Dipolariton formation in quantum dot molecules strongly coupled to optical resonators

In this theoretical work, we study a double quantum dot interacting strongly with a microcavity, while undergoing resonant tunneling. Effects of interdot tunneling on the light-matter hybridized states are determined, and tunability of their brightness degrees and associated dipole moments is demonstrated. These results predict dipolariton generation in artificial molecules coupled to optical resonators, and provide a promising scenario for control of emission efficiency and coherence times of exciton polaritons.


INTRODUCTION
In recent years, interest for light generation from low dimensional structures coupled to electrodynamics cavities has increased noticeably [1][2][3]. In particular, quantum dots (QDs) have proved to be an excellent tool for experimental observation of purely quantum phenomena, like single photon emission and photon entanglement, both of which can be enhanced through an optical resonator by strengthening the coupling between the QD and the electromagnetic field [4,5].
Regarding ability for implementation of electronic devices, the use of artificial atoms instead of natural ones results advantageous, given the obvious convenience of working with stable solid structures rather than with tiny and elusive atoms, aiming on-chip light-matter hybrid structures [15].
In turn, microcavities confine light in a small volume and increase radiation-matter coupling as described by the Purcell effect [16,17]. In such a strong coupling regime, the system eigenvectors are hybridized states of the QD and the cavity field. These kind of mixed states of light and mater are known as "exciton polaritons" (EP) [27]. Strong radiation-matter coupling for a QD inside a planar cavity has been successfully observed and progressively improved along this century [9,14,18].
On the other hand, coupling by resonant tunneling between adjacent QDs (artificial molecules) has been proposed as an efficient mechanism to improve tunability in zero dimensional systems [19,20]. Between different alternatives to control tunneling in double quantum dot (DQD) structures, bias tuning has been found so far as the most successful [21][22][23].
In this work, we study the properties of EP modes for a DQD embedded in a microcavity, in such a way that interdot coupling and strong radiation matter interaction are simultaneously considered, and formation of polaritons with adjustable dipole moment (dipolaritons) and reduced brightness (dark polaritons), is explored [24]. to the firs rung of the Jaynes-Cummings (JC) ladder [25].
In absence of a bias field, the direct exciton (DX) coupled to a photonic mode would form a conventional polariton with a coupling energy given by the Rabi frequency Ω (which in turn depends on the radiation-matter constant g) [14]. On its side, the indirect exciton (IX) is assumed to be a dark state, given the reduced overlap between electron and hole.
Application of an external bias F on the DQD allows for tuning of the indirect exciton energy, and resonant tunneling between the | 0, DX and | 0, IX states can be achieved.
The tunneling rate J depends on the potential barrier experienced by the confined single particles, and is in principle unmodified by the cavity. For simplicity, hole tunneling can be reasonably neglected and then, only electron hoping is considered [23]. The Hamiltonian for the n-th JC rung in the above described basis reads ( = 1) where ω C is the cavity mode frequency, e is the electron charge, d is interdot distance between the IX and DX (the cavity and the DX),n =â †â +σ † dx,gσ − g,dx +σ † ix,gσ − g,ix is the polariton number operator (withâ andâ † the photon annihilation and creation operators, respectively), andσ † dx,g = |DX g| (σ † ix,g = |IX g|) is the transition dipole operator between the DX (IX) and the DQD ground state.
To calculate the dynamics of the system at very low temperature, where phonon dissipation effects can be ignored, we use the imaginary part of the effective Hamiltonian yielded by equation (1) in which κ represents the cavity scape rate of photons and γ DX is the direct exciton recombination rate (we neglect the indirect exciton recombination because of the poor electron-hole overlap in this configuration, i.e. γ DX = 0). (1)

By diagonalizing the Hamiltonian in equation
where α = LP, M P, U P ; for each EP mode α, we define the bright polariton degree and the exciton dipole moment BP D indicates how strong is the mixing between the DX and the cavity mode, and EDM accounts for the dipole moment associated to the corresponding EP mode. To evidence how polaritonic lifetimes can be tuned along a wide range, we calculate the system dynamics by diagonalizing the complex matrix of equation (2) [27]. Figure 4 shows the bias field dependence of the recombination rates and lifetimes of all three polaronic branches. The parameters γ DX = 2π0.1 GHz and κ = 2π16 GHz were used in the simulation.
Those curves reveal how the lower and upper branches allow tuning the polariton lifetimes between tens and hundreds of picoseconds, by application of moderate electric fields (|F | < 20 kV/cm).

CONCLUSION
The eigenenergy modes of a quantum dot molecule strongly coupled to a microcavity have been studied. By obtaining the dressed states, the corresponding fractional components and