We study the ability to control d-dimensional quantum systems (qudits) encoded in the hyperfine spin of alkali-metal atoms through the application of radio- and microwave-frequency magnetic fields in the presence of inhomogeneities in amplitude and detuning. Such a capability is essential to the design of robust pulses that mitigate the effects of experimental uncertainty and also for application to tomographic addressing of particular members of an extended ensemble. We study the problem of preparing an arbitrary state in the Hilbert space from an initial fiducial state. We prove that inhomogeneous control of qudit ensembles is possible based on a semi-analytic protocol that synthesizes the target through a sequence of alternating rf and microwave-driven SU(2) rotations in overlapping irreducible subspaces. Several examples of robust control are studied, and the semi-analytic protocol is compared to a brute force, full numerical search. For small inhomogeneities, < 1%, both approaches achieve average fidelities greater than 0.99, but the brute force approach performs superiorly, reaching high fidelities in shorter times and capable of handling inhomogeneities well beyond experimental uncertainty. The full numerical search is also applied to tomographic addressing whereby two different nonclassical states of the spin are produced in two halves of the ensemble.
Hyperfine spectroscopy and fast, all-optical arbitrary state initialization and readout of a single, ten-level ${}^{73}$Ge vacancy nuclear spin qudit in diamond
Collective effects in the interaction of light with ensembles of identical scatterers play an important role in many fields of physics. However, often the term ``identical'' is not accurate due to the presence of hyperfine fields which induce inhomogeneous transition shifts and splittings. Here we develop a formalism based on the Green function method to model the linear response of such inhomogeneous ensembles in one-dimensional waveguides. We obtain a compact formula for the collective spectrum, which exhibits deviations from the uniform frequency shift and broadening expected of two level s…
We show that [VO(TPP)] (vanadyl tetraphenylporphyrinate) is a promising system suitable to implement quantum computation algorithms based on encoding information in multi-level (qudit) units. Indeed, it embeds an electronic spin 1/2 coupled through hyperfine interaction to a nuclear spin 7/2, both characterized by remarkable coherence. We demonstrate this by an extensive broadband nuclear magnetic resonance study, which allow us to characterize the nuclear spin-Hamiltonian and to measure the spin dephasing time as a function of the magnetic field. In addition, we combine targeted measurements …
All-optical universal control of nuclear-spin qudits in trapped neutral atoms
Institute of Experimental Physics, Graz University of Technology（格拉茨工业大学实验物理研究所）；Institute of Physics, University of Graz（格拉茨大学物理研究所）；PlanQC GmbH（PlanQC有限公司）
As an extension of two-level quantum bits (qubits), multilevel systems, so-called qudits, where d represents the Hilbert space dimension, have been predicted to reduce the number of iterations in quantum computation algorithms. This has been tested in the well-known [TbPc2]0 SMM, which allowed the implementation of the Grover algorithm in a single molecular unit. In the quest for molecular systems possessing an increased number of accessible nuclear spin states, we explore herein a dimeric Tb2-SMM via single crystal μ-SQUID measurements at sub-Kelvin temperatures. We observe ferromagnetic inte…
We develop a procedure of generalized continuous dynamical decoupling (GCDD) for an ensemble of $d$-level systems (qudits), allowing one to protect the action of an arbitrary multi-qudit gate from general noise. We first present our GCDD procedure for the case of an arbitrary qudit and apply it to the case of a Hadamard gate acting on a qutrit. This is done using a model that, in principle, could be implemented using the three magnetic hyperfine states of the ground energy level of $^{87}\mathrm{Rb}$ and laser beams whose intensities and phases are modulated according to our prescription. We s…
Quantum bit or qubit is a two-level system, which builds the foundation for quantum computation, simulation, communication and sensing. Quantum states of higher dimension, i.e., qutrits (D = 3) and especially qudits (D = 4 or higher), offer significant advantages. Particularly, they can provide noise-resistant quantum cryptography, simplify quantum logic and improve quantum metrology. Flying and solid-state qudits have been implemented on the basis of photonic chips and superconducting circuits, respectively. However, there is still a lack of room-temperature qudits with long coherence time an…
Nuclear spins of dopant atoms in semiconductors are promising candidates as quantum bits, due to the long lifetime of their quantum states. Conventionally, coherent control of nuclear spins is done using ac magnetic fields. Using the example of a phosphorus atom in silicon, we theoretically demonstrate that hyperfine interaction can enhance the speed of magnetic control: the electron on the donor amplifies the ac magnetic field felt by the nuclear spin. Based on that result, we show that hyperfine interaction also provides a means to control the nuclear spin efficiently using an ac electric fi…
Continuous spectral hole burning and spin-level population oscillations are studied in an inhomogeneously broadened diamond-based spin ensemble composed of substitutional nitrogen and nitrogen-vacancy centres created through neutron irradiation and annealing. The burnt spectral features highlight a detuning-dependent homogeneous hole linewidth that is up to three orders of magnitude narrower than the total inhomogeneous ensemble linewidth. Continuous population oscillations are observed to quickly decay beyond a pump and probe detuning of 5 Hz, and are numerically modelled using a five-level s…
This work introduces the so-called synchrosqueezed wavelet transform, to shed light on the dipolar fluctuations of a thermal ensemble of nuclear spins in a diamond crystal structure, hyperfine-coupled to a central spin. The raw time series of the nuclear spin bath coherent dynamics is acquired through the two-point correlation function computed using the cluster correlation expansion method. The dynamics can be conveniently analyzed according to zero-, single-, and double-quantum transitions derived from the dipolar pairwise spin flips. We show that in the early-time behavior when the coherenc…
Using an operator approach based on a commutator scheme that has been previously applied to Richardson's reduced BCS model and the inhomogeneous Dicke model, we obtain general exact solvability requirements for an anisotropic central spin model with $XXZ$-type hyperfine coupling between the central spin and the spin bath, without any prior knowledge of integrability of the model. We outline the basic steps of the usage of the operator approach, and pedagogically summarize them into two \emph{Lemmas} and two \emph{Constraints}. Through a step-by-step construction of the eigen-problem, we show t…
Hole spins in semiconductors are a potential qubit alternative to electron spins. In nuclear-spin-rich host crystals like GaAs, the hyperfine interaction of hole spins with nuclei is considerably weaker than that for electrons, leading to potentially longer coherence times. Here we demonstrate optical pumping and coherent population trapping for acceptor-bound holes in a strained GaAs epitaxial layer. We find $μ$s-scale longitudinal spin relaxation time T$_1$ and an inhomogeneous dephasing time T$_2^*$ of $\sim$7~ns. We attribute the spin relaxation mechanism to a combination effect of a hole-…
Gate Synthesis in Dephasing-Limited Nitrogen-Vacancy Ensembles
Institut quantique, Université de Sherbrooke（舍布鲁克大学量子研究所）；Département de physique, Université de Sherbrooke（舍布鲁克大学物理系）；Keysight Technologies Canada（是德科技加拿大）；Département de génie électrique et de génie informatique, Université de Sherbrooke（舍布鲁克大学电气与计算机工程系）
Rare-earth ions in crystals are a proven solid-state platform for quantum technologies in the ensemble regime and attractive for new opportunities at the single ion level. Among the trivalent rare earths, ${}^{171}\mathrm{Yb}^{3+}$ is unique in that it possesses a single 4f excited-state manifold and is the only paramagnetic isotope with a nuclear spin of 1/2. In this work, we present measurements of the optical and spin properties of $^{171}$Yb$^{3+}$:YVO$_4$ to assess whether this distinct energy level structure can be harnessed for quantum interfaces. The material was found to possess large…
Optically interfaced spins in the solid promise scalable quantum networks. Robust and reliable optical properties have so far been restricted to systems with inversion symmetry. Here, we release this stringent constraint by demonstrating outstanding optical and spin properties of single silicon vacancy centres in silicon carbide. Despite the lack of inversion symmetry, the system's particular wave function symmetry decouples its optical properties from magnetic and electric fields, as well as from local strain. This provides a high-fidelity spin-to-photon interface with exceptionally stable an…
Optically active defects in solids with accessible spin states are promising candidates for solid state quantum information and sensing applications. To employ these defects as quantum building blocks, coherent manipulation of their spin state is required. Here we realize coherent control of ensembles of boron vacancy (V$_B^-$) centers in hexagonal boron nitride (hBN). Specifically, by applying pulsed spin resonance protocols, we measure spin-lattice relaxation time ($T_1$) of 18 $μ$s and spin coherence time ($T_2$) of 2 $μ$s at room temperature. The spin-lattice relaxation time increases by t…
Coherent Microwave Control of Optically Addressable Donor Qubits in ZnO
University of Washington（华盛顿大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；California Institute of Technology（加州理工学院）；Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院量子信息与物质研究所）；University of Tokyo（东京大学）；RIKEN（理化学研究所）
