Miniaturization of force probes into nanomechanical oscillators enables ultrasensitive investigations of forces on dimensions smaller than their characteristic length scale. Meanwhile it also unravels the force field vectorial character and how its topology impacts the measurement. Here we expose an ultrasensitive method to image 2D vectorial force fields by optomechanically following the bidimensional Brownian motion of a singly clamped nanowire. This novel approach relies on angular and spectral tomography of its quasi frequency-degenerated transverse mechanical polarizations: immersing the nanoresonator in a vectorial force field does not only shift its eigenfrequencies but also rotate eigenmodes orientation as a nano-compass. This universal method is employed to map a tunable electrostatic force field whose spatial gradients can even take precedence over the intrinsic nanowire properties. Enabling vectorial force fields imaging with demonstrated sensitivities of attonewton variations over the nanoprobe Brownian trajectory will have strong impact on scientific exploration at the nanoscale.Introduction-Nanosciences were revolutionized by the invention of atomic force microscopy [1] which enabled first perceptions of the nanoworld, by measuring proximity forces exerted by a sample on a micromechanical oscillator. The subsequent emergence of nanomechanical oscillators and evolutions in readout techniques [2][3][4] lead to impressive improvements in force sensitivity [5], enabling detection of collective spin dynamics [6][7][8], single electron spin [9], mass sensing of atoms [10,11] or inertial sensing [12]. Attractive perspectives arise too when nanoresonators are hybridized to single quantum systems, such as molecular magnets [13], spin or solid states qubits [14][15][16][17]. This reduction of the probe size naturally motivates the exploration of force fields on dimensions smaller than their characteristic length scale where a great physical richness is expected, in particular for nanoscale imaging or investigations of fundamental interactions such as proximity forces or near field couplings. In this situation, measurements are performed in presence of strong force field gradients whose vectorial structure becomes crucially relevant and should be fully accounted to describe the measurement process itself [18].
Reminiscent of the bound character of a qubit's dynamics confined on the Bloch sphere, the observation of a Mollow triplet in the resonantly driven qubit fluorescence spectrum represents one of the founding signatures of quantum electrodynamics. Here we report on its observation in a hybrid spin-nanomechanical system, where a nitrogen-vacancy spin qubit is magnetically coupled to the vibrations of a silicon carbide nanowire. A resonant microwave field turns the originally parametric hybrid interaction into a resonant process, where acoustic phonons are now able to induce transitions between the dressed qubit states, leading to synchronized spin-oscillator dynamics. We further explore the vectorial character of the hybrid coupling to the bidimensional deformations of the nanowire. The demonstrated microwave assisted synchronization of the spin-oscillator dynamics opens novel perspectives for the exploration of spin-dependent forces, the key ingredient for quantum state transfer.
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