Observation of Non-Markovian Dynamics of a Single Quantum Dot in a Micropillar Cavity

We measure the detuning-dependent dynamics of a quasiresonantly excited single quantum dot coupled to a micropillar cavity. The system is modeled with the dissipative Jaynes-Cummings model where all experimental parameters are determined by explicit measurements. We observe non-Markovian dynamics when the quantum dot is tuned into resonance with the cavity leading to a nonexponential decay in time. Excellent agreement between experiment and theory is observed with no free parameters providing the first quantitative description of an all-solid-state cavity QED system based on quantum dot emitters.

Figure 1

Illustration of the three distinct dynamical regimes for a coupled QD cavity, with the physical system in the left-hand panel and the resulting dynamics obtained from Eq. (2) in the right-hand panel. (a) Weak coupling regime: the QD decays exponentially with a Purcell enhanced rate ($F_P\gamma$). (b) Intermediate regime: the QD dynamics is non-Markovian leading to a nonexponential decay in time. For reference the dashed curve shows an exponential decay. (c) Coherent regime: the QD population undergoes Rabi oscillations. In regimes (b) and (c) the coherent backaction of the radiation field on the QD leads to non-Markovian dynamics.

Figure 2

(a) An example of an emission spectrum obtained with $p$-shell excitation at $T=10\mathrm{K}$. (b) Measured decay curves close to and far from cavity resonance. The data recorded at $\Delta =-17\mu \mathrm{eV}$ are modeled with the non-Markovian model obtained by solving Eq. (2) [dark gray (blue) solid line] with an additional slow exponential decay accounting for recombination of dark excitons. The green dashed curve represents the case where the Markov approximation has been assumed. The black curve shows the instrument response function (IRF) of the measurements that is used to convolute the theory in order to model the experimental data. Off resonance the Markov approximation is excellent [light gray (orange) solid line]. (c) The fast parts of the modeled decay curves recorded at $\Delta =-17\mu \mathrm{eV}$ (blue solid line) displaying a pronounced offset from the Markovian theory (green dotted curve).

Figure 3

(a) The detuning-dependent decay rate of the QD extracted by assuming the Markov approximation and with no approximations (non-Markovian). The large deviation between the two approaches clearly illustrates the importance of non-Markovian effects. The theory curve is calculated using only the experimentally measured parameters. (b) The slow decay rate ${\gamma }_s$ and (c) the reduced ${\tilde{\chi }}^2$ for the Markovian fits versus detuning obtained by modeling decay curves like the ones shown in Fig. 2b.