Molecular Eigenstates Research Articles

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^{1}Σ^{+}). 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, quantum sensing, and dipolar spinor physics.

Tracing the Background‐Suppressed Vibrational Decay Time of a Molecular Monolayer with Time‐Resolved Surface‐Enhanced Broadband Coherent Anti‐Stokes Raman Scattering

AbstractThe sensitivity of molecular spectroscopy based on surface‐enhanced coherent anti‐Stokes Raman scattering (SECARS) is limited by the spectrally overlapping background from nonresonant four‐wave mixing (FWM). While the SECARS signal is mediated by the molecular vibrational eigenstates and exhibits long lifetime (a few picoseconds), the FWM background stems from the instantaneous electronic polarization and decays rapidly with the vanishment of excitation. Therefore, CARS and FWM can be separated by time‐resolved CARS (trCARS) using ultrashort pulsed lasers. The broad spectral bandwidth also enables broadband CARS (BCARS) for simultaneous identification of multiple vibrational signatures. This work combines trCARS and BCARS with an optimized plasmonic system to demonstrate time‐resolved surface‐enhanced BCARS) and show its capability in obtaining background‐suppressed broadband vibrational spectra from a monolayer of 4‐Aminothiophenol (4‐ATP) molecules self‐assembled on a gold grating. The vibrational dephasing time of the ring‐breathing mode for the 4‐ATP monolayer on the gold grating (≈1.00 ± 0.17 ps) is significantly shortened compared to that for 4‐ATP powder on a glass substrate (2.10 ± 0.05 ps). This work presents an effective method to suppress FWM background and investigate the vibrational dynamics of molecules in the vicinity of plasmonic nanostructures.

Geometric quantum adiabatic methods for quantum chemistry

Quantum algorithms have been successfully applied in quantum chemistry to obtain the ground-state energy of small molecules. Although accurate near the equilibrium geometry, the results can become unreliable when the chemical bonds are broken at large distances. For any adiabatic approach, this is usually caused by serious issues, such as energy gap closing or level crossing along the adiabatic evolution path. In this work, we propose a quantum algorithm based on adiabatic evolution to obtain molecular eigenstates and eigenenergies in quantum chemistry, which exploits a smooth geometric deformation by continuously varying bond lengths and bond angles. We demonstrate its utility in several examples on a noiseless quantum simulator, including ${\mathrm{H}}_{2}\mathrm{O}, {\mathrm{CH}}_{2}$, and a chemical reaction of ${\mathrm{H}}_{2}+{\mathrm{D}}_{2}\ensuremath{\rightarrow}$ 2HD, by uniformly stretching chemical bonds. We find that this new algorithm solves the problems related to energy gap closing and level crossing along the adiabatic evolution path at large atomic distances. The new method performs more stably and achieves better accuracy than our previous adiabatic method [Yu and Wei, Phys. Rev. Research 3, 013104 (2021)]. Furthermore, our fidelity analysis demonstrates that even with finite bond length changes, our algorithm still achieves high fidelity for the ground state.

Seemingly asymmetric atom-localized electronic densities following laser-dissociation of homonuclear diatomics.

Recent experiments on laser-dissociation of aligned homonuclear diatomic molecules show an asymmetric forward-backward (spatial) electron-localization along the laser polarization axis. Most theoretical models attribute this asymmetry to interference effects between gerade and ungerade vibronic states. Presumably due to alignment, these models neglect molecular rotations and hence infer an asymmetric (post-dissociation) charge distribution over the two identical nuclei. In this paper, we question the equivalence that is made between spatial electron-localization, observed in experiments, and atomic electron-localization, alluded by these theoretical models. We show that (seeming) agreement between these models and experiments is due to an unfortunate omission of nuclear permutation symmetry, i.e., quantum statistics. Enforcement of the latter requires mandatory inclusion of the molecular rotational degree of freedom, even for perfectly aligned molecules. Unlike previous interpretations, we ascribe spatial electron-localization to the laser creation of a rovibronic wavepacket that involves field-free molecular eigenstates with opposite space-inversion symmetry i.e., even and odd parity. Space-inversion symmetry breaking would then lead to an asymmetric distribution of the (space-fixed) electronic density over the forward and backward hemisphere. However, owing to the simultaneous coexistence of two indistinguishable molecular orientational isomers, our analytical and computational results show that the post-dissociation electronic density along a specified space-fixed axis is equally shared between the two identical nuclei-a result that is in perfect accordance with the principle of the indistinguishability of identical particles.

Fluorine intercalated graphene: Formation of a two-dimensional spin lattice through pseudoatomization

A suspended layer made up of ferromagnetically ordered spins could be created between two mono/multilayer graphene through intercalation. Stability and electronic structure studies show that, when fluorine molecules are intercalated between two mono/multilayer graphene, their bonds get stretched enough ($\sim$ 1.9$-$2.0 {\AA}) to weaken their molecular singlet eigenstate. Geometrically, these stretched molecules form a pseudoatomized fluorine layer by maintaining a van der Waals separation of $\sim$ 2.6 {\AA} from the adjacent carbon layers. As there is a significant charge transfer from the adjacent carbon layers to the fluorine layers, a mixture of triplet and doublet states stabilize to induce local spin-moments at each fluorine sites and in turn form a suspended 2D spin lattice. The spins of this lattice align ferromagnetically with nearest neighbour coupling strength as large as $\sim$ 100 meV. Our finite temperature \textit {ab initio} molecular dynamics study reveals that the intercalated system can be stabilized up to a temperature of 100 K with an average magnetic moment of $\sim$ 0.6 $\mu_{B}$/F. However, if the graphene layers can be held fixed, the room temperature stability of such a system is feasible.

Toward the laser control of electronic decoherence.

Controlling electronic decoherence in molecules is an outstanding challenge in chemistry. Recent advances in the theory of electronic decoherence [B. Gu and I. Franco, J. Phys. Chem. Lett. 9, 773 (2018)] have demonstrated that it is possible to manipulate the rate of electronic coherence loss via control of the relative phase in the initial electronic superposition state. This control emerges when there are both relaxation and pure-dephasing channels for decoherence and applies to initially separable electron-nuclear states. In this paper, we demonstrate that (1) such an initial superposition state and the subsequent quantum control of electronic decoherence can be created via weak-field one-photon photoexcitation with few-cycle laser pulses of definite carrier envelope phase (CEP), provided the system is initially prepared in a separable electron-nuclear state. However, we also demonstrate that (2) when stationary molecular states (which are generally not separable) are considered, such one-photon laser control disappears. Remarkably, this happens even in situations in which the initially factorizable state is an excellent approximation to the stationary state with fidelity above 98.5%. The laser control that emerges for initially separable states is shown to arise because these states are superpositions of molecular eigenstates that open up CEP-controllable interference routes at the one-photon limit. Using these insights, we demonstrate that (3) the laser control of electronic decoherence from stationary states can be recovered by using a two-pulse control scheme, with the first pulse creating a vibronic superposition state and the second one inducing interference. This contribution advances a viable scheme for the laser control of electronic decoherence and exposes a surprising artifact that is introduced by widely used initially factorizable system-bath states in the field of open quantum systems.

Angular momentum radiation from current-carrying molecular junctions

We consider the radiation of angular momentum (AM) from current-carrying molecular junctions. Using the nonequilibrium Green's function method, we derive a convenient formula for the AM radiation and apply it to a prototypical benzene molecule junction. We discuss the selection rules for inelastic transitions between the molecular angular momentum eigenstates due to a 6-fold rotational symmetry. Our study provides important insights into the generation of light with AM from DC-biased molecular junctions.

Gate-Efficient Simulation of Molecular Eigenstates on a Quantum Computer

A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with short circuit depth that finish within the available coherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. Complementing the theoretical work by Barkoutsos et al. [PRA 98, 022322 (2018)], we report on the experimental implementation of a variational algorithm on a superconducting qubit platform to compute the eigenstate energies of molecular hydrogen. We utilize a parametrically driven tunable coupler to realize exchange-type gates that are configurable in amplitude and phase on two fixed-frequency superconducting qubits. With gate fidelities around 95% we are able to compute the eigenstates within an accuracy of 50 mHartree on average, a limit set by the coherence time of the tunable coupler.

Quantum hardware simulating four-dimensional inelastic neutron scattering

Magnetic molecules, modelled as finite-size spin systems, are test-beds for quantum phenomena and could constitute key elements in future spintronics devices, long-lasting nanoscale memories or noise-resilient quantum computing platforms. Inelastic neutron scattering is the technique of choice to probe them, characterizing molecular eigenstates on atomic scales. However, although large magnetic molecules can be controllably synthesized, simulating their dynamics and interpreting spectroscopic measurements is challenging because of the exponential scaling of the required resources on a classical computer. Here, we show that quantum computers have the potential to efficiently extract dynamical correlations and the associated magnetic neutron cross-section by simulating prototypical spin systems on a quantum hardware. We identify the main gate errors and show the potential scalability of our approach. The synergy between developments in neutron scattering and quantum processors will help design spin clusters for future applications.

Coupling of the First and Second Excited States of R6G Dye with the Fabry–Perot Cavity

Coupling of macroscopic ensembles of highly concentrated R6G molecules with aluminum and silver Fabry–Perot cavities of different sizes, in which one or two standing wave modes are in resonance with the absorption transition(s) of the dye molecules, have been studied. (i) It has been found that strong coupling of the cavity with one molecular eigenstate (S0→S1 transition) does not perturb the energies of the other molecular states. (ii) The S0→S2 absorption transition is too weak to strongly couple to the resonant cavity (“λ” standing wave mode). However, the resonant cavity causes a blue shift of the S0→S2 excitation band. (iii) The splitting of the dispersion curve is theoretically predicted and experimentally observed at strong coupling of the cavity resonance (“λ” standing wave mode) with the material resonances of Ag, including bound electron and “epsilon equal zero” transitions.

Quantum-mechanical definition of atoms and their mutual interactions in Born-Oppenheimer molecules

The apparent absence of meaningful assignments of electrons and indistinguishable nuclei to particular atoms in a chemical aggregate would seem to preclude the quantum-mechanical definition of atomic Hamiltonian operators within molecules and matter. The electronic energies of individual constituent atoms, as well as the interactions between them, are accordingly widely perceived as objectively undefined in molecular quantum theory, requiring additional auxiliary conditions to achieve quantitative specificity, giving rise to a plethora of individual preferences. Here we address the issue of assignments of electrons to atoms within molecules at the Born-Oppenheimer classical fixed-nuclei level of theory and provide thereby quantum-mechanical definitions of atomic operators and of the interactions between them. In the spirit of early work of Longuet-Higgins, a van der Waals subgroup of the full molecular electronic symmetric group is shown to facilitate assignments of electrons to particular atomic nuclei in a molecule. The orthonormal (Eisenschitz-London) outer products of atomic eigenstates that provide separable Hilbert space representations of this symmetric subgroup furthermore support totally antisymmetric solutions of the molecular Schr\odinger equation. Self-adjoint atomic and atomic-interaction operators within a molecule defined in this way are seen to have universal Hermitian matrix representatives and physically significant expectation values in totally antisymmetric molecular eigenstates. Adiabatic Born-Oppenheimer molecular energies emerge naturally from the development in the form of sums of the energies of individual atomic constituents and of their atomic-pairwise interactions, in the absence of additional auxiliary conditions. A detailed and nuanced quantitative description of electronic structure and bonding is provided thereby which includes the interplay between atomic promotion and interaction energies, common representations of atomic-state hybridization and interatomic charge apportionment, potentially measurable multiatom entanglements upon coherent dissociations of molecules, and other attributes of the development revealed by selected illustrative calculations. These include applications to the ground and electronically excited states of diatomic and triatomic hydrogen molecules, which exhibit significant accommodation among the atomic promotion and interaction energies, as well as entanglements among atomic states, over the entire range of molecular geometries traversed in the course of two- and three-atom dissociations.

Negative differential resistance and rectification effects in zigzag graphene nanoribbon heterojunctions: Induced by edge oxidation and symmetry concept

By applying non-equilibrium Green's functions (NEGF) in combination with tight-binding (TB) model, we investigate and compare the electronic transport properties of H-terminated zigzag graphene nanoribbon (H/ZGNR) and O-terminated ZGNR/H-terminated ZGNR (O/ZGNR–H/ZGNR) heterostructure under finite bias. Moreover, the effect of width and symmetry on the electronic transport properties of both models is also considered. The results reveal that asymmetric H/ZGNRs have linear I–V characteristics in whole bias range, but symmetric H-ZGNRs show negative differential resistance (NDR) behavior which is inversely proportional to the width of the H/ZGNR. It is also shown that the I–V characteristic of O/ZGNR–H/ZGNR heterostructure shows a rectification effect, whether the geometrical structure is symmetric or asymmetric. The fewer the number of zigzag chains, the bigger the rectification ratio. It should be mentioned that, the rectification ratios of symmetric heterostructures are much bigger than asymmetric one. Transmission spectrum, density of states (DOS), molecular projected self-consistent Hamiltonian (MPSH) and molecular eigenstates are analyzed subsequently to understand the electronic transport properties of these ZGNR devices. Our findings could be used in developing nanoscale rectifiers and NDR devices.

When can time-dependent currents be reproduced by the Landauer steady-state approximation?

We establish well-defined limits in which the time-dependent electronic currents across a molecular junction subject to a fluctuating environment can be quantitatively captured via the Landauer steady-state approximation. For this, we calculate the exact time-dependent non-equilibrium Green's function (TD-NEGF) current along a model two-site molecular junction, in which the site energies are subject to correlated noise, and contrast it with that obtained from the Landauer approach. The ability of the steady-state approximation to capture the TD-NEGF behavior at each instant of time is quantified via the same-time correlation function of the currents obtained from the two methods, while their global agreement is quantified by examining differences in the average currents. The Landauer steady-state approach is found to be a useful approximation when (i) the fluctuations do not disrupt the degree of delocalization of the molecular eigenstates responsible for transport and (ii) the characteristic time for charge exchange between the molecule and leads is fast with respect to the molecular correlation time. For resonant transport, when these conditions are satisfied, the Landauer approach is found to accurately describe the current, both on average and at each instant of time. For non-resonant transport, we find that while the steady-state approach fails to capture the time-dependent transport at each instant of time, it still provides a good approximation to the average currents. These criteria can be employed to adopt effective modeling strategies for transport through molecular junctions in interaction with a fluctuating environment, as is necessary to describe experiments.

Molecular response properties in equation of motion coupled cluster theory: A time-dependent perspective.

Molecular response properties for ground and excited states and for transitions between these states are defined by solving the time-dependent Schrödinger equation for a molecular system in a field of a time-periodic perturbation. In equation of motion coupled cluster (EOM-CC) theory, molecular response properties are commonly obtained by replacing, in configuration interaction (CI) molecular response property expressions, the energies and eigenstates of the CI eigenvalue equation with the energies and eigenstates of the EOM-CC eigenvalue equation. We show here that EOM-CC molecular response properties are identical to the molecular response properties that are obtained in the coupled cluster-configuration interaction (CC-CI) model, where the time-dependent Schrödinger equation is solved using an exponential (coupled cluster) parametrization to describe the unperturbed system and a linear (configuration interaction) parametrization to describe the time evolution of the unperturbed system. The equivalence between EOM-CC and CC-CI molecular response properties only holds when the CI molecular response property expressions-from which the EOM-CC expressions are derived-are determined using projection and not using the variational principle. In a previous article [F. Pawłowski, J. Olsen, and P. Jørgensen, J. Chem. Phys. 142, 114109 (2015)], it was stated that the equivalence between EOM-CC and CC-CI molecular response properties only held for a linear response function, whereas quadratic and higher order response functions were mistakenly said to differ in the two approaches. Proving the general equivalence between EOM-CC and CC-CI molecular response properties is a challenging task, that is undertaken in this article. Proving this equivalence not only corrects the previous incorrect statement but also first and foremost leads to a new, time-dependent, perspective for understanding the basic assumptions on which the EOM-CC molecular response property expressions are founded. Further, the equivalence between EOM-CC and CC-CI molecular response properties highlights how static molecular response properties can be obtained from finite-field EOM-CC energy calculations.

Rectifying properties of oligo(phenylene ethynylene) heterometallic molecular junctions: molecular length and side group effects.

The rectifying properties of α,ω-dithiol terminated oligo(phenylene ethynylene) molecules sandwiched between heterometallic electrodes, including the molecular length and side group effects, are theoretically investigated using the fully self-consistent nonequilibrium Green's function method combined with density functional theory. The results show nonlinear variation with changes in molecule length: when the molecule becomes longer, the current decreases at first and then increases while the rectification shifts in the opposite direction. This stems from the change in molecular eigenstates and the coupling between the molecule and electrodes caused by different molecular lengths. The rectifying behavior of heterometallic molecular junctions can be attributed to the asymmetric molecule-electrode contacts, which lead to asymmetric electronic tunneling spectra, molecular eigenvalues, molecular orbitals, and potential drop at reversed equivalent bias voltages. Our results provide a fundamental understanding of the rectification of heterometallic molecular junction, and a prediction of rectifiers with different rectification properties from those in the experiment, using electrodes with reduced sizes.

Spin-excited states and rectification in an organic spin rectifier

Spin-excited states in an asymmetric magnetic organic co-oligomer diode are investigated theoretically. The results demonstrate that the structural asymmetry of the co-oligomer is modulated by the spin-excited states, which is embodied in the wave functions of the eigenstates as well as the spin density wave. By calculating the transport property, a robust spin-current rectification concomitant with a charge-current rectification is observed in all spin-excited states. However, the current through the diode is suppressed distinctly by the spin-excited states, while the rectification ratios may be reduced or enhanced depending on the bias and the excited spins. The intrinsic mechanism is analyzed from the spin-dependent transmission combined with the change of molecular eigenstates under bias. Finally, the temperature-induced spin excitation is simulated. Significant rectification behavior is obtained even at room temperature.

Quantum dynamics experienced by a single molecular eigenstate excited by incoherent light.

Contrary to conventional wisdom that all dynamics are a result of interference (or "dephasing") between many (at least two) energy eigenstates, we show that when a continuum of states is present, even a single molecular eigenstate undergoes "steady-state" quantum dynamics. Moreover, this type of dynamics can be initiated by incoherent (e.g., solar) light sources. Continua are invariably involved in molecular systems due to a variety of sources such as the ever present bath modes, spontaneously emitted photons; the detachment of electrons, or the dissociation of chemical bonds. Contrary to a single bound energy eigenfunction which is a real ("standing-waves") function that carries no flux and, hence, has no dynamics, a single (complex) continuum energy eigenfunction carries "steady-state" flux given by the group velocity of the energetically narrow wave packet it represents. When this energy eigenfunction is a multimode resonance embedded in a continuum via a chain of intramolecular couplings, this dynamics may be initiated by any (light) source, and is controlled, contrary to coherent wave packet dynamics, by the position of the resonance rather than its width.

Strong-laser-induced quantum interference

Intense femtosecond pulses of infrared light are frequently used to manipulate molecules. It is now shown that such control even extends to making different molecular eigenstates interfere with each other — an effect that could potentially pave the way to using molecules for quantum information processing.

Wave packets get a kick

Intense femtosecond pulses of infrared light can manipulate molecules. It is now shown that such control even extends to making different molecular eigenstates interfere with each other in a way never considered before — a potential tool for optically engineered chemical reactions and for ultrafast information encoding and manipulation.

Dipole-Resonance Assisted Isomerization in the Electronic Ground State Using Few-Cycle Infrared Pulses

A computational investigation of HCN → HNC isomerization in the electronic ground state by one- and few-cycle infrared pulses is presented. Starting from a vibrationally pre-excited reagent state, isomerization yields of more than 50% are obtained using single one- to five-cycle pulses. The principal mechanism includes two steps of population transfer by dipole-resonance (DR), and hence, the success of the method is closely linked to the polarity of the system and, in particular, the stepwise change of the dipole moment from reactant to transition state and on to products. The yield drops massively if the diagonal dipole matrix elements are artificially set to zero. In detail, the mechanism includes DR-induced preparation of a delocalized vibrational wavepacket, which traverses the barrier region and is finally trapped in the product well by DR-dominated de-excitation. The excitation and de-excitation steps are triggered by pulse lobes of opposite field direction. As the number of optical cycles is increased, the leading field lobes prepare a vibrational superposition state by off-resonant ladder climbing, which is then subjected to the three steps of the principal isomerization mechanism. DR excitation is more efficient from a preformed vibrational wavepacket than from a molecular eigenstate. The entire process can be loosely described as Tannor-Kosloff-Rice type transfer mechanism on a single potential surface effected by a single pulse, individual field lobes assuming the roles of pump- and dump-pulses. Pre-excitation to a transient wavepacket can be enhanced by applying a separate, comparatively weak few-cycle prepulse, in which the prepulse prepares a vibrational wavepacket. The two-pulse setup corresponds to a double Tannor-Kosloff-Rice control scheme on a single potential surface.