Analysis of the finite difference time domain technique to solve the Schrödinger equation for quantum devices

Soriano, Antonio; Navarro, Enrique A.; Portí, J.A.; Such, V.

doi:10.1063/1.1753661

Cited by 84 publications

(73 citation statements)

References 4 publications

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“…To test the stability of the generalized FDTD schem Equation (27) and Equation (30) with discrete absorbing boundary conditions, Equation (39), we employed the present schemes and the original FDTD scheme to simuspace and then hitting an es in late a particle moving in free energy potential as tested in [3]. To this end, we initiated a particle at a wavelength of  in a Gaussian envelop of width  with the following two equations:…”

Section: Numerical Examplesmentioning

confidence: 99%

A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation

Moxley¹,

Zhu²,

Dai³

2012

AJCM

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The Finite-Difference Time-Domain (FDTD) method is a well-known technique for the analysis of quantum devices. It solves a discretized Schrödinger equation in an iterative process. However, the method provides only a second-order accurate numerical solution and requires that the spatial grid size and time step should satisfy a very restricted condition in order to prevent the numerical solution from diverging. In this article, we present a generalized FDTD method with absorbing boundary condition for solving the one-dimensional (1D) time-dependent Schrödinger equation and obtain a more relaxed condition for stability. The generalized FDTD scheme is tested by simulating a particle moving in free space and then hitting an energy potential. Numerical results coincide with those obtained based on the theoretical analysis.

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Section: Numerical Examplesmentioning

confidence: 99%

A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation

Moxley¹,

Zhu²,

Dai³

2012

AJCM

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“…As was mentioned above, the equations of motion are analytically unsolvable, and were integrated numerically with the technique [64].…”

Section: Ultrastrong Coupling: Results and Discussionmentioning

confidence: 99%

“…One can see that the resonance condition [65] corresponds to Equation (29) for m = 0. The frequency given by Equation (30) is associated with the Rabi frequency in [64]. The frequency of intra-molecular oscillations driven by the donor-acceptor tunneling in [65] may be identified as a Bloch frequency in Equation (29).…”

Section: The Case Of Small Bloch-frequencymentioning

confidence: 99%

The New Concept of Nano-Device Spectroscopy Based on Rabi–Bloch Oscillations for THz-Frequency Range

Levie¹,

Slepyan²

2017

Applied Sciences

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Abstract:We considered one-dimensional quantum chains of two-level Fermi particles coupled via the tunneling driven both by ac and dc fields in the regimes of strong and ultrastrong coupling. The frequency of ac field is matched with the frequency of the quantum transition. Based on the fundamental principles of electrodynamics and quantum theory, we developed a general model of quantum dynamics for such interactions. We showed that the joint action of ac and dc fields leads to the strong mutual influence of Rabi-and Bloch oscillations, one to another. We focused on the regime of ultrastrong coupling, for which Bloch-and Rabi-frequencies are significant values of the frequency of interband transition. The Hamiltonian was solved numerically, with account of anti-resonant terms. It manifests by the appearance of a great number of narrow high-amplitude resonant lines in the spectra of tunneling current and dipole moment. We proposed the new concept of terahertz (THz) spectroscopy, which is promising for different applications in future nanoelectronics and nano-photonics.

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“…Then alternating iterations of Eqns. 6 simulate the motion of the waveform in time [18][19][20][21][22][23].…”

Section: Appendix a A Finite Difference Time Domainmentioning

confidence: 99%

Hybrid quantum systems for enhanced nonlinear optical susceptibilities

Sullivan¹,

Mossman²,

Kuzyk³

2016

J. Opt. Soc. Am. B

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Significant effort has been expended in the search for materials with ultra-fast nonlinear-optical susceptibilities, but most fall far below the fundamental limits. This work applies a theoretical materials development program that has identified a promising new hybrid made of a nanorod and a molecule. This system uses the electrostatic dipole moment of the molecule to break the symmetry of the metallic nanostructure that shifts the energy spectrum to make it optimal for a nonlinearoptical response near the fundamental limit. The structural parameters are varied to determine the ideal configuration, providing guidelines for making the best structures.

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Analysis of the finite difference time domain technique to solve the Schrödinger equation for quantum devices

Cited by 84 publications

References 4 publications

A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation

A Generalized FDTD Method with Absorbing Boundary Condition for Solving a Time-Dependent Linear Schrodinger Equation

The New Concept of Nano-Device Spectroscopy Based on Rabi–Bloch Oscillations for THz-Frequency Range

Hybrid quantum systems for enhanced nonlinear optical susceptibilities

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