Researchers have deterministically generated two-electron spin states within a quantum dot molecule (QDM), a structure that can advance measurement-based quantum information processing. While one-dimensional chains of entangled photons are now routinely created using single quantum dots, building the two-dimensional entanglement structures needed for complex quantum computing has proven challenging; current methods using probabilistic fusion gates struggle as systems grow.

This work directly addresses this bottleneck by decoupling the control of orbital hybridization and charge status within the QDM, enabling repeated optical addressing of hybridized states for timescales exceeding 50 microseconds at 1.7 K. The team demonstrates initialization into a well-defined singlet ground state.

Stacked Quantum Dots Enable Singlet-Triplet Qubit Control

Multi-photon states exhibiting two-dimensional entanglement are essential for measurement-based quantum information processing, a requirement currently hindering progress in the field. Existing methods rely on probabilistic fusion gates to build these 2D structures from one-dimensional chains of entangled photons, but this approach struggles to scale effectively as quantum systems increase in complexity. Researchers are now exploring deterministic methods, and a recent demonstration utilizes vertically stacked and coupled quantum dots to generate these 2D entanglement structures.

The device, consisting of a single self-assembled quantum dot molecule formed from two interacting InGaAs dots separated by approximately 10 nanometers, achieves high charge storage times exceeding 50 microseconds and spin lifetimes greater than 10 microseconds. These durations are longer than those observed in other quantum dot systems. This improved coherence is critical because it allows for more complex quantum operations before information is lost.

Independent control over the charge state and orbital coupling within the quantum dot molecule is a key feature of this design. The team focused on a specific operating regime, labeled (1, 1), where single-dot orbitals are hybridized, noting that accessing a different configuration, (0, 2), was limited by current flow within the device. Achieving this level of control is vital for manipulating the spin states of electrons within the dots, a necessary step towards building more robust quantum bits.

“These timescales are certainly larger than the typical spin coherence times in self-assembled quantum dots of a few nanoseconds,” the researchers report, highlighting the improvement over previous systems. The demonstrated ability to deterministically generate these entangled states, building on prior work showing deterministic spin-photon entanglement in single quantum dots, opens a pathway to creating deterministic two-dimensional photonic cluster states. Future work will concentrate on reducing the tunnel coupling strength between the spins, enabling entanglement mediated on timescales comparable to spin-photon entanglement generation, and ultimately, coherent control of the two-spin system within the quantum dot molecule.

Orbital Hybridization Achieved via Selective Optical Charging

Selective optical charging allows for independent tuning of a quantum dot molecule’s orbital coupling and charge status, overcoming a longstanding limitation in creating stable, tunable entangled states. Previously, a single axial electric field controlled both properties simultaneously, hindering precise manipulation of two-electron spin systems; this new method bypasses that constraint by employing resonant optical driving and charge storage devices.

The team demonstrated charge preparation fidelities, a significant improvement in the reliability of initializing quantum states within the device. Calculations of singlet-triplet relaxation rates show a strong dependence on the applied electric field, with rates decreasing as voltage decreases.

Coulomb Blockade Facilitates Two-Electron QDM Initialization

The energy separation between resonant and non-resonant signals directly reveals the singlet-triplet splitting, measured at 718(16)μeV for this sample, providing a precise value for characterizing the initialized two-electron states. This measurement is enabled by a device configuration where the (1,1)-regime, with hybridized single-dot orbitals, is accessible, unlike the (0,2)-configuration which induces current flow in the diode and remains experimentally inaccessible.

Deterministic charging of the quantum dot molecule relies on the Coulomb blockade, a principle used to control charge status by exploiting the energy required to add electrons to the system. Preparation of the two-electron state via the lower dot trion initializes electrons in a (2,0)_S configuration, but electrical switching between orbital configurations could potentially introduce unwanted mixing of spin states.

To investigate this potential effect, researchers performed experiments demonstrating optical spin pumping, a process where population can be moved between singlet and triplet states without a magnetic field, and measured spin relaxation across a range of orbital energy detunings. This capability allows for a direct comparison to the behavior of a single electron within the quantum dot molecule, revealing nuanced control over the coupled electron system.

Optical pumping schemes were employed for both a single electron in the (1,0)-configuration and two electrons in the (2,0)-configuration, utilizing yellow arrows to indicate optically driven transitions and dashed blue and green arrows to represent possible recombination paths for the X⁻ and X²⁻ states. Calculations, adapted to the specific size, shape, and composition of the quantum dot molecule, were performed using the configuration interaction method to model the electric field dependence of the lowest-energy two-electron states. These computations involved diagonalizing the Coulomb Hamiltonian and presenting the calculated energies of the two-spin eigenstates when an electric field is applied in Faraday geometry, further refining the understanding of spin state manipulation.

Electrical Tuning of Quantum Dot Molecule Orbital Coupling

This extended duration stems from independent control over charge status and orbital coupling within the stacked quantum dot structure, enabling prolonged charge storage and enhanced spin lifetimes. Researchers observed that these relaxation times exhibited a strong dependence on the energy difference between ground and excited two-spin states, a relationship corroborated by k·p calculations modeling phonon-mediated spin relaxation. The model traces field-dependent excitonic states, with agreement observed between calculations of voltage-dependent eigenenergies for the lower dot of the neutral exciton and singly charged exciton, confirming assignments of these states. Optical pumping techniques yielded charge preparation fidelities.

Nanosecond Optical Pumping of QDM Spin States

Hybridized states within quantum dot molecules (QDMs) remain stable under repeated optical addressing, a finding demonstrated by the ability to maintain charge within the QDM for over 50 microseconds at 1.7 Kelvin. This extended charge retention, crucial for sustained quantum operations, occurs even while manipulating the spin and orbital characteristics of electrons within the device. These hybridized states allow for selective optical charging, adding either one or two electron spins to the QDM without immediate charge loss.

The team elucidated relaxation dynamics of both single- and two-electron spin states using optical pumping, revealing a decaying triplet signal indicative of spin pumping, a process where resonant laser light returns the system to a singlet state. Measurements showed a decay rate of 5.8(3)μs⁻¹ for the triplet signal, confirming optical transitions between spin states.

This contrasts with single-electron systems, where phonon-assisted tunneling occurs on picosecond to 100 picosecond timescales, effectively inhibiting optical pumping and maintaining a stable signal. The difference in behavior stems from the faster timescale of inelastic interdot tunneling in single-electron systems compared to the optical pumping rate.

The researchers demonstrated Pauli blockade and optical pumping of the (2, 0) system via a direct transition, further validating the control over spin states. This ability to repeatedly address and manipulate hybridized states, coupled with nanosecond optical pumping, represents an advancement in maintaining coherence and controlling spin dynamics within QDMs.

Slow S-T Relaxation Below 5meV Energy Splitting

Relaxation between singlet and triplet states slows dramatically when energy splitting falls below 5 milli-electronvolts, with measured rates as low as 0.01 microseconds inverse observed in the quantum dot molecule. This extended charge retention is particularly notable because increasing the energy splitting beyond 5 meV causes the relaxation rate to jump by over two orders of magnitude, a change driven by sequential multi-phonon spin relaxation involving excited-state triplets.

The observed behavior demonstrates a pathway toward independent control over requirements for generating cluster states, including initialization of the two-spin system and prolonged spin storage. The team modeled voltage-dependent relaxation rates as a function of a reference voltage and rate, and found a consistent value until 0.54 volts. Beyond that point, the rate of decrease in relaxation changes, continuing at least until a gate voltage is applied.

This strong dependence on the energy splitting of the orbital states involved is further evidenced by changes in the orbital character of the singlet ground state, transitioning from a (2,0) configuration to (1,1) as visualized by a shift in color from white to blue. Changes in the energy splitting between the (1,1) triplet state and the singlet ground state also reveal a minimum around 10 kilovolts per centimeter, where the splitting reaches 718 micro-electronvolts.

The adiabatic theorem predicts singlet mixing requires switching speeds matching the energy difference, but the maximum bandwidth of the waveform generator used is 100 megahertz, over three orders of magnitude too slow to induce such mixing. This decoupling, combined with the observed slow relaxation rates, offers a promising route toward building more stable and versatile quantum systems for information processing.

Bragg Grating Enhances Photon Collection from Stacked Dots

Researchers have now demonstrated an alternative approach utilizing vertically stacked and coupled quantum dots, forming a quantum dot molecule (QDM) containing two interacting spins, to deterministically generate cluster states with 2D entanglement. The team fabricated a circular Bragg grating (CBG) directly above the QDM using deterministically fabricated electron-beam lithography, a process that precisely aligns the grating to the selected QDM. This CBG, combined with a backside distributed Bragg reflector (DBR), enhances photon collection efficiency across a bandwidth sufficient to simultaneously address transitions in both the upper and lower quantum dots.

Spectroscopic probing of the orbital states within the QDM involved voltage-dependent photoluminescence using a continuous wave laser at 850 nanometers, exciting quasi-free charge carriers in the wetting layer. Measured relaxation rates were observed across a voltage range transitioning from a (2,0)-configuration ground state to a hybridized regime.

The S-T relaxation is shown to be very slow for energy splittings Δ_S−T<5meV, with relaxation rates as low as 0.01μs^−1. The device structure incorporates a 50-nanometer-thick aluminum gallium arsenide barrier beneath the lower dot, preventing electron escape and facilitating electron storage within the flatter, larger confinement energy lower dot. This configuration, coupled with the Bragg grating, represents a step toward more efficient and scalable quantum entanglement generation.

Voltage-Dependent Photoluminescence Identifies QDM Charge Complexes

Different charged complexes within the QDM are identified by fitting the voltage-dependent emission energy of observed lines using a few-body Hamiltonian, detailed in Appendix B, providing a consistent model for neutral exciton states $X^{0}$ , singly charged excitons $X^{−}$ , and doubly charged excitons $X^{2} -$ . The shorthand notation (e_l,e_u) represents the number of electrons in each dot for states not involving a hole.

Deterministic optical electron charging is demonstrated by mapping voltage and energy points where one-electron and two-electron charging is possible, with luminescence from the lower dot directly observed in the photoluminescence regime ( $V_{G}$ >0V) for both $X^{0}$ and $X^{−}$ complexes, alongside simulations from the few-particle Hamiltonian. These results reveal the ability to precisely control charge states within the QDM, a key requirement for scalable quantum information processing, and offer a pathway toward generating multi-photon states with 2D entanglement structures necessary for measurement-based quantum computing.

👉 More information
🗞 Ultra-Slow Orbital and Spin Dynamics in an Electrically Tunable Quantum Dot Molecule
✍️ Christopher Thalacker et al.
🧠 DOI: http://link.aps.org/doi/10.1103/qgr2-968q

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