Group-velocity slowdown in a double quantum dot molecule

The slowdown of optical pulses due to quantum-coherence effects is investigated theoretically for an “active material” consisting of InGaAs-based double quantum dot molecules. These are designed to exhibit a long-lived coherence between two electronic levels, which is an essential part of a quantum-coherence scheme that makes use of electromagnetically induced transparency effects to achieve group-velocity slowdown. We apply a many-particle approach based on realistic semiconductor parameters that allows us to calculate the quantum dot material dynamics including microscopic carrier scattering and polarization dephasing dynamics. The group-velocity reduction is characterized in the frequency domain by a quasiequilibrium slowdown factor and in the time domain by the probe-pulse slowdown obtained from a calculation of the spatiotemporal material dynamics coupled to the propagating optical field. The group-velocity slowdown in the quantum dot molecule is shown to be substantially higher than what is achievable from similar transitions in typical InGaAs-based single quantum dots. The dependencies of slowdown and shape of the propagating probe pulses on lattice temperature and drive intensities are investigated.

Figure 1

Schematic drawing of setup for the calculation of group-velocity slowdown with a $V$ scheme formed by levels in the QD molecules as shown in Fig. 2. For the determination of the slowdown factor, the drive field is assumed to be cw; for the dynamical calculation a “quasi-cw” drive pulse with duration much larger than the probe pulse is used.

Figure 2

Schematic picture of the lowest-level wave functions and the geometry of the asymmetric double-QD molecule described in the text. The resonant probe and drive fields in a $V$-type quantum-coherence scheme are also shown.

Figure 3

Gain $g$ and slowdown $S^{\prime }$ versus probe detuning for $T=300$ K, $I_d=0.25{\mathrm{MW}/\mathrm{cm}}^2$ (a),(b); $T=300$ K, $I_d=0.7{\mathrm{MW}/\mathrm{cm}}^2$ (c),(d); and $T=150$ K, $I_d=0.25{\mathrm{MW}/\mathrm{cm}}^2$ (e),(f). The unexcited exciton transition energy is denoted by ${\epsilon }_x$.

Figure 4

Peak gain (a) and peak slowdown (b) versus drive intensity for a lattice temperature of 300 K (dashed line) and 150 K (solid line).

Figure 5

Slowdown-bandwidth product versus drive intensity for a lattice temperature of 300 K (dashed line) and 150 K (solid line).

Figure 6

Gain (a) and slowdown (b) versus drive-pulse intensity after a propagation distance of 1 $\mu$m for a cosh${}^{-2}$ probe pulse with a FWHM of 17.6 ps (dashed line) and 35.3 ps (dotted line) and a lattice temperature of 300 K. For comparison, the gain and slowdown factor for a cw probe (black solid line) without propagation effects is plotted.

Figure 7

Same plot as in Fig. 6 for a lattice temperature of 150 K.

Figure 8

Temporal shape of the probe-pulse field versus propagation distance for a drive-pulse intensity of $0.7$ MW cm${}^{-2}$. The shape of the reference pulse versus propagation distance is plotted at $z=0\mu$m, $z=50\mu$m, and $z=100\mu$m for comparison. The initial shape of the probe and reference pulse is a cosh${}^{-2}$. The lattice temperature is 300 K.

Figure 9

Same as Fig. 8 for a drive-pulse intensity of $1.8$ MW cm${}^{-2}$. The reference pulse is shown for $z=0\mu$m, $z=100\mu$m, and $z=200\mu$m.

Figure 10

Temporal shape of the probe-pulse field versus propagation distance for a drive-pulse intensity of $0.7$ MW cm${}^{-2}$. The shape of the reference pulse versus propagation distance is plotted at $z=0\mu$m, $z=50\mu$m, and $z=100\mu$m for comparison. The initial shape of the probe and reference pulse is a cosh${}^{-2}$. The lattice temperature is 150 K.

Figure 11

Same as Fig. 10 for a drive-pulse intensity of $1.8$ MW cm${}^{-2}$. The reference pulse is shown for $z=0\mu$m, $z=100\mu$m, and $z=200\mu$m.

Figure 12

Temporal field shape of the probe pulse for a drive-pulse intensity of 1.8 MW/cm${}^2$ after propagation distance of 0 $\mu$m (solid), 100 $\mu$m (dashed), 200 $\mu$m (dashed-dotted), 250 $\mu$m (dotted). The initial shape of the probe pulse is a cosh${}^{-2}$. The lattice temperature is 150 K.

Figure 13

Schematic picture of the geometry of the single QD described in the text. The resonant probe and drive fields in a $V$-type quantum-coherence scheme are also shown.

Figure 14

Peak gain (a) and peak slowdown (b) versus drive intensity for a lattice temperature of 150 K (solid line) and 300 K (dashed line) for a deep single QD.

Figure 15

Peak gain (a) and peak slowdown (b) versus drive intensity for the QD molecule (solid line) and the deep single QD. The lattice temperature is 150 K.