4NATURE MATERIAL

Nuclear spin effects in semiconductor quantum dots

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E. A. Chekhovich1M. N. Makhonin1A. I. Tartakovskii1A. Yacoby2H. Bluhm3, 4K. C. Nowack5, 6L. M. K. Vandersypen5

Abstract

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Abstract? Introduction?

Hyperfine interaction and detection of nuclear polarization? Dynamic nuclear polarization?

Interaction of valence-band holes with nuclear spins?

Narrowing of nuclear field distribution in 'closed-loop' DNP? Nuclear magnetic resonance in single quantum dots? Future directions and other materials? References?

Acknowledgements? Author information

The interaction of an electronic spin with its nuclear environment, an issue known as the central spin problem, has been the subject of considerable attention due to its relevance for spin-based quantum computation using semiconductor quantum dots. Independent control of the nuclear spin bath using nuclear magnetic resonance techniques and dynamic nuclear polarization using the central spin itself offer unique possibilities for manipulating the nuclear bath with significant consequences for the coherence and controlled manipulation of the central spin. Here we review some of the recent optical and transport experiments that have explored this central spin problem using semiconductor quantum dots. We focus on the interaction between 104–106 nuclear spins and a spin of a single electron or valence-band hole. We also review the experimental techniques as well as the key theoretical ideas and the implications for quantum information science. At a glance Figures View all figures

1. Figure 1: Optical measurements of nuclear spin effects in quantum dots.

a, A schematic representation of the electron wavefunction in the dot (shown in orange) overlapping with a large number of nuclei (blue circles). Electron spin is shown with a black arrow, and randomly orientated nuclear spins are shown with blue arrows. b, Transmission electron microscopy image of an InP/GaInP self-assembled quantum dot, with darker area corresponding to the In-rich region. c, A typical micro-photoluminescence set-up. A sample is attached to a

three-dimensional piezo-positioner, allowing it to move with respect to a tight laser spot (~2 μm) obtained using a lens with a high numerical aperture. d, Micro-photoluminescence spectra measured for a single InGaAs/GaAs QD in an external magnetic field Bz = 5.3 T along the QD growth axis, z. Circularly polarized non-resonant optical excitation is used. In both cases dynamic nuclear polarization is apparent, as the exciton Zeeman splitting between the peaks in the spectrum measured with σ+ polarized excitation (circles), EXZ(σ+), is larger than that for σ?, EXZ(σ?) (squares).

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2. Figure 2: Electrical probing of nuclear spin effects in gate-defined quantum dots.

a, Schematic of a gate-defined double QD. b, Measurement of the current through a double QD (left) and sensing of the occupation of each dot using a nearby charge detector (right). c, Pauli spin blockade is used to convert spin to charge information. The Pauli exclusion principle forbids electrons with parallel spins (spin triplet) to occupy the same dot (left), whereas double occupancy is allowed for spin singlet (right). d, Energy levels of a double QD as a function of the relative energy detuning, ε, between the (1,1) and (0,2) charge configurations. This detuning can be controlled through gate voltages VgL and VgR in b. S(1,1) and S(0,2) denote the spin singlets in (1,1) and (0,2). Because of Pauli exclusion only S(0,2) is relevant in the (0,2) region. Near the transition, S(1,1) and S(0,2) hybridize because of the inter-dot tunnel

coupling tc. T+ = |↑↑, T0 = 1/√ 2(|↑↓ + |↓↑) and T? = |↓↓ are the three (1,1) triplets. The states T+ and T? split off owing to Bext. Far left in the (1,1) region, the eigenstates turn into |↑↓ and |↓↑ because of the difference of Bnuc in the two dots, ΔBnuc (left inset). The degeneracy point of S = 1/√ 2(|↑↓ ? |↓↑)and T+ (middle inset) can be used for polarizing nuclear spins. e, Time trace of ΔBnuc. Each data point reflects the frequency gμBΔBnuc/h of an oscillation between S and T0, showing the probability to obtain a singlet PS (inset). Figure reproduced with permission from: a, ref. 43, ? 2008 NPG; e, ref. 44, ? 2010 APS. Full size image View in article

3. Figure 3: Dynamic nuclear polarization in optically pumped quantum dots.

a, Bistable behaviour of nuclear polarization in a positively charged InP/GaInP quantum dot pumped non-resonantly with circularly polarized light in external magnetic field along the growth axis Bz =0.85 T. The plot shows the Zeeman splitting of the positively charged exciton, X+, measured in photoluminescence as the laser excitation power is scanned from high to low and back. Directions of the scans are shown with arrows for σ+ pumping, inducing Overhauser field Bnuc (felt by optically excited electrons) antiparallel to Bz and leading to the reduction of the electron Zeeman splitting. This causes positive feedback for DNP and results in switching and bistability of Bnuc (refs 23,24,35). In contrast,

under σ? pumping, Bnuc is parallel to Bz, causing the slow-down of DNP as Bnuc increases. b, Decay times for nuclear spin polarization in an InGaAs QD in a Schottky diode as a function of bias measured at temperatures of 4 K (dark red) and 0.2 K (green) and Bext = 5 T. The decay of the Overhauser field is mediated by the electron cotunnelling between the dot and the electron reservoir in the contact, particularly pronounced at the edges of the charging plateau around 505 and 575 mV in this graph. The decay time increases up to 105 s for T = 0.2 K at biases away from the cotunnelling regime. Panel b reproduced with permission from ref. 60, ? 2011 APS. Full size image View in article

4. Figure 4: Dynamic nuclear polarization in gate-defined quantum dots.

a, DNP leads to a hysteretic leakage current in the spin blockade regime as a function of increasing and decreasing magnetic field. b, Average charge occupation of a double quantum dot in the spin blockade regime (measured via the

change in voltage across the quantum point contact (QPC) sensor, δVQPC) under the influence of an alternating electric field. When the excitation frequency f is resonant with the electron Zeeman splitting, it drives electron–nuclear flip-flops (inset), thus lifting the spin blockade and changing the average occupation (darker regions). As the field Bext (directed along z) is swept upwards, a nuclear polarization partly counteracts the change of Bext, thus moving the resonance away from its equilibrium position (black diagonal line) by up to 840 mT. c, Control of the hyperfine field gradient in a double quantum dot operated as an S–T0 qubit. DNP is obtained by sweeping the detuning through the S–T+ transition (top), causing spin transfer between electrons and nuclei. Each data point on the lower panel reflects a measurement of ΔBnuc as shown in the inset to Fig. 2e. DNP pulses were applied between successive measurements. They increase or decrease ΔBnuc depending on whether the DNP cycle starts from an S (green) or T+ state (black). Figure reproduced with permission from: a, ref. 68, ? 2004 APS; b, ref. 47, ? 2007 APS; c, ref. 44, ? 2010 APS. Full size image View in article

5. Figure 5: Dynamics of nuclear spins in a gated double-dot structure.

a, Spectra of the fluctuation of the nuclear hyperfine field at relatively low frequency, obtained from time traces of the singlet probability PS of the qubit after precession in the Overhauser field over a fixed evolution time τS. A significant speeding up of the dynamics is observed at low magnetic fields. The shape of the spectrum can be explained in terms of nuclear spin diffusion. b, Hahn-echo signal in a S–T0 qubit as a function of the total evolution time, τ, for different values of magnetic field. Exchanging the two electrons at time τ/2 via a gate voltage pulse causes them to see the same static

hyperfine field, so that only fluctuations during τreduce the probability of the electrons to return to their initial state, which is reflected in the echo amplitude. Curves are offset for clarity and normalized. Data are shown as dots, fits as solid lines. c, Illustration of the semiclassical model used for the fits (see main text). Figure reproduced with permission from: a, ref. 75, ? 2008 APS; b,c, ref. 28, ? 2010 NPG.