Four qubits Hamiltonian of the Rs. molischianum light-harvesting complex II ring

TL;DR

This paper constructs a four-qubit Hamiltonian model of the Rs. molischianum LH-II ring, analyzing energy levels, entanglement, and potential cavity QED experiments to better understand its quantum properties.

Contribution

It introduces a simplified four-qubit Hamiltonian for the LH-II ring and explores its entanglement and interaction with electromagnetic fields, linking biological systems with quantum physics.

Findings

Eigenstates show increasing entanglement up to maximum of 1

Hamiltonian models energy levels associated with electronic excitations

Potential for experimental cavity QED studies of the biological complex

Abstract

We will construct a simple four qubits Hamiltonian of the Rs. molischianum purple bacteria light harvesting complex II (LH-II) ring which yields energy levels that carry the ring's oscillator strength. In an excitonic representation, these levels are associated with the second and the third lowest electronic excitations of the ring. We will assume that qubits form a closed loop lattice and the interaction between qubits is only due to the exchange effect. As we will show, eigenstates are constructed in a such way that as we subsequently divide qubits of the Rs. molischianum LH-II ring into the subsystem A consisting of only one qubit and the subsystem B consisting of the remaining qubits, respective entropies of entanglement increase until the value of 1 for the maximally entangled state (bipartite system) is reached. Since the Hamiltonian in essence introduces a two-level approximation for the LH-II ring, we will go one step further and assume that interactions between qubits closed loop lattices and an electromagnetic field are described by the Jaynes-Cummings Hamiltonian. This assumption is interesting by itself, since it leads to behavior where the qubits lattice and field oscillate back and fourth exchanging a quantum of energy, at the Rabbi frequency. This opens a challenging opportunity to experimentally study the Rs. molischianum LH-II ring in the regime of cavity QED.