Population inversion in quantum dot ensembles via adiabatic rapid passage

Electrical detection of adiabatic rapid passage (ARP) in quantum dot ensembles is explored by extension of a simple physical model. We include exciton and biexciton states and model the current flow into the external circuit which occurs following ionization of the exciton and tunneling of the separate carriers. The inversion produced by ARP is robust with respect to fluctuations in coupling and detuning, and we show directly that this manifests itself as only minor variation in the current drawn per dot, as the number of dots in an ensemble is increased. This approach therefore can provide a means of initializing many dots simultaneously into a specific excited state.

Figure 1

The calculated diagonal density-matrix elements for the two-level model excited by a bandwidth-limited optical pulse resonant with the exciton transition, as a function of time. From (a) to (d), the optical power is increased in steps of factors of 2. The solid line represents the ground state and the dashed line the excited state.

Figure 2

(Color online) The calculated diagonal density-matrix elements for the two-level model excited by a chirped pulse as a function of time. From (a) to (d), the optical power is increased in steps of factors of 2. The solid line represents the ground state and the dashed line the excited state. (e) shows the envelope of the electric field of the chirped pulse on an arbitrary scale and (f) the linear variation in the instantaneous frequency with time through the pulse, expressed as a percentage of the central frequency.

Figure 3

(Color online) Panels (a)–(c): single-dot photocurrent as a function of the dimensionless chirp ${\alpha }^{\prime }/{\tau }_0^2=\alpha {\tau }^2$ and pulse energy. The ratio of the exciton to biexciton coupling ${\zeta }_x/{\zeta }_b$ is (a) 100, (b) 10, and (c) 1, corresponding to excitation pulses ranging from almost (a) circular to (c) linear polarization. Panel (d): photocurrent from an ensemble of 50 such dots with ${\zeta }_x/{\zeta }_b=100$. The grayscale is in electrons per dot per pulse, with a contour at 1 [for panels (a), (b), and (d)] and at 2 [for panel (c)]. In panel (d), fluctuations in the dot energies and coupling strengths preclude populating the dots with resonant pulses, destroying the Rabi oscillations. Chirped pulses however lead to robust excitonic inversion, with occupations close to one electron per dot per pulse over a large parameter region.