A silicon-based single-electron interferometer coupled to a fermionic sea

We study Landau-Zener-Stückelberg-Majorana (LZSM) interferometry under the influence of projective readout using a charge qubit tunnel-coupled to a fermionic sea. This allows us to characterize the coherent charge-qubit dynamics in the strong-driving regime. The device is realized within a silicon complementary metal-oxide-semiconductor (CMOS) transistor. We first read out the charge state of the system in a continuous nondemolition manner by measuring the dispersive response of a high-frequency electrical resonator coupled to the quantum system via the gate. By performing multiple fast passages around the qubit avoided crossing, we observe a multipassage LZSM interferometry pattern. At larger driving amplitudes, a projective measurement to an even-parity charge state is realized, showing a strong enhancement of the dispersive readout signal. At even larger driving amplitudes, two projective measurements are realized within the coherent evolution resulting in the disappearance of the interference pattern. Our results demonstrate a way to increase the state readout signal of coherent quantum systems and replicate single-electron analogs of optical interferometry within a CMOS transistor.

Figure 1

Dispersive detection of a DQD. (a) Scanning electron microscope image of a device connected to an rf-reflectometry setup via the top gate. A nearby on-PCB coplanar waveguide delivers MW signals. (b) Device schematic. Top: cross section perpendicular to current flow direction, indicating the location of the corner QDs, where BOX indicates the buried oxide layer. Bottom: top view of the device, with transparent top gate for clarity; five electronic transitions between dots and reservoirs marked by arrows. ${\mathrm{\Delta }}_{\text{c}}$ represents the tunnel coupling and ${\mathrm{\Gamma }}_{\text{L}}\text{(R)}$ the relaxation rates between the left (right) dot and the reservoirs. (c) Resonator phase response $\mathrm{\Delta }\phi$ as a function of top-gate and back-gate voltages ($V_{\text{TG}},V_{\text{BG}}$). The white dashed line emphasizes the ICT and the black solid arrow indicates the position of the trace in panel (d). DQD electron numbers appear in parentheses. (d) $\mathrm{\Delta }\phi$ as a function of $V_{\text{TG}}$, showing the relative intensity of the ICT and the DST.

Figure 2

Multipassage LZSM interferometry. Schematic of the probability distribution after the first (a) and second (b) passage. (c) $\mathrm{\Delta }\phi$ calculated (left of panel) vs experimental (right of panel), both panels mirrored in the horizontal direction with respect to one another. (d) Optical interferometry analog showing the photon paths (electron charge states), the beam splitters (fast passage through the anticrossing), and refocusing mirrors (microwave electric fields). Here the process is repeated $N$ times.

Figure 3

Multilevel LZSM interferometry. (a) Calculated DQD energy level diagram as a function of reduced detuning ${\varepsilon }_0/E_{\text{C}}$; ${\alpha }_{-}=0.05$ and $E_{\text{m}}/E_{\text{C}}=10$, where $E_{\text{m}}$ is the mutual charging energy. (b) $\mathrm{\Delta }\phi$ measured as a function of the detuning, ${\varepsilon }_0$, and MW amplitude, $A_{\text{mw}}$, for $f_{\text{mw}}=21$ GHz. Regions of constant $\mathrm{\Delta }\phi$, with well-defined electron numbers, are indicated in parentheses. The (10)-(01) anticrossing and the (00)-(10) and (01)-(11) crossings are indicated by black dashed lines. Incoherent, multipassage, double-passage, and single-passage LZSM regions are indicated by the blue star, red star, green circle, and yellow triangle, respectively. (c) $\mathrm{\Delta }\phi$ vs ${\varepsilon }_0$ trace at $A_{\text{mw}}=0.55$ meV and $f_{\text{mw}}=11$ GHz. Symbols as in (b).

Figure 4

Double-passage LZSM interferometry. LZ transition schematic at the (10)-(11) (a) and (01)-(11) (b) crossings. The blue arrow indicates $P_{\text{LZ}}\approx 1$ and the red arrow thickness shows the strength of the relaxation process. (c) $\mathrm{\Delta }\phi$ calculated (left) vs experimental [right, a section of Fig. 3]. (d) Optical interferometry analog now including the detector $D_{11}$ after the second passage [fast relaxation at the (01)-(11) transition]. (e) Optical interferometry analog for the single-passage regime including an additional detector $D_{00}$ after the first passage [relaxation at the (10)-(00) transition].