Arbitrary Excited States Research Articles

Generalized Unruh effect: A potential resolution to the black hole information paradox

We generalize the vacuum-Unruh effect to arbitrary excited states in the Fock space and find that the Unruh mode at the horizon induces coherent excitation on the canonical background ensemble measured by an accelerated observer. When there is only one type of Unruh mode in the system, for example, the ones outgoing from a black hole horizon, the mapping from an arbitrary density matrix on the maximal foliation to a vector space spanned by the pseudo-thermal density matrix on the partitioned spacetime wedge is one-to-one. Hence we propose that the information of the particles that are inside a collapsing shell, thus inside the asymptotic black hole horizon is at least partially retrievable by measuring the deviation of the Hawking radiation from the black body radiation spectrum. This work shows that the long-standing black hole information confusion might come from overlooking the possibility that the information could be preserved much better than we have expected in a seemingly non-unitary process when the partitions of the system are strongly entangled.

Is there a better way of representing stationary wave functions than basis expansion?

We extend our previously developed approach for finding the exact analytical form of ground state wave function of single-electron Schrödinger equations to target arbitrary excited states of 1D model chemical systems of hydrogen atom and H 2 + $$ {\mathrm{H}}_2^{+} $$ with soft Coulomb potential. Our representation of the wave functions is formally unified by a factorized formula involving a polynomial prefactor encoding the nodal information, a non-integer power prefactor, and an exponentially decaying term modulated by a modulator function. We show that our method leads to faster energy convergence than the basis expansion method, and hence is a better way of representing the wave function. This conclusion is also validated in the real-world H 2 + $$ {\mathrm{H}}_2^{+} $$ .

Optical Images of Molecular Vibronic Couplings from Tip-Enhanced Fluorescence Excitation Spectroscopy.

Tip-based photoemission spectroscopic techniques have now achieved subnanometer resolution that allows visualization of the chemical structure and even the ground-state vibrational modes of a single molecule. However, the ability to visualize the interplay between electronic and nuclear motions of excited states, i.e., vibronic couplings, is yet to be explored. Herein, we theoretically propose a new technique, namely, tip-enhanced fluorescence excitation (TEFE). TEFE takes advantage of the highly confined plasmonic field and thus can offer a possibility to directly visualize the vibronic effect of a single molecule in real space for arbitrary excited states in a given energy window. Numerical simulations for a single porphine molecule confirm that vibronic couplings originating from Herzberg–Teller (HT) active modes can be visually identified. TEFE further enables high-order vibrational transitions that are normally suppressed in the other plasmon-based processes. Images of the combination vibrational transitions have the same pattern as that of their parental HT active mode’s fundamental transition, providing a direct protocol for measurements of the activity of Franck–Condon modes of selected excited states. These findings strongly suggest that TEFE is a powerful strategy to identify the involvement of molecular moieties in the complicated electron–nuclear interactions of the excited states at the single-molecule level.

Variational quantum packaged deflation for arbitrary excited states

Determining the spectral structure of molecular Hamiltonians is one of the most important and challenging research fields in quantum chemistry. In the near future, such a problem may be solvable by means of quantum simulation. However, constrained by a handful of qubits and noisy quantum gates available in the near-term quantum devices, hybrid quantum-classical algorithms based on variational methods such as variational quantum eigensolver have become a preferable choice. Here we propose an interesting variational quantum algorithm for obtaining the excited states of many-body Hamiltonians. To obtain the kth excited states, the previous variational quantum deflation algorithm requires the use of k different variational circuits, which is now reduced to only two circuits with our algorithm. The feasibility of the algorithm was numerically tested on the hydrogen molecule with and without random noise, where the chemical accuracy is reached for both cases. This algorithm is expected to significantly reduce the resource requirements of quantum simulation.

Excited State Search Using Quantum Annealing

Quantum annealing (QA) is one of the ways to search the ground state of the problem Hamiltonian. Here, we propose the QA scheme to search arbitrary excited states of the problem Hamiltonian. In our scheme, an $n$-th excited state of the trivial Hamiltonian is initially prepared and is adiabatically changed into an $n$-th excited state of the target Hamiltonian. Although our scheme is general such that we can search any excited states, we especially discuss the first excited state search in this paper. As a comparison, we consider a non-adiabatic scheme to find the first excited state with non-adiabatic transitions from the ground state. By solving the Lindblad master equation, we evaluate the performance of each scheme under the influence of decoherence. Our conclusion is that the adiabatic scheme show better performance than the non-adiabatic scheme as long as the coherence time of qubits is sufficiently long. These results are important for applications in the area of quantum chemistry, quantum simulation, and post-quantum cryptography.

Sum rule of quantum uncertainties: coupled harmonic oscillator system with time-dependent parameters

Uncertainties $$(\Delta x)^2$$ and $$(\Delta p)^2$$ are analytically derived in an N-coupled harmonic oscillator system when spring and coupling constants are arbitrarily time-dependent and each oscillator is in an arbitrary excited state. When $$N = 2$$ , those uncertainties are shown as just arithmetic average of uncertainties of two single harmonic oscillators. We call this property as “sum rule of quantum uncertainty”. However, this arithmetic average property is not generally maintained when $$N \ge 3$$ , but it is recovered in N-coupled oscillator systems if and only if $$(N-1)$$ quantum numbers are equal. The generalization of our results to a more general quantum system is briefly discussed.

A Projective Method for the Calculation of Excited-State Electronic Coupling: Isolating Charge Transfer/Recombination Processes in Organic Photovoltaics.

Electronic coupling between excited states is a vital parameter required to describe ultrafast energy and charge transfer processes that occur in photoresponsive organic materials. In such systems, short-range Coulombic, exchange, overlap, and configuration interaction effects must all be accounted for. Although a number of methods are available, the evaluation of coupling between arbitrary excited states remains challenging. In this contribution, a flexible and scalable method for the calculation of short-range electronic coupling between excited states is developed. Excitation- or charge-localized states are projected onto the adiabatic states of a dimeric molecular system using an efficient wave function overlap algorithm. In addition to correctly treating Coulombic, exchange, and overlap contributions, the inclusion of multistate interactions is inherent in the procedure. The method is then used to disentangle excitation energy transfer, charge transfer, and charge recombination processes in donor/acceptor systems relevant to organic photovoltaics, with a view toward the development of material design principles. Calculations were performed within single-excitation frameworks, but the scheme has the potential to be extended to multireference/higher-order excitation quantum-chemical methods.

Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states.

In this work, we revisited the idea of using the coupled-cluster (CC) ground state formalism to target excited states. Our main focus was targeting doubly excited states and double core hole states. Typical equation-of-motion (EOM) approaches for obtaining these states struggle without higher-order excitations than doubles. We showed that by using a non-Aufbau determinant optimized via the maximum overlap method, the CC ground state solver can target higher energy states. Furthermore, just with singles and doubles (i.e., CCSD), we demonstrated that the accuracy of ΔCCSD and ΔCCSD(T) (triples) far surpasses that of EOM-CCSD for doubly excited states. The accuracy of ΔCCSD(T) is nearly exact for doubly excited states considered in this work. For double core hole states, we used an improved ansatz for greater numerical stability by freezing core hole orbitals. The improved methods, core valence separation (CVS)-ΔCCSD and CVS-ΔCCSD(T), were applied to the calculation of the double ionization potential of small molecules. Even without relativistic corrections, we observed qualitatively accurate results with CVS-ΔCCSD and CVS-ΔCCSD(T). Remaining challenges in ΔCC include the description of open-shell singlet excited states with the single-reference CC ground state formalism as well as excited states with genuine multireference character. The tools and intuition developed in this work may serve as a stepping stone toward directly targeting arbitrary excited states using ground state CC methods.

Ab initio simulations of x-ray emission spectroscopy with the GW+ Bethe-Salpeter equation method

In order to calculate x-ray emission spectroscopy (XES) spectra, we apply the $GW+$Bethe-Salpeter equation ($\mathrm{GW}+\mathrm{BSE}$) method on a basis of extended quasiparticle theory, which enables one to treat an arbitrary excited state as an initial state, because the initial state in the XES process is a highly excited state with a core hole. Compared to the preexisting experimental data of XES fluorescence photon energy, the calculated $\mathrm{GW}+\mathrm{BSE}$ results give values with about 1-eV accuracy, which is comparable to the previous results using the time-dependent density functional theory with the short-range corrected exchange-correlation functional, the equation of motion-coupled cluster single and double, and delta self-consistent field methods. Our $\mathrm{GW}+\mathrm{BSE}$ results reproduce corresponding experimental XES spectra without missing any peak. The method can assign the excitonic configuration of each peak in XES spectra with the quasiparticle levels. As a result, the analysis of excitonic structure for each peak gives obvious interpretation concerning the relation between excitonic states and valence states.

Generation of intense water window X-ray pulses by superposition of an initial state of the helium atom driven by a three-color field

We theoretically study the generation of high-order harmonics and attosecond pulses from the superposition of an initial state in helium atom driven by a three-color laser field. It is shown that when the initial state is chosen to be a single electronic state, due to the rapid depletion of the ground state, the efficiency of the spectral continuum will be decreased as the initial state increases. When the initial state is chosen to be the coherent superposition of the ground state and an arbitrary excited state, the efficiency of the spectral continuum can be enhanced compared to that from the single initial state. Further, with the optimization of the three-color laser beam, not only can the harmonic cutoff be extended to the water window X-ray region but also the spectral continuum is contributed by the single harmonic emission peak with the dominant short quantum path. Consequently, two combinations of the laser parameters can be found to generate the water window spectral continuum. By properly superposing some harmonics on the spectral continuum, a number of intense water window pulses with the duration of sub-35 as can be produced.

Krylov-Projected Quantum MonteCarlo Method.

We present an approach to the calculation of arbitrary spectral, thermal, and excited state properties within the full configuration interaction quzantum MonteCarlo framework. This is achieved via an unbiased projection of the Hamiltonian eigenvalue problem into a space of stochastically sampled Krylov vectors, thus, enabling the calculation of real-frequency spectral and thermal properties and avoiding explicit analytic continuation. We use this approach to calculate temperature-dependent properties and one- and two-body spectral functions for various Hubbard models, as well as isolated excited states in abinitio systems.

Excited state entanglement in one-dimensional quantum critical systems: Extensivity and the role of microscopic details

We study entanglement via the subsystem purity relative to bipartitions of arbitrary excited states in (1+1)-dimensional conformal field theory, equivalent to the scaling limit of one dimensional quantum critical systems. We compute the exact subpurity as a function of the relative subsystem size for numerous excited states in the Ising and three-state Potts models. We find that it decays exponentially when the system and the subsystem sizes are comparable until a saturation limit is reached near half-partitioning, signaling that excited states are maximally entangled. The exponential behavior translates into extensivity for the second R\'enyi entropy. Since the coefficient of this linear law depends only on the excitation energy, this result shows an interesting, new relationship between energy and quantum information and elucidates the role of microscopic details.

Photoelectron angular distributions of excited atoms in intense laser fields

Angular distributions of photoionization differential rates for an atom in arbitrary excited states ionized by intense laser fields with arbitrary polarization are reported. Relativistic effects are incorporated into the Keldysh theory, yielding semi-analytical expressions of ionization rates for hydrogenic initial states in intense linear, circular, and elliptical laser polarizations. Angular distributions are compared for different angular momentum quantum numbers, magnetic quantum numbers, and Keldysh parameters $\ensuremath{\gamma}$. The angular distributions are shown to depend strongly on $\ensuremath{\gamma}$, thus also reflecting the influence of relativistic effects. The sign of the magnetic quantum number, corresponding to different electron rotations, is shown to have a significant effect on photoelectron angular distributions in circularly polarized laser fields.

Post collision interactions in fully differential cross sections for four-body charge transfer processes

Recently, experimental fully differential cross sections have been reported for proton–helium collisions. In this work we will examine single capture, transfer with target excitation and double capture for proton–helium collisions. For single capture, the proton captures one electron from helium and leaves the other electron in the ground state. For the transfer-excitation case, the target is excited to arbitrary excited states. In the case of double capture, the proton captures both of the electrons from helium and leaves the collision as an H− ion. We introduce a fully quantum mechanical four-body model that includes the final state post collision interactions between all two-particle pairs exactly. In the initial state, the two-particle interactions are included asymptotically by using an Eikonal wavefunction. The results of this model are in better agreement with experimental data than previous quantum mechanical calculations.

Generalized variational principle for excited states using nodes of trial functions

The familiar variational principle provides an upper bound to the ground-state energy of a given Hamiltonian. This allows one to optimize a trial wave function by minimizing the expectation value of the energy. This approach is also trivially generalized to excited states, so that given a trial wave function of a certain symmetry, one can compute an upper bound to the lowest-energy level of that symmetry. In order to generalize further and build an upper bound of an arbitrary excited state of the desired symmetry, a linear combination of basis functions is generally used to generate an orthogonal set of trial functions, all bounding their respective states. However, sometimes a compact wave-function form is sought, and a basis-set expansion is not desirable or possible. Here we present an alternative generalization of the variational principle to excited states that does not require explicit orthogonalization to lower-energy states. It is valid for one-dimensional systems and, with additional information, to at least some n-dimensional systems. This generalized variational principle exploits information about the nodal structure of the trial wave function, giving an upper bound to the exact energy without the need to build a linear combination of basis functions. To illustrate the theorem we apply it to a nontrivial example: the 1s2s (1)S excited state of the helium atom.

Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order alpha(Zalpha)6] and for the two-loop Lamb shift [of order alpha2(Zalpha)6] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of states, defined as Delta N = n3deltaE(nS) - delta E(1S). We present numerical results for one-loop and two-loop corrections for excited S, P, and D states. In particular, the normalized Lamb shift difference of states is calculated with an uncertainty of order 0.1 kHz.

Non-perturbative contributions to the plane-wave string mass matrix

D-instanton contributions to the mass matrix of arbitrary excited string states of type IIB string theory in the maximally supersymmetric plane-wave background are calculated to leading order in the string coupling using a supersymmetric light-cone boundary state formalism. The explicit non-perturbative dependence of the mass matrix on the complex string coupling, the plane-wave mass parameter and the mode numbers of the excited states is determined.

An atomistic approach to conduction between nanoelectrodes through a single molecule.

Capacitance and other properties of nanoelectrodes, finite-size metal clusters envisaged for use in complex molecular-electronic devices, are discussed. The applicability of classical electrostatics (Coulomb's and Gauss' law, Poisson's equation, etc.) to atomistic systems is investigated and the self-energy necessary to store a finite charge on an atom is found to be of central importance. In particular, the neglect of electron exchange is found to introduce severe limitations, with quantum calculations predicting fundamentally different electronic structures. Also, the well-known poor representation of the atomic self-energy inherent to modern DFT is discussed, along with its implications for molecular electronics calculations. An INDO/S method is introduced with new parameters for gold. This is the simplest approximate computational scheme that correctly includes quantum electrostatic, resonance, and spin effects, and is capable of describing arbitrary excited electronic states. Encouraging results are obtained for some trial problems. In particular, voltage differential between the electrodes in electrode-molecule-electrode conduction is obtained, not through an a priori prescription but rather by moving whole electrons between the electrodes and analyzing the response. The voltage drops across the molecule-electrode junctions and the central molecular region are then deduced. This alternative to the current Landauer-based 1-particle transmission equations for electrode-molecule-electrode conduction is discussed in terms of the use of the electronic states of the system. It provides a proper description not only of conduction via electrode-to-molecule charge or hole transfer but also of conduction via simultaneous charge and hole transfer via low-lying excited molecular electronic states, including the ability to account for electroluminescence and other chemical effects. In addition, various aspects of our research on the quantitative prediction of the I(V) curves for electrode-molecule-electrode conduction are reviewed, including demonstration of the equivalence of the formalisms generated by the Datta and the Mujica-Ratner groups, and the development of analytically solvable paradigms, including the conduction through a linear-chain Hückel wire.

Variational Principle for a Particle in a Box

The particle-in-a-box problem is reexamined, using different model wave functions, to illustrate the use of the variational principle applied to the simplest solvable quantum mechanical problem. The scheme presented here provides a useful paradigm for the LCAO approach used in atomic and molecular calculations. Suitable polynomial basis functions are introduced that provide a way for controlling both the accuracy and the number of independent variational parameters used in the energy calculations, when the coordinate origin is taken either at the left-hand edge or the center of the box. Links with the Bransden and Joachain calculations on the first two even parity states are made. The approximate ground state wave function, x(x - L), is also redefined by introducing a variation parameter in the form of a prescription based on the value of the position coordinate. Finally, a straightforward method is presented for determining an approximate energy for an arbitrary excited state, based on the use of any app...

Density-matrix renormalization-group method for excited states

The density-matrix renormalization-group (DMRG) method can provide approximate ground-state wave functions for many one-dimensional systems with a high degree of accuracy. Conventional DMRG techniques, however, cannot be expected to give accurate excited-state information because the excited states of interest are not explicitly included in the calculations. We discuss techniques for extending DMRG to accurately target and investigate arbitrary excited states. As an example we apply the method to investigate the properties of excitons within the extended Hubbard model. Our results show that excited-state calculations within the standard DMRG procedure give results that are quantitatively incorrect.