Optically detected measurement of the ground-state population of an ensemble of neutral donors in GaAs

Strong resonant elastic light scattering (RELS) from the donor-bound exciton transition in GaAs $\left(1.514\mathrm{eV}\right)$ occurs at neutral donors in the ground $\left(1S\right)$ state, but not at neutral donors in excited hydrogenic states. When $1.6\mathrm{THz}$ radiation is incident on an ensemble of neutral donors, we observe up to a 30% decrease in the RELS, corresponding to a decrease in the population of neutral donors in their ground states. This signature allows for optical detection of the ground-state population of donors, and is similar to quantum nondemolition measurement techniques used for readout of ion trap quantum computers. In this scheme, Auger recombination of the bound exciton, which changes the state of the donor during measurement, limits the measurement fidelity and maximum near infrared laser excitation intensity.

Figure 1

Schematic energy level diagram (not to scale) illustrating the use of the donor bound exciton state for readout. Initial states are hydrogenic orbitals of the electron bound the the neutral donor $\left(D^0\right)$, shown relative to the conduction band (CB), or ionization potential. Several donor bound exciton $\left(D^{0}X\right)$ rotational states are shown. (a) Neutral donors in the $1S$ state $\left(D^{0}1S\right)$ absorb near infrared laser light tuned to resonance with the $D^{0}X$ transition, and return to the ground state with high probability by reemitting light of the same energy (cycling transition). The presence of scattered light indicates the donor is in the ground (bright) state. (b) Donors in excited hydrogenic (dark) states do not scatter light because because optical transitions are weak and excitation is off-resonance.

Figure 2

Nonidealities associated with $D^{0}X$ decay. The $D^{0}X$ state decays via one of two pathways: (i) Direct recombination of the bound exciton is fast $(<1\mathrm{ns})$ and leaves the donor in the ground $\left(D^{0}1S\right)$ state. (ii) Exciton recombination with simultaneous excitation of the electron bound to the donor (Auger recombination) changes the state of the donor during measurement. These “two electron satelite” (TES) transitions occur at a much slower rate, and result in leakage of electrons into excited hydrogenic states during measurement (see also Fig. 3).

Figure 3

$5\mathrm{K}$ PL spectrum (log scale) of GaAs $(N_d-N_a=3\times {10}^{14}{\mathrm{cm}}^{-3})$ taken with CCD and grating spectrometer at $35\mu \mathrm{eV}$ $\left(0.02\mathrm{nm}\right)$ resolution. Laser excitation was at $1.52\mathrm{eV}$, $1\mathrm{mW}{\mathrm{cm}}^{-2}$ intensity. Labels identify transitions associated with the free exciton $\left(\mathit{\text{free}}X\right)$, the neutral donor-bound exciton $\left(D^{0}X\right)$, the ionized donor-bound exciton $\left(D^{+}X\right)$, and the neutral acceptor-bound exciton $\left(A^{0}X\right)$. $L$ denotes the rotational quantum number of the $D^{0}X$ initial state. (Inset) Linear scale PL of direct exciton recombination from the two lowest $D^{0}X$ rotational levels.

Figure 4

$5\mathrm{K}$ resonant emission spectra. The solid line is a typical emission spectrum including both RELS and PL. In this spectrum, the laser is resonant with the $D^{0}X$ $L=1$ transition (labeled RELS). PL from the $D^{0}X$ $L=0$ transition is also present. The open circles trace the RELS peak height obtained from a series of spectra at various excitation energies. The dashed line is a guide to the eye. The linewidths of the two transitions are due to inhomogeneous broadening. (Inset) Experimental geometry for collection of NIR emission.

Figure 5

RELS modulation versus incident NIR laser frequency (intensity $\sim 1\mathrm{mW}{\mathrm{cm}}^{-2}$). Sample temperature is $5\mathrm{K}$ and the incident THz power is $\sim 20\mathrm{mW}{\mathrm{cm}}^{-2}$. The error bars are due to fluctuations in the intensity of the molecular gas laser. Labels denote the spectral features shown in Fig. 3 (inset) and Fig. 4.

Figure 6

RELS modulation versus incident THz intensity. Open circles are data points. A fit to a two-level absorption saturation curve of the form $A[1-{(1+I∕I_0)}^{-1}]$ is included as a guide to illustrate the asymptotic behavior (solid line). The fit parameters are $I_0=13.7$ and $A=31$.