Bose-Einstein condensation of 84Sr

Realizing topological edge states with Rydberg-atom synthetic dimensions

A discrete degree of freedom can be engineered to match the Hamiltonian of particles moving in a real-space lattice potential. Such synthetic dimensions are powerful tools for quantum simulation because of the control they offer and the ability to create configurations difficult to access in real space. Here, in an ultracold ⁸⁴Sr atom, we demonstrate a synthetic-dimension based on Rydberg levels coupled with millimeter waves. Tunneling amplitudes between synthetic lattice sites and on-site potentials are set by the millimeter-wave amplitudes and detunings respectively. Alternating weak and strong tunneling in a one-dimensional configuration realizes the single-particle Su-Schrieffer-Heeger (SSH) Hamiltonian, a paradigmatic model of topological matter. Band structure is probed through optical excitation from the ground state to Rydberg levels, revealing symmetry-protected topological edge states at zero energy. Edge-state energies are robust to perturbations of tunneling-rates that preserve chiral symmetry, but can be shifted by the introduction of on-site potentials.

Synthetic dimensions, states of a system engineered to act as if they were a reconfigurable extra spatial dimension, have been demonstrated with different systems previously. Here the authors create a synthetic dimension using Rydberg atoms and configure it to support topological edge states.

Quantum control of reactions and collisions at ultralow temperatures

At temperatures close to absolute zero, the molecular reactions and collisions are dominantly governed by quantum mechanics. Remarkable quantum phenomena such as quantum tunneling, quantum threshold behavior, quantum resonances, quantum interference, and quantum statistics are expected to be the main features in ultracold reactions and collisions. Ultracold molecules offer great opportunities and challenges in the study of these intriguing quantum phenomena in molecular processes. In this article, we review the recent progress in the preparation of ultracold molecules and the study of ultracold reactions and collisions using ultracold molecules. We focus on the controlled ultracold chemistry and the scattering resonances at ultralow temperatures. The challenges in understanding the complex ultracold reactions and collisions are also discussed.

Confinement of an alkaline-earth element in a grating magneto-optical trap

We demonstrate a compact magneto-optical trap (MOT) of alkaline-earth atoms using a nanofabricated diffraction grating chip. A single input laser beam, resonant with the broad ¹S₀ → ¹P₁ transition of strontium, forms the MOT in combination with three diffracted beams from the grating chip and a magnetic field produced by permanent magnets. A differential pumping tube limits the effect of the heated, effusive source on the background pressure in the trapping region. The system has a total volume of around 2.4 l. With our setup, we have trapped up to 5 × 10^{6 88}Sr atoms at a temperature of ∼6 mK, and with a trap lifetime of ∼1 s. Our results will aid the effort to miniaturize quantum technologies based on alkaline-earth atoms.

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.

Resonant Rydberg Dressing of Alkaline-Earth Atoms via Electromagnetically Induced Transparency

We develop an approach to generate finite-range atomic interactions via optical Rydberg-state excitation and study the underlying excitation dynamics in theory and experiment. In contrast to previous work, the proposed scheme is based on resonant optical driving and the establishment of a dark state under conditions of electromagnetically induced transparency (EIT). Analyzing the driven dissipative dynamics of the atomic gas, we show that the interplay between coherent light coupling, radiative decay, and strong Rydberg-Rydberg atom interactions leads to the emergence of sizable effective interactions while providing remarkably long coherence times. The latter are studied experimentally in a cold gas of strontium atoms for which the proposed scheme is most efficient. Our measured atom loss is in agreement with the theoretical prediction based on binary effective interactions between the driven atoms.

Injection locking of a low cost high power laser diode at 461 nm

Stable laser sources at 461 nm are important for optical cooling of strontium atoms. In most existing experiments, this wavelength is obtained by frequency doubling infrared lasers, since blue laser diodes either have low power or large emission bandwidths. Here, we show that injecting less than 10 mW of monomode laser radiation into a blue multimode 500 mW high power laser diode is capable of slaving at least 50% of the power to the desired frequency. We verify the emission bandwidth reduction by saturation spectroscopy on a strontium gas cell and by direct beating of the slave with the master laser. We also demonstrate that the laser can efficiently be used within the Zeeman slower for optical cooling of a strontium atomic beam.

Mid-infrared optical parametric oscillators and frequency combs for molecular spectroscopy

Review of mid-infrared optical parametric oscillators and frequency combs for high-resolution spectroscopy, including applications in trace gas detection and fundamental research.

The ground-state potential energy curve of the radium dimer from relativistic coupled cluster calculations

The potential energy curve for the ground-state of radium dimer (Ra2) is provided by means of atomic and molecular relativistic coupled cluster calculations. The short-range part of this curve is defined by an equilibrium bond length of 5.324 Å, a dissociation energy of 897 cm(-1), and a harmonic vibrational frequency of 20.5 cm(-1). The asymptotic behavior at large interatomic distances is characterized by the van der Waals coefficients C6 = 5.090 × 10(3), C8 = 6.978 × 10(5), and C10 = 8.786 × 10(7) atomic units. The two regions are matched in an analytical potential to provide a convenient representation for use in further calculations, for instance, to model cold collisions between radium atoms. This might become relevant in future experiments on ultracold, optically trapped, radioactive radium atoms that are used to search for a permanent electric dipole moment.

Ultracold Fermi gases with emergent SU(N) symmetry

We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include (1) the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, (2) the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, (3) the realization of a Mott insulator of (173)Yb atoms, (4) the creation of various kinds of Fermi-Bose mixtures and (5) the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases such as reaching the temperature scale required to observe magnetic and more exotic quantum orders. The challenge of dealing with collisional relaxation of excited electronic levels is also discussed.

Spectroscopy of cold LiCa molecules formed on helium nanodroplets

We report on the formation of mixed alkali-alkaline earth molecules (LiCa) on helium nanodroplets and present a comprehensive experimental and theoretical study of the ground and excited states of LiCa. Resonance enhanced multiphoton ionization time-of-flight (REMPI-TOF) spectroscopy and laser induced fluorescence (LIF) spectroscopy were used for the experimental investigation of LiCa from 15000 to 25500 cm(-1). The 4(2)Σ(+) and 3(2)Π states show a vibrational structure accompanied by distinct phonon wings, which allows us to determine molecular parameters as well as to study the interaction of the molecule with the helium droplet. Higher excited states (4(2)Π, 5(2)Σ(+), 5(2)Π, and 6(2)Σ(+)) are not vibrationally resolved and vibronic transitions start to overlap. The experimental spectrum is well reproduced by high-level ab initio calculations. By using a multireference configuration interaction (MRCI) approach, we calculated the 19 lowest lying potential energy curves (PECs) of the LiCa molecule. On the basis of these calculations, we could identify previously unobserved transitions. Our results demonstrate that the helium droplet isolation approach is a powerful method for the characterization of tailor-made alkali-alkaline earth molecules. In this way, important contributions can be made to the search for optimal pathways toward the creation of ultracold alkali-alkaline earth ground state molecules from the corresponding atomic species. Furthermore, a test for PECs calculated by ab initio methods is provided.

Dimerized solids and resonating plaquette order in SU(N)-Dirac fermions

We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.

Strongly coupled plasmas via Rydberg blockade of cold atoms

We propose and analyze a new scheme to produce ultracold neutral plasmas deep in the strongly coupled regime. The method exploits the interaction blockade between cold atoms excited to high-lying Rydberg states and therefore does not require substantial extensions of current ultracold plasma experiments. Extensive simulations reveal a universal behavior of the resulting Coulomb coupling parameter, providing a direct connection between the physics of strongly correlated Rydberg gases and ultracold plasmas. The approach is shown to reduce currently accessible temperatures by more than an order of magnitude, which opens up a new regime for ultracold plasma research and cold ion-beam applications with readily available experimental techniques.

A simplified 461-nm laser system using blue laser diodes and a hollow cathode lamp for laser cooling of Sr

We develop a simplified light source at 461 nm for laser cooling of Sr without frequency-doubling crystals but with blue laser diodes. An anti-reflection coated blue laser diode in an external cavity (Littrow) configuration provides an output power of 40 mW at 461 nm. Another blue laser diode is used to amplify the laser power up to 110 mW by injection locking. For frequency stabilization, we demonstrate modulation-free polarization spectroscopy of Sr in a hollow cathode lamp. The simplification of the laser system achieved in this work is of great importance for the construction of transportable optical lattice clocks.

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.

Controlling condensate collapse and expansion with an optical Feshbach resonance

We demonstrate control of the collapse and expansion of an (88)Sr Bose-Einstein condensate using an optical Feshbach resonance near the (1)S(0)-(3)P(1) intercombination transition at 689 nm. Significant changes in dynamics are caused by modifications of scattering length by up to ± 10a(bg), where the background scattering length of (88)Sr is a(bg) = -2a(0) (1a(0) = 0.053 nm). Changes in scattering length are monitored through changes in the size of the condensate after a time-of-flight measurement. Because the background scattering length is close to zero, blue detuning of the optical Feshbach resonance laser with respect to a photoassociative resonance leads to increased interaction energy and a faster condensate expansion, whereas red detuning triggers a collapse of the condensate. The results are modeled with the time-dependent nonlinear Gross-Pitaevskii equation.

Adiabatic loading of one-dimensional SU(N) alkaline-earth-atom fermions in optical lattices

Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.

Creation of ultracold Sr(2) molecules in the electronic ground state

We report on the creation of ultracold (84)Sr(2) molecules in the electronic ground state. The molecules are formed from atom pairs on sites of an optical lattice using stimulated Raman adiabatic passage (STIRAP). We achieve a transfer efficiency of 30% and obtain 4×10(4) molecules with full control over the external and internal quantum state. STIRAP is performed near the narrow (1)S(0)-(3)P(1) intercombination transition, using a vibrational level of the 1(0(u)(+)) potential as an intermediate state. In preparation of our molecule association scheme, we have determined the binding energies of the last vibrational levels of the 1(0(u)(+)), 1(1(u)) excited-state and the X (1)Σ(g)(+) ground-state potentials. Our work overcomes the previous limitation of STIRAP schemes to systems with magnetic Feshbach resonances, thereby establishing a route that is applicable to many systems beyond alkali-metal dimers.

Narrow linewidth laser system realized by linewidth transfer using a fiber-based frequency comb for the magneto-optical trapping of strontium

A narrow linewidth diode laser system at 689 nm is realized by phase-locking an extended cavity diode laser to one tooth of a narrow linewidth optical frequency comb. The optical frequency comb is phase-locked to a narrow linewidth laser at 1064 nm, which is frequency stabilized to a high-finesse optical cavity. We demonstrate the magneto-optical trapping of Sr using an intercombination transition with the developed laser system.

Few-body physics with ultracold atomic and molecular systems in traps

Few-body physics has played a prominent role in atomic, molecular and nuclear physics since the early days of quantum mechanics. It is now possible-thanks to tremendous progress in cooling, trapping and manipulating ultracold samples-to experimentally study few-body phenomena in trapped atomic and molecular systems with unprecedented control. This review summarizes recent studies of few-body phenomena in trapped atomic and molecular gases, with an emphasis on small trapped systems. We start by introducing the free-space scattering properties and then investigate what happens when two particles, bosons or fermions, are placed in an external confinement. Next, various three-body systems are treated analytically in limiting cases. Our current understanding of larger two-component Fermi systems and Bose systems is reviewed, and connections with the corresponding bulk systems are established. Lastly, future prospects and challenges are discussed. Throughout this review, commonalities with other systems such as nuclei or quantum dots are highlighted.

Quantum simulation of an extra dimension

We present a general strategy to simulate a D+1-dimensional quantum system using a D-dimensional one. We analyze in detail a feasible implementation of our scheme using optical lattice technology. The simplest nontrivial realization of a fourth dimension corresponds to the creation of a bi-volume geometry. We also propose single- and many-particle experimental signatures to detect the effects of the extra dimension.

Strongly dipolar Bose-Einstein condensate of dysprosium

We report the Bose-Einstein condensation (BEC) of the most magnetic element, dysprosium. The Dy BEC is the first for an open f-shell lanthanide (rare-earth) element and is produced via forced evaporation in a crossed optical dipole trap loaded by an unusual, blue-detuned and spin-polarized narrowline magneto-optical trap. Nearly pure condensates of 1.5 × 10(4) (164)Dy atoms form below T = 30 nK. We observe that stable BEC formation depends on the relative angle of a small polarizing magnetic field to the axis of the oblate trap, a property of trapped condensates only expected in the strongly dipolar regime. This regime was heretofore only attainable in Cr BECs via a Feshbach resonance accessed at a high-magnetic field.

Experimental determination of the ²⁴Mg I (3s3p)³P₂ lifetime

We present the first experimental determination of the electric-dipole forbidden (3s3p)³P₂→(3s²)¹S₀ (M2) transition rate in ²⁴Mg and compare to state-of-the-art theoretical predictions. Our measurement exploits a magnetic trap isolating the sample from perturbations and a magneto-optical trap as an amplifier converting each ³P₂→¹S₀ decay event into millions of photons readily detected. The transition rate is determined to be (4.87 ± 0.3)×10⁻⁴  s⁻¹ corresponding to a ³P₂ lifetime of 2050(-110)(+140) sec. This value is in agreement with recent theoretical predictions, and to our knowledge the longest lifetime ever determined in a laboratory environment.

Measurement of optical Feshbach resonances in an ideal gas

Using a narrow intercombination line in alkaline earth atoms to mitigate large inelastic losses, we explore the optical Feshbach resonance effect in an ultracold gas of bosonic (88)Sr. A systematic measurement of three resonances allows precise determinations of the optical Feshbach resonance strength and scaling law, in agreement with coupled-channel theory. Resonant enhancement of the complex scattering length leads to thermalization mediated by elastic and inelastic collisions in an otherwise ideal gas. Optical Feshbach resonance could be used to control atomic interactions with high spatial and temporal resolution.

Three-sublattice ordering of the SU(3) Heisenberg model of three-flavor fermions on the square and cubic lattices

Combining a semiclassical analysis with exact diagonalizations, we show that the ground state of the SU(3) Heisenberg model on the square lattice develops three-sublattice long-range order. This surprising pattern for a bipartite lattice with only nearest-neighbor interactions is shown to be the consequence of a subtle quantum order-by-disorder mechanism. By contrast, thermal fluctuations favor two-sublattice configurations via entropic selection. These results are shown to extend to the cubic lattice, and experimental implications for the Mott-insulating states of three-flavor fermionic atoms in optical lattices are discussed.

Ultracold RbSr molecules can be formed by magnetoassociation

We investigate the interactions between ultracold alkali-metal atoms and closed-shell atoms using electronic structure calculations on the prototype system Rb+Sr. There are molecular bound states that can be tuned across atomic thresholds with a magnetic field and previously neglected terms in the collision Hamiltonian that can produce zero-energy Feshbach resonances with significant widths. The largest effect comes from the interaction-induced variation of the Rb hyperfine coupling. The resonances may be used to form paramagnetic polar molecules if the magnetic field can be controlled precisely enough.

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.