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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.

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 $\Lambda$ 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.

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 $y$.

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.

We report numerically exact quantum scattering calculations on magnetic Feshbach resonances in ultracold, strongly anisotropic atom-molecule [Rb($^2$S) + SrF($^2\Sigma^+$)] 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.

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.

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.

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$(X^1\Sigma)$. 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.

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., Comment: The following article has been accepted by The Journal of Chemical Physics. After it is published, it will be found at https://pubs.aip.org/aip/jcp

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.

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.

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., Comment: 8 pages, 3 figures

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.

We propose a hybrid quantum-classical algorithm for solving the time-independent Schr\"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix by inverting the Hamiltonian matrix expressed in the basis of square-integrable functions. The computational bottleneck of the classical algorithm -- symmetric matrix inversion -- is addressed here using the variational quantum linear solver (VQLS), a recently developed noisy intermediate-scale quantum (NISQ) algorithm for solving systems of linear equations. We apply our algorithm to single and multichannel quantum scattering problems, obtaining accurate vibrational relaxation probabilities in collinear atom-molecule collisions. We also show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules. Our results demonstrate that it is possible to calculate scattering cross sections and rates for complex molecular collisions on NISQ quantum processors, opening up the possibility of scalable digital quantum computation of gas-phase bimolecular collisions and reactions of relevance to astrochemistry and ultracold chemistry., Comment: 8 pages,6 figures

Ultracold chemical reactions of weakly bound triplet-state alkali-metal dimer molecules have recently attracted much experimental interest. We perform rigorous quantum scattering calculations with a new $ab\, initio$ potential energy surface to explore the chemical reaction of spin-polarized NaLi($a^3\Sigma^+$) and Li($^2$S) to form Li$_2$($a^3\Sigma_u^+$) and Na($^2$S). The reaction is exothermic, and proceeds readily at ultralow temperatures. Significantly, we observe strong sensitivity of the total reaction rate to small variations of the three-body part of the Li$_2$Na interaction at short range, which we attribute to a relatively small number of open Li$_2$($a^3\Sigma_u^+$) product channels populated in the reaction. This provides the first signature of highly non-universal dynamics seen in rigorous quantum reactive scattering calculations of an ultracold exothermic insertion reaction involving a polar alkali-dimer molecule, opening up the possibility of probing microscopic interactions in atom+molecule collision complexes via ultracold reactive scattering experiments., Comment: 26 pages, 5 figures (Supporting information: 12 pages, 5 figures)

We consider the coherent control of ultracold molecule-molecule scattering, impacted by a dense set of rovibrational resonances. To characterize the resonance spectrum, a rudimentary model based on multichannel quantum defect theory has been used to study the control of the scattering cross section and the reaction rate. Complete control around resonance energies is shown to be possible, but thermal averaging over a large number of resonances significantly reduces the extent of control of reaction rates due to the random distribution of optimal control parameters between resonances. We show that measuring the extent of coherent control could be used to extract meaningful information about the relative contribution of direct scattering versus collision complex formation, as well as about the statistical regime.

We explore the quantum dynamics of nuclear spin relaxation in cold collisions of $^1\Sigma^+$ molecules with structureless atoms in an external magnetic field. To this end, we develop a rigorous coupled-channel methodology, which accounts for rotational and nuclear spin degrees of freedom of $^1\Sigma^+$ molecules, their interaction with an external magnetic field, as well as for anisotropic atom-molecule interactions. We apply the methodology to study collisional relaxation of the nuclear spin sublevels of $^{13}$CO molecules immersed in a cold buffer gas of $^4$He atoms. We find that nuclear spin relaxation in the ground rotational manifold of CO occurs extremely slowly due to the absence of direct couplings between the nuclear spin sublevels. The rates of collisional transitions between the $N=1$ nuclear spin states of CO are generally much higher due to the direct nuclear spin-rotation coupling between the states. These transitions obey selection rules, which depend on the values of space-fixed projections of rotational and nuclear spin angular momenta for the initial and final molecular states. For some initial states, we also observe a strong magnetic field dependence, which can be understood using the first Born approximation. We use our calculated nuclear spin relaxation rates to investigate the thermalization of a single nuclear spin state of CO$(N=0)$ immersed in a cold buffer gas of He. The calculated nuclear spin relaxation times ($T_1\simeq 0.5$ s at $T=1$ K) display a steep temperature dependence decreasing rapidly at elevated temperatures due to the increased population of rotationally excited states, which undergo nuclear spin relaxation at a much faster rate. Thus, long relaxation times of $N=0$ nuclear spin states in cold collisions with buffer gas atoms can only be maintained at sufficiently low temperatures ($kT\ll 2B_e$), where $B_e$ is the rotational constant., Comment: 41 pages, 12 figures

We propose a general protocol for on-demand generation of robust entangled states of nuclear and/or electron spins of ultracold $^1\Sigma$ and $^2\Sigma$ polar molecules using electric dipolar interactions. By encoding a spin-1/2 degree of freedom in a combined set of spin and rotational molecular levels, we theoretically demonstrate the emergence of effective spin-spin interactions of the Ising and XXZ forms, enabled by efficient magnetic control over electric dipolar interactions. We show how to use these interactions to create long-lived cluster and squeezed spin states.

We show that the integral cross sections for state-to-state quantum scattering of cold molecules in a magnetic field can be efficiently computed using the total angular momentum representation despite the presence of unphysical Zeeman states in the eigenspectrum of the asymptotic Hamiltonian. We demonstrate that the unphysical states arise due to the incompleteness of the space-fixed total angular momentum basis caused by using a fixed cutoff value $J_\text{max}$ for the total angular momentum of the collision complex $J$. As a result, certain orbital angular momentum ($l$) basis states lack the full range of $J$ values required by the angular momentum addition rules, resulting in the appearance of unphysical states. We find that by augmenting the basis with a full range of $J$-states for every $l$, it is possible to completely eliminate the unphysical states from quantum scattering calculations on molecular collisions in external fields. To illustrate the procedure, we use the augmented basis sets to calculate the state-to-state cross sections for rotational and spin relaxation in cold collisions of $^{40}$CaH$(X^2\Sigma^+,v=0,N=1, M_N=1, M_S=1/2)$ molecules with $^4$He atoms in a magnetic field. We find excellent agreement with benchmark calculations, validating our proposed procedure. We find that $N$-conserving spin relaxation to the lowest-energy Zeeman state of the $N=1$ manifold, $|11\frac{1}{2}\rangle\to |1-1-\frac{1}{2}\rangle$ is nearly completely suppressed due to the lack of spin-rotation coupling between the fully spin-stretched Zeeman states. Our results demonstrate the possibility of rigorous, computationally efficient, and unphysical state-free quantum scattering calculations on cold molecular collisions in an external magnetic field.

We present a theoretical study of quantum coherent dynamics of a three-level $\Lambda$ system driven by a thermal environment (such as blackbody radiation), which serves as an essential building block of photosynthetic light-harvesting models and quantum heat engines. By solving the nonsecular Bloch-Redfield master equations, we obtain analytical results for the ground-state population and coherence dynamics and classify the dynamical regimes of the incoherently driven $\Lambda$-system as underdamped and overdamped depending on whether the ratio $\Delta/[r f(p)]$ is greater or less than one, where $\Delta$ is the ground-state energy splitting, $r$ is the incoherent pumping rate, and $f(p)$ is a function of the transition dipole alignment parameter $p$. In the underdamped regime, we observe long-lived coherent dynamics that lasts for $\tau_c\simeq 1/r$, even though the initial state of the $\Lambda$-system contains no coherences in the energy basis. In the overdamped regime for $p = 1$, we observe the emergence of coherent quasi-steady states with the lifetime $\tau_{c} = 1.34 (r/\Delta^{2})$, which have low von Neumann entropy compared to the conventional thermal states. We propose an experimental scenario for observing noise-induced coherent dynamics in metastable He$^*$ atoms driven by x-polarized incoherent light. Our results suggest that thermal excitations can generate experimentally observable long-lived quantum coherent dynamics in the ground-state subspace of atomic and molecular $\Lambda$ systems in the absence of coherent driving.

We show that the cross sections for a broad range of resonant {\it inelastic} processes accompanied by excitation exchange (such as spin-exchange, F\"orster resonant, or angular momentum exchange) exhibit an unconventional near-threshold scaling $E^{\Delta m_{12}}$, where $E$ is the collision energy, $\Delta m_{12}=m_1'+m_2'-m_1-m_2$, and $m_i$ and $m_i'$ are the initial and final angular momentum projections of the colliding species ($i=1,\,2$). In particular, the inelastic cross sections for $\Delta m_{12}=0$ transitions display an unconventional $E^0$ scaling similar to that of elastic cross sections, and their rates vanish as $T^{\Delta m_{12}+1/2}$. For collisions dominated by even partial waves (such as those of identical bosons in the same internal state) the scaling is modified to $\sigma_\text{inel}\propto E^{\Delta m_{12} +1} $ if $\Delta m_{12}$ is odd. We present accurate quantum scattering calculations that illustrate these modified threshold laws for resonant spin exchange in ultracold Rb+Rb and O$_2$+O$_2$ collisions. Our results illustrate that the threshold scaling of collision cross sections is determined only by the energetics of the underlying process (resonant vs. exothermic) rather than by whether the internal states of colliding particles is changed in the collision.

We use numerically exact quantum dynamics calculations to demonstrate universal stereoselectivity of cold collisions of $^2\Pi$ molecules with $^1$S-state atoms in an external electric field. We show that cold collisions of OH molecules in their low-field-seeking $f$ states, whose dipole moments are oriented against the field direction, are much more likely to lead to inelastic scattering than those of molecules oriented along the field direction, causing nearly perfect steric asymmetry in the inelastic collision cross sections. The universal nature of this effect is due to the threshold suppression of inelastic scattering between the degenerate $\pm M$ Stark sublevels of the high-field-seeking $e$-state, where $M$ is the projection of the total angular momentum of the molecule on the field axis. Above the $\Lambda$-doublet threshold, the stereodynamics of inelastic atom-molecule collisions can be tuned via electric-field-induced resonances, which enable effective control of Ne + OH scattering over the range of collision energies achievable in current merged beam experiments.

We demonstrate that it is possible to efficiently control ultracold chemical reactions of alkali-metal atoms colliding with open-shell alkali-metal dimers in their metastable triplet states by choosing the internal hyperfine and rovibrational states of the reactants as well as by inducing magnetic Feshbach resonances with an external magnetic field. We base these conclusions on coupled-channel statistical calculations that include the effects of hyperfine contact and magnetic-field-induced Zeeman interactions on ultracold chemical reactions of hyperfine-resolved ground-state Na and the triplet NaLi(a$^3\Sigma^+$) producing singlet Na$_2$($^1\Sigma^+_g$) and a Li atom. We find that the reaction rates are sensitive to the initial hyperfine states of the reactants. The chemical reaction of fully spin-polarized, high-spin states of rotationless NaLi(a$^3\Sigma^+, v = 0, N = 0$) molecules with fully spin-polarized Na is suppressed by a factor of 10-100 compared to that of unpolarized reactants. We interpret these findings within the adiabatic state model, which treats the reaction as a sequence of nonadiabatic transitions between the initial non-reactive high-spin state and the final low-spin states of the reaction complex. In addition, we show that magnetic Feshbach resonances can similarly change reaction rate coefficients by several orders of magnitude. Some of these resonances are due to resonant trimer bound states dissociating to the $N=2$ rotational state of NaLi(a$^3\Sigma^+, v = 0$) and would thus exist in systems without hyperfine interactions., Comment: 6 pages, 3 figures

We explore coherent control of Penning and associative ionization in cold collisions of metastable He$^*({2}^3\text{S})$ atoms via the quantum interference between different states of the He$_2^*$ collision complex. By tuning the preparation coefficients of the initial atomic spin states, we can benefit from the quantum interference between molecular channels to maximize or minimize the cross sections for Penning and associative ionization. In particular, we find that we can enhance the ionization ratio by 30% in the cold regime. This work is significant for the coherent control of chemical reactions in the cold and ultracold regime., Comment: 14 pages, 6 figures

We show that quantum interference-based coherent control is a highly efficient tool for tuning ultracold molecular collision dynamics, and is free from the limitations of commonly used methods that rely on external electromagnetic fields. By varying {the relative populations and} phases of an initial coherent superpositions of degenerate molecular states, we demonstrate complete coherent control over integral scattering cross sections in the ultracold $s$-wave regime of both the initial and final collision channels. The proposed control methodology is applied to ultracold O$_2$~+~O$_2$ collisions, showing extensive control over $s$-wave spin-exchange cross sections and product branching ratios over many orders of magnitude.

Rigorous quantum scattering calculations on ultracold molecular collisions in external fields present an outstanding computational problem due to strongly anisotropic atom-molecule interactions that depend on the relative orientation of the collision partners, as well as on their vibrational degrees of freedom. Here, we present the first numerically exact three-dimensional quantum scattering calculations on strongly anisotropic atom-molecule (Li+CaH) collisions in an external magnetic field based on the parity-adapted total angular momentum representation and a new three-dimensional potential energy surface (PES) for the triplet Li-CaH collision complex using the unrestricted coupled cluster method with single, double and perturbative triple excitations [UCCSD(T)] and a large quadruple-zeta type basis set. We find that while the full three-dimensional treatment is necessary for the accurate description of Li ($M_S=1/2$)+CaH ($v=0,N=0,M_S=1/2$) collisions as a function of magnetic field, the magnetic resonance density and statistical properties of spin-polarized atom-molecule collisions are not strongly affected by vibrational degrees of freedom, justifying the rigid-rotor approximation used in previous calculations. We observe rapid, field-insensitive vibrational quenching in ultracold Li ($M_S=1/2$)+CaH ($v=1,N=0, M_S=1/2$) collisions, leading to efficient collisional cooling of CaH vibrations., Comment: 12 pages, 10 figures, 64 references

We explore the properties of steady-state Fano coherences generated in a three-level V-system continuously pumped by polarized incoherent light in the absence of coherent driving. The ratio of the stationary coherences to excited-state populations $\mathcal{C} = (1+\frac{\Delta^2}{\gamma(r+\gamma)} )^{-1}$ is maximized when the excited-state splitting $\Delta$ is small compared to either the spontaneous decay rate $\gamma$ or the incoherent pumping rate $r$. We demonstrate that an intriguing regime exists where the $\mathcal{C}$ ratio displays a maximum as a function of the dephasing rate $\gamma_d$. We attribute the surprising dephasing-induced enhancement of stationary Fano coherences to the environmental suppression of destructive interference of individual incoherent excitations generated at different times. We identify the imaginary Fano coherence with the non-equilibrium flux across a pair of qubits coupled to two independent thermal baths, unraveling a direct connection between the seemingly unrelated phenomena of incoherent driving of multilevel quantum systems and non-equilibrium quantum transport in qubit networks. The real part of the steady-state Fano coherence is found to be proportional to the deviation of excited-state populations from their values in thermodynamic equilibrium, making it possible to observe signatures of steady-state Fano coherences in excited-state populations. We put forward an experimental proposal for observing steady-state Fano coherences by detecting the total fluorescence signal emitted by Calcium atoms excited by polarized vs. isotropic incoherent light. Our analysis paves the way toward further theoretical and experimental studies of non-equilibrium coherent steady states in thermally driven atomic and molecular systems, and for the exploration of their potential role in biological processes., Comment: Abstract shortened to fit the 1,920 char limit (see draft for the complete version)

We present a joint experimental and theoretical study of spin coherence properties of 39K, 85Rb, 87Rb, and 133Cs atoms trapped in a solid parahydrogen matrix. We use optical pumping to prepare the spin states of the implanted atoms and circular dichroism to measure their spin states. Optical pumping signals show order-of-magnitude differences depending on both matrix growth conditions and atomic species. We measure the ensemble transverse relaxation times (T2*) of the spin states of the alkali-metal atoms. Different alkali species exhibit dramatically different T2* times, ranging from sub-microsecond coherence times for high mF states of 87Rb, to ~100 microseconds for 39K. These are the longest ensemble T2* times reported for an electron spin system at high densities (n > 10^16 cm^-3). To interpret these observations, we develop a theory of inhomogenous broadening of hyperfine transitions of ^2S atoms in weakly-interacting solid matrices. Our calculated ensemble transverse relaxation times agree well with experiment, and suggest ways to longer coherence times in future work.

While attaining external field control of bimolecular chemical reactions has long been a coveted goal of physics and chemistry, the role of hyperfine interactions and dc magnetic fields in achieving such control has remained elusive. We develop an extended coupled-channel statistical theory of barrierless atom-diatom chemical reactions, and apply it to elucidate the effects of magnetic fields and hyperfine interactions on the ultracold chemical reaction Li($^2\text{S}_{1/2}$) + CaH($^2\Sigma^+$) $\to$ LiH($^1\Sigma^+$) + Ca($^1\text{S}_{0}$) on a newly developed set of ab initio potential energy surfaces. We observe large field effects on the reaction cross sections, opening up the possibility of controlling ultracold barrierless chemical reactions by tuning selected hyperfine states of the reactants with an external magnetic field., Comment: 4.2 pages plus Supplemental Material

We measure the transverse relaxation of the spin state of an ensemble of ground-state rubidium atoms trapped in solid parahydrogen at cryogenic temperatures. We find the spin dephasing time of the ensemble (T$_2^*$) is limited by inhomogeneous broadening. We determine that this broadening is dominated by electrostatic interactions with the host matrix, and can be reduced by preparing nonclassical spin superposition states. Driving these superposition states gives significantly narrower electron paramagnetic resonance lines and the longest reported electron spin $T_2^*$ in any solid-phase system other than solid helium.

Currently, quantum scattering calculations cannot be used for quantitative predictions of molecular scattering observables at ultralow temperatures. This is a result of two problems: the extreme sensitivity of the scattering observables to details of potential energy surfaces (PES) for interactions between the collision partners, and the exceedingly large size of molecular basis sets required for the numerically exact integration of the Schr\"{o}dinger equation in the presence of external fields. Here, we suggest a new statistical approach to address both of the above problems. We show that ensembles of scattering calculations with different PESs are characterized by cumulative probability distributions, which are insensitive to the size of the molecular basis sets and can, therefore, be obtained from calculations with restricted basis sets. This opens the possibility of making predictions of experimentally relevant observables for a wide variety of molecular systems, currently considered out of reach of quantum dynamics theory. We demonstrate the method by computing the success probability of sympathetic cooling of CaH and SrOH molecules by Li atoms and SrF molecules by Rb atoms., Comment: 5 pages, 4 figures, 35 references

Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta $J$ of the collision complex. We show that by restricting the number of total angular momentum basis states to include only the states with helicities $K\le K_\text{max}$ it is possible to obtain accurate elastic and inelastic cross sections for He+CaH, Li+CaH and Li+SrOH collisions at a small fraction of the computational cost of the full coupled-channel calculations (where $K$ is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field. For dipolar-mediated spin relaxation in ultracold Li+CaH and Li+SrOH collisions, we find that a minimal helicity basis set ($K_\text{max}=0$) gives quantitatively accurate results at ultralow collision energies, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in Li+CaH and Li+SrOH inelastic cross sections in the few partial wave-regime ($K_\text{max}=3$) as well as indirect spin relaxation in He+CaH collisions ($K_\text{max}=1$). Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different $K$ and the couplings between the rotational states of the same $K$ induced by the anisotropy of the interaction potential.

We present a joint experimental and theoretical study of spin dynamics of a single $^{88}$Sr$^+$ ion colliding with an ultracold cloud of Rb atoms in various hyperfine states. While spin-exchange between the two species occurs after 9.1(6) Langevin collisions on average, spin-relaxation of the Sr$^+$ ion Zeeman qubit occurs after 48(7) Langevin collisions which is significantly slower than in previously studied systems due to a small second-order spin-orbit coupling. Furthermore, a reduction of the endothermic spin-exchange rate was observed as the magnetic field was increased. Interestingly, we found that, while the phases acquired when colliding on the spin singlet and triplet potentials vary largely between different partial waves, the singlet-triplet phase difference, which determines the spin-exchange cross-section, remains locked to a single value over a wide range of partial-waves which leads to quantum interference effects., Comment: 5 pages, 5 figures and Supplemental Material

We explore the suitability of ultracold collisions between spin-polarized SrF($^2\Sigma^+$) molecules and Rb($^2$S) atoms as elementary steps for the sympathetic cooling of SrF($^2\Sigma^+$) molecules in a magnetic trap. To this end, we carry out quantum mechanical scattering calculations on ultracold Rb+SrF collisions in a magnetic field based on an accurate potential energy surface for the triplet electronic state of Rb-SrF developed ab initio using a spin-restricted coupler cluster method with single, double and noniterative triple excitations [RCCSD(T)]. The Rb-SrF interaction has a global minimum with a well depth of 3444 cm$^{-1}$ in a bent geometry and a shallow local minimum in the linear geometry. Despite such a strong and anisotropic interaction, we find that converged close-coupling scattering calculations on Rb+SrF collisions in a magnetic field are still possible using rotational basis sets including up to 125 closed rotational channels in the total angular momentum representation. Our calculations show that electronic spin relaxation in fully spin-polarized Rb-SrF collisions occurs much more slowly than elastic scattering over a wide range of magnetic fields (1-1000 G) and collision energies ($10^{-5}-10^{-3}$ K) suggesting good prospects of sympathetic cooling of laser-cooled SrF($^2\Sigma^+$) molecules with spin-polarized Rb($^2$S) atoms in a magnetic trap. We show that incoming $p$-wave scattering plays a significant role in ultracold collisions due to the large reduced mass of the Rb-SrF collision pair. The calculated magnetic field dependence of the inelastic cross sections at 1.4 $\mu$K displays a rich resonance structure including a low-field $p$-wave resonance, which suggests that external magnetic fields can be used to enhance the efficiency of sympathetic cooling in heavy atom-molecule mixtures.

We explore the coherent dynamics of a three-level V-system interacting with a thermal bath in the regime where thermal excitation occurs much faster than spontaneous decay. We present analytic solutions of the Bloch-Redfield quantum master equations, which show that strong incoherent pumping can generate long-lived quantum coherences among the excited states of the V-system in the overdamped regime defined by the condition $\Delta/(\bar{n}\gamma)

We use accurate ab initio and quantum scattering calculations to explore the prospects for sympathetic cooling of the heavy molecular radical SrOH($^2\Sigma$) by ultracold Li atoms in a magnetic trap. A two-dimensional potential energy surface (PES) for the triplet electronic state of Li-SrOH is calculated ab initio using the partially spin-restricted coupled cluster method with single, double and perturbative triple excitations and a large correlation-consistent basis set. The highly anisotropic PES has a deep global minimum in the skewed Li-HOSr geometry with $D_e=4932$ cm$^{-1}$ and saddle points in collinear configurations. Our quantum scattering calculations predict low spin relaxation rates in fully spin-polarized Li+SrOH collisions with the ratios of elastic to inelastic collision rates well in excess of 100 over a wide range of magnetic fields (1-1000 G) and collision energies (10$^{-5}-0.1$~K) suggesting favorable prospects for sympathetic cooling of SrOH molecules with spin-polarized Li atoms in a magnetic trap. We find that spin relaxation in Li+SrOH collisions occurs via a direct mechanism mediated by the magnetic dipole-dipole interaction between the electron spins of Li and SrOH, and that the indirect (spin-rotation) mechanism is strongly suppressed. The upper limit to the Li+SrOH reaction rate coefficient calculated for the singlet PES using adiabatic capture theory is found to decrease from $4\times 10^{-10}$~cm$^3$/s to a limiting value of $3.5\times 10^{-10}$ cm$^3$/s with decreasing temperature from 0.1 K to 1 $\mu$K.

We have used laser ablation and helium buffer-gas cooling to produce the titanium-helium van der Waals molecule at cryogenic temperatures. The molecules were detected through laser-induced fluorescence spectroscopy. Ground-state Ti-He binding energies were determined for the ground and first rotationally excited states from studying equilibrium thermodynamic properties, and found to agree well with theoretical calculations based on newly calculated ab initio Ti-He interaction potentials, opening up novel possibilities for studying the formation, dynamics, and non-universal chemistry of van der Waals clusters at low temperatures.

Light induced processes in nature occur by irradiation with slowly turned-on incoherent light. The general case of time-dependent incoherent excitation is solved here analytically for V-type systems using a newly developed master equation method. Clear evidence emerges for the disappearance of radiatively induced coherence as turn-on times of the radiation exceed characteristic system times. The latter is the case, in nature, for all relevant dynamical time scales for other than nearly degenerate energy levels. We estimate that, in the absence of non-radiative relaxation and decoherence, turn-on times slower than 1 ms (still short by natural standards) induce Fano coherences between energy eigenstates that are separated by less than 0.9 cm$^{-1}$.

We present accurate ab initio and quantum scattering calculations on a prototypical hybrid ion-atom system Yb$^+$-Rb, recently suggested as a promising candidate for the experimental study of open quantum systems, quantum information processing, and quantum simulation. We identify the second-oder spin-orbit (SO) interaction as the dominant source of hyperfine relaxation and decoherence in cold Yb$^+$-Rb collisions. Our results are in good agreement with recent experimental observations [L. Ratschbacher et al., Phys. Rev. Lett. 110, 160402 (2013)] of hyperfine relaxation rates of trapped Yb$^+$ immersed in an ultracold Rb gas. The calculated rates are 4 times smaller than predicted by the Langevin capture theory and display a weak $T^{-0.3}$ temperature dependence, indicating significant deviations from statistical behavior. Our analysis underscores the deleterious nature of the SO interaction and implies that light ion-atom combinations such as Yb$^+$-Li should be used to minimize hyperfine relaxation and decoherence of trapped ions in ultracold atomic gases., Comment: 5 pages, 3 figures

We present closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter $\zeta=\frac{1}{2}(\gamma_1+\gamma_2)/\Delta_p$, where $\gamma_i$ are the radiative decay rates of the excited levels $i=1,2$, and $\Delta_p=\sqrt{\Delta^2 + (1-p^2)\gamma_1\gamma_2}$ depends on the excited-state level splitting $\Delta>0$ and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit ($\zeta\gg1$), approach a long-lived quasi-steady state in the overdamped limit ($\zeta\ll 1$), and display an intermediate behavior at critical damping ($\zeta= 1$). The sudden incoherent turn-on generates a mixture of excited eigenstates $|e_1\rangle$ and $|e_2\rangle$ and their in-phase coherent superposition $|\phi_+\rangle = \frac{1}{\sqrt{2\bar{r}}}(\sqrt{r_1} |e_1\rangle + \sqrt{r_2}|e_2\rangle)$, which is remarkably long-lived in the overdamped limit (where $r_1$ and $r_2$ are the incoherent pumping rates). Formation of this coherent superposition {\it enhances} the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, we identify additional asymptotic quasistationary coherences, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when $r_1=r_2$ and the transition dipole moments are fully aligned., Comment: revised version

We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The modified Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis, and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state, and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.

We use quantum and classical adiabatic capture theories to study the chemical reaction Li + CaH -> LiH + Ca. Using a recently developed ab initio potential energy surface, which provides an accurate representation of long-range interactions in the entrance reaction channel, we calculate the adiabatic channel potentials by diagonalizing the atom-molecule Hamiltonian as a function of the atom-molecule separation. The resulting adiabatic channel potentials are used to calculate both the classical and quantum capture probabilities as a function of collision energy, as well as the temperature dependencies of the partial and total reaction rates. The calculated reaction rate agrees well with the measured value at 1 K [V. Singh et al., Phys. Rev. Lett. 108, 203201 (2012)], suggesting that the title reaction proceeds without an activation barrier. The calculated classical adiabatic capture rate agrees well with the quantum result in the multiple partial wave regime of relevance to the experiment. Significant differences are found only in the ultracold limit (T < 1 mK), demonstrating that adiabatic capture theories can predict the reaction rates with nearly quantitative accuracy in the multiple partial wave regime.

We develop a theoretical method for solving the quantum mechanical reactive scattering problem in the presence of external fields based on a hyperspherical coordinate description of the reaction complex combined with the total angular momentum representation for collisions in external fields. The method allows us to obtain converged results for the chemical reaction LiF + H -> Li + HF in an electric field. Our calculations demonstrate that, by inducing couplings between states of different total angular momenta, electric fields with magnitudes <150 kV/cm give rise to resonant scattering and a significant modification of the total reaction probabilities, product state distributions and the branching ratios for reactive vs inelastic scattering., Comment: 11 pages, 8 figures, including the Supplemental Material

We present a theoretical study of noise-induced quantum coherences in a model three-level V-type system interacting with incoherent radiation, an important prototype for a wide range of physical systems ranging from trapped ions to biomolecules and quantum dots. By solving the quantum optical equations of motion for the V-type system, we obtain analytical expressions for the noise-induced coherences and show that they exhibit an oscillating behavior in the limit of large excited level spacing $\Delta$ ($\Delta /\gamma \gg 1$, where $\gamma$ is the radiative decay rate). Most remarkably, we find that in the opposite limit of small level spacing $\Delta/\gamma \ll 1$, appropriate for large molecules, (a) the coherences can survive for an arbitrarily long time $\tau=(2/\gamma) (\Delta/\gamma)^{-2}$ before eventually decaying to zero, and (b) coherences at short times can be substantial. We further show that the long-lived coherences can be robust against environmental relaxation and decoherence, and discuss implications to the design of quantum heat engines and incoherent light excitation of biological systems.

Rydberg atoms excited by cold blackbody radiation are shown to display long-lived quantum coherences on timescales of tens of picoseconds. By solving non-Markovian equations of motion with no free parameters we obtain the time evolution of the density matrix, and demonstrate that the blackbody-induced temporal coherences manifest as slowly decaying (100 ps) quantum beats in time-resolved fluorescence. An analytic model shows the dependence of the coherent dynamics on the energy splitting between atomic eigenstates, transition dipole moments, and coherence time of the radiation. Experimental detection of the fluorescence signal from a trapped ensemble of $10^8$ Rydberg atom is discussed, but shown to be technically challenging at present, requiring CMB amplification somewhat beyond current practice., Comment: 9 pages, 6 figures

We show that weakly bound He-containing van der Waals molecules can be produced and magnetically trapped in buffer-gas cooling experiments, and provide a general model for the formation and dynamics of these molecules. Our analysis shows that, at typical experimental parameters, thermodynamics favors the formation of van der Waals complexes composed of a helium atom bound to most open-shell atoms and molecules, and that complex formation occurs quickly enough to ensure chemical equilibrium. For molecular pairs composed of a He atom and an S-state atom, the molecular spin is stable during formation, dissociation, and collisions, and thus these molecules can be magnetically trapped. Collisional spin relaxations are too slow to affect trap lifetimes. However, helium-3-containing complexes can change spin due to adiabatic crossings between trapped and untrapped Zeeman states, mediated by the anisotropic hyperfine interaction, causing trap loss. We provide a detailed model for Ag3He molecules, using ab initio calculation of Ag-He interaction potentials and spin interactions, quantum scattering theory, and direct Monte Carlo simulations to describe formation and spin relaxation in this system. The calculated rate of spin-change agrees quantitatively with experimental observations, providing indirect evidence for molecular formation in buffer-gas-cooled magnetic traps., Comment: 20 pages, 13 figures