Phonon-assisted tunnelling in a double quantum dot molecule immersed in a cavity

Abstract

The effects caused by phonon-assisted tunnelling (PhAT) in a double quantum dot (QD) molecule immersed in a cavity were studied under the quantum Markovian master equation formalism in order to account for dissipation phenomena.We explain how for higher PhAT rates, a stronger interaction between a QD and the cavity at off-resonance takes place through the resonant interaction of another QD and the cavity, where the QDs interact through tunnelling. A closer look at the system's allowed optical transitions as a function of PhAT rates showed coalescence of the transition energies, leading to a loss of spectroscopic resolution in the photoluminescence (PL) spectrum. This coalescence occurs at several exceptional points, suggesting a quantum dynamical phase transition.

Light emission properties in a double quantum dot molecule immersed in a cavity: Phonon-assisted tunneling

“…The three optical transitions from the 1st to 0th excitation manifolds are shown in each panel in dashed lines. The left and central panels show a coalescence behavior, caused by a dynamical phase transition where spectroscopic resolution is lost due to the action of PhAT [5]. For low tunneling rates, the lateral transitions show luminescence, while the central transition remains inactive, as shown in the left panel.…”

“…The interaction between each QD and the cavity mode is taken to be described by the dipole approximation in the rotating wave approximation, which is outlined by the Jaynes-Cummings interaction [17]. Hereafter, we follow the construction of our previous work [5]. Thus, the Hamiltonian of the double QD-cavity system is…”

“…where σ † j (σ j ) is the creation (annihilation) operator for the j-th two-level QD with frequency ω j , a † (a) is the creation (annihilation) operator for the cavity mode with frequency ω 0 , T is the tunnelling rate and g j is the QD-cavity interaction constant between the mode and the j-th QD. However, the physical system entangles with the surrounding environment, leading to decoherence processes that are well-described in the Born-Markov approximation by the quantum master equation [18,5]:…”

“…and its characteristic polynomial gives analytic expressions for the eigenvalues. Their imaginary part are the transition frequencies between the 0th and 1st excitation manifolds, whereas their real part are the corresponding half widths at half maximum [5]. Finally, the g (2) second-order coherence function is defined as…”

Dark Exciton Giant Rabi Oscillations with no External Magnetic Field

“…A formal solution of this equation for a time-independent Liouvillian is ρ(t) = k e Λ k t Tr[ k ρ(0)] k , where Λ k are the complex eigenvalues of L with corresponding eigenmatrices k . The eigenvalues are associated to the emission peaks [42][43][44] as they show both the peak location Im{Λ k } and the full width at half maximum − Re{Λ k }. On the other hand, the eigenmatrices account for information about which states are involved in each transition [45].…”