Microlens schematic

A microlens fabricated above a quantum dot allows more efficient harvesting of photons from “dark excitons,” considered a candidate for quantum bits, or qubits, in some quantum-computing concepts. [Image: Tobias Heindel]

In the ongoing search for the best quantum bit, or qubit, to form a basis for the long-envisioned new generation of quantum computers, some researchers have nominated the spin states of so-called dark excitons (coupled pairs of electrons and electron holes in semiconductors) as one candidate. But dark excitons are, by definition, dark—that is, they do not emit photons. That makes extracting spin-state information from the system, and thus reading out the qubit for actual computing, a bit of a puzzle.

A research team in Germany and Israel has now proposed what they suggest is a scalable method to nudge dark excitons resting inside semiconductor quantum dots into divulging their spin state with a photon, and to amplify that signal through ingeniously fabricated microlenses (APL Photon., doi: 10.1063/1.5004147). The team believes that its approach could offer a foundation on which to build solid-state components of quantum information systems, such as “the realization of a solid-state-based quantum memory.”

Spin-blockaded pairs

There is, of course, no shortage of qubit candidates for quantum computing on the scene today; research groups are actively experimenting with systems based on trapped atoms or ions, ultra-cooled superconducting circuits, and solid-state, spin-based systems in diamond nitrogen-vacancy centers or semiconductor quantum dots.

Dark excitons fall in the solid-state, spin-based category. Technically, dark excitons are electron-hole pairs, confined in a quantum dot (a semiconductor nanocrystal that functions as a sort of artificial atom), in which the electron and hole have identical spins. As a result, they are “spin-blockaded”; they cannot easily radiatively recombine (owing to the Pauli exclusion principle), and thus can hang around for up to a microsecond before relaxing to a lower energy level.

While a microsecond doesn’t seem like a particularly long time, it’s a thousand times longer than the residence times of so-called bright excitons, which radiatively recombine and emit a photon in a nanosecond or so. It’s also comfortably long enough for dark excitons to function as qubits in quantum-computing schemes. The big challenge has been the darkness itself—the lack of a photon to show the presence of the dark exciton and reveal its spin state.

Reading “biexcitons”

In 2010, a multinational research team (including David Gershoni of the Technion, Israel, also a coauthor on the new study) solved one piece of the puzzle, by figuring out a way to access the optically inactive dark excitons with light. The key was to consider not single dark excitons, but coupled pairs, which exist in a so-called spin-blockaded biexciton state.

When such a biexciton state (trapped in a semiconductor quantum dot) eventually relaxes, it leaves a dark exciton behind, and also emits a photon heralding its presence. The spin state of the remaining dark exciton can then be accessed by adding an additional electron (or electron hole) to the system. That, in turn, causes the dark exciton to become bright and emit a photon, the polarization of which can be read to infer the dark exciton’s spin state.

A microlens boost

While the 2010 demo showed that extracting information from dark excitons was possible, the technique had some problems. The biggest was that it was nondeterministic, and thus the photon harvest was meager. Scaling up the system would require much more efficient, reliable photon extraction and collection.

To get to that point, the research team in the new APL Photonics study, led by Tobias Heindel of the Technical University of Berlin, began with a system of dark excitons trapped within semiconductor quantum dots. They then added an optical component to provide some extra photon-catching power: A tiny microlens, fitted over individual quantum dots.

The lenses are fashioned via 3-D in situ electron beam lithography of a capping layer over pre-selected, target quantum dots. According to the researchers, the use of microlenses to boost the excitons’ optical signal, rather than narrowband microcavity resonators, is a plus, as it allows photons to be harvested efficiently over a broad spectral range.

The team reports that the experiments using this setup “clearly reveal the coherent precession of the [dark exciton] spin,” a finding that the team believes “provide[s] evidence for the robustness of the [dark exciton] as a long-lived coherent spin qubit and pave[s] the way for wider applications.” The team is working on additional tweaks—such as a backside gold mirror beneath the quantum dot and a 3-D-printed micro-objective above the microlens—that, according to the researchers, could push photon extraction efficiencies as high as 80 percent. The work, they conclude, “constitutes an important step toward scalable implementations of quantum information schemes” based on dark excitons.