proton and deuteron (1933).

physics.hist-ph↗

arXiv2011

Interaction between polar molecules subject to a far-off-resonant optical field: Entangled dipoles up- or down-holding each other

We show that the electric dipole-dipole interaction between a pair of polar molecules undergoes an all-out transformation when superimposed by a far-off resonant optical field. The combined interaction potential becomes tunable by variation of wavelength, polarization and intensity of the optical field and its dependence on the intermolecular separation exhibits a crossover from an inverse-power to an oscillating behavior. The ability thereby offered to control molecular interactions opens up avenues toward the creation and manipulation of novel phases of ultracold polar gases among whose characteristics is a long-range entanglement of the dipoles' mutual orientation. We devised an accurate analytic model of such optical-field-dressed dipole-dipole interaction potentials, which enables a straightforward access to the optical-field parameters required for the design of intermolecular interactions in the laboratory.

physics.atom-ph↗

arXiv2011

Entanglement of polar symmetric top molecules as candidate qubits

Proposals for quantum computing using rotational states of polar molecules as qubits have previously considered only diatomic molecules. For these the Stark effect is second-order, so a sizable external electric field is required to produce the requisite dipole moments in the laboratory frame. Here we consider use of polar symmetric top molecules. These offer advantages resulting from a first-order Stark effect, which renders the effective dipole moments nearly independent of the field strength. That permits use of much lower external field strengths for addressing sites. Moreover, for a particular choice of qubits, the electric dipole interactions become isomorphous with NMR systems for which many techniques enhancing logic gate operations have been developed. Also inviting is the wider chemical scope, since many symmetric top organic molecules provide options for auxiliary storage qubits in spin and hyperfine structure or in internal rotation states.

quant-ph↗

arXiv2011

Supersymmetry identifies molecular Stark states whose eigenproperties can be obtained analytically

We made use of supersymmetric (SUSY) quantum mechanics to find a condition under which the Stark effect problem for a polar and polarizable closed-shell diatomic molecule subject to collinear electrostatic and nonresonant radiative fields becomes exactly solvable. The condition, $Δω= \frac{ω^2}{4 (m+1)^2}$, connects values of the dimensionless parameters $ω$ and $Δω$ that characterize the strengths of the permanent and induced dipole interactions of the molecule with the respective fields. The exact solutions are obtained for the $|\tilde{J}=m,m;ω,Δω>$ family of "stretched" states. The field-free and strong-field limits of the combined-fields problem were found to exhibit supersymmetry and shape-invariance, which is indeed the reason why they are analytically solvable. By making use of the analytic form of the $|\tilde{J}=m,m;ω,Δω>$ wavefunctions, we obtained simple formulae for the expectation values of the space-fixed electric dipole moment, the alignment cosine, the angular momentum squared, and derived a "sum rule" which combines the above expectation values into a formula for the eigenenergy. The analytic expressions for the characteristics of the strongly oriented and aligned states provide a direct access to the values of the interaction parameters required for creating such states in the laboratory.

physics.chem-ph↗

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

Stark-selected beam of ground-state OCS molecules characterized by revivals of impulsive alignment

We make use of an inhomogeneous electrostatic dipole field to impart a quantum-state-dependent deflection to a pulsed beam of OCS molecules, and show that those molecules residing in the absolute ground state, $X ^1Σ^+$, $\ket{00^00}$, J=0, can be separated out by selecting the most deflected part of the molecular beam. Past the deflector, we irradiate the molecular beam by a linearly polarized pulsed nonresonant laser beam that impulsively aligns the OCS molecules. Their alignment, monitored via velocity-map imaging, is measured as a function of time, and the time dependence of the alignment is used to determine the quantum state composition of the beam. We find significant enhancements of the alignment (\costhetasqtd $= 0.84$) and of state purity ($> 92$%) for a state-selected, deflected beam compared with an undeflected beam.

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↗

arXiv2011

Entanglement of polar molecules in pendular states

In proposals for quantum computers using arrays of trapped ultracold polar molecules as qubits, a strong external field with appreciable gradient is imposed in order to prevent quenching of the dipole moments by rotation and to distinguish among the qubit sites. That field induces the molecular dipoles to undergo pendular oscillations, which markedly affect the qubit states and the dipole-dipole interaction. We evaluate entanglement of the pendular qubit states for two linear dipoles, characterized by pairwise concurrence, as a function of the molecular dipole moment and rotational constant, strengths of the external field and the dipole-dipole coupling, and ambient temperature. We also evaluate a key frequency shift, $\triangleω$, produced by the dipole-dipole interaction. Under conditions envisioned for the proposed quantum computers, both the concurrence and $\triangleω$ become very small for the ground eigenstate. In principle, such weak entanglement can be sufficient for operation of logic gates, provided the resolution is high enough to detect the $\triangleω$ shift unambiguously. In practice, however, for many candidate polar molecules it appears a challenging task to attain adequate resolution. Simple approximate formulas fitted to our numerical results are provided from which the concurrence and $\triangleω$ shift can be obtained in terms of unitless reduced variables.

quant-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↗