Manipulation of the nuclear spin ensemble in a quantum dot with chirped magnetic resonance pulses

Abstract

The nuclear spins in nano-structured semiconductors play a central role in quantum applications [1][2][3][4] . The nuclear spins represent a useful resource for generating local magnetic 5 fields but nuclear spin noise represents a major source of dephasing for spin qubits 2,3 . Controlling the nuclear spins enhances the resource while suppressing the noise. Nuclear magnetic resonance (NMR) techniques are challenging: the group-III and group-V isotopes have large spins with widely different gyromagnetic-ratios; in strained material there are large atom-dependent quadrupole-shifts 6 ;nano-scale NMR is hard to detect 7,8 . We report NMR on 100, 000 nuclear spins of a quantum dot using chirped radio-frequency pulses. Following polarization, we demonstrate a reversal of the nuclear spin. We can flip the nuclear spin back-and-forth a hundred times. We demonstrate that chirped-NMR is a powerful way of determining the chemical composition, the initial nuclear spin temperatures and quadrupole frequency distributions for all the main isotopes. The key observation is a plateau in the NMR signal as a function of sweep-rate: we achieve inversion at the first quantum transition for all isotopes simultaneously. These experiments represent a generic technique for manipulating nano-scale inhomogeneous nuclear spin ensembles and open the way to probe the coherence of such mesoscopic systems.NMR signals can be boosted by polarizing the nuclei. This is particularly beneficial on the nano-scale where NMR signals are invariably small and hard to detect. The nuclear spins in a self-assembled quantum dot can be polarized optically by exploiting the hyperfine interaction with an electron spin 3,5 . Extremely long-lived polarizations 4,9-11 up to about 50% have been achieved. The nuclear spin polarization results in a shift of the optical resonance, the Overhauser shift, facilitating its sensitive detection 5 . These features have enabled the observation of isotope-selective NMR of the nuclear spins associated with strain-free GaAs quantum dots 12,13 . Self-assembled quantum dots, attractive for single photon generation and opticallycontrolled spin qubits 2 , have highly inhomogeneous nuclear spins 5,[14][15][16] Here we use chirped NMR pulses. The main concept is that by sweeping over a large frequency range, the pulse addresses each nuclear spin at some point. For a spin-1 2 nucleus, a 2-level system, the Hamiltonian in the rotating frame is,where h is the Planck constant, I the nuclear spin, γ the gyromagnetic ratio of the nuclear isotope (in frequency units) and ∆ν(t) is the time-dependent detuning between the radio frequency (RF) excitation and the Larmor frequency ν L = γB z . The coupling between the RF magnetic field B x and the spin, the second term in the Hamiltonian, leads to an avoided crossing in the eigen-energies with splitting hν RF , Fig. 1a , where ν RF = γB x . On traversing the avoided crossing from large and negative ∆ν to large and positive ∆ν with a single pulse (N = 1) at sweep rate α, the probability that t...

Resonant driving of a single photon emitter embedded in a mechanical oscillator

“…(Note that in equation (4) this factor 2 is included in the definition of λ .) Assuming the QD is mainly composed of GaAs 37 , a  = −8.33 eV and b  = −2.0 eV 23 , we find  GHz and  GHz, in excellent agreement with the results from Section III.…”

Electron dynamics in transport and optical measurements of self‐assembled quantum dots

“…These self‐assembled QDs, , like an atom, show energy quantization, direct and indirect (exchange) Coulomb interaction as well as angular momentum and spin‐dependent optical, , and electrical properties, . Moreover, recent discoveries of nuclear spin manipulation, and decoupling from these nuclear spins () make self‐assembled dots highly attractive for quantum applications where long spin coherence is needed.…”

Few-second-long correlation times in a quantum dot nuclear spin bath probed by frequency-comb nuclear magnetic resonance spectroscopy

“…Here we focus on the spin I = 3/2 nuclei 71 Ga and 75 As. The strain-induced quadrupolar shifts result in an inhomogeneously broadened NMR spectrum 21,22 , as shown schematically by the green line in Fig. 1b.…”

“…By contrast, pulsed NMR reveals the spin bath coherence time T 2 , which characterizes the dynamics of the transverse nuclear magnetization 7,8,20 and is much shorter than τ c . The problem is further exacerbated in self-assembled quantum dots, where quadrupolar effects lead to inhomogeneous NMR broadening exceeding 10 MHz (refs 21,22), so that pulsed NMR requires practically unattainable rf field amplitudes exceeding 1 T.…”

“…1a. Here we exploit the hyperfine interaction of the nuclei with the optically excited electron 17,21,22 both to polarize the nuclei (pump pulse) and to measure the nuclear spin polarization in terms of the Overhauser shift E hf in the quantum dot photoluminescence spectrum (probe pulse). The rf magnetic field depolarizing nuclear spins is induced by a small copper coil.…”