Electronic properties of a quasi-two-dimensional electron gas in semiconductor quantum wells under intense laser fields

A systematic study on the influence of two intense, long-wavelength, nonresonant laser fields on the electron energy levels and density of states (DOS) in $\mathrm{GaAs}∕\mathrm{AlGaAs}$ quantum wells is performed within a Green’s function approach. The carrier confinement pattern and its associated DOS are shown to be modified by the laser beams. For laser field polarizations parallel to the growth direction only the effective potential is changed whereas for in-plane polarizations only the DOS is altered in the sense that it is field-driven. The results show that for a $\mathrm{GaAs}∕\mathrm{AlGaAs}$ quantum well the effect of the laser field radiation is to induce strong blueshifts in the electronic energy levels. The DOS dependence on the laser-induced confinement characteristics changes from the usual ladder profile to a functional form that reminds us of a one-dimensional system.

Figure 1

Heterostructure growth direction ($z$ axis) and polarization/propagation directions for the laser field beams. The dark layer is the $\mathrm{GaAs}$ channel, which is sandwiched by two $\mathrm{AlGaAs}$ layers (light gray). The dark arrows indicate the propagation directions. Note that the laser radiation propagating along the $y$ axis ($z$ axis) is polarized parallel to the $z$ axis ($x$ axis).

Figure 2

Modifications in the conduction band edge and bound state energy levels for a $150\text{−}\AA$-wide $\mathrm{GaAs}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ single QW induced by an intense ${\mathrm{CO}}_2$ laser field polarized parallel to the growth axis ($z$ axis). The dashed lines represent the energies in the absence of external fields. The solid lines are for $F_{0z}=180\mathrm{kV}∕\mathrm{cm}$, corresponding to a laser-dressing parameter ${\alpha }_{0z}\sim 15\AA$. Note the fourth bound state energy level, initially just below the barriers, is made unbound as a consequence of the changes in the effective potential.

Figure 3

Blueshifts induced by an intense ${\mathrm{CO}}_2$ laser field on the bound state energy levels for a $200\text{−}\AA$-wide ${\mathrm{GaAs}∕\mathrm{Al}}_{0.35}{\mathrm{Ga}}_{0.65}\mathrm{As}$ single QW as a function of the laser-dressing parameter, which was modified only through the laser intensity. The behavior is almost linear, and the fifth energy level is made unbound for ${\alpha }_{0z}$ above $\sim 11.5\AA$.

Figure 4

The DOS for electrons confined in a $150\text{−}\AA$-wide $\mathrm{GaAs}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ single QW illuminated by two crossed ILFs. The EM radiation propagating along the $y$ axis is an intense ${\mathrm{CO}}_2$ laser field polarized parallel to the growth direction (i.e.,$F_z\widehat{z}$), whereas the one propagating along the $z$ axis is an intense $\mathrm{THz}$ laser field $\left({\omega }_x∕2\pi =1.0\mathrm{THz}\right)$ polarized along the $x$ axis (i.e., $F_x\widehat{x}$). The dashed line is for the DOS in the absence of external fields. The other (solid) lines are for $F_{0z}=180\mathrm{kV}∕\mathrm{cm}$. The thinner (thicker) line is for $F_{0x}=5\left(15\right)\mathrm{kV}∕\mathrm{cm}$, with an additional (DFKE) blueshift of $4.15\left(37.02\right)\mathrm{meV}$ due to the $\mathrm{THz}$ laser field.

Figure 5

The DOS for electrons confined in a $150\text{−}\AA$ wide $\mathrm{GaAs}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ single QW illuminated by two crossed, ILFs. The dashed line is for the DOS in the absence of external fields. The other lines are for $F_{0z}=180\mathrm{kV}∕\mathrm{cm}$ and $F_{0x}=5\mathrm{kV}∕\mathrm{cm}$ (${\mathrm{CO}}_2$ and $\mathrm{THz}$ laser sources, respectively). The thicker (thinner) solid line is for ${\omega }_x∕2\pi =0.5\left(1.0\right)\mathrm{THz}$. The dash-dotted line is for ${\omega }_x∕2\pi =5\mathrm{THz}$. Emphasis is given for the DOS around the ground state energy.