Scalable qubit architecture based on holes in quantum dot molecules

Spins confined in quantum dots are a leading candidate for solid-state quantum bits that can be coherently controlled by optical pulses. There are, however, many challenges to developing a scalable multibit information processing device based on spins in quantum dots, including the natural inhomogeneous distribution of quantum dot energy levels, the difficulty of creating all-optical spin manipulation protocols compatible with nondestructive readout, and the substantial electron-nuclear hyperfine interaction-induced decoherence. Here, we present a scalable qubit design and device architecture based on the spin states of single holes confined in a quantum dot molecule. The quantum dot molecule qubit enables a new strategy for optical coherent control with dramatically enhanced wavelength tunability. The use of hole spins allows the suppression of decoherence via hyperfine interactions and enables coherent spin rotations using Raman transitions mediated by a hole-spin-mixed optically excited state. Because the spin mixing is present only in the optically excited state, dephasing and decoherence are strongly suppressed in the ground states that define the qubits and nondestructive readout is possible. We present the qubit and device designs and analyze the wavelength tunability and fidelity of gate operations that can be implemented using this strategy. We then present experimental and theoretical progress toward implementing this design.

Figure 1

(a) Schematic band diagram of proposed qubit QDM. Direct (D) and Indirect (I) optical transitions are schematically indicated. (b) Cross-sectional STM of a QDM demonstrating the stacking of QDs and the possibility of lateral offsets. (c) Photonic cavity architecture incorporating multiple QDMs. (d) Schematic cross section of device heterostructure.

Figure 2

(a) and (b) Calculated energy levels for the $X^{+}$ (a) and $h$${}^{+}$ (b) states as a function of applied electric field in the presence of a 1-T magnetic field parallel to the optical axis. Right column indicates the dominant atomic-like basis states for each group of molecular states. (c) Hole-spin contributions to one-hole eigenstate as a function of applied electric field.

Figure 3

(a) Energy of direct and indirect PL from the neutral exciton in a single QDM as a function of applied electric field. (b) Ratio of PL intensity (indirect/direct) as a function of applied electric field. AC1 indicates the region in which the direct and indirect transitions anticross. AC2 indicates a region in which the energy and intensity of the direct transition is influenced by an anticrossing with an excited indirect transition (not shown).

Figure 4

Proposed strategy for (a) spin initialization, (b) manipulation, and (c) readout using optical transitions of QDMs. Top (bottom) rows indicate the spin projections of electrons (holes) in the top (right column) and bottom (left column) QDs.

Figure 5

(a) Energies of optical transitions in our designed QDM as a function of applied electric field. The two topmost lines (red) indicate the transitions between the two qubit states and the target $X^{+}$ state ($|t\rangle$). The second highest pair of lines (black) indicate the energy of transitions involving the unwanted $X^{+}$ state ($|u\rangle$). Other colors indicate the energies of all other transitions with the same polarization (${\sigma }^{-}$) that have been included in our calculations. Inset indicates where these transitions lie relative to the anticrossing of the $X^{+}$ state. (b) Dipole strengths of each optical transition as a function of applied field. Color and dashing as in top panel. Dipole strengths are measured relative to the dipole for a direct transition, which is given a strength of 1. (c) Calculated fidelity of a $\pi /2$ rotation using the two target transitions in the presence of all parasitic transitions and taking into account dipole variations. The lower axis indicates the QDM's detuning from an ideal laser for each value of the applied electric field.

Figure 6

Fidelity as function of angle of rotation for ‘traditional' approach (dashed black line) in which the laser is detuned and our new approach (solid red line) in which the QDM is tuned relative to a fixed laser. The $\pi$-rotation is implemented by a resonant set of pulses, in which case the two approaches coincide. Inset: temporal profile of the hyperbolic secant pulses used in our simulations (intensity in a.u.). The bandwidth of the pulse is $0.02$ meV; the optical decay time is taken to be 1ns.

Figure 7

Fidelity of spin rotation as a function of the angle of rotation for a multi-QDM system with variations in their optical resonances. Each curve corresponds to a different value of the E field; from top to bottom at $\phi =\pi /2$: 13.8, 14.7, 15.3, 15.6, 16, 16.4, 16.8, 17.2, 13.4, 17.7, 18.1, 19.3 kV/cm. The pulse envelope is similar to that used in Fig. 6 but with half the bandwidth, so about double in temporal length.

Figure 8

Experimental and calculated spectra from the positive trion in a QDM with a 4-nm barrier in a 6-T longitudinal magnetic field. (a) Experimental spectra, (b) calculation with $hm=0$, (c) calculation with $hm=0.2$ meV. The circles highlight four regions where the features observed experimentally are only reproduced by the calculation including nonzero $hm$.

Figure 9

(a) Single hole energy as a function of the electric field in a QDM subject to $B=6$ T. The QDs have $H=2$ nm, $R=15$ nm, $D=1.8$ nm, and are offset by $4.2$ nm. (b) Spin anticrossing gap as a function of the QDM offset for QDs with different aspect ratio. Triangles correspond to $(R,D)=(15,1.8)$ nm, circles to $(R,D)=(13,1.7)$ nm, and squares to $(R,D)=(10,1.6)$ nm.