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arXiv:0811.3560 · Physical Review Letters

Nuclear State Preparation via Landau-Zener-Stückelberg Transitions in Double Quantum Dots

Hugo Ribeiro, Guido Burkard

Published May 28, 2009• 76 citations
arXivHTMLPDF

Abstract

We theoretically model a nuclear-state preparation scheme that increases the coherence time of a two-spin qubit in a double quantum dot. The two-electron system is tuned repeatedly across a singlet-triplet level anticrossing with alternating slow and rapid sweeps of an external bias voltage. Using a Landau-Zener-Stückelberg model, we find that in addition to a small nuclear polarization that weakly affects the electron spin coherence, the slow sweeps are only partially adiabatic and lead to a weak nuclear spin measurement and a nuclear-state narrowing which prolongs the electron spin coherence. This resolves some open problems brought up by a recent experiment [D. J. Reilly, Science 321, 817 (2008).10.1126/science.1159221]. Based on our description of the weak measurement, we simulate a system with up to n=200 nuclear spins per dot. Scaling in n indicates a stronger effect for larger n.

DOI
10.1103/physrevlett.102.216802

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Physical Review B•Jul 28, 2009•7 citations
We theoretically model a nuclear-state preparation scheme that increases the coherence time of a two-spin qubit in a double quantum dot. The two-electron system is tuned repeatedly across a singlet-triplet level anticrossing with alternating slow and rapid sweeps of an external bias voltage. Using a Landau-Zener-Stückelberg model, we find that in addition to a small nuclear polarization that weakly affects the electron spin coherence, the slow sweeps are only partially adiabatic and lead to a weak nuclear spin measurement and a nuclear-state narrowing which prolongs the electron spin coherence. This resolves some open problems brought up by a recent experiment [D. J. Reilly, Science 321, 817 (2008).10.1126/science.1159221]. Based on our description of the weak measurement, we simulate a system with up to n=200 nuclear spins per dot. Scaling in n indicates a stronger effect for larger n.
Landau-Zener-Stuckelberg-Majorana (LZSM) physics has been exploited to coherently manipulate two-electron spin states in a GaAs double quantum dot (DQD) at a singlet (S)-triplet (T+) anti-crossing. The anti-crossing results from the hyperfine interaction with the nuclear spins of the host material [1,2]. However, the fluctuations of the nuclear spin bath result in spin dephasing within T ∗ 2 ∼ 10− 20 ns. As a consequence, the sweep through the anti-crossing would have to be performed on a timescale comparable to T ∗ 2 to achieve LZSM oscillations with 100% visibility. Moreover, the S-T+ anti-crossing is located near the (1, 1)− (2, 0) interdot charge transition, where (nl, nr) denotes the number of electrons in the left and right quantum dot. As a result the singlet state involved in the dynamics is a superpostion of (1, 1) and (2, 0) singlet states. Here we show that it is possible to increase the oscillation visibility while keeping sweep times less than T ∗ 2 using a tailored pulse with a detuning dependent level velocity. The pulse includes a slow level velocity portion that is chosen to coincide with the passage through the S-T+ anti-crossing and two fast level velocity portions. The latter minimize the time spent in regions where spin and charge degrees of freedom are entangled, which renders the qubit susceptible to charge noise. The slow level velocity portion of the pulse results in a stronger effective coupling between the spins states, which increases the oscillations visibility [3,4]. In particular, we were able to obtain a visibility of ∼ 0.5 for LZSM oscillations. This constitutes an important step towards the implementation of a Hadamard gate.
We theoretically study the interplay of spin-orbit and hyperfine interactions in dynamical nuclear polarization in two-electron semiconductor double quantum dots near the singlet-triplet ($S\ensuremath{-}{T}_{+}$) anticrossing. The goal of the scheme under study is to extend the singlet-triplet ($S\ensuremath{-}{T}_{0}$) qubit decoherence time T2∗{T}_{2}^{*}T2∗​ by dynamically transferring the polarization from the electron spins to the nuclear spins. This polarization transfer is achieved by cycling the electron spins over the $S\ensuremath{-}{T}_{+}$ anticrossing. Here, we investigate, both quantitatively and qualitatively, how this hyperfine-mediated dynamical polarization transfer is influenced by the Rashba and Dresselhaus spin-orbit interaction. In addition to T2∗{T}_{2}^{*}T2∗​, we determine the singlet return probability Ps{P}_{s}Ps​, a quantity that can be measured in experiments. Our results suggest that the spin-orbit interaction establishes a mechanism that can polarize the nuclear spins in the direction opposite to that of hyperfine-mediated nuclear spin polarization. In materials with relatively strong spin-orbit coupling, this interplay of spin-orbit and hyperfine-mediated nuclear spin polarizations prevents any notable increase in the $S\ensuremath{-}{T}_{0}$ qubit decoherence time T2∗{T}_{2}^{*}T2∗​.
In many realizations of electron spin qubits the dominant source of decoherence is the fluctuating nuclear spin bath of the host material. The slowness of this bath lends itself to a promising mitigation strategy where the nuclear spin bath is prepared in a narrowed state with suppressed fluctuations. Here, this approach is realized for a two-electron spin qubit in a GaAs double quantum dot and a nearly tenfold increase in the inhomogeneous dephasing time T₂* is demonstrated. Between subsequent measurements, the bath is prepared by using the qubit as a feedback loop that first measures its nuclear environment by coherent precession, and then polarizes it depending on the final state. This procedure results in a stable fixed point at a nonzero polarization gradient between the two dots, which enables fast universal qubit control.
In moderately strong magnetic fields, the difference in Land\'e ggg factors in each of the dots of a two-electron double quantum dot (DQD) may induce oscillations between singlet and triplet states of an entangled pair and lead to a nonequilibrium electron spin polarization in the system. The calculated bipolar polarization reflects the strong spin correlation in the spatially separated pair of electrons that occupy almost degenerate states in a coupled DQD. We will show that this polarization may partially survive the rapid inhomogeneous decoherence caused by random nuclear magnetic fields.
We report repeated single-shot measurements of the two-electron spin state in a GaAs double quantum dot. The readout allows measurement with a fidelity above 90% with a approximately 7 micros cycle time. Hyperfine-induced precession between singlet and triplet states of the two-electron system are directly observed, as nuclear Overhauser fields are quasistatic on the time scale of the measurement cycle. Repeated measurements on millisecond to second time scales reveal the evolution of the nuclear environment.
We investigate the utilization of external magnetic field for the manipulation of the quantum states in a two-electron double quantum dot. The singlet and triplet states are coupled through the hyperfine interaction between the electrons and surrounding nuclei. When the magnetic field is changed as a function of time, the singlet-triplet transition is possible for certain values of magnetic field, when the singlet state becomes degenerate with the triplet state. The transition probability depends on the sweeping speed of the magnetic field through the averaged Landau-Zener formula. We evaluate proper time scales for efficient control of the quantum dot, evaluate the singlet probabilities for different time-dependent magnetic fields, and study the average of the final singlet probability, averaged over the orientations of the nuclear spins surrounding the quantum dot.