Alkaline-earth-like (AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states ∣0〉 and ∣1〉 are excited to Rydberg states ∣ r 〉 with detuning Δ and 0, respectively, where a MHz-scale detuning Δ arises from a weak magnetic field on the order of 1 G. With a proper ratio between Δ and Ω, the qubit state ∣1〉 can be fully excited to the Rydberg state while ∣0〉 remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.
Alkaline-earth-like (AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states ∣0〉 and ∣1〉 are excited to Rydberg states ∣ r 〉 with detuning Δ and 0, respectively, where a MHz-scale detuning Δ arises from a weak magnetic field on the order of 1 G. With a proper ratio between Δ and Ω, the qubit state ∣1〉 can be fully excited to the Rydberg state while ∣0〉 remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.
Abstract In this brief review, the opportunities that the alkaline-earth elements offer for studying new aspects of Rydberg physics are discussed. For example, the bosonic alkaline-earth isotopes have zero nuclear spin which eliminates many of the complexities present in alkali Rydberg atoms, permitting simpler and more direct comparison between theory and experiment. The presence of two valence electrons allows the production of singlet and triplet Rydberg states that can exhibit a variety of attractive or repulsive interactions. The availability of weak intercombination lines is advantageous for laser cooling and for applications such as Rydberg dressing. Excitation of one electron to a Rydberg state leaves behind an optically active core ion allowing, for high- L states, the optical imaging of Rydberg atoms and their (spatial) manipulation using light scattering. The second valence electron offers the possibility of engineering long-lived doubly excited states such as planetary atoms. Recent advances in both theory and experiment are highlighted together with a number of possible directions for the future.
Hyperentanglement (HE), the simultaneous entanglement between two particles in more than one degree of freedom, is relevant to both fundamental physics and quantum technology. Previous study on HE has been focusing on photons. Here, we study HE in individual neutral atoms. In most alkaline-earth-like atoms with two valence electrons and a nonzero nuclear spin, there are two stable electronic states, the ground state and the long-lived clock state, which can define an electronic qubit. Meanwhile, their nuclear spin states can define a nuclear qubit. By the Rydberg blockade effect, we show that the controlled-Z (cz) operation can be generated in the electronic qubits of two nearby atoms, and simultaneously in their nuclear qubits as well, leading to a cz$\ensuremath{\bigotimes}$cz operation which is capable to induce HE. The possibility to induce HE in individual neutral atoms offers opportunities to study quantum science and technology based on neutral atoms.
The theory is developed for one- and two-atom interactions when the atom has a Rydberg electron attached to a hyperfine-split core state. This situation is relevant for some of the rare-earth and alkaline-earth atoms that have been proposed for experiments on Rydberg-Rydberg interactions. For the rare-earth atoms, the core electrons can have a very substantial total angular momentum J and a nonzero nuclear spin I. In the alkaline-earth atoms there is a single (s) core electron whose spin can couple to a nonzero nuclear spin for odd isotopes. The resulting hyperfine splitting of the core state can lead to substantial mixing between the Rydberg series attached to different thresholds. Compared to the unperturbed Rydberg series of the alkali-metal atoms, the series perturbations and near degeneracies from the different parity states could lead to qualitatively different behavior for single-atom Rydberg properties (polarizability, Zeeman mixing and splitting, etc.) as well as Rydberg-Rydberg interactions (C5 and C6 matrices).
Neutral alkaline earth(like) atoms have recently been employed in atomic arrays with individual readout, control, and high-fidelity Rydberg-mediated entanglement. This emerging platform offers a wide range of new quantum science applications that leverage the unique properties of such atoms: ultranarrow optical ``clock'' transitions and isolated nuclear spins. Specifically, these properties offer an optical qubit (o) as well as ground (g) and metastable (m) nuclear spin qubits, all within a single atom. We consider experimentally realistic control of this omg architecture and its coupling to Rydberg states for entanglement generation, focusing specifically on ytterbium-171 (171Yb) with nuclear spin I=21. We analyze the S-series Rydberg states of 171Yb, described by the three spin-21 constituents (two electrons and the nucleus). We confirm that the F=23 manifold, a unique spin configuration, is well suited for entangling nuclear spin qubits. Further, we analyze the F=21 series, described by two overlapping spin configurations, using a multichannel quantum defect theory. We study the multilevel dynamics of the nuclear spin states when driving the clock or Rydberg transition with Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{c}=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}200\phantom{\rule{0.28em}{0ex}}\text{kHz}$ or ${\mathrm{\ensuremath{\Omega}}}_{R}=2\ensuremath{\pi}\ifmmode\times\else\texttimes\fi{}6\phantom{\rule{0.28em}{0ex}}\text{MHz}$, respectively, finding that a modest magnetic field ($\ensuremath{\approx}200\phantom{\rule{0.28em}{0ex}}\text{G}$) and feasible laser polarization intensity purity ($\ensuremath{\lesssim}0.99$) are sufficient for gate fidelities exceeding 0.99. We also study single-beam Raman rotations of the nuclear spin qubits and identify a ``magic'' linear polarization angle with respect to the magnetic field at which purely ${\ensuremath{\sigma}}_{x}$ rotations are possible.
We present a novel class of Rydberg-mediated nuclear-spin entanglement in divalent atoms with global laser pulses. First, we show a fast nuclear-spin controlled phase gate of an arbitrary phase realizable either with two laser pulses when assisted by Stark shifts, or with three pulses. Second, we propose to create an electrons–nuclei-entangled state, which is named a super bell state (SBS) for it mimics a large Bell state incorporating three small Bell states. Third, we show a protocol to create a three-atom electrons-nuclei entangled state which contains the three-body W and Green-berger–Horne–Zeilinger (GHZ) states simultaneously. These protocols possess high intrinsic fidelities, do not require single-site Rydberg addressing, and can be executed with large Rydberg Rabi frequencies in a weak, Gauss-scale magnetic field. The latter two protocols can enable measurement-based preparation of Bell, hyperentangled, and GHZ states, and, specifically, SBS can enable quantum dense coding where one can share three classical bits of information by sending one particle.
Recently, alkaline-earth (-like) atoms and alkaline earth metals (AEL) gained experimental and theoretical interest principally related to the possibility offered in metrological field by the excitation of visible and UV clock transitions. AEL atoms, in their neutral \nform and in the ground state, have a null total electronic momentum, resulting nearly insensitive to external magnetic fields. While the absence of magnetic coupling does not allow the simply interactions tuning by exploiting Feshbach resonances as it occurs \nin alkaline atoms, these atoms are characterized by highly symmetric ground states allowing the simulation of SU(N) systems. This characteristic, that can be attributed in AEL atoms to the decoupling between electronic and nuclear atomic momenta, can be \nexploited to perform quantum simulation of a wealth of novel systems and constitutes a fundamental property of isotopes that have a nonzero nuclear spin, as it occurs for all the fermionic species and in particular for 173Yb and 87Sr. This feature also ensures the \nabsence of spin-changing collisions in ground state sublevels, implying that nuclear-spin mixtures are observationally stable. This attribute is fundamental for the study of transitions between different nuclear-spin states, for example by exploiting the two-photon \nRaman coupling. The degeneracy related to the SU(N) symmetry can be controllably removed by applying a two-photon Raman coupling, allowing for the simulation of systems with broken symmetries. \nBesides the possibility to induce couplings within the nuclear-spin degree of freedom, AEL atoms also offer the possibility to access a second, electronic degree of freedom; the possibility to address visible doubly-forbidden transitions between long-lived electronic \nclock states comprises a fantastic tool that allowed the building of optical lattice clocks improving metrological measurements and offering a richer platform for simulating complex systems. \nThe main difference between the two internal degrees of freedom offered by AEL atoms is that the possibility to address ultranarrow optical clock transitions exists also for AEL bosonic isotopes in which the nuclear-spin degree of freedom is not present because the \ntotal atomic momentum is absent. \nThe possibilities related to the excitation of long-lived metastable triplet levels, that, referring only to the lowest lying atomic levels are 3P(0;2) (in Russell-Saunders approximation they result doubly forbidden with respect to the electric dipole operator), are \nmultiple. If bosonic atoms are considered, the metrological applications based on the clock transition at the state of the art have performances comparable to optical lattice clocks realized with fermionic isotopes. Bosonic isotopes, requiring external fields in order \nto excite transitions from the ground state to long-lived states, have been proposed as good candidates in order to build a reliable and fast system in which controllable qu-bits could be realized. Most of these applications, and in particular the possibility to create \nquantum computers with neutral atoms, crucially rely on the control of the scattering properties of atoms in different electronic states. \nRegarding fermionic isotopes, the clock transitions recently allowed for the demonstration of spin-orbit coupling and quantum simulation via the synthetic dimension approach. As recently discovered, the clock transitions from the ground to the 3P(0;2) states give rise to rich interactions possibilities between atoms in the fundamental and in the metastable states. The spin-exchange interaction that has been observed between ground and metastable states, supports also a new kind of Feshbach resonance, called Orbital Feshbach Resonance (OrbFR). As occurs in magnetic Feshbach resonances for alkali atoms, also the OrbFR, that occurs in AEL atoms, supports the existence of extremely shallow homonuclear molecules. After considering the (s-wave) scattering parameters of all the AEL atoms that have been characterized experimentally, 173Yb is the only isotope in which the production and manipulation of Orbital Feshbach molecules (produced e.g. with photoassociation) is experimentally viable. Molecules generated by employing this atom, may lead to the investigation of fermionic superfluidity in still-unexplored regimes. In this thesis we report the characterization of interactions in bosonic 174Yb isotope by probing the clock transition between the singlet 1S0 ground state and the triplet 3P0 \nmetastable excited state. Interactions and inelastic losses between ground-state and excited metastable-state atoms have been experimentally determined with high accuracy, resulting consistent with an indipendent evaluation realized in the same period by Yb \nBEC group at LKB. \nThe obtained values for the interactions among ground and metastable atoms for the specified isotope constitute a first step in order to design an experimental system in which quantum information can be realized by means of exploiting the clock transition of bosonic Yb atoms. \nThis work, by exploiting the internal degrees of freedom of 173Yb atoms, reports a study on Orbital Feshbach molecules, showing experimentally the possibility to employ the nuclear degree of freedom in 173Yb atoms to manipulate and precisely detect homo-nuclear photoassociated molecules. \nThis first result regarding this new kind of shallow-bound molecules allowed the characterization of interactions between ground-state and metastable-state of 173Yb atoms. \nThis first intensive study of orbital Feshbach molecules is a fundamental step for future studies on the possibilities offered by these homo-nuclear molecules. \nFinally, we exploited the ground state SU(N) symmetry and its controlled breaking via Raman coupling (in 173Yb N = 1...6) to simulate the physical processes that are supposed to be driven by the hybridation of d-orbitals of iron atoms in iron based-superconductors, \nin which orbital-selective Mott insulating phases have been experimentally observed and are suspected to be the fundamental ingredient to achieve high-temperature superconductivity in these compounds.