Super-resolved Imaging Of Trapped Ions

In recent decades,the rapid development of quantum computing,quantum communication,and quantum metrology fields has led to the second quantum revolution.The improvement of experimental techniques allows richer and more precise quantum manipulation methods on single or multiple qubits.This progress potentially makes the speed of computation faster,the protocol of communication securer,and detection of physical parameters more precise.For experimental systems such as atoms,ions,molecules,and solid-states,far-field optical manipulations have been widely used in quantum manipulation,detection,and imaging.Taking the trapped ion as an example,the tightly focused beam array is employed to realize ion addressing and entanglement between arbitrary ions.With the state-dependent fluorescence technique,state detection is demonstrated with high fidelity.Imaging is accomplished with the objective,which collects scattering photons from the qubit within Doppler cooling cycles.For imaging systems,spatial resolution is a very important parameter.Basically,it determines the minimum distance between resolvable points and the sensitivity of single ion's position.However,the resolution is fundamentally limited by the wavelength and numerical aperture of the objective lens according to the diffraction theory of Abbe,leading to the minimum resolution which cannot surpass the half wavelength.To break the diffraction limit,we propose and demonstrate the super-resolved imaging scheme using a single trapped ion.The principle is based on ground state depletion,which is similar to the stimulated emission depletion microscopy.We utilize the doughnut beam to selectively depopulate the spin.It will remain unchanged when located in the center area due to the low intensity.Otherwise,the spin will be depopulated.In this way,the spatial information is encoded in the quantum state.This research can be mainly organized into four parts.(1)We investigate the holographic beam reshaping technique based on digital micromirror devices.The key points lie in the aberration correction and beam reshaping with holographic patterns.We employ multi-step phase shift method to measure the aberration of the whole optical system.Then the holographic patterns considering the corrected aberration are computed and projected.With this method,various modes of Laguerre-Gaussian and Hermit-Gaussian beams are generated.In contrast to other techniques of beam reshaping,this method is adaptive and able to produce modes of higher purity.(2)We demonstrate the super-resolved imaging on single trapped ions.We analyzed two factors determining the spatial resolution,i.e.,the intensity and duration of the depletion beam.The limit of resolution is also discussed.The achieved resolution is 175 nm with objectives of NA=0.1,which is beyond the optical diffraction limit and improves over 13 times than fluorescence microscopy.(3)With this technique,the dynamics of trapped ion is investigated.We take a video of a single ion's secular motion in a period of hundreds of nanoseconds.We achieve a 50 ns of temporal resolution and 10 nm precision of the trajectories.(4)Bayesian optimization for wavefront sensing is proposed and investigated from the point of simulation and experiment.This algorithm takes the 8 orders Zernike coefficients as input parameter and Strehl ratio of point spread function of images as output.The optimal solution is generated by iterating many steps until a Strehl ratio closing 1.0 is found.The performance in the case of small and large aberration is investigated.We verify the merits of fast converging speed and robustness to initial conditions compared with other algorithms.This algorithm performs better than(1).We developed a super-resolved imaging tool for cold atoms and extend one dimension imaging to two dimensions.This technique can be extended into many other quantum systems such as trapped ion chain,s optical lattices,optical tweezers,and cavity QED.The applications include resolving single atoms from ensembles to achieve higher precision of detection and improving the sensitivity of parameters like displacement and electric force.