Amorphous two-dimensional optical lattices with coherently controlled morphologies in quantum well structures

It is shown theoretically that the interface morphology of a quantum well structure and coherent control of its optical properties can be used to generate an amorphous two-dimensional optical lattice. This is done by considering the interaction of an $n$-doped double-quantum-well structure containing three conduction subbands with an infrared laser beam responsible for the generation of quantum interference in the transitions between these subbands. We show that when a well/barrier interface in this structure contains large-scale monolayer growth islands the lateral variation of the conduction subband energies changes the effects of quantum coherence in these transitions along the quantum well plane. In the presence of electron tunneling in the double-quantum-well structure this leads to lateral modulation of the complex susceptibilities of these transitions, allowing the infrared laser beam to coherently suppress or enhance refractive indices of these transitions in specific regions in this plane while they become transparent. In other regions, the same laser field generates large amount of gain or absorption with different refractive indices. It is shown that for a signal field propagating along the quantum well plane these processes can generate an amorphous optical lattice with a morphology determined by the roughness of the quantum well interfaces and the frequency and intensity of the infrared laser. In the absence of such an infrared laser this plane is transparent to the signal field and has a uniform refractive index.

Figure 1

Schematic illustration of microscopic and macroscopic fluctuations, respectively, at the lower and upper interfaces of an ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}∕\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ QW structure. It is assumed that before deposition of the upper ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ layer the growth process is interrupted for a period of time. $L$ refers to the nominal width of the QW structure.

Figure 2

(Color online) Schematic illustrations of the potential profiles of the double-QW structures in regions of the QW plane where the wider (left) QW thickness is 20 (solid line), 21 (dashed line), or 19 ML (dotted line). The two-sided arrow represents the control field and the one-sided arrow refers to the signal field.

Figure 3

(Color online) An oblique illustration of the interface between the left ${\mathrm{Al}}_{0.42}{\mathrm{Ga}}_{0.58}\mathrm{As}$ barrier (top) and the nominally 20-ML-wide GaAs well (bottom). The terraces and valleys refer, respectively, to $+1$ and $-1$ ML fluctuations in the GaAs well thickness.

Figure 4

(Color online) Absorption coefficient (a) and refractive index change (b) of the 1-2 transitions in the 19 (dashed lines), 20 (solid lines), and 21 ML systems (dotted lines). The control field intensity is assumed to be $0.6\mathrm{MW}∕{\mathrm{cm}}^2$ and its wavelength is $5.59\mu \mathrm{m}$. The arrows refer to ${\lambda }_{\mathrm{s}}=8.58\mu \mathrm{m}$.

Figure 5

(Color online) Lateral response of the 19-, 20-, and 21-ML systems with the interface morphology shown in Fig. 3 when the signal field wavelength is $8.58\mu \mathrm{m}$. (a) refers to the absorption coefficient and (b) to the refractive index change in the QW plane. All other specifications are the same as those in Fig. 4.

Figure 6

(Color online) Absorption coefficient (a) and refractive index change (b) of the 1-2 transitions in the 19-ML (dashed lines), 20-ML (solid lines), and 21-ML (dotted lines) systems. The control field intensity is assumed to be $0.6\mathrm{MW}∕{\mathrm{cm}}^2$ and its wavelength is $5.23\mu \mathrm{m}$. The arrows refer to ${\lambda }_s=9.45\mu \mathrm{m}$.

Figure 7

(Color online) Lateral response of the QW structure shown in Fig. 2 with the interface morphology shown in Fig. 3 when the signal field wavelength is $9.45\mu \mathrm{m}$. (a) refers to the absorption coefficient and (b) to the refractive index change. Other specifications are the same as those in Fig. 6.

Figure 8

(Color online) Absorption coefficient (a) and refractive index change (b) of the 1-2 transitions in the 19-ML (dashed lines), 20-ML (solid lines), and 21-ML (dotted lines) systems. The control field intensity is assumed to be $0.6\mathrm{MW}∕{\mathrm{cm}}^2$ and its wavelength is $4.92\mu \mathrm{m}$. Thick arrows refer to ${\lambda }_s=8.58\mu \mathrm{m}$ and thin arrows to ${\lambda }_s=9.21\mu \mathrm{m}$.

Figure 9

(Color online) Lateral response of the QW structure shown in Fig. 2 with the interface morphology shown in Fig. 3 when the signal field wavelength is $8.58\mu \mathrm{m}$. (a) refers to the absorption coefficient and (b) to the refractive index change. Other specifications are the same as those in Fig. 8.