Alkaline-earth-metal atoms as few-qubit quantum registers

Frequency references based on molecular iodine for the study of Yb atoms using the 1S0 - 3P1 intercombination transition at 556 nm

We used precision spectroscopy to analyze the R(53)24-1, P(49)24-1, and R(95)25-1 lines of molecular iodine (¹²⁷I₂) to establish optical frequency references for the laser cooling of Yb atoms using the ¹S₀ - ³P₁ intercombination transition at 556 nm. A laser frequency instability of < 2 × 10^-12 (for 0.01 s < τ < 3000 s, τ is the average time of the measurement) was attained using the observed Doppler-free hyperfine transitions of the iodine lines. The absolute frequencies of the observed 63 hyperfine transitions were determined with an uncertainty of 7 kHz (fractional uncertainty of 1.3 × 10^-11). Highly accurate hyperfine constants were determined by fitting the measured hyperfine splittings to a four-term Hamiltonian that includes the electric quadrupole, spin-rotation, tensor spin-spin, and scalar spin-spin interactions with an uncertainty of approximately 1 kHz. The observed hyperfine transitions of molecular iodine provide new frequency references for research using atomic Yb, because these transitions are close to the intercombination transition of Yb at 556 nm.

Photovoltaic transistor of atoms due to spin-orbit coupling in three optical traps

In this paper, spin-orbit coupling induced photovoltaic effect of cold atoms has been studied in a three-trap system which is an two-dimensional extension of a two-trap system reported previously. It is proposed here that atom coherent length is one of the important influences to the resistance of this photovoltaic battery. Current properties of the system for different geometrical structures of the trapping potentials are discussed. Numerical results show extension in the number of traps could cause current increase directly. Quantum master equation at finite temperature is used to treat this open system. This work may give a theoretical basis for further development of the photovoltaic effect of neutral atoms.

Multi-reference ab initio calculations of Hg spectral data and analysis of magic and zero-magic wavelengths

We have identified magic wavelengths for ¹S₀ ↔ ³P_1,2 (m_J = 0) transitions and zero-magic wavelengths for the ³P_1,2 (m_J = 0) states of ²⁰⁰Hg atoms, analysed the robustness of the magic conditions with respect to wavelength and polarization imperfections. We show that the most experimentally feasible magic wavelength for the ¹S₀ ↔ ³P₂ transition is 351.8 nm of π polarized light. Relevant transition wavelengths and transition strengths are calculated using the state-of-the-art Complete Active Space Self-Consistent-Field (CASSCF) method with a perturbative inclusion of spin-orbit coupling. The transition wavelengths are a posteriori corrected for the dynamical energy using the second-order perturbation theory.

Single-layer polymeric tetraoxa[8]circulene modified by s-block metals: toward stable spin qubits and novel superconductors

Tunable electronic properties of low-dimensional materials have been the object of extensive research, as such properties are highly desirable in order to provide flexibility in the design and optimization of functional devices. In this study, we account for the fact that such properties can be tuned by embedding diverse metal atoms and theoretically study a series of new organometallic porous sheets based on two-dimensional tetraoxa[8]circulene (TOC) polymers doped with alkali or alkaline-earth metals. The results reveal that the metal-decorated sheets change their electronic structure from semiconducting to metallic behaviour due to n-doping. Complete active space self-consistent field (CASSCF) calculations reveal a unique open-shell singlet ground state in the TOC-Ca complex, which is formed by two closed-shell species. Moreover, Ca becomes a doublet state, which is promising for magnetic quantum bit applications due to the long spin coherence time. Ca-doped TOC also demonstrates a high density of states in the vicinity of the Fermi level and induced superconductivity. Using the ab initio Eliashberg formalism, we find that the TOC-Ca polymers are phonon-mediated superconductors with a critical temperature T_C = 14.5 K, which is within the range of typical carbon based superconducting materials. Therefore, combining the proved superconductivity and the long spin lifetime in doublet Ca, such materials could be an ideal platform for the realization of quantum bits.

Symmetry Breaking and Error Correction in Open Quantum Systems

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system-a Lindbladian-a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Z_{n} symmetry-breaking transitions for both cases. In the case of Z_{2}, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.

State-Dependent Optical Lattices for the Strontium Optical Qubit

We demonstrate state-dependent optical lattices for the Sr optical qubit at the tune-out wavelength for its ground state. We tightly trap excited state atoms while suppressing the effect of the lattice on ground state atoms by more than 4 orders of magnitude. This highly independent control over the qubit states removes inelastic excited state collisions as the main obstacle for quantum simulation and computation schemes based on the Sr optical qubit. Our results also reveal large discrepancies in the atomic data used to calibrate the largest systematic effect of Sr optical lattice clocks.

2000-Times Repeated Imaging of Strontium Atoms in Clock-Magic Tweezer Arrays

We demonstrate single-atom resolved imaging with a survival probability of 0.99932(8) and a fidelity of 0.99991(1), enabling us to perform repeated high-fidelity imaging of single atoms in tweezers thousands of times. We further observe lifetimes under laser cooling of more than seven minutes, an order of magnitude longer than in previous tweezer studies. Experiments are performed with strontium atoms in 813.4 nm tweezer arrays, which is at a magic wavelength for the clock transition. Tuning to this wavelength is enabled by off-magic Sisyphus cooling on the intercombination line, which lets us choose the tweezer wavelength almost arbitrarily. We find that a single not retroreflected cooling beam in the radial direction is sufficient for mitigating recoil heating during imaging. Moreover, this cooling technique yields temperatures below 5  μK, as measured by release and recapture. Finally, we demonstrate clock-state resolved detection with average survival probability of 0.996(1) and average state detection fidelity of 0.981(1). Our work paves the way for atom-by-atom assembly of large defect-free arrays of alkaline-earth atoms, in which repeated interrogation of the clock transition is an imminent possibility.

Ab initio studies of the ground and first excited states of the Sr-H2 and Yb-H2 complexes

Accurate intermolecular potential-energy surfaces (IPESs) for the ground and first excited states of the Sr-H₂ and Yb-H₂ complexes were calculated. After an extensive methodological study, the coupled cluster with single, double, and non-iterative triple excitation method with the Douglas-Kroll-Hess Hamiltonian and correlation-consistent basis sets of triple-ζ quality extended with 2 sets of diffuse functions and a set of midbond functions were chosen. The obtained ground-state IPESs are similar in both complexes, being relatively isotropic with two minima and two transition states (equivalent by symmetry). The global minima correspond to the collinear geometries with R = 5.45 and 5.10 Å and energies of -27.7 and -31.7 cm^-1 for the Sr-H₂ and Yb-H₂ systems, respectively. The calculated surfaces for the Sr(³P)-H₂ and Yb(³P)-H₂ states are deeper and more anisotropic, and they exhibit similar patterns within both complexes. The deepest surfaces, where the singly occupied p-orbital of the metal atom is perpendicular to the intermolecular axis, are characterised by the global minima of ca. -2053 and -2260 cm^-1 in the T-shape geometries at R = 2.41 and 2.29 Å for Sr-H₂ and Yb-H₂, respectively. Additional calculations for the complexes of Sr and Yb with the He atom revealed a similar, strong dependence of the interaction energy on the orientation of the p-orbital in the Sr(³P)-He and Yb(³P)-He states.

Spectrum Estimation of Density Operators with Alkaline-Earth Atoms

We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing and time keeping with alkaline-earth atoms are discussed.

Symmetry-Protected Topological States for Interacting Fermions in Alkaline-Earth-Like Atoms

We discuss the quantum simulation of symmetry-protected topological (SPT) states for interacting fermions in quasi-one-dimensional gases of alkaline-earth-like atoms such as ^{173}Yb. Taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these atoms, we consider Raman-assisted spin-orbit couplings in the clock states, which, together with the spin-exchange interactions in the clock-state manifolds, give rise to SPT states for interacting fermions. We numerically investigate the phase diagram of the system, and study the phase transitions between the SPT phase and the symmetry-breaking phases. The interaction-driven topological phase transition can be probed by measuring local density distribution of the topological edge modes.

Second harmonic generation at 399 nm resonant on the 1S0-1P1 transition of ytterbium using a periodically poled LiNbO3 waveguide

We demonstrate a compact and robust method for generating a 399-nm light resonant on the ¹S₀ - ¹P₁ transition in ytterbium using a single-pass periodically poled LiNbO₃ waveguide for second harmonic generation (SHG). The obtained output power at 399 nm was 25 mW when a 798-nm fundamental power of 380 mW was coupled to the waveguide. We observed no degradation of the SHG power for 13 hours with a low power of 6 mW. The obtained SHG light has been used as a seed light for injection locking, which provides sufficient power for laser cooling ytterbium.

Synthetic Spin-Orbit Coupling in an Optical Lattice Clock

We propose the use of optical lattice clocks operated with fermionic alkaline-earth atoms to study spin-orbit coupling (SOC) in interacting many-body systems. The SOC emerges naturally during the clock interrogation, when atoms are allowed to tunnel and accumulate a phase set by the ratio of the "magic" lattice wavelength to the clock transition wavelength. We demonstrate how standard protocols such as Rabi and Ramsey spectroscopy that take advantage of the sub-Hertz resolution of state-of-the-art clock lasers can perform momentum-resolved band tomography and determine SOC-induced s-wave collisions in nuclear-spin-polarized fermions. With the use of a second counterpropagating clock beam, we propose a method for engineering controlled atomic transport and study how it is modified by p- and s-wave interactions. The proposed spectroscopic probes provide clean and well-resolved signatures at current clock operating temperatures.

Realizing exactly solvable SU(N) magnets with thermal atoms

We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the S _n symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.

Time-reversal-symmetric single-photon wave packets for free-space quantum communication

Readout and retrieval processes are proposed for efficient, high-fidelity quantum state transfer between a matter qubit, encoded in the level structure of a single atom or ion, and a photonic qubit, encoded in a time-reversal-symmetric single-photon wave packet. They are based on controlling spontaneous photon emission and absorption of a matter qubit on demand in free space by stimulated Raman adiabatic passage. As these processes do not involve mode selection by high-finesse cavities or photon transport through optical fibers, they offer interesting perspectives as basic building blocks for free-space quantum-communication protocols.

Control of resonant interaction between electronic ground and excited states

We observe magnetic Feshbach resonances in a collision between the ground and metastable states of two-electron atoms of ytterbium (Yb). We measure the on-site interaction of doubly occupied sites of an atomic Mott-insulator state in a three-dimensional optical lattice as a collisional frequency shift in a high-resolution laser spectroscopy. The observed spectra are well fitted by a simple theoretical formula, in which two particles with an s-wave contact interaction are confined in a harmonic trap. This analysis reveals a wide variation of the interaction with a resonance behavior around a magnetic field of about 1.1 G for the energetically lowest magnetic sublevel of 170Yb, as well as around 360 mG for the energetically highest magnetic sublevel of 174Yb. The observed Feshbach resonance can only be induced by an anisotropic interatomic interaction. This scheme will open the door to a variety of studies using two-electron atoms with tunable interaction.

Spin-orbit suppression of cold inelastic collisions of aluminum and helium

We present a quantitative study of suppression of cold inelastic collisions by the spin-orbit interaction. We prepare cold ensembles of >10(11) Al(2P(1/2)) atoms via cryogenic buffer-gas cooling and use a single-beam optical pumping method to measure their magnetic (m(J)-changing) and fine-structure (J-changing) collisions with 3He atoms at millikelvin temperatures over a range of magnetic fields from 0.5 to 6 T. The experimentally determined rates are in good agreement with the functional form predicted by quantum scattering calculations using ab initio potentials. This comparison provides direct experimental evidence for a proposed model of suppressed inelasticity in collisions of atoms in 2P(1/2) states [T. V. Tscherbul et al., Phys. Rev. A 80, 040701(R) (2009)], which may allow for sympathetic cooling of other 2P(1/2) atoms (e.g., In, Tl and metastable halogens).

Long-range interacting many-body systems with alkaline-earth-metal atoms

Alkaline-earth-metal atoms can exhibit long-range dipolar interactions, which are generated via the coherent exchange of photons on the (3)P(0) - (3)D(1) transition of the triplet manifold. In the case of bosonic strontium, which we discuss here, this transition has a wavelength of 2.6 μm and a dipole moment of 4.03 D, and there exists a magic wavelength permitting the creation of optical lattices that are identical for the states (3)P(0) and (3)D(1). This interaction enables the realization and study of mixtures of hard-core lattice bosons featuring long-range hopping, with tunable disorder and anisotropy. We derive the many-body master equation, investigate the dynamics of excitation transport, and analyze spectroscopic signatures stemming from coherent long-range interactions and collective dissipation. Our results show that lattice gases of alkaline-earth-metal atoms permit the creation of long-lived collective atomic states and constitute a simple and versatile platform for the exploration of many-body systems with long-range interactions. As such, they represent an alternative to current related efforts employing Rydberg gases, atoms with large magnetic moment, or polar molecules.

Creation of quantum-degenerate gases of ytterbium in a compact 2D-/3D-magneto-optical trap setup

We report on the first experimental setup based on a 2D-/3D-magneto-optical trap (MOT) scheme to create both Bose-Einstein condensates and degenerate Fermi gases of several ytterbium isotopes. Our setup does not require a Zeeman slower and offers the flexibility to simultaneously produce ultracold samples of other atomic species. Furthermore, the extraordinary optical access favors future experiments in optical lattices. A 2D-MOT on the strong (1)S0 → (1)P1 transition captures ytterbium directly from a dispenser of atoms and loads a 3D-MOT on the narrow (1)S0 → (3)P1 intercombination transition. Subsequently, atoms are transferred to a crossed optical dipole trap and cooled evaporatively to quantum degeneracy.

Precision measurement of transition matrix elements via light shift cancellation

We present a method for accurate determination of atomic transition matrix elements at the 10(-3) level. Measurements of the ac Stark (light) shift around "magic-zero" wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s - 6p matrix elements in rubidium by measuring the light shift around the 421 and 423 nm zeros through diffraction of a condensate off a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3235(9)ea(0) and 0.5230(8)ea(0) for the 5s - 6p(1/2) and 5s - 6p(3/2) elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.

p-Wave cold collisions in an optical lattice clock

We study ultracold collisions in fermionic ytterbium by precisely measuring the energy shifts they impart on the atoms' internal clock states. Exploiting Fermi statistics, we uncover p-wave collisions, in both weakly and strongly interacting regimes. With the higher density afforded by two-dimensional lattice confinement, we demonstrate that strong interactions can lead to a novel suppression of this collision shift. In addition to reducing the systematic errors of lattice clocks, this work has application to quantum information and quantum simulation with alkaline-earth atoms.

Resolved atomic interaction sidebands in an optical clock transition

We report the observation of resolved atomic interaction sidebands (ISB) in the (87)Sr optical clock transition when atoms at microkelvin temperatures are confined in a two-dimensional optical lattice. The ISB are a manifestation of the strong interactions that occur between atoms confined in a quasi-one-dimensional geometry and disappear when the confinement is relaxed along one dimension. The emergence of ISB is linked to the recently observed suppression of collisional frequency shifts. At the current temperatures, the ISB can be resolved but are broad. At lower temperatures, ISB are predicted to be substantially narrower and useful spectroscopic tools in strongly interacting alkaline-earth gases.

Projective measurement of a single nuclear spin qubit by using two-mode cavity QED

We report the implementation of projective measurement on a single 1/2 nuclear spin of the (171)Yb atom by measuring the polarization of cavity-enhanced fluorescence. To obtain cavity-enhanced fluorescence having a nuclear-spin-dependent polarization, we construct a two-mode cavity QED system, in which two cyclic transitions are independently coupled to each of the orthogonally polarized cavity modes, by manipulating the energy level of (171)Yb. This system can associate the nuclear spin degrees of freedom with the polarization of photons, which will facilitate the development of hybrid quantum systems.

Degenerate Fermi gas of (87)Sr

We report quantum degeneracy in a gas of ultracold fermionic (87)Sr atoms. By evaporatively cooling a mixture of spin states in an optical dipole trap for 10.5 s, we obtain samples well into the degenerate regime with T/T(F)=0.26(-0.06)(+0.05). The main signature of degeneracy is a change in the momentum distribution as measured by time-of-flight imaging, and we also observe a decrease in evaporation efficiency below T/T(F) ∼0.5.

Many-body treatment of the collisional frequency shift in fermionic atoms

Recent experiments have measured collisional frequency shifts in polarized fermionic alkaline-earth atoms using 1S0-3P0 Rabi spectroscopy. Here, we provide a first-principles nonequilibrium theoretical description of the interaction frequency shifts starting from the microscopic many-body Hamiltonian. Our formalism describes the dependence of the frequency shift on excitation inhomogeneity, interactions, temperature, and many-body dynamics, provides a fundamental understanding of the effects of the measurement process, and explains the observed density shift data.

Bose-Einstein condensation of 84Sr

We report Bose-Einstein condensation of (84)Sr in an optical dipole trap. Efficient laser cooling on the narrow intercombination line and an ideal s-wave scattering length allow the creation of large condensates (N(0) approximately 3 x 10(5)) even though the natural abundance of this isotope is only 0.6%. Condensation is heralded by the emergence of a low-velocity component in time-of-flight images.

Bose-Einstein condensation of strontium

We report on the attainment of Bose-Einstein condensation with ultracold strontium atoms. We use the (84)Sr isotope, which has a low natural abundance but offers excellent scattering properties for evaporative cooling. Accumulation in a metastable state using a magnetic-trap, narrowline cooling, and straightforward evaporative cooling in an optical trap lead to pure condensates containing 1.5 x 10(5) atoms. This puts (84)Sr in a prime position for future experiments on quantum-degenerate gases involving atomic two-electron systems.

Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons

We have quantified collisional losses, decoherence and the collision shift in a one-dimensional optical lattice clock on the highly forbidden transition (1)S(0)-(3)P(0) at 698 nm with bosonic (88)Sr. We were able to distinguish two loss channels: inelastic collisions between atoms in the upper and lower clock state and atoms in the upper clock state only. Based on the measured coefficients, we determine the operation parameters at which a 1D-lattice clock with (88)Sr shows no degradation due to collisions on the fractional uncertainty level of 10(-16).

Spin-1/2 optical lattice clock

We experimentally investigate an optical clock based on ;{171}Yb (I = 1/2) atoms confined in an optical lattice. We have evaluated all known frequency shifts to the clock transition, including a density-dependent collision shift, with a fractional uncertainty of 3.4 x 10;{-16}, limited principally by uncertainty in the blackbody radiation Stark shift. We measured the absolute clock transition frequency relative to the NIST-F1 Cs fountain clock and find the frequency to be 518 295 836 590 865.2(0.7) Hz.