# Hunt Research Group

## Katharine Hunt

Katharine Clarke Hunt completed her Ph.D. in theoretical chemistry in 1978 at the University of Cambridge in the UK. In the next year, she held a post-doctoral fellowship at MIT. She joined the Department of Chemistry in 1979. She became a University Distinguished Professor in 1992 and chaired the Department from 1998-2002. She spent two sabbaticals at Stanford University. In Fall 2023, she was a Distinguished Fellow of the Institute for Advanced Studies of the University of Luxembourg.

**Quantum transitions induced by time-dependent fields**

The Hunt group has developed a nonadiabatic theory of quantum transitions based on a suggestion by Landau and Lifshitz. We take the excited-state coefficients from Dirac’s theory of quantum transition probabilities and separate them into adiabatic and nonadiabatic terms. The adiabatic terms characterize the adaptation of the initial state to a perturbation, while the nonadiabatic terms characterize excitations across an energy gap. The energy separates cleanly into adiabatic terms as well, and the power absorbed from an electromagnetic field by a molecule is equal to the time derivative of the nonadiabatic term in the energy. If the quantum system remains coherent during a process, then our nonadiabatic theory and Dirac’s theory are equivalent. However, differ if decoherence and population relaxation occur due to coupling to the environment. Then the nonadiabatic theory accurately describes the remaining coherences and state populations based on the Liouville equation for the time evolution of the density matrix with an added.

**Collision-induced spectroscopic processes and astrophysical applications**

** **The Hunt group has carried out high-accuracy *ab initio* calculations of the dipole moments induced during collisions of nonpolar molecules.
The induced dipoles give rise to collision-induced absorption and emission processes
in the infrared and far infrared. Our recent work has focused on the interaction-induced
dipoles of hydrogen molecules colliding with hydrogen atoms, helium atoms, and other
hydrogen molecules. Calculated spectra obtained from our results have been added
to the HITRAN database of the Harvard/Smithsonian Center for Astrophysics. Our results
are in use to characterize the spectra of very old, very cool white dwarf stars, and
to model the spectra of the outer planets, “hot Jupiters,” and “warm Neptunes.” On
a more speculative level, the results may have applications to the formation of the
first stars in the universe.

**Quantum computing and the entropy of Schr****ödinger’s cat states**

The Hunt group has examined the entropies of Schrödinger’s cat states
consisting of n qubits on noisy intermediate-scale quantum (NISQ) computers. We have
looked at the Shannon entropy of measurement outcomes and the von Neumann entropy,
determined by quantum state tomography. The Shannon entropy should be one, independent
of the number of qubits n. Instead, this entropy S rises almost linearly with the
number of qubits. The slope of S *versus* n provides a sensitive indicator of the quality of a quantum computer; we have found
different slopes for computers with the same quantum volume. The von Neumann entropy
should be zero for a pure quantum state, but it is non-zero due to the fault levels
of the quantum computers. We are currently examining time-evolution of the quantum
states using adiabatic quantum computing methods and Trotterization of the propagator.

**Van der Waals dispersion forces**

In 1939, Richard Feynman suggested an electrostatic interpretation of the van der Waals dispersion forces on the nuclei in interacting atoms in spherically symmetric (S) states. He stated that for atoms at long range, the quantum mechanical correlations between the electronic positions permitted a build-up of electronic charge in the region between the nuclei, thus producing a local dipole on each center. Feynman stated that then each nucleus was attracted by the distorted charge distribution of its “own” electrons, thus producing the attractive force. He noted that the local dipole and the van der Waals force both vary as the inverse seventh power of the separation between the nuclei, suggesting a common physical origin. About 30 years later, Joe Hirschfelder and Morton Eliason used perturbation theory to show numerically that Feynman’s statement was valid for interacting hydrogen atoms initially in the 1s state, at least to four figures. Larger systems could not be analyzed at that time. In 1990, Hunt provided an analytical proof of Feynman’s statement within the polarization approximation. Research in the group is now focusing on a highly accurate full configuration-interaction analysis of the van der Waals forces, with full inclusion of the anti-symmetrization of the wave function and electron exchange.

**Bell and Clauser-Horne-Shimony Holt inequalities**

With a group of high-school interns working in Summer 2019 and 2020, Hunt investigated whether violations of the Bell and Clauser-Horne-Shimony-Holt (CHSH) equalities could be detected on current quantum computers. The Bell inequalities are related to measurements of properties in a set of three (A, B, and C), where each property can be +1 or -1. Spin up and spin down along three different axes fit this prescription. The CHSH inequalities govern a linear combination of correlation functions of measurements. The inequalities are obeyed by all classical properties of this type, but they are violated in some quantum cases. The consequence of the violation of the Bell inequalities is that no "hidden variable" theory can be consistent with quantum mechanics unless it also permits faster than light communication of information. So, it is quite important. Violations of the inequalities are well known, and in fact the theory and measurement of the violations was the basis of the 2022 Nobel Prize in Physics, awarded to John Clauser, Anton Zeilinger, and Alain Aspect. We did not know at the outset whether current quantum computers would be accurate enough to show the violations. With one exception, the quantum computers that we tested showed the violations. The results came into quite good agreement with quantum predictions after use of an error mitigation strategy suggested in IBM’s qiskit documentation.

**Women in science**

** **While in Luxembourg to work on research topics with Alexandre Tkatchenko’s group in
Physics,** **Hunt gave a talk in the Bridge Forum Dialogue series at the Banque de Luxembourg.
She spoke about eminent women scientists, their accomplishments, and the obstacles
they had to overcome. The text of this talk and a pdf are provided at the link.