arXiv subjects

Bretislav Friedrich

Publications and source records attributed to Bretislav Friedrich.

At least 19 recordsLinked to original sources

arXiv2026

Emergence of a Luttinger Liquid Phase in an Array of Chiral Molecules

We propose a robust platform for simulating chiral quantum magnetism using linear arrays of trapped asymmetric top molecules, specifically 1,2-propanediol ($\mathrm{C_{3}H_{8}O_{2}}$). By mapping the Stark-dressed rotational states onto an effective spin-$1/2$ subspace, we rigorously derive a generalized $XXZ$ Heisenberg Hamiltonian governing the underlying many-body dynamics. Unlike standard solid-state models where the topological Dzyaloshinskii-Moriya Interaction (DMI) is introduced phenomenologically, we demonstrate that DMI emerges \textit{ab initio} from the molecular stereochemistry. Specifically, the interference between the transition dipole moments of heterochiral enantiomer pairs (L-R), which breaks inversion symmetry, generates a tunable DMI that stabilizes a Chiral Luttinger Liquid phase. Through a comprehensive phase-diagram analysis, we identify an optimal experimental regime characterized by intermolecular separations of $ r \approx 1.5~\mathrm{nm} $ and intermediate electric-field strengths $ d\varepsilon/B \approx 2.5 $. In this window, the system is protected from trivial field-polarized phases and exhibits a robust gapless spin-spiral texture. Our results establish 1,2-propanediol arrays as a versatile quantum simulator, providing a direct microscopic link between molecular chirality and topological many-body phases.

quant-ph↗

arXiv2024

The Spectrum of He$^+$ as a Proving Ground for Bohr's Model of the Atom: A Legacy of Williamina Fleming's Astrophysical Discovery

In 1896, Edward Charles Pickering (1846-1919), Director of the Harvard College Observatory (HCO), reported in a trio of publications the observation of "peculiar spectra" of the southern star $ζ$ Puppis, which he attributed to an "element not yet found in other stars or on earth." Supported by laboratory spectra obtained by Alfred Fowler (1868-1940), Niels Bohr (1885-1962) showed in 1913 that this "element" was in fact ionized helium, He$^+$. Its spectrum has become known as the Pickering Series, even though Pickering credited Williamina Fleming (1857-1911) for the discovery. Fleming was one of HCO's "computers" and the future Curator of the Astronomical Photographic Glass Plate Collection. The series of spectral lines associated with Pickering's name played a unique role on the path to quantum mechanics by serving as a proving ground for Bohr's model of the atom. Our examination of the discovery of the Pickering series relied on the records held at the Center for Astrophysics $\vert$ Harvard \& Smithsonian (the successor institution to HCO), especially the Notebooks and Diaries of Williamina Fleming and others as well as on the Center's Glass Plate Collection. Glimpses of the "peculiar sociology" of a research institution, half of whose staff were women employed on grossly unequal terms with men, are given in the course of the narrative.

physics.atom-ph↗

arXiv2022

Mapping atomic trapping in an optical superlattice onto the libration of a planar rotor in electric fields

We show that two seemingly unrelated problems - the trapping of an atom in an optical superlattice (OSL) and the libration of a planar rigid rotor in combined electric and optical fields - have isomorphic Hamiltonians. Formed by the interference of optical lattices whose spatial periods differ by a factor of two, OSL gives rise to a periodic potential that acts on atomic translation via the AC Stark effect. The latter system, also known as the generalized planar pendulum (GPP), is realized by subjecting a planar rigid rotor to combined orienting and aligning interactions due to the coupling of the rotor's permanent and induced electric dipole moments with the combined fields. The mapping makes it possible to establish correspondence between concepts developed for the two eigenproblems individually, such as localization on the one hand and orientation/alignment on the other. Moreover, since the GPP problem is conditionally quasi-exactly solvable (C-QES), so is atomic trapping in an OSL. We make use of both the correspondence and the quasi-exact solvability to treat ultracold atoms in an optical superlattice as a semifinite-gap system. The band structure of this system follows from the eigenenergies and their genuine and avoided crossings obtained previously for the GPP as analytic solutions of the Whittaker-Hill equation. These solutions characterize both the squeezing and the tunneling of atoms trapped in an optical superlattice and pave the way to unraveling their dynamics in analytic form.

cond-mat.quant-gas↗

arXiv2022

An Electro-Optical Trap for Polar Molecules

A detailed treatment of an electro-optical trap for polar molecules, realized by embedding an optical trap within a uniform electrostatic field, is presented and the trap's properties analyzed and discussed. The electro-optical trap offers significant advantages over an optical trap that include an increased trap depth and conversion of alignment of the trapped molecules to marked orientation. Tilting the polarization plane of the optical field with respect to the electrostatic field diminishes both the trap depth and orientation and lifts the degeneracy of the $\pm M$ states of the trapped molecules. These and other features of the electro-optical trap are explained in terms of the eigenproperties of the polar and polarizable molecules subject to the combined permanent and induced electric dipole interactions at play.

physics.atom-ph↗

arXiv2022

One hundred years ago Alfred Landé unriddled the Anomalous Zeeman Effect and presaged Electron Spin

In order to commemorate Alfred Landé's unriddling of the anomalous Zeeman Effect a century ago, we reconstruct his seminal contribution to atomic physics in light of the atomic models available at the time. Landé recognized that the coupling of quantized electronic angular momenta via their vector addition within an atom was the origin of all the apparent mysteries of atomic structure as manifested by the anomalous Zeeman effect. We show to which extent Landé's ideas influenced the development of quantum physics, particularly Wolfgang Pauli's path to the exclusion principle. We conclude with Landé's brief biography.

physics.hist-ph↗

arXiv2021

Realization of Heisenberg models of spin systems with polar molecules in pendular states

We show that ultracold polar diatomic or linear molecules, oriented in an external electric field and mutually coupled by dipole-dipole interactions, can be used to realize the exact Heisenberg XYZ, XXZ and XY models without invoking any approximation. The two lowest lying excited pendular states coupled by microwave or radio-frequency fields are used to encode the pseudo-spin. We map out the general features of the models by evaluating the models' constants as functions of the molecular dipole moment, rotational constant, strength and direction of the external field as well as the distance between molecules. We calculate the phase diagram for a linear chain of polar molecules based on the Heisenberg models and discuss their drawbacks, advantages, and potential applications.

quant-ph↗

arXiv2021

Dynamics of translational and rotational thermalization of AlF molecules via collisions with cryogenic helium

We investigated helium-mediated translational and rotational thermalization of the aluminum monofluoride (AlF) molecule at cryogenic temperatures via a new $ab \ initio$ potential energy surface (PES) and quantum multichannel scattering theory. Our examination of the elastic and rotationally inelastic channels revealed that helium is an efficient quencher of AlF at temperatures relevant to buffer gas cooling experiments ($\sim1$ mK to $10$ K). We also showed that this conclusion is robust against possible inaccuracies of the PES.

physics.chem-ph↗

arXiv2021

Quantum dynamics of a polar rotor acted upon by an electric rectangular pulse of variable duration

As demonstrated in our previous work [J. Chem. Phys. 149, 174109 (2018)], the kinetic energy imparted to a quantum rotor by a non-resonant electromagnetic pulse with a Gaussian temporal profile exhibits quasi-periodic drops as a function of the pulse duration. Herein, we show that this behaviour can be reproduced with a simple waveform, namely a rectangular electric pulse of variable duration, and examine, both numerically and analytically, its causes. Our analysis reveals that the drops result from the oscillating populations that make up the wavepacket created by the pulse and that they are necessarily accompanied by drops in the orientation and by a restoration of the pre-pulse alignment of the rotor. Handy analytic formulae are derived that allow to predict the pulse durations leading to diminished kinetic energy transfer and orientation. Experimental scenarios are discussed where the phenomenon could be utilized or be detrimental.

quant-ph↗

arXiv2021

Quantum dynamics of a planar rotor driven by suddenly switched combined aligning and orienting interactions

We investigate, both analytically and numerically, the quantum dynamics of a planar (2D) rigid rotor subject to suddenly switched-on or switched-off concurrent orienting and aligning interactions. We find that the time-evolution of the post-switch populations as well as of the expectation values of orientation and alignment reflects the spectral properties and the eigensurface topology of the planar pendulum eigenproblem established in our earlier work [Frontiers in Physics 2, 37 (2014); Eur. Phys. J. D 71, 149 (2017)]. This finding opens the possibility to examine the topological properties of the eigensurfaces experimentally as well as provides the means to make use of these properties for controlling the rotor dynamics in the laboratory.

quant-ph↗

arXiv2020

Spin-momentum entanglement in a Bose-Einstein condensate

Entanglement is at the core of quantum information processing and may prove essential for quantum speed-up. Inspired by both theoretical and experimental studies of spin-momentum coupling in systems of ultra-cold atoms, we investigate the entanglement between the spin and momentum degrees of freedom of an optically trapped BEC of $^{87}$Rb atoms. We consider entanglement that arises due to the coupling of these degrees of freedom induced by Raman and radio-frequency fields and examine its dependence on the coupling parameters by evaluating von Neumann entropy as well as concurrence as measures of the entanglement attained. Our calculations reveal that under proper experimental conditions significant spin-momentum entanglement can be obtained, with von Neumann entropy of 80% of the maximum attainable value. Our analysis sheds some light on the prospects of using BECs for quantum information applications.

quant-ph↗

arXiv2018

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime

We study, analytically as well as numerically, the dynamics that arises from the interaction of a polar polarizable rigid rotor with single unipolar electromagnetic pulses of varying length, $Δτ$, with respect to the rotational period of the rotor, $τ_r$. In the sudden, non-adiabatic limit, $Δτ\ll τ_r$, we derive analytic expressions for the rotor's wavefunctions, kinetic energies, and field-free evolution of orientation and alignment. We verify the analytic results by solving the corresponding time-dependent Schrödinger equation numerically and extend the temporal range of the interactions considered all the way to the adiabatic limit, $Δτ\gg τ_r$, where general analytic solutions beyond the field-free case are no longer available. The effects of the orienting and aligning interactions as well as of their combination on the post-pulse populations of the rotational states are visualized as functions of the orienting and aligning kick strengths in terms of populations quilts. Quantum carpets that encapsulate the evolution of the rotational wavepackets provide the space-time portraits of the resulting dynamics. The population quilts and quantum carpets reveal that purely orienting, purely aligning, or even-break combined interactions each exhibit a sui generis dynamics. In the intermediate temporal regime, we find that the wavepackets as functions of the orienting and aligning kick strengths show resonances that correspond to diminished kinetic energies at particular values of the pulse duration.

quant-ph↗

arXiv2018

Symmetric Tops Subject to Combined Electric Fields: Conditional Quasi-Solvability via the Quantum Hamilton-Jacobi Theory

We make use of the Quantum Hamilton-Jacobi (QHJ) theory to investigate conditional quasi-solvability of the quantum symmetric top subject to combined electric fields (symmetric top pendulum). We derive the conditions of quasi-solvability of the time-independent Schroedinger equation as well as the corresponding finite sets of exact analytic solutions. We do so for this prototypical trigonometric system as well as for its anti-isospectral hyperbolic counterpart. An examination of the algebraic and numerical spectra of these two systems reveals mutually closely related patterns. The QHJ approach allows to retrieve the closed-form solutions for the spherical and planar pendula and the Razavy system that had been obtained in our earlier work via Supersymmetric Quantum Mechanics as well as to find a cornucopia of additional exact analytic solutions.

math-ph↗

arXiv2018

Microsolvation of phthalocyanine molecules in superfluid helium nanodroplets as revealed by the optical line shape at the electronic origin

We investigate the solvent shift of phthalocyanine (Pc) doped into superfluid helium droplets and probed by optical spectroscopy at the electronic origin. Our present work complements extant studies and provides results that in part contradict previous conclusions. In particular, the solvent shift does not increase monotonously with droplet radius all the way up to the bulk limit, but exhibits a turnaround instead. Moreover, a substructure is resolved, whose characteristics depend on the droplet size. This behavior can hardly be reconciled with that of a freely rotating Pc-helium complex.

physics.chem-ph↗

arXiv2017

Conditional quasi-exact solvability of the quantum planar pendulum and of its anti-isospectral hyperbolic counterpart

We have subjected the planar pendulum eigenproblem to a symmetry analysis with the goal of explaining the relationship between its conditional quasi-exact solvability (C-QES) and the topology of its eigenenergy surfaces, established in our earlier work [Frontiers in Physical Chemistry and Chemical Physics 2, 1-16, (2014)]. The present analysis revealed that this relationship can be traced to the structure of the tridiagonal matrices representing the symmetry-adapted pendular Hamiltonian, as well as enabled us to identify many more -- forty in total to be exact -- analytic solutions. Furthermore, an analogous analysis of the hyperbolic counterpart of the planar pendulum, the Razavy problem, which was shown to be also C-QES [American Journal of Physics 48, 285 (1980)], confirmed that it is anti-isospectral with the pendular eigenproblem. Of key importance for both eigenproblems proved to be the topological index $κ$, as it determines the loci of the intersections (genuine and avoided) of the eigenenergy surfaces spanned by the dimensionless interaction parameters $η$ and $ζ$. It also encapsulates the conditions under which analytic solutions to the two eigenproblems obtain and provides the number of analytic solutions. At a given $κ$, the anti-isospectrality occurs for single states only (i.e., not for doublets), like C-QES holds solely for integer values of $κ$, and only occurs for the lowest eigenvalues of the pendular and Razavy Hamiltonians, with the order of the eigenvalues reversed for the latter. For all other states, the pendular and Razavy spectra become in fact qualitatively different, as higher pendular states appear as doublets whereas all higher Razavy states are singlets.

quant-ph↗

arXiv2016

Quantum computation using arrays of N polar molecules in pendular states

We investigate several aspects of realizing quantum computation using entangled polar molecules in pendular states. Quantum algorithms typically start from a product state |00...0> and we show that up to a negligible error, the ground states of polar molecule arrays can be considered as the unentangled qubit basis state |00...0>. This state can be prepared by simply allowing the system to reach thermal equilibrium at low temperature (<1 mK). We also evaluate entanglement, characterized by the concurrence of pendular state qubits in dipole arrays as governed by the external electric field, dipole-dipole coupling and number N of molecules in the array. In the parameter regime that we consider for quantum computing, we find that qubit entanglement is modest, typically no greater than 0.0001, confirming the negligible entanglement in the ground state. We discuss methods for realizing quantum computation in the gate model, measurement based model, instantaneous quantum polynomial time circuits and the adiabatic model using polar molecules in pendular states.

quant-ph↗

arXiv2016

Effect of rotational-state-dependent molecular alignment on the optical dipole force

The properties of molecule-optical elements such as lenses or prisms based on the interaction of molecules with optical fields depend in a crucial way on the molecular quantum state and its alignment created by the optical field. However, in previous experimental studies, the effects of state-dependent alignment have never been included in estimates of the optical dipole force acting on the molecules while previous theoretical investigations took the state-dependent molecular alignment into account only implicitly. Herein, we consider the effects of molecular alignment explicitly and, to this end, introduce an effective polarizability which takes proper account of molecular alignment and is directly related to the alignment-dependent optical dipole force. We illustrate the significance of including molecular alignment in the optical dipole force by a trajectory study that compares previously used approximations with the present approach. The trajectory simulations were carried out for an ensemble of linear molecules subject to either propagating or standing-wave optical fields for a range of temperatures and laser intensities. The results demonstrate that the alignment-dependent effective polarizability can serve to provide correct estimates of the optical dipole force, on which a state-selection method applicable to nonpolar molecules could be based. We note that an analogous analysis of the forces acting on polar molecules subject to an inhomogeneous static electric field reveals a similarly strong dependence on molecular orientation.

physics.chem-ph↗

arXiv2016

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

We examine the rotational states of a pair of polar $^2Σ$ 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 $ΔJ_{i}=0,\pm 1$, $ΔN_{i}=0,\pm 2$, and $ΔM_{i}=0,\pm 1$ 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.

physics.chem-ph↗

arXiv2016

Prospects for Quantum Computing with an Array of Ultracold Polar Paramagnetic Molecules

Arrays of trapped ultracold molecules represent a promising platform for implementing a universal quantum computer. DeMille has detailed a prototype design based on Stark states of polar $^1Σ$ molecules as qubits. Herein, we consider an array of polar $^2Σ$ molecules which are, in addition, inherently paramagnetic and whose Hund's case (b) free-rotor states are Bell states. We show that by subjecting the array to combinations of concurrent homogeneous and inhomogeneous electric and magnetic fields, the entanglement of the array's Stark and Zeeman states can be tuned and the qubit sites addressed. Two schemes for implementing an optically controlled CNOT gate are proposed and their feasibility discussed in the face of the broadening of spectral lines due to dipole-dipole coupling and the inhomogeneity of the electric and magnetic fields.

quant-ph↗