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Register a new userTracking the precession of single nuclear spins by weak measurements
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Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analyzing the structure and function of molecules, and for performing three-dimensional imaging of the spin density. At the heart of NMR spectrometers is the detection of electromagnetic radiation, in the form of a free induction decay (FID) signal, generated by nuclei precessing around an applied magnetic field. While conventional NMR requires signals from 1e12 or more nuclei, recent advances in sensitive magnetometry have dramatically lowered this number to a level where few or even individual nuclear spins can be detected. It is natural to ask whether continuous FID detection can still be applied at the single spin level, or whether quantum back-action modifies or even suppresses the NMR response. Here we report on tracking of single nuclear spin precession using periodic weak measurements. Our experimental system consists of carbon-13 nuclear spins in diamond that are weakly interacting with the electronic spin of a nearby nitrogen-vacancy center, acting as an optically readable meter qubit. We observe and minimize two important effects of quantum back-action: measurement-induced decoherence and frequency synchronization with the sampling clock. We use periodic weak measurements to demonstrate sensitive, high-resolution NMR spectroscopy of multiple nuclear spins with a priori unknown frequencies. Our method may provide the optimum route for performing single-molecule NMR at atomic resolution.
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Quantum sensors have recently achieved to detect the magnetic moment of few or single nuclear spins and measure their magnetic resonance (NMR) signal. However, the spectral resolution, a key feature of NMR, has been limited by relaxation of the sensor to a few kHz at room temperature. The spectral resolution of NMR signals from single nuclear spins can be improved by, e.g., using quantum memories, however at the expense of sensitivity. Classical signals on the other hand can be measured with exceptional spectral resolution by using continuous measurement techniques, without compromising sensitivity. To apply these techniques to single-spin NMR, it is critical to overcome the impact of back action inherent of quantum measurements. Here we report sequential weak measurements on a single $^{13}$C nuclear spin. The back-action of repetitive weak measurements causes the spin to undergo a quantum dynamics phase transition from coherent trapping to coherent oscillation. Single-spin NMR at room-temperature with a spectral resolution of 3.8 Hz is achieved. These results enable the use of measurement-correlation schemes for the detection of very weakly coupled single spins.
Precise characterization of a hyperfine interaction is a prerequisite for high fidelity manipulations of electron and nuclear spins belonging to a hybrid qubit register in diamond. Here, we demonstrate a novel scheme for determining a hyperfine interaction, using single-quantum and zero-quantum Ramsey fringes, by applying it to the system of a Nitrogen Vacancy (NV) center and a $^{13}$C nuclear spin in the 1$^{mathrm{st}}$ shell. The zero-quantum Ramsey fringe, analogous to the quantum beat in a $Lambda$-type level structure, particularly enhances the measurement precision for non-secular hyperfine terms. Precisions less than 0.5 MHz in the estimation of all the components in the hyperfine tensor were achieved. Furthermore, for the first time we experimentally determined the principal axes of the hyperfine interaction in the system. Beyond the 1$^{mathrm{st}}$ shell, this method can be universally applied to other $^{13}$C nuclear spins interacting with the NV center.
Weak measurements may result in extra quantity of quantumness of correlations compared with standard projective measurement on a bipartite quantum state. We show that the quantumness of correlations by weak measurements can be consumed for information encoding which is only accessible by coherent quantum interactions. Then it can be considered as a resource for quantum information processing and can quantify this quantum advantage. We conclude that weak measurements can create more valuable quantum correlation.
We propose a method to achieve high degree control of nanomechanical oscillators by coupling their mechanical motion to single spins. By manipulating the spin alone and measuring its quantum state heralds the cooling or squeezing of the oscillator even for weak spin-oscillator couplings. We analytically show that the asymptotic behavior of the oscillator is determined by a spin-induced thermal filter function whose overlap with the initial thermal distribution of the oscillator determines its cooling, heating or squeezing. Counterintuitively, the rate of cooling dependence on the instantaneous thermal occupancy of the oscillator renders robust cooling or squeezing even for high initial temperatures and damping rates. We further estimate how the proposed scheme can be used to control the motion of a thin diamond cantilever by coupling it to its defect centers at low temperature.
The understanding of weak measurements and interaction-free measurements has greatly expanded the conceptual and experimental toolbox to explore the quantum world. Here we demonstrate single-shot variable-strength weak measurements of the electron and the nuclear spin states of a single $^{31}$P donor in silicon. We first show how the partial collapse of the nuclear spin due to measurement can be used to coherently rotate the spin to a desired pure state. We explicitly demonstrate that phase coherence is preserved throughout multiple sequential single-shot weak measurements, and that the partial state collapse can be reversed. Second, we use the relation between measurement strength and perturbation of the nuclear state as a physical meter to extract the tunneling rates between the $^{31}$P donor and a nearby electron reservoir from data, conditioned on observing no tunneling events. Our experiments open avenues to measurement-based state preparation, steering and feedback protocols for spin systems in the solid state, and highlight the fundamental connection between information gain and state modification in quantum mechanics.
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