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Timur V. Tscherbul

Publications and source records attributed to Timur V. Tscherbul.

At least 19 recordsLinked to original sources
arXiv2026

Identical-Particle Symmetry-Enabled Complete Coherent Control of Ultracold Atomic and Molecular Collisions

We show that exchange symmetry in collisions of identical particles enables symmetry-protected coherent control of the total scattering cross section. For identical fermions, antisymmetrization enforces a common control phase among contributing channels within a given parity sector, yielding maximal control visibility. For identical bosons, phase-locking persists but with reduced visibility due to additional exchange (satellite) contributions. Collisions of distinguishable particles lack this symmetry-imposed phase-locking, leading to lower controllability and visibility. We elucidate these principles through coupled-channel quantum-scattering calculations for lithium-lithium collisions, comparing the $^{6}\mathrm{Li}{-}^{6}\mathrm{Li}$ (identical fermions), $^{7}\mathrm{Li}{-}^{7}\mathrm{Li}$ (identical bosons), and $^{6}\mathrm{Li}{-}^{7}\mathrm{Li}$ (distinguishable) systems. Furthermore, in the identical-particle cases, symmetry-enforced phase-locking enables full control over the parity of the final state even beyond the ultracold regime. This mechanism is broadly applicable to identical-particle collisions, including homonuclear molecules for which established approaches--DC electric fields or microwave shielding--are ineffective or unavailable.

physics.atom-ph↗
arXiv2026

A quadratic-scaling algorithm with guaranteed convergence for quantum coupled-channel calculations

Rigorous quantum dynamics calculations provide essential insights into complex scattering phenomena across atomic and molecular physics, chemical reaction dynamics, and astrochemistry. However, the application of the gold-standard quantum coupled-channel (CC) method has been fundamentally constrained by a steep cubic scaling of computational cost $[{O}(N^3)]$. Here, we develop a general, rigorous, and robust method for solving the time-independent Schrödinger equation for a single column of the scattering S-matrix with quadratic scaling $[{O}(N^2)]$ in the number of channels. The Weinberg-regularized Iterative Series Expansion (WISE) algorithm resolves the divergence issues affecting iterative techniques by applying a regularization procedure to the kernel of the multichannel Lippmann-Schwinger integral equation. The method also explicitly incorporates closed-channel effects, including those responsible for multichannel Feshbach resonances. We demonstrate the power of this approach by performing rigorous calculations on He + CO and CO + N$_2$ collisions, achieving exact quantum results with quadratic scaling guaranteed by a contour-integral construction. Our results establish a highly scalable computational paradigm, enabling state-to-state quantum scattering computations for complex molecular systems.

physics.chem-ph↗
arXiv2025

A rigorous adiabatic approach to ultracold atom-molecule collisions in a magnetic field

We extend the rigorous adiabatic coupled-channel formalism to ultracold nonreactive atom-molecule collisions in the presence of an external magnetic field. The wavefunction of the collision complex is expanded in adiabatic basis states obtained by solving the eigenvalue problem for the adiabatic Hamiltonian (the total Hamiltonian of the collision complex minus the radial kinetic energy) on a grid of atom-molecule distances $R$. The resulting coupled-channel equations are solved using the diabatic-by-sector method. We show that the adiabatic approach provides accurate cross sections for cold and ultracold Mg ($^1$S) + NH ($^3Σ^-$) collisions in a magnetic field with ~2 times fewer channels than the standard diabatic basis. We further develop an efficient $R$-dependent basis truncation protocol (RBT), in which the elements of the log-derivative matrix are sampled and discarded as it is propagated from small to large $R$. While RBT can be applied in both the adiabatic and diabatic bases, we show that the adiabatic basis can be reduced to just the open channels at long range, leading to an overall computational gain of ~15-30 for the propagation part of the calculation. The gain is particularly significant in situations where substantial errors in the calculated cross sections ($<$50\%) can be tolerated or long-range interactions are involved, making the adiabatic basis formulation a promising approach to strongly anisotropic collisions and chemical reactions in the presence of an external magnetic field.

physics.chem-ph↗
arXiv2025

Rigorous quantum calculations for atom-molecule chemical reactions in electric fields: from single to multiple partial wave regimes

We present an efficient method for rigorous quantum calculations of cross sections for atom-molecule reactive scattering in the presence of a dc electric field. The wavefunction of the reaction complex is expanded in an overcomplete set of arrangement-dependent Fock-Delves hyperspherical basis functions and the interactions of the reactants and products with electric fields are accounted for in the total angular momentum representation. A significant computational challenge affecting our previously developed approach [Phys. Rev. Lett. $\mathbf{115}$, 023201 (2015)] is addressed by an efficient asymptotic frame transformation between the hyperspherical and Jacobi coordinates in the presence of an external field. Using accurate {\it ab initio} potential energy surfaces, we calculate total and state-resolved cross sections for the chemical reactions LiF$(v=1,j=0)$ + H $\to$ Li + HF($v'=0,j'$) and F + HD$(v=0,j=0)$ $\to$ HF + D, DF + H as functions of collision energy and electric field strength. The field dependence of the cross sections for the LiF + H chemical reaction exhibits resonance structure mediated by tunneling-driven interactions between reactants and products. No significant field effects are found for the F + HD $\to$ HF + D, DF + H chemical reaction at 1 Kelvin, even for state-resolved transitions and with field magnitudes reaching 200 kV/cm. Our calculations illustrate the essential role of basis set convergence for the proper interpretation of external field effects on chemical reaction dynamics. While reduced-basis calculations for the F + HD reaction indicate significant effects of electric fields on product state distributions, these effects vanish when the number of total angular momentum basis states is increased.

physics.chem-ph↗
arXiv2025

Rotational decoherence dynamics in ultracold molecules induced by a tunable spin environment: The Central Rotor Model

We show that quantum rotational wavepacket dynamics in molecules can be described by a new system-environment model, which consists of a rotational subsystem coupled to a magnetically tunable spin bath formed by the nuclear spins within the molecule. The central rotor model shares similarities with the paradigmatic central spin model, but features much richer rotational dynamics that is sensitive to the molecule's environment, which can be initiated and probed with short laser pulses used to control molecular orientation and alignment. We present numerical simulations of the nuclear-spin-bath-induced rotational decoherence dynamics of KRb molecules, which exhibit remarkable sensitivity to an external magnetic field. Our results show that ultracold molecular gases provide a natural platform for the experimental realization of the CRM.

quant-ph↗
arXiv2024

Time-Reversal Symmetry-Protected Coherent Control of Ultracold Molecular Collisions

Coherent control of atomic and molecular scattering relies on the preparation of colliding particles in superpositions of internal states, establishing interfering pathways that can be used to tune the outcome of a scattering process. However, incoherent addition of different partial wave contributions to the integral cross sections (partial wave scrambling), commonly encountered in systems with complex collisional dynamics, poses a significant challenge, often limiting control. This work demonstrates that time-reversal symmetry can overcome these limitations by constraining the relative phases of S-matrix elements, thereby protecting coherent control against partial wave scrambling, even for collisions mediated by highly anisotropic interactions. Using the example of ultracold O$_2$-O$_2$ scattering, we show that coherent control is robust against short-range dynamical complexity. Furthermore, the time-reversal symmetry also protects the control against a distribution of collisional energy. These findings show that ultracold scattering into the final states that are time-reversal-invariant, such as the J = 0, M = 0 rotational state, can always be optimally controlled by using time-reversal-invariant initial superpositions. Beyond the ultracold regime, we observe significant differences in the controllability of crossed-molecular beam vs. trap experiments with the former being easier to control, emphasizing the cooperative role of time-reversal and permutation symmetries in maintaining control at any temperature. These results open new avenues for the coherent control of complex inelastic collisions and chemical reactions both in and outside of the ultracold regime.

physics.atom-ph↗
arXiv2024

Bringing multilevel quantum master equations into Lindblad form for complete positivity tests: Two approaches

While quantum master equations (QMEs) are the primary workhorse in quantum information science, quantum optics, spectroscopy, and quantum thermodynamics, bringing an arbitrary $N$-level QME into Lindbladian form and verifying complete positivity of the associated quantum dynamical map remain open challenges for $N\ge 3$. We explore and implement two independent methods to accomplish these tasks, which enable one to directly compute the Kossakowski matrix of an arbitrary Markovian QME from its Liouvillian. In the first method, due to Hall, Cresser, Li, and Andersson, the Kossakowski matrix elements are obtained by evaluating the action of the Liouvillian on the orthonormal SU($N$) basis matrices and then computing a sum of matrix-product traces. The second method, developed in this work, is based on the real $N$-level coherence vector and relies on the Moore-Penrose pseudo-inverse of a rectangular matrix composed of the structure constants of SU$(N)$. We show that both methods give identical results, and apply them to establish the complete positivity of the partial secular Bloch-Redfield QME for the $Λ$ and V-systems driven by incoherent light. We find that the eigenvalues of the Kossakowski matrix of these seemingly different three-level systems are identical, implying close similarities of their dissipative dynamics. By facilitating the expression of multilevel Markovian QMEs in Lindblad form, our results enable testing the QMEs for complete positivity without solving them, as well as restoring complete positivity by keeping only non-negative eigenvalues of the Kossakowski matrix.

quant-ph↗
arXiv2024

Highly spin-polarized molecules via collisional microwave pumping

We propose a general technique to produce cold spin-polarized molecules, in which rotationally excited states are first populated by coherent microwave excitation, and then allowed to spin-flip and relax via collisional quenching, which populates a single final spin state. We illustrate the high selectivity of the technique for $^{13}$C$^{16}$O molecules immersed in a cold buffer gas of helium atoms, achieving a high degree ($\geq$95\%) of nuclear spin polarization at 1 K.

physics.chem-ph↗
arXiv2024

Universality and threshold laws for collision lifetimes at ultralow temperatures

While collision lifetimes are a fundamental property of few-body scattering events, their behavior at ultralow temperatures is not completely understood. We derive a general expression for the Smith lifetime Q-matrix using multichannel quantum defect theory, which allows us to obtain the average time delay in the incident $s$-wave collision channel in the limit of zero collision energy $E$, $Q_{11}=A/\sqrt{E} + B$, where $A$ and $B$ are constants. We show that the time delay is dominated by elastic scattering, and contains an additional multichannel contribution independent of the two-body scattering length. We also obtain the expressions for the collision lifetime using the universal model of Idziaszek and Julienne [Phys. Rev. Lett. 104, 113202 (2010)]. The lifetime acquires an imaginary part in the presence of inelastic loss due to the lack of unitarity of the S-matrix, and shortens with increasing the short-range loss parameter $y$.

physics.chem-ph↗
arXiv2024

Magnetic Feshbach resonances in ultracold atom-molecule collisions

We report numerically exact quantum scattering calculations on magnetic Feshbach resonances in ultracold, strongly anisotropic atom-molecule [Rb($^2$S) + SrF($^2Σ^+$)] collisions based on state-of-the-art ab initio potential energy surfaces. We find broad resonances mediated by the intermolecular spin-exchange interaction, as well as narrow resonances due to the intramolecular spin-rotation interaction, which are unique to atom-molecule collisions. Remarkably, the density of resonances in atom-molecule collisions is not much higher than that in atomic collisions despite the presence of a dense manifold of molecular rotational states, which can be rationalized by analyzing the adiabatic states of the collision complex.

physics.atom-ph↗
arXiv2024

Multichannel quantum defect theory with a frame transformation for ultracold atom-molecule collisions in magnetic fields

We extend the powerful formalism of multichannel quantum defect theory combined with a frame transformation to ultracold atom-molecule collisions in magnetic fields. By solving the coupled-channel equations with hyperfine and Zeeman interactions omitted at short range, the extended theory enables a drastically simplified description of the intricate quantum dynamics of ultracold molecular collisions in terms of a small number of short-range parameters. We apply the formalism to ultracold Mg + NH collisions in a magnetic field, achieving a 10$^4$-fold reduction in computational effort.

physics.chem-ph↗
arXiv2024

Hyperfine-to-rotational energy transfer in ultracold atom-molecule collisions

Energy transfer between different mechanical degrees of freedom in atom-molecule collisions has been widely studied and largely understood. However, systems involving spins remain less explored, especially with a state-to-state precision. Here, we directly observed the energy transfer from atomic hyperfine to molecular rotation in the $^{87}$Rb ($|F_a,M_{F_a}\rangle = |2,2\rangle$) + $^{40}$K$^{87}$Rb (in the rovibronic ground state $N=0$) $\longrightarrow$ Rb ($ |1,1\rangle$) + KRb ($N=0,1,2$) exothermic collision. We probed the quantum states of the collision products using resonance-enhanced multi-photon ionization followed by time-of-flight mass spectrometry. We also carried out state-of-the-art quantum scattering calculations, which rigorously take into account the coupling between the spin and rotational degrees of freedom at short range, and assume that the KRb monomer can be treated as a rigid rotor moving on a single potential energy surface. The calculated product rotational state distribution deviates from the observations even after extensive tuning of the atom-molecule potential energy surface, suggesting that vibrational degrees of freedom and conical intersections play an important part in ultracold Rb + KRb collisions. Additionally, our ab initio calculations indicate that spin-rotation coupling is dramatically enhanced near a conical intersection, which is energetically accessible at short range. The observations confirm that spin is coupled to mechanical rotation at short range and establish a benchmark for future theoretical studies.

physics.atom-ph↗
arXiv2024

Hyperfine and Zeeman interactions in ultracold collisions of molecular hydrogen with atomic lithium

We present a rigorous quantum scattering study of the effects of hyperfine and Zeeman interactions on cold Li - H$_{2}$ collisions in the presence of an external magnetic field using a recent ab initio potential energy surface. We find that the low-field-seeking states of H$_{2}$ predominantly undergo elastic collisions: the ratio of elastic-to-inelastic collisions exceeds 100 for collision energies below 1.5 K. Furthermore, we demonstrate that most inelastic collisions conserve the space-fixed projection of the nuclear spin. We show that the anisotropic hyperfine interaction between the nuclear spin of H$_{2}$ and the electron spin of Li can have a significant effect on inelastic scattering in the ultracold regime, as it mediates two processes: the electron spin relaxation in lithium, and the nuclear spin - electron spin exchange. Given the predominance of elastic collisions and the propensity of inelastic collisions to retain H$_{2}$ in its low-field-seeking states, our results open up the possibility of sympathetic cooling of molecular hydrogen by atomic lithium, paving the way for future exploration of ultracold collisions and high-precision spectroscopy of H$_{2}$ molecules.

physics.chem-ph↗
arXiv2024

Interference is in the eye of the beholder: application to the coherent control of collisional processes

Interference is widely regarded as a foundational attribute of quantum mechanics. However, for a given experimental arrangement, interference can either contribute or not contribute to the outcome depending upon the basis in which it is measured. This observation is both foundational and particularly relevant to coherent control of molecular processes, an approach based upon quantum interference. Here we address this issue and its relevance to controlling molecular processes via the "coherent control scattering (CCS) matrix", a formalism that allows an analysis of modifications in interference structure resulting from a change of basis. This analysis reveals that the change in interference structure can be attributed to the non-commutativity of the transformation matrix with the CCS matrix, and the non-orthogonality of the transformation. Additionally, minimal interference is shown to be associated with the CCS eigenbasis, and that the Fourier transform of the eigenvectors of the CCS matrix provides the maximal interference and hence the best coherent control. The change of controllability through a change of basis is illustrated with an example of $^{85}$Rb+ $^{85}$Rb scattering. In addition, the developed formalism is applied to explain recent experimental results on He + D$_2$ inelastic scattering demonstrating the presence or absence of interference depending on the basis.

physics.atom-ph↗
arXiv2024

Magnetically tunable electric dipolar interactions of ultracold polar molecules in the quantum ergodic regime

By leveraging the hyperfine interaction between the rotational and nuclear spin degrees of freedom, we demonstrate extensive magnetic control over the electric dipole moments, electric dipolar interactions, and ac Stark shifts of ground-state alkali-dimer molecules such as KRb$(X^1Σ)$. The control is enabled by narrow avoided crossings and the highly ergodic character of molecular eigenstates at low magnetic fields, offering a general and robust way of continuously tuning the intermolecular electric dipolar interaction for applications in quantum simulation and sensing.

physics.atom-ph↗
arXiv2023

Ultracold molecular collisions in magnetic fields: Efficient incorporation of hyperfine structure in the total rotational angular momentum representation

The effects of hyperfine structure on ultracold molecular collisions in external fields are largely unexplored due to major computational challenges associated with rapidly proliferating hyperfine and rotational channels coupled by highly anisotropic intermolecular interactions. We explore a new basis set for incorporating the effects of hyperfine structure and external magnetic fields in quantum scattering calculations on ultracold molecular collisions. The basis is composed of direct products of the eigenfunctions of the total {\it rotational} angular momentum (TRAM) of the collision complex $J_r$ and the electron/nuclear spin basis functions of the collision partners. The separation of the rotational and spin degrees of freedom ensures rigorous conservation of $J_r$ even in the presence of external magnetic fields and isotropic hyperfine interactions. The resulting block-diagonal structure of the scattering Hamiltonian enables coupled-channel calculations on highly anisotropic atom-molecule and molecule-molecule collisions to be performed independently for each value of $J_r$, with an added advantage of eliminating the unphysical states present in the total angular momentum representation. We illustrate the efficiency of the TRAM basis by calculating state-to-state cross sections for ultracold He + YbF collisions in a magnetic field. The size of the TRAM basis required to reach numerical convergence is 8 times smaller than that of the uncoupled basis used previously, providing a computational gain of three orders of magnitude. The TRAM basis is therefore well suited for rigorous quantum scattering calculations on ultracold molecular collisions in the presence of hyperfine interactions and external magnetic fields.

physics.atom-ph↗
arXiv2023

Population Oscillations and Ubiquitous Coherences in multilevel quantum systems driven by incoherent radiation

We consider incoherent excitation of multilevel quantum systems, e.g. molecules with multiple vibronic states. We show that (1) the geometric constraints of the matter-field coupling operator guarantee that noise-induced coherences will be generated in all systems with four or more energy eigenstates and (2) noise-induced coherences can lead to population oscillations due to quantum interference via coherence transfer between pairs of states in the ground and excited manifolds. Our findings facilitate the experimental detection of noise-induced coherent dynamics in complex quantum systems.

quant-ph↗
arXiv2023

Sympathetic cooling and slowing of molecules with Rydberg atoms

We propose to sympathetically slow and cool polar molecules in a cold, low-density beam using laser-cooled Rydberg atoms. The elastic collision cross sections between molecules and Rydberg atoms are large enough to efficiently thermalize the molecules even in a low density environment. Molecules traveling at 100 m/s can be stopped in under 30 collisions with little inelastic loss. Our method does not require photon scattering from the molecules and can be generically applied to complex species for applications in precision measurement, quantum information science, and controlled chemistry.

physics.atom-ph↗