Controlling the quantum dynamics of a mesoscopic spin bath in diamond

Abstract

Understanding and mitigating decoherence is a key challenge for quantum science and technology. The main source of decoherence for solid-state spin systems is the uncontrolled spin bath environment. Here, we demonstrate quantum control of a mesoscopic spin bath in diamond at room temperature that is composed of electron spins of substitutional nitrogen impurities. The resulting spin bath dynamics are probed using a single nitrogen-vacancy (NV) centre electron spin as a magnetic field sensor. We exploit the spin bath control to dynamically suppress dephasing of the NV spin by the spin bath. Furthermore, by combining spin bath control with dynamical decoupling, we directly measure the coherence and temporal correlations of different groups of bath spins. These results uncover a new arena for fundamental studies on decoherence and enable novel avenues for spin-based magnetometry and quantum information processing.

Figure 1. Magnetic resonance spectroscopy of a spin bath using a single spin sensor.

(a) Schematic of the system: a single NV centre electronic spin (S = 1) is surrounded by a bath of electron spins (S = 1/2) belonging to substitutional N impurities. The applied external magnetic field B is aligned with the symmetry axis of the NV centre, which is oriented along the [111] crystallographic direction. Nitrogen impurities exhibit a static Jahn-Teller distortion, which results in an elongation of one of the four N-C bonds. As a result, the defect has a symmetry axis, also called the Jahn-Teller axis (indicated red), which is oriented along randomly along one of the crystallographic axes. There are therefore two geometric types of bath spins which are distinguished by their orientation of the Jahn-Teller axis relative to the external field B: those that have their JT axis at an angle α = 0°, and those with α = 109.5°. (b) Measurement sequence for spin bath spectroscopy. A spin echo sequence is applied to the NV spin using MW pulses; the bath spins are controlled by RF pulses. The evolution of the NV spin during the sequence is sketched in the Bloch spheres at the bottom, both for the case of no spin bath control (solid line), and for the case of spin bath control applied (dashed line) (see Supplementary information for details). (c) Upper panel: Magnetic resonance spectroscopy of the spin bath. A magnetic field of 132 G is applied along the NV centre symmetry axis. Roman numbers label the different groups of N electron bath spins, according to their nuclear spin projections m_I and angle α between their Jahn-Teller axis and the external magnetic field: I,V: m_I = ±1 and α = 0°, II,IV: m_I = ±1 and α = 109.5°_, III: m_I = 0 and α = 0° or 109.5°. Lower panel: Calculation of the spectrum (see Supplementary information).

Figure 2. Coherent control of the spin bath.

(a) Coherent driven oscillations of group II bath spins, using RF pulses of 298 MHz. Revivals in NV echo amplitude are observed whenever the bath spins from group II perform a 2π rotation. The maximum Rabi frequency extracted from fitting the upper trace at 20 dBm source power is f₁ = (20.5 ± 0.1) MHz. (b) Independent coherent control of each group of bath spins. Solid lines are fits to with t the length of the RF pulse (see Supplementary information).

Figure 3. Control of NV spin coherence by spin bath manipulation.

(a) Spin echo double resonance (SEDOR) experiment. The RF pulses have been calibrated to rotate a preselected group of bath spins over a π angle. The NV spin echo curve is fit to , SEDOR curves are fit to (see Supplementary information). (b) Dynamical suppression of NV centre spin dephasing through spin bath control. Free evolution of the NV spin is shown with (blue) and without (red) RF π-pulse applied to the bath spins. Solid lines are fits that include the detuning () of the MW driving field compared to the NV spin splitting, and local hyperfine interaction of 2.2 MHz with the host nuclear N spin. This hyperfine interaction is responsible for the observed beating pattern (see Supplementary information). The overall signal decays with a Gaussian envelope, with decay constant in the absence of the spin bath control (red) and with decay constant in the case where the bath control pulses are applied (blue).

Figure 4. Coherent dynamics and temporal correlations of the spin bath.

(a) Measurement of decay during free evolution of spin bath groups I and II. The two sensing stages marked by τ_s serve to sample the magnetic environment before and after the Ramsey sequence is applied to the bath spins. The NV spin sensor is turned off while the RF Ramsey sequence is applied to the bath spins (see main text for details). Instead of detuning the RF pulse field with respect to the transition to observe fringes, an artificial detuning f_ais introduced by changing the phase of the final RF π/2-pulse linearly with pulse separation . Solid lines are fits to (see Supplementary information for details). Additional contributions resulting from the off-resonant driving of spins from the nearest neighbouring group is taken into account by an extra oscillating term with frequency , which is given by the detuning of this group with respect to the pulse carrier. The fast modulation of Ramsey fringes for group I (upper panel) result from off-resonant driving of the more abundant spins from group II (). From the fits we extract the decay constants and . (b) Spin echo on spin bath groups I and II. The phase of the final RF π/2-pulse is changed as a function of total free evolution time τ as with f_a = 10 MHz, resulting in oscillations in the NV spin echo amplitude with free evolution time τ. Solid lines are fits to from which the decay times T_2,I = (1.9 ± 0.6) µs and T_2,II = (0.89 ± 0.13) µs are extracted (see Supplementary information). (c) Measurement of temporal correlations on the full environment and on spin bath group II alone. During the sensing stages marked by, MW and RF π-pulses can be applied simultaneously to the NV spin and to the bath spins to selectively measure the correlation time of a particular group of bath spins. Solid lines are fits to (see Supplementary information).