Tunneling through Coulombic barriers: quantum control of nuclear fusion
Rajdeep Saha · Andreas Markmann · Victor S. Batista
Abstract and summary · read the original at the source · none found
In one page
Fusing two deuterons means bringing two positive charges close enough to touch, and the Coulomb repulsion between them is a barrier millions of electronvolts high. The usual answer is heat and pressure — hit the barrier hard enough and a few nuclei go over the top. Rajdeep Saha, Andreas Markmann and Victor Batista, at Yale, ask a different question: can you make nuclei go through it on purpose? Their scheme borrows from coherent control and from spin-echo magnetic resonance. A train of low-energy electron-impact ionization pulses, each timed so that it flips the phase of one component of the deuteron’s wavepacket, rearranges the interference between the channels open to that wavepacket. Amplitude is driven into the classically forbidden region under the barrier and out into the fusion continuum beyond. In their simulation the survival probability barely moves without pulses and falls by more than half with them, while the total energy of the system hardly changes at all.
Why it matters hereChapter 12 treats fusion as the energy substrate the rest of the thesis stands on, and this paper is a clean statement of the site’s central fusion mechanism in ordinary quantum chemistry: the tunnelling rate, not the barrier, is the adjustable quantity. Chapter 2 owns the reason it matters — the pulses do their work by changing the phase structure the wavepacket sees, which is exactly the kind of handle a driven electromagnetic environment offers on a nucleus that is otherwise untouchable.
What it claims
01The proposal in one line: a train of repetitive low-energy electron-impact ionization pulses can speed up quantum tunnelling of a proton or deuteron through a Coulombic barrier, by acting on the interference phenomena that govern the wavepacket rather than on the barrier itself.Abstract; Section 1 Introduction, closing paragraph
Published and peer-reviewed02The pulse is a phase kick, not an energy injection. Each electron scattering event transiently carries one vibrational component onto the singly ionized surface and back, and its duration is chosen to produce a phase shift of pi along that component — the unitary operator known as a two-pi pulse in optics and a 180-degree pulse in spin-echo magnetic resonance. Repetitive application of it is the whole control scheme, and it is the same bang-bang dynamical decoupling idea the group had already used with optical pulses.Section 2 Methods and model system, equation 3 with Figure 3
Published and peer-reviewed03The model is a deuteron in a one-dimensional box two and a half atomic units across — a size set by the plasma density, standing for a deuteron among its nearest neighbours in a dense plasma — interacting with a second deuteron at the origin through the sum of two repulsive Coulomb potentials, with an absorbing optical potential inside the nuclear radius playing the part of the outgoing helium and neutron continuum. The decay of the wavefunction amplitude into that absorber is what counts as fusion. The initial state is the one impulsive ionization of a deuterium molecule leaves behind, and the propagation uses the split-operator Fourier transform method.Section 2, equation 2 with Figure 2
Published and peer-reviewed04The result: without pulses the survival probability of the bound population decays negligibly. Pulsing every hundred atomic units of time takes more than twenty per cent of the population out through the barrier, and pulsing every five atomic units takes more than half. The slope of the survival curve at early time gives the tunnelling rate and its asymptotic value gives the product yield.Section 3 Results, equation 7 with Figure 4
Published and peer-reviewed05The energy bookkeeping is the point of the paper. The pulses redistribute population among the levels — destructive interference among bound components, constructive interference inside the barrier and beyond — without significantly changing the total energy of the system, and the energy fluctuations that do appear are of order seven hartree against a Coulombic barrier of order ten to the fifth hartree. Tunnelling proceeds from states below one hundred in the box basis, which is to say from low-energy collisions.Section 3, equation 8 with Figures 5 and 6
Published and peer-reviewed06What would have to hold for it to be seen, in the authors’ own words: sufficiently high collision cross sections, meaning high density or high temperature, and the survival of quantum coherence over the time scale of the reactive scattering event — the predicted control should be observable unless the decoherence time is much shorter than two hundred femtoseconds. Their suggested application is electron-impact ionization pulsing during the final ignition step of inertial confinement, where they argue it could yield the efficiency gains needed to reach break-even.Section 4 Conclusions and outlook
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Read it · abstract
Abstract
A general coherent control scheme for speeding up quantum tunneling of proton transfer through Coulombic barriers is analysed. The quantum control scenario is based on repetitive electron impact ionization pulses that affect the ensuing interference phenomena responsible for quantum dynamics and force the proton to tunnel into classically forbidden regions of configuration space. The scheme is demonstrated for the simplest model of nuclear fusion, hinting at the possible enhancement of reactive scattering based on low energy collisions.
Rajdeep Saha, Andreas Markmann and Victor S. Batista, Department of Chemistry, Yale University, New Haven, Connecticut. Molecular Physics 110, numbers 9 to 10, pages 995 to 999 (2012), invited article.
(Abstract only — the article itself is copyright Taylor and Francis and carries no open licence; see the rights note above for the copy that was read and where each claim is located in it. The complete article is at doi.org/10.1080/00268976.2012.679635. Read it beside the screening work, where the effective barrier really is altered by the material a nucleus sits in — Screening energy for low energy nuclear reactions in condensed matter, Enhancement of the electron screening effect for d + d fusion reactions in metallic environments and Experimental techniques for the investigation of the electron screening effect for d+d fusion reactions in metallic environments — and beside the lattice confinement fusion results that put the same idea on a bench: Experimental Observations of Nuclear Activity in Deuterated Materials Subjected to a Low-Energy Photon Beam, Novel nuclear reactions in bremsstrahlung-irradiated deuterated metals and the Lattice Confinement Fusion (LCF) Overview.)
The way in
https://doi.org/10.1080/00268976.2012.679635PUBLICATION. Invited article in Molecular Physics, volume 110, numbers 9 to 10, pages 995 to 999, issue dated 10 to 20 May 2012; received 1 February 2012, final version received 21 March 2012. All three authors are at the Department of Chemistry, Yale University, New Haven, Connecticut. LICENCE, CHECKED 2026-09-09. The Crossref deposit for this DOI registers no licence and carries no abstract; OpenAlex and Unpaywall both record the work as closed, and the printed article carries the notice ‘2012 Taylor and Francis’. No Creative Commons statement exists on the article or anywhere else that was reached, so no text of the paper is reproduced here beyond its own abstract. SOURCE READ. An arXiv copy was searched for by title, by the phrase ‘quantum control of nuclear fusion’ and by the two co-authors together, and arXiv holds none. The authors’ own copy is posted by the Batista group at Yale as entry 99 of its publication list, files.batistalab.com/publications/molphys.pdf, and that five-page PDF — the complete article with its six figures and twenty-six references — was retrieved and read in full on 2026-09-09. Every claim below is located by the article’s own section, equation or figure number in that copy. THE ABSTRACT. The abstract reproduced below is the article’s own, printed on its first page and identical word for word to the one OpenAlex carries for this DOI; Crossref holds none. Equations are described in words, since the extracted text carries the original typesetting only as characters. FUNDING as printed in the acknowledgement: supercomputer time from NERSC, support from Lawrence Livermore National Laboratory grant B590847, and National Science Foundation grants CHE-0911520 for quantum dynamics methods and ECCS-0404191 for quantum control.
How to cite it
Rajdeep Saha, Andreas Markmann, Victor S. Batista (2012) Tunneling through Coulombic barriers: quantum control of nuclear fusion. doi:10.1080/00268976.2012.679635
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