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1. Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences

   https://doi.org/10.22331/q-2024-03-28-1304  

   Takou, Evangelia; Barnes, Edwin; Economou, Sophia E (March 2024, Quantum)

   Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZ ${}_M$-like states with minimal cross-talk. We introduce the $M$-tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZ ${}_M$-like states of up to $M=10$qubits within time constraints that saturate bounds on $M$-way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary $M$-tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary $M$-tangling power which incorporates the impact of electronic dephasing errors on the $M$-way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation. 

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2. Precise high-fidelity electron–nuclear spin entangling gates in NV centers via hybrid dynamical decoupling sequences

   https://doi.org/10.1088/1367-2630/ab9bc0  

   Dong, Wenzheng; Calderon-Vargas, F. A.; Economou, Sophia E. (July 2020, New Journal of Physics)

   Abstract Color centers in solids, such as the nitrogen-vacancy center in diamond, offer well-protected and well-controlled localized electron spins that can be employed in various quantum technologies. Moreover, the long coherence time of the surrounding spinful nuclei can enable a robust quantum register controlled through the color center. We design pulse sequence protocols that drive the electron spin to generate robust entangling gates with these nuclear memory qubits. We find that compared to using Carr-Purcell-Meiboom-Gill (CPMG) alone, Uhrig decoupling sequence and hybrid protocols composed of CPMG and Uhrig sequences improve these entangling gates in terms of fidelity, spin control range, and spin selectivity. We provide analytical expressions for the sequence protocols and also show numerically the efficacy of our method on nitrogen-vacancy centers in diamond. Our results are broadly applicable to color centers weakly coupled to a small number of nuclear spin qubits. 

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3. Theory of long range interactions for Rydberg states attached to hyperfine split cores

   Robicheaux, F.; Booth, D.; Saffman, M. (January 2018, 49th annual meeting of the APS division of atomic, molecular and optical physics)

   Theory for one and two atom interactions is developed for the case when the atoms have a Rydberg electron attached to a hyper- fi ne split core state, a situation relevant for some rare earth and some alkaline earth atoms proposed for experiments on Rydberg-Rydberg in- teractions. For the rare earth atoms, the core electrons can have a very substantial total angular momentum, J, and a non-zero nuclear spin, I. For alkaline earth atoms there is a single, s, core electron whose spin can couple to a non-zero nuclear spin for odd isotopes. The hyper fine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the un- perturbed Rydberg series of the alkali atoms, series perturbations and near degeneracies from the different parity states could lead to quali- tatively different behavior for single atom Rydberg properties (polariz- ability, Zeeman mixing and splitting, etc) as well as Rydberg-Rydberg interactions (C5 and C6 matrices). 

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4. Directly imaging spin polarons in a kinetically frustrated Hubbard system

   Prichard, Max; Spar, B; Morera, I; Demler, E; Yan, Z; Bakr, W (May 2024, Nature)

   The emergence of quasiparticles in quantum many-body systems underlies the rich phenomenology in many strongly interacting materials. In the context of doped Mott insulators, magnetic polarons are quasiparticles that usually arise from an interplay between the kinetic energy of doped charge carriers and superexchange spin interactions. However, in kinetically frustrated lattices, itinerant spin polarons—bound states of a dopant and a spin flip—have been theoretically predicted even in the absence of superexchange coupling. Despite their important role in the theory of kinetic magnetism, a microscopic observation of these polarons is lacking. Here we directly image itinerant spin polarons in a triangular-lattice Hubbard system realized with ultracold atoms, revealing enhanced antiferromagnetic correlations in the local environment of a hole dopant. In contrast, around a charge dopant, we find ferromagnetic correlations, a manifestation of the elusive Nagaoka effect. We study the evolution of these correlations with interactions and doping, and use higher-order correlation functions to further elucidate the relative contributions of superexchange and kinetic mechanisms. The robustness of itinerant spin polarons at high temperature paves the way for exploring potential mechanisms for hole pairing and superconductivity in frustrated systems. Furthermore, our work provides microscopic insights into related phenomena in triangular-lattice moiré materials. 

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5. Spin-dynamics of pairs of submerged-4f-shell atoms in cylindrically symmetric harmonic traps: connecting multi-channel models to effective analytical approaches

   https://doi.org/10.1088/1367-2630/adc764  

   Li, Hui; Tiesinga, Eite; Li, Ming; Kotochigova, Svetlana (April 2025, New Journal of Physics)

   Abstract We study spin dynamics and quantum magnetism with ultracold highly-magnetic atoms. In particular, we focus on the interactions among rare-earth atoms localized in a site of an optical-lattice potential, modeled as a cylindrically symmetric harmonic oscillator in the presence of a weak external magnetic field. The interactions between the atoms are modeled using a multi-channel Hamiltonian containing multiple spin–spin and anisotropic spin–orbit interactions with strengths that depend on the separation between the atoms. We studied the eigenenergies of the atom pair in a site for different lattice geometries and magnetic field strengths. In parallel, we compared these energies to those found from a simplified approach, where the complex-collisional physics is replaced by a two-length-scale pseudopotential containing the contact and magnetic dipole–dipole interactions. The eigenenergies of this model can be computed analytically within the Born approximation as well as non-perturbatively for strong contact interactions. We have shown that the pseudopotential model can accurately represent the multi-channel Hamiltonian in certain parameter regimes of the shape of the site of an optical lattice. The pseudopotential forms the starting point for many-body, condensed matter simulations involving many atom pairs in different sites of an optical lattice. 

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