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arXiv:0707.2997 · Europhysics Letters (EPL)

Modelling chemical reactions using semiconductor quantum dots

A. Smirnov, Sergey E. Savel'ev, Lev G. Mourokh, Franco Nori

Published Nov 13, 2007• 40 citations
arXivHTMLPDF

Abstract

We propose the use of semiconductor quantum dots for simulating chemical reactions, as electrons are redistributed among such artificial atoms. We show that it is possible to achieve various reaction regimes and obtain different reaction products by varying the speed of voltage changes applied to the gates forming quantum dots. Considering the simplest possible reaction, H 2 +H→H+H 2 , we show how the necessary initial state can be obtained and what voltage pulses should be applied to achieve a desirable final product. Our calculations have been performed using the Pechukas gas approach, which can be extended for more complicated reactions.

DOI
10.1209/0295-5075/80/67008

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We propose the use of semiconductor quantum dots for simulating chemical reactions, as electrons are redistributed among such artificial atoms. We show that it is possible to achieve various reaction regimes and obtain different reaction products by varying the speed of voltage changes applied to the gates forming quantum dots. Considering the simplest possible reaction, H 2 +H→H+H 2 , we show how the necessary initial state can be obtained and what voltage pulses should be applied to achieve a desirable final product. Our calculations have been performed using the Pechukas gas approach, which can be extended for more complicated reactions.
Quantum computers can potentially simulate quantum-mechanical phenomena, so chemical reactions are a potential application of them. In particular, the time evolution of the wavefunctions should be simulated because chemical reactions are accompanied by structural changes. In this study, to pave the way to achieving such wavefunction simulations, we decompose chemical reactions into their main parts and comprehensively show the minimum essential circuits for simulating each part. An antisymmetrized initial state is constructed using ancillae. Chemical reactions should be simulated in two different ways, where the difference is whether the ancillae are released or not. When they are released, the whole electronic system is simulated. When they are not released, orbital information is obtained. These ways are hence complementary.
We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates.
Studying chemical reactions, particularly in the gas phase, relies heavily on computing scattering matrix elements. These elements are essential for characterizing molecular reactions and accurately determining reaction probabilities. However, the intricate nature of quantum interactions poses challenges, necessitating the use of advanced mathematical models and computational approaches to tackle the inherent complexities. In this study, we develop and apply a quantum computing algorithm for the calculation of scattering matrix elements. In our approach, we employ the time-dependent method based on the Møller operator formulation where the S-matrix element between the respective reactant and product channels is determined through the time correlation function of the reactant and product Møller wavepackets. We successfully apply our quantum algorithm to calculate scattering matrix elements for 1D semi-infinite square well potential and on the colinear hydrogen exchange reaction. As we navigate the complexities of quantum interactions, this quantum algorithm is general and emerges as a promising avenue, shedding light on new possibilities for simulating chemical reactions on quantum computers.
Suggestion of modifications of finite-dimensional quantum-electrodynamic (QED) models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible between the cavities. Super dark states of diatomic systems are described, in which the motion of atoms between cavities is impossible due to quantum interference. Chemical processes with two level atoms and three level atoms with lambda spectrum are schematically modeled by solving the single quantum master equation with the Lindblad operators of photon leakage from the cavity and influx into it; association and dissociation reactions then differ only in the initial states. An example is given of the optical interpretation of the transition of an electron from atom to atom in terms of the multilevel Tavis-Cummings-Hubbard model with an estimate of the accuracy. Polyatomic chemical reactions are too complex for accurate modeling. Our method of rough interpretation helps to obtain their long-term results, for example, the form of stationary states of reagents, such as dark and super dark states.
Suggestion of modifications of finite-dimensional QED models are proposed for interpreting chemical reactions in terms of artificial atoms and molecules on quantum dots placed in optical cavities. Moving both photons and atoms is possible between the cavities. Super dark states of diatomic systems are described, in which the motion of atoms between cavities is impossible due quantum interference. Chemical processes with two level atoms and three level atoms with lambda spectrum are schematically modeled by solving the single quantum master equation with the Lindblad operators of photon leakage from the cavity and influx into it; association and dissociation reactions then differ only in the initial states. An example is given of the optical interpretation of the transition of an electron from atom to atom in terms of the multilevel Tavis-Cummings-Hubbard model with an estimate of the accuracy. Polyatomic chemical reactions are too complex for accurate modeling. Our method of rough interpretation helps to obtain their long-term results, for example, the form of stationary states of reagents, such as dark and super dark states.
As the size and proximity of components on modern computer chips approaches quantum mechanical limits, various novel solutions have been proposed to ensure further increases in processing speed and reliability. Of these, small semiconductor devices called quantum dots may constitute the logic gates of future quantum computers - processors taking advantage of phenomena such as entanglement and quantum teleportation to enable ultra-fast computation speeds. Quantum dots behave much like designer atoms in that their absorption/emission energies can be adjusted lo desired values. A quantum mechanical model of semiconductor quantum dots having equal size and interacting with a single-mode electric field tuned to some fraction of the transition frequency has been developed Due to the similarities between two-level atoms and quantum dots, techniques common in quantum optics have been employed to describe the time evolution of the resulting exciton-field system. it is assumed that the quantum dots are initially prepared in a Bell entangled state and that the field is in a coherent state. Collapse and revivals in the entanglement are found when the mean photon number of the coherent state is very large.