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Physical Review A

Quantum excitation transfer, entanglement, and coherence in a trimer of two-level systems at finite temperature

Ethan Wyke, Abuenameh Aiyejina, Roger Andrews

Published Jun 1, 2020• 8 citations
Publisher

Abstract

The excitation probabilities, concurrence, and relative entropy of coherence for an array of three coupled two-level systems are studied analytically and numerically at various temperatures. We determine the excitation probabilities for each site, the concurrence between the outer sites, and the relative entropy of coherence of the system for three energy configurations of the trimer and various temperatures. We find that a well configuration (i.e., negative detuning of the inner site) at all temperatures localizes the excitation on the inner site, while a barrier configuration (i.e., positive detuning of the inner site) causes the excitation to be localized on the outer sites. We determine the decay times for the probabilities, concurrence, and relative entropy of coherence for all energy configurations at each temperature. The barrier configuration creates the largest concurrence at zero temperature; however, we find that the uniform configuration is able to resist the loss of quantum coherence and entanglement at higher temperatures more so than any of the other configurations.

DOI
10.1103/physreva.101.062101

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We study coherent energy transfer of a single excitation and quantum entanglement in a dimer, which consists of a donor and an acceptor modeled by two two-level systems. Between the donor and the acceptor, there exists a dipole-dipole interaction, which provides the physical mechanism for coherent energy transfer and entanglement generation. The donor and the acceptor couple to two independent heat baths with diagonal couplings that do not dissipate the energy of the noncoupling dimer. Special attention is paid to the effect on single-excitation energy transfer and entanglement generation of the energy detuning between the donor and the acceptor and the temperatures of the two heat baths. It is found that, the probability for single-excitation energy transfer largely depends on the energy detuning in the low temperature limit. Concretely, the positive and negative energy detunings can increase and decrease the probability at steady state, respectively. In the high temperature limit, however, the effect of the energy detuning on the probability is negligibly small. We also find that the probability is negligibly dependent on the bath temperature difference of the two heat baths. In addition, it is found that quantum entanglement can be generated in the process of coherent energy transfer. As the bath temperature increases, the generated steady-state entanglement decreases. For a given bath temperature, the steady-state entanglement decreases with the increase of the absolute value of the energy detuning.
The entanglement of two qubits, each defined as an effective two-level, spin 1/2 system, is investigated for the case that the qubits interact via a Heisenberg XY interaction and are subject to decoherence due to population relaxation and thermal effects. For zero temperature, the time-dependent concurrence is studied analytically and numerically for some typical initial states, including a separable (unentangled) initial state. An analytical formula for non-zero steady state concurrence is found for any initial state, and optimal parameter values for maximizing steady state concurrence are given. The steady state concurrence is found analytically to remain non-zero for low, finite temperatures. We also identify the contributions of global and local coherence to the steady state entanglement.
We analyze a quantum wire that consists of a linear chain of three qutrits with nearest-neighbor interactions and detuning on the central qutrit. We derive the detuning conditions for perfect state transfer of a double excitation and for maximal entanglement between the first and third qutrits. We also analytically determine the times for perfect state transfer and maximal entanglement, which are found to be periodic. We also show that perfect state transfer is a necessary condition for maximal entanglement, with the first occurrence of maximal entanglement at half the time for the first occurrence of perfect state transfer.
We derive and simulate the wavefunctions and double-excitation probabilities for dimer and trimer three-level systems. Perfect state transfer occurs for pulse strengths that are odd multiples of π /2 when the parameter Jt equals odd multiples of π /2 and π /2 for the dimer and trimer, respectively. Near-perfect state transfer with a single photon occurred for photon coupling strength g =2 J when Jt=1.99,19.87 in the dimer and Jt=2.62,25.51 in the trimer. The nature of perfect state transfer is due to localization and transfer of double excitations for given pulse strengths and times.
The dynamics of tripartite entanglement and intramolecular energy for one harmonic- and two anharmonic-vibrational modes in a symmetric trimer molecule is studied for various initial states, where the entanglement is quantified in terms of concurrence and the interacting energy among three modes is calculated to establish a link between entanglement and energy. It is shown that the concurrence and the interacting energy behave dominantly positive correlation for the localized state in the anharmonic-vibrational mode, while they are dominantly anti-correlated for the localized state in the harmonic-vibrational mode. The relation between bipartite entanglement and the energy in a subsystem is discussed as well. Those are useful for quantum computing and quantum information in high dimensional states prepared in polyatomic molecules.