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Register a new userDynamics of observables and exactly solvable quantum problems: Using time-dependent density functional theory to control quantum systems
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We use analytic (current) density-potential maps of time-dependent (current) density functional theory (TD(C)DFT) to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schrodinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum NOT gate.
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Two coupled two-level systems placed under external time-dependent magnetic fields are modeled by a general Hamiltonian endowed with a symmetry that enables us to reduce the total dynamics into two independent two-dimensional sub-dynamics. Each of the sub-dynamics is shown to be brought into an exactly solvable form by appropriately engineering the magnetic fields and thus we obtain an exact time evolution of the compound system. Several physically relevant and interesting quantities are evaluated exactly to disclose intriguing phenomena in such a system.
Time-Dependent Density Functional Theory (TDDFT) has recently been extended to describe many-body open quantum systems (OQS) evolving under non-unitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a non-interacting open Kohn-Sham system yielding the correct non-equilibrium density evolution. A pseudo-eigenvalue equation analogous to the Casida equations of usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C$^{2+}$ atom in an optical resonator interacting with a bath of photons. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on Gorling-Levy perturbation theory is calculated.
We present a systematic analysis and classification of several models of quantum batteries involving different combinations of two level systems and quantum harmonic oscillators. In particular, we study energy transfer processes from a given quantum system, termed charger, to another one, i.e. the proper battery. In this setting, we analyze different figures of merit, including the charging time, the maximum energy transfer, and the average charging power. The role of coupling Hamiltonians which do not preserve the number of local excitations in the charger-battery system is clarified by properly accounting them in the global energy balance of the model.
Colloidal quantum dots (QDs) of group III-V are considered as promising candidates for next-generation environmentally friendly light emitting devices, yet there appears to be only limited understanding of the underlying electronic and excitonic properties. Using large-scale density functional theory with the hybrid B3LYP functional solving the single-particle states and time-dependent density functional theory accounting for the many-body excitonic effects, we have identified the structural, electronic and excitonic optical properties of InP, GaP and GaInP QDs containing up to a thousand atoms or more. The calculated optical gap of InP QD appears in excellent agreement with available experiments, and it scales nearly linearly with the inverse diameter. The radiative exciton decay lifetime is found to increase surprisingly linearly with increasing the dot size. For GaP QDs, we predict an unusual electronic state crossover at diameter around 1.5 nm whereby the nature of the lowest unoccupied molecular orbital (LUMO) state switches its symmetry from $Gamma_{5}$-like at larger diameter to $Gamma_{1}$-like at smaller diameter. After the crossover, the absorption intensity of the band-edge exciton states is significantly enhanced. Finally, we find that Vegards law holds very well for GaInP random alloyed quantum dots down to ultra-small sizes with less than a hundred atoms. The obtained energy gap bowing parameter of this common-cation compound in QD regime appears positive, size-dependent and much smaller than its bulk parentage. The volume deformation, dominating over the charge exchange and structure relaxation effects, is mainly responsible for the QD energy gap bowing. The present work provides a road map for a variety of electronic and optical properties of colloidal QDs in group III-V that can guide spectroscopic studies.
Imaginary-time time-dependent Density functional theory (it-TDDFT) has been proposed as an alternative method for obtaining the ground state within density functional theory (DFT) which avoids some of the difficulties with convergence encountered by the self-consistent-field (SCF) iterative method. It-TDDFT was previously applied to clusters of atoms where it was demonstrated to converge in select cases where SCF had difficulty with convergence. In the present work we implement it-TDDFT propagation for {it periodic systems} by modifying the Quantum ESPRESSO package, which uses a plane-wave basis with multiple $boldsymbol{k}$ points, and has the options of non-collinear and DFT+U calculations using ultra-soft or norm-conserving pseudo potentials. We demonstrate that our implementation of it-TDDFT propagation with multiple $boldsymbol{k}$ points is correct for DFT+U non-collinear calculations and for DFT+U calculations with ultra-soft pseudo potentials. Our implementation of it-TDDFT propagation converges to the exact SCF energy (up to the decimal guaranteed by double precision) in all but one case where it converged to a slightly lower value than SCF, suggesting a useful alternative for systems where SCF has difficulty to reach the Kohn-Sham ground state. In addition, we demonstrate that rapid convergence can be achieved if we use adaptive-size imaginary-time-steps for different kinetic-energy plane-waves.
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