Three-point functions in ABJM and Bethe Ansatz

We develop an integrability-based framework to compute structure constants of two sub-determinant operators and a single-trace non-BPS operator in ABJM theory in the planar limit. In this first paper, we study them at weak coupling using a relation to an integrable spin chain. We first develop a nested Bethe ansatz for an alternating SU(4) spin chain that describes single-trace operators made out of scalar fields. We then apply it to the computation of the structure constants and show that they are given by overlaps between a Bethe eigenstate and a matrix product state. We conjecture that the determinant operator corresponds to an integrable matrix product state and present a closed-form expression for the overlap, which resembles the so-called Gaudin determinant. We also provide evidence for the integrability of general sub-determinant operators. The techniques developed in this paper can be applied to other quantities in ABJM theory including three-point functions of single-trace operators.

Quantum Dark Solitons in the 1D Bose Gas: From Single to Double Dark-Solitons

We study quantum double dark-solitons, which give pairs of notches in the density profiles, by constructing corresponding quantum states in the Lieb–Liniger model for the one-dimensional Bose gas. Here, we expect that the Gross–Pitaevskii (GP) equation should play a central role in the long distance mean-field behavior of the 1D Bose gas. We first introduce novel quantum states of a single dark soliton with a nonzero winding number. We show them by exactly evaluating not only the density profile but also the profiles of the square amplitude and phase of the matrix element of the field operator between the N-particle and (N−1)-particle states. For elliptic double dark-solitons, the density and phase profiles of the corresponding states almost perfectly agree with those of the classical solutions, respectively, in the weak coupling regime. We then show that the scheme of the mean-field product state is quite effective for the quantum states of double dark solitons. Assigning the ideal Gaussian weights to a sum of the excited states with two particle-hole excitations, we obtain double dark-solitons of distinct narrow notches with different depths. We suggest that the mean-field product state should be well approximated by the ideal Gaussian weighted sum of the low excited states with a pair of particle-hole excitations. The results of double dark-solitons should be fundamental and useful for constructing quantum multiple dark-solitons.

Ultrafast carrier dynamics at organic donor-acceptor interfaces - A quantum-based assessment of the hopping model

We investigate the charge transfer dynamics of photogenerated excitons at the donor-acceptor interface of an organic solar cell blend under the influence of molecular vibrations. This is examined using an effective Hamiltonian, parametrized by density functional theory calculations, to describe the full quantum behaviour of the relevant molecular orbitals, which are electronically coupled with each other and coupled to over one hundred vibrations (via Holstein coupling). This electron-phonon system is treated in a numerically quasi-exact fashion using the matrix-product-state ansatz. We provide insight into different mechanisms of charge separation and their relation to the electronic driving energy for the separation process. We find ultrafast electron transfer, which for small driving energy is dominated by kinetic processes and at larger driving energies by dissipative phonon emission connected to the prevalent vibration modes. Using this fully quantum mechanical model we perform a benchmark comparison to a recently developed semi-classical hopping approach, which treats the hopping and vibration time scales consistently. We find qualitatively and quantitatively good agreement between the results of the sophisticated matrix-product-state based quantum dynamics and the simple and fast time-consistent-hopping approach.

Experimental study of quantum coherence decomposition and trade-off relations in a tripartite system

Quantum coherence is the most fundamental of all quantum quantifiers, underlying other well-known quantities such as entanglement. It can be distributed in a multipartite system in various ways—for example, in a bipartite system it can exist within subsystems (local coherence) or collectively between the subsystems (global coherence), and exhibits a trade-off relation. In this paper, we experimentally verify these coherence trade-off relations in adiabatically evolved nuclear spin systems using an NMR spectrometer. We study the full set of coherence trade-off relations between the original state, the bipartite product state, the tripartite product state, and the decohered product state. We also experimentally verify the monogamy inequality and show that both the quantum systems are polygamous during the evolution. We find that the properties of the state in terms of coherence and monogamy are equivalent. This illustrates the utility of using coherence as a characterization tool for quantum states.