Thermal entanglement in a triple quantum dot system

Abstract

We present studies of thermal entanglement of a three-spin system in triangular symmetry. Spin correlations are described within an effective Heisenberg Hamiltonian, derived from the Hubbard Hamiltonian, with super-exchange couplings modulated by an effective electric field. Additionally a homogenous magnetic field is applied to completely break the degeneracy of the system. We show that entanglement is generated in the subspace of doublet states with different pairwise spin correlations for the ground and excited states. At low temperatures thermal mixing between the doublets with the same spin destroys entanglement, however one can observe its restoration at higher temperatures due to the mixing of the states with an opposite spin orientation or with quadruplets (unentangled states) always destroys entanglement. Pairwise entanglement is quantified using concurrence for which analytical formulae are derived in various thermal mixing scenarios. The electric field plays a specific role -it breaks the symmetry of the system and changes spin correlations. Rotating the electric field can create maximally entangled qubit pairs together with a separate spin (monogamy) that survives in a relatively wide temperature range providing robust pairwise entanglement generation at elevated temperatures.

Entanglement switching via the Kondo effect in triple quantum dots

“…As expected, there are two regimes of interest, depending on the inter-dot couplings (t 2 higher or lower compared to a transition value t 2c ), similar to the result of a recent analysis of thermal entanglement of isolated TQDs [51].…”

“…The main reason for the renormalization can, in fact, be understood from an effective spin model by tracing out the empty and doubly occupied states, and representing the conduction band using a single spin S D [29][30][31]35,37,38,51,55], (13) with the exchange couplings J 1,2,3 = 4t 2 1,2,3 /U . First we consider a simple TQD system with J D = 0, i.e., without the coupling to spin S D .…”

“…The transition at t 2c ∼ t 1 is explained by the level crossing of the corresponding doublet eigenstates of the isolated TQD [29][30][31]35,37,38,51]. It should be noted that two-channel Kondo effects found in a quantum dot trimer coupled to the leads through two adjacent quantum dots [36][37][38] do not occur in the system considered here.…”

“…Recently it was shown that in isolated TQD the entanglement is generated in the subspace of doublet states with different pairwise spin correlations for the ground and excited states [51]. The mixing of the states with an opposite spin orientation always monotonically destroys entanglement.…”

Regular and singular Fermi liquid in triple quantum dots: Coherent transport studies

“…Pauli exclusion principle), therefore superexchange processes dominates [41,52,39,40]. The ground state is given by doublet states.…”