Probing the Quantum States of a Single Atom Transistor at Microwave Frequencies

Abstract

The ability to apply gigahertz frequencies to control the quantum state of a single P atom is an essential requirement for the fast gate pulsing needed for qubit control in donor-based silicon quantum computation. Here, we demonstrate this with nanosecond accuracy in an all epitaxial single atom transistor by applying excitation signals at frequencies up to ≈13 GHz to heavily phosphorus-doped silicon leads. These measurements allow the differentiation between the excited states of the single atom and the density of states in the one-dimensional leads. Our pulse spectroscopy experiments confirm the presence of an excited state at an energy ≈9 meV, consistent with the first excited state of a single P donor in silicon. The relaxation rate of this first excited state to the ground state is estimated to be larger than 2.5 GHz, consistent with theoretical predictions. These results represent a systematic investigation of how an atomically precise single atom transistor device behaves under radio frequency excitations.

Unusual Quantum Transport Mechanisms in Silicon Nano-Devices

“…In view of this, it is now possible to obtain extremely precise control of the quantum properties of electrons confined in silicon CMOS compatible structures even during fabrication [ 4 , 5 ] and it is also possible to engineer devices precise to a single atom level [ 21 , 22 , 23 , 24 ]. These new enhanced fabrication capabilities have translated into an improved ability for the control of all the quantum degrees of freedom (for example spin, charge, pseudo-spin) of electrons [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 20 , 21 , 22 , 23 , 24 ] and holes [ 25 ] in silicon nanostructures [ 4 , 5 ]. Finally, although there are still a few open questions in this area, for example see Reference [ 4 ], the achievements described above have translated into improved control of the electronic signature that can be observed in these devices.…”

“…These degeneracies can in turn be broken by all other atomic effects that go under the name of valley-splitting see Figure 1 a). For isolated dopant-atoms in the silicon lattice, i.e., single atom transistors [ 8 , 9 , 10 , 11 , 12 , 13 , 17 , 21 , 22 , 23 , 24 ], in the most ideal situation, the final configuration gives a 1-fold degenerate 1s state (A1), below a 3-fold degenerate 1s and another 2-fold 1s state, as shown in Figure 1 b), while other intermediate situations are possible [ 8 , 9 ]. As an example, the lower energetic valley-orbital states are fundamental for the observation of the Kondo and the Kondo-Fano effects described in the section below.…”

“…Consequently, even when they are operating at 4.2 K and at GHz frequencies of excitation, non-adiabatic effects are not as efficient in causing errors in SAPs, as opposed to QDs pumps [ 12 , 13 ]. Furthermore, for SAPs the relaxation rates (Γ relaxation , see also schematic in Figure 7 a) controlling the relaxation of the electrons from excited states to the ground states are considerably faster [ 24 ] when compared to the equivalent ones observed in QD pumps [ 48 ]. Here, it is very important to emphasize that the fast relaxation rate effects observed naturally in SAPs are directly linked to the energy spectrum that the multi-valley physics imposes on these silicon systems [ 12 , 13 , 24 ].…”

Electrooptomechanical Equivalent Circuits for Quantum Transduction

“…(24), the mechanical frequency ! m,V entering this definition now contains static shifts from both the EM and OM interactions, (23) and (72), combining to…”

“…(89) in terms of the upper and lower sideband optical currents I o,± (⌦) (⌦ > 0) Furthermore, while the mechanical capacitance C m is still defined by Eq. (24), the mechanical frequency ω m,V entering this definition now contains static shifts from both the EM and OM interactions, (23) and (72), combining to…”