Photon assisted tunneling in pairs of silicon donors

Shallow donors in silicon are favorable candidates for the implementation of solid-state quantum computer architectures because of the promising combination of atomiclike coherence properties and scalability from the semiconductor manufacturing industry. Quantum processing schemes require (among other things) controlled information transfer for readout. Here we demonstrate controlled electron tunneling at 10 K from P to Sb impurities and vice versa with the assistance of resonant terahertz photons.

Figure 1

For a Poisson distribution, the probability that there are no donors in a volume $V$ is $e^{-nV}$, so the cumulative probability that there are other donors within radius $r$ from one impurity of interest is just 1–exp(–4π$n{r}^3$/3), where the lines shown are for different values of $n$. Hence 98.5% of impurities have a neighbor within a distance $n^{-1/3}$. (It also follows that the probability density function for the interdonor distance is 4π$r^{2}n$ exp(–4π$n{r}^3$/3) per unit radius and the expected interdonor distance is ⟨$r$⟩ = 0.554$n^{-1/3}$.) Also indicated along the abscissa are the center-to-center distances for touching orbitals (i.e., the Bohr diameters) found by scaling the binding energies [11].

Figure 2

Small-signal (a) and nonequilibrium (b) transmission spectroscopy of the codoped silicon sample. Transition energies [12] are labeled according to the excited state (all originating from the 1$s$($A_1$) ground state) for (a) antimony and (b) phosphorus (1-2$p_0$, 2-2$p_{\pm }$, 3-3$p_0$, 4-3$p_{\pm }$, 5-4$p_{\pm }$, 6-5$p_{\pm }$, and 7-conduction band). In (a) the transmission signal at 4.2 K has been normalized to the instrument response. In (b) the differential transmission of the probe at 10 K is shown at fixed delay between probe and pump pulses of +15 ps (pumped), normalized with the signal at −150 ps (unpumped).

Figure 3

The logarithm and reciprocal of normalized Δ$T$, the change in probe transmission due to the pump, as a function of the delay between the pulses. The excitation was directly from $P_{1s}$ into the continuum at 11.1 THz. The transmission recovery is well described by reciprocal decay (with $t_R=65$ ps) as can be seen from the linear relationship between 1/Δ$T$ and delay.

Figure 4

As Fig. 3 for different samples and resonant transitions as labeled. Every panel has the same axes, and the ticks on the right-hand ordinate are integer steps in ln(Δ$T$). For each experiment on the codoped sample (right column) the same transition was measured in the corresponding monodoped sample (left column) with identical conditions. The monodoped samples are well described by single exponential decays with the following relaxation times: $1s\to 2p_0$, P: $T_1=175$ ps; $1s\to 2p_{\pm }$, P: $T_1=95$ ps; $1s\to 2p_{\pm }$, Sb: $T_1=135$ ps. For the codoped sample the recovery was fitted with both components: $1s\to 2p_0$, P: $T_1=142$ ps, $t_R=70$ ps; $1s\to 2p_{\pm }$, P: $T_1=100$ ps, $t_R=64$ ps; $1s\to 2p_{\pm }$, Sb: $T_1=166$ ps, $t_R=67$ ps.