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arXiv:1201.3859 · Physical Review Letters

Quantum Interference between Three Two-Spin States in a Double Quantum Dot

Sergei Studenikin, G. C. Aers, Ghislain Granger, Louis Gaudreau, A. Kam, P. Zawadzki, Z. R. Wasilewski, Andy S. Sachrajda

Published May 31, 2012• 28 citations
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Abstract

Qubits based on the singlet (S) and the triplet (T(0), T(+)) states in double quantum dots have been demonstrated in separate experiments. It has been recently proposed theoretically that under certain conditions a quantum interference could occur from the interplay between these two qubit species. Here we report experiments and modeling that confirm these theoretical predictions and identify the conditions under which this interference occurs. Density matrix calculations show that the interference pattern manifests primarily via the occupation of the common singlet state. The S/T(0) qubit is found to have a much longer coherence time as compared to the S/T(+) qubit.

DOI
10.1103/physrevlett.108.226802

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Exchange-coupled singlet-triplet spin qubits in two gate-defined double quantum dots are considered theoretically. Using charge density operators to describe the double-dot orbital states, we calculate the Coulomb couplings between the qubits and identify optimal bias points for single- and two-qubit operations, as well as convenient idle positions. The same intuitive formulation is used to derive dephasing rates of these qubits due to the fluctuating charge environment, thereby providing the main considerations for a quantum computation architecture that is within current experimental capabilities.
We simulate the control of the spin states in a two-electron double quantum dot when an external detuning potential is used to pass the system through an anticrossing. The hyperfine coupling of the electron spins with the surrounding nuclei causes not only anticrossing of the spin states but also decoherence of the spin states. We calculate numerically the singlet–triplet decoherence for different detuning values and find good agreement with the experimental measurement results for a similar setup. We predict an interference effect due to the coupling of the T 0 and T + states.
We present a theoretical study of a four-electron four-quantum-dot system based on molecular-orbital methods, which hosts a pair of singlet-triplet spin qubits. We took into account the admixture of electron wave functions in all dots, and we found that this mixing of wave functions has consequences to the energy spectrum, exchange interaction, and gate crosstalk of the system. Specifically, we found that when the two singlet-triplet qubits are close enough, some of the states are no longer dominated by the computational basis states, and the exchange interaction cannot simply be understood as the energy difference between the singlet and triplet states. Using the Hund-Mulliken calculation of the Hubbard parameters, we characterized the effective exchange interaction of the system, and we found good agreement with results calculated by taking energy differences where applicable. We studied the two commonly conceived schemes coupling two qubits, namely the exchange and capacitive coupling, and we found that when the interqubit distance is at certain intermediate values, the two kinds of coupling are comparable in strength, complicating the analyses of the evolution of the two qubits. We also investigated the gate crosstalk in the system due to the quantum-mechanical mixing of electron states, and we found that while this effect is typically very weak, it should not be ignored if the spacing between the qubits is similar to or less than the distance between the double dots that constitute the qubit.
We study electron-phonon interaction induced decoherence between two-electron singlet and triplet states in a semiconductor double quantum dot using a spin-boson model. We investigate the onset and time evolution of this dephasing, and study its dependence on quantum dot parameters such as dot size and double dot separations, as well as the host materials (GaAs and Si). At the short time limit, electron-phonon interaction only causes an incomplete initial Gaussian decay of the off-diagonal density matrix element in the singlet-triplet Hilbert space; a complete long-time exponential decay due to phonon relaxation would eventually dominate over two-spin decoherence. We analyze two-spin decoherence in both symmetric and biased double quantum dots, identifying their difference in electron-phonon coupling and the relevant consequences.
We investigate theoretically the hyperfine-induced dephasing of two-electron-spin states in a double quantum dot with a finite singlet-triplet splitting JJJ. In particular, we derive an effective pure dephasing Hamiltonian, which is valid when the hyperfine-induced mixing is suppressed due to the relatively large JJJ and the external magnetic field. Using both a quantum theory based on resummation of ring diagrams and semiclassical methods, we identify the dominant dephasing processes in regimes defined by values of the external magnetic field, the singlet-triplet splitting, and inhomogeneity in the total effective magnetic field. We address both free induction and Hahn echo decay of superposition of singlet and unpolarized triplet states (both cases are relevant for singlet-triplet qubits realized in double quantum dots). We also study hyperfine-induced exchange gate errors for two single-spin qubits. Results for III-V semiconductors as well as silicon-based quantum dots are presented.