Environment-assisted quantum control of a solid-state spin via coherent dark states

Journal name:
Nature Physics
Year published:
Published online

Understanding the interplay between a quantum system and its environment lies at the heart of quantum science and its applications. So far most efforts have focused on circumventing decoherence induced by the environment by either protecting the system from the associated noise1, 2, 3, 4, 5 or by manipulating the environment directly6, 7, 8, 9. Recently, parallel efforts using the environment as a resource have emerged, which could enable dissipation-driven quantum computation and coupling of distant quantum bits10, 11, 12, 13, 14. Here, we realize the optical control of a semiconductor quantum-dot spin by relying on its interaction with an adiabatically evolving spin environment. The emergence of hyperfine-induced, quasi-static optical selection rules enables the optical generation of coherent spin dark states without an external magnetic field. We show that the phase and amplitude of the lasers implement multi-axis manipulation of the basis spanned by the dark and bright states, enabling control via projection into a spin-superposition state. Our approach can be extended, within the scope of quantum control and feedback15, 16, to other systems interacting with an adiabatically evolving environment.

At a glance


  1. Optical spin access via environment-dictated quantization axis.
    Figure 1: Optical spin access via environment-dictated quantization axis.

    a, The hyperfine interaction between the resident electron spin (black arrow) and a large bath of nuclear spins (orange arrows) is modelled as a classical effective magnetic field, the Overhauser field (OH, large orange arrow). b, Level structure and selection rules for different orientations of the OH field. The curved arrows represent dipole-allowed transitions, the straight arrows represent the excitation laser used in c. The dashed curved arrows represent the weakly allowed spin-flip transitions due to the Overhauser field. For the first two configurations the optical transitions are all of comparable strength, whereas the last configuration exhibits an imbalance in the strengths of the dipole-allowed (solid arrows) and dipole-forbidden (dashed arrows) transitions. c, Low-power (Ω = 0.224Γ) resonance fluorescence intensity autocorrelation (blue line) fitted with an exponential decay (red line). The data is post-selected for a rms-detuning of ~0.23Γ (Supplementary Section 1). The inset shows the bunching amplitude for different post-selected detunings. The red curve is a spin pumping simulation with an OH field dispersion of 18 ± 1 mT. Horizontal axes are in units of the radiative transition linewidth Γ = 216 ± 2 MHz and the lifetime τ = 737 ± 6 ps. Error bars represent the standard error in the amplitudes of fits to exponential decays for each measurement.

  2. Environment-assisted coherent population trapping.
    Figure 2: Environment-assisted coherent population trapping.

    a, Two lasers, each set to Ω = 0.224Γ, with orthogonal linear polarization (H, V) and variable detuning, are used to excite the QD. b, Simulation of two-laser absorption of the QD at zero magnetic field and without spectral wandering. Experimentally measured values of laser powers, radiative lifetime and OH field dispersion are used. A hyperfine-induced ground-state splitting of 400 MHz gives the best fit to the data. c, Two-laser measurement of QD absorption with experimental parameters corresponding to b. d,e, Linecuts across Δ1 + Δ2 = 0 (dashed black line shown in c) for two different applied magnetic fields in the Faraday configuration. The corresponding linecut extracted from the simulation of b with spectral wandering is shown in red. f, Magnetic field dependence of the visibility of the spectral signature of CPT, after correcting for saturation and incoherent spin pumping effects (Supplementary Information). The measured OH field dispersion is shown as a vertical orange line. The error bars are calculated by propagation of both the min–max values of the count rates around Δ1 = Δ2 = 0, and standard errors in the amplitude of Voigt fits to single-laser line shapes used for normalization.

  3. Phase dependence of coherent dark states.
    Figure 3: Phase dependence of coherent dark states.

    a, Experimental set-up used to measure the effect of fast phase jumps on QD absorption. A single laser is split into two paths: one is phase-modulated with an electro-optic modulator (EOM) and the other is frequency shifted to compensate for the ground-state Zeeman splitting under 8.4 mT (applied to lift the excited state degeneracy for this experiment). Photon detection events are recorded and correlated with voltage pulses sent to the EOM; AOM: acousto-optic modulator; PBS: polarizing beam splitter; APD: avalanche photodiode; λ/2: half-wave plate. b, QD level structure at an arbitrary OH field and 8.4 mT external field, with phase and frequency differences corresponding to the experimental set-up described in a. c, Example time-resolved fluorescence measurement (lower graph) when an electrical pulse (upper graph) is sent to the EOM. The middle graph shows the phase change rate, corresponding to an effective frequency shift. The Bloch spheres depict qualitatively the effect of the phase jump on the electron spin state at different times in the cycle, both in the hyperfine-dictated and dressed bases (B is bright state, D is dark state).

  4. Quantum control of an electron spin via state projection.
    Figure 4: Quantum control of an electron spin via state projection.

    Amplitude of the intermittent fluorescence extracted from fits to exponential decays, as a function of voltage pulse amplitude applied to the EOM, normalized to the mean count rate. The blue curve is a sinusoidal fit, and the error bars represent the standard deviation of the background-subtracted (Supplementary Information) counts in each measurement. Vπ is the EOM voltage required for a π phase shift. The Bloch spheres depict the effect of the corresponding phase jump on an electron spin prepared in the dark state. The transparent vector represents the initially prepared dark state, and the opaque vector shows the final state.


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Author information

  1. These authors contributed equally to this work.

    • Jack Hansom &
    • Carsten H. H. Schulte


  1. Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, UK

    • Jack Hansom,
    • Carsten H. H. Schulte,
    • Claire Le Gall,
    • Clemens Matthiesen &
    • Mete Atatüre
  2. EPSRC National Centre for III-V Technologies, University of Sheffield, Sheffield S1 3JD, UK

    • Edmund Clarke
  3. CNRS-CRHEA, rue Bernard Grégory, 06560 Valbonne France

    • Maxime Hugues
  4. Joint Quantum Institute/National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

    • Jacob M. Taylor


J.H., C.H.H.S., J.M.T. and M.A. devised the experiments. J.H., C.H.H.S. and C.L.G. performed the experiments and analysed the data. J.H., C.H.H.S., C.L.G., C.M., J.M.T. and M.A. contributed to the discussion of the results and the manuscript preparation. J.M.T. performed the theoretical modelling shown in Fig. 2. J.H. performed theoretical modelling of the data shown in Fig. 1. E.C. and M.H. grew the sample. C.M. processed the devices.

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