We demonstrate coherent manipulation of the nuclear degrees of freedom of ultracold ground-state strontium 87 atoms, thus providing a toolkit for fully exploiting the corresponding large Hilbert space as a quantum resource and for quantum simulation experiments with SU(N)-symmetric matter. By controlling the resonance conditions of Raman transitions with a tensor light shift, we can perform rotations within a restricted Hilbert space of two isolated spin states among the 2F+1 = 10 possible states. These manipulations correspond to engineering unitary operations deriving from generators of the SU(N) algebra beyond what can be done by simple spin precession. We present Ramsey interferometers involving an isolated pair of Zeeman states with no measurable decoherence after 3 seconds. We also demonstrate that one can harvest the large spin degrees of freedom as a qudit resource by implementing two interferometer schemes over four states. The first scheme senses in parallel multiple external fields acting on the atoms, and the second scheme simultaneously measures multiple observables of a collective atomic state - including non-commuting ones. Engineering unitary transformations of the large spin driven by other generators than the usual spin-F representation of the SU(2) group offers new possibilities from the point of view of quantum metrology and quantum many-body physics, notably for the quantum simulation of large-spin SU(N)-symmetric quantum magnetism with fermionic alkaline-earth atoms.

Superconducting microwave resonators are crucial elements of microwave circuits, offering a wide range of potential applications in modern science and technology. While conventional low-T[Formula: see text] superconductors are mainly employed, high-T[Formula: see text] cuprates could offer enhanced temperature and magnetic field operating ranges. Here, we report the realization of [Formula: see text] superconducting coplanar waveguide resonators, and demonstrate a continuous evolution from a lossy undercoupled regime, to a lossless overcoupled regime by adjusting the device geometry, in good agreement with circuit model theory. A high-quality factor resonator was then used to perform electron spin resonance measurements on a molecular spin ensemble across a temperature range spanning two decades. We observe spin-cavity hybridization indicating coherent coupling between the microwave field and the spins in a highly cooperative regime. The temperature dependence of the Rabi splitting and the spin relaxation time point toward an antiferromagnetic coupling of the spins below 2 K. Our findings indicate that high-Tc superconducting resonators hold great promise for the development of functional circuits. Additionally, they suggest novel approaches for achieving hybrid quantum systems based on high-T[Formula: see text] superconductors and for conducting electron spin resonance measurements over a wide range of magnetic fields and temperatures.

Superconducting microwave resonators are crucial elements of microwave circuits, offering a wide range of potential applications in modern science and technology. While conventional lowT(c) superconductors are mainly employed, high-T-c cuprates could offer enhanced temperature and magnetic field operating ranges. Here, we report the realization of YBa(2)Cu(3)O(7-delta )superconducting coplanar waveguide resonators, and demonstrate a continuous evolution from a lossy undercoupled regime, to a lossless overcoupled regime by adjusting the device geometry, in good agreement with circuit model theory. A high-quality factor resonator was then used to perform electron spin resonance measurements on a molecular spin ensemble across a temperature range spanning two decades. We observe spin-cavity hybridization indicating coherent coupling between the microwave field and the spins in a highly cooperative regime. The temperature dependence of the Rabi splitting and the spin relaxation time point toward an antiferromagnetic coupling of the spins below 2 K. Our findings indicate that high-Tc superconducting resonators hold great promise for the development of functional circuits. Additionally, they suggest novel approaches for achieving hybrid quantum systems based on high-T-c superconductors and for conducting electron spin resonance measurements over a wide range of magnetic fields and temperatures.

We propose and demonstrate an experimental method to measure by absorption imaging the size and local column density of a cloud of atoms, even when its smallest dimension is smaller than the resolution of the imaging system. To do this, we take advantage of the fact that, for a given total number of atoms, a smaller and denser cloud scatters less photons when the gas is optically thick. The method relies on making an ansatz on the cloud shape along the unresolved dimension(s) and on providing an additional information, such as the total number of atoms. We demonstrate the method on in situ absorption images of elongated Sr-87 Fermi gases. We find significant nonlinear corrections to the estimated size and local density of the cloud compared to a standard analysis. This allows us to recover an undistorted longitudinal density profile and to measure transverse sizes as small as one-fourth of our imaging resolution. The ultimate limit of our method is the wavelength that is used for imaging.

We introduce a spin-orbit coupling scheme, where a retroreflected laser beam selectively diffracts two spin components in opposite directions. Spin sensitivity is provided by sweeping through a magnetic-field sensitive transition while dark states ensure that spontaneous emission remains low. The scheme is adiabatic and thus inherently robust. This tailored spin-orbit coupling allows simultaneous measurements of the spin and momentum distributions of a strontium degenerate Fermi gas, and thus opens the path to momentum-resolved spin-correlation measurements on SU(N) quantum magnets.

We present a spectroscopy scheme for the 7 kHz wide 689 nm intercombination line of strontium. We rely on shelving detection, where electrons are first excited to a metastable state by the spectroscopy laser before their state is probed using the broad transition at 461 nm. As in the similar setting of calcium beam clocks, this enhances dramatically the signal strength as compared to direct saturated fluorescence or absorption spectroscopy of the narrow line. We implement shelving spectroscopy both in directed atomic beams and hot vapor cells with isotropic atomic velocities. We measure a fractional frequency instability similar to 2 x 10(-12) at 1s limited by technical noise-about one order of magnitude above shot noise limitations for our experimental parameters. Our work illustrates the robustness and flexibility of a scheme that can be very easily implemented in the reference cells or ovens of most existing strontium experiments, and may find applications for low-complexity clocks.

Understanding quantum thermalization through entanglement build up in isolated quantum systems addresses fundamental questions on how unitary dynamics connects to statistical physics. Spin systems made of long-range interacting atoms offer an ideal experimental platform to investigate this question. Here, we study the spin dynamics and approach towards local thermal equilibrium of a macroscopic ensemble of S = 3 chromium atoms pinned in a three dimensional optical lattice and prepared in a pure coherent spin state, under the effect of magnetic dipole–dipole interactions. Our isolated system thermalizes under its own dynamics, reaching a steady state consistent with a thermal ensemble with a temperature dictated from the system’s energy. The build up of quantum correlations during the dynamics is supported by comparison with an improved numerical quantum phase-space method. Our observations are consistent with a scenario of quantum thermalization linked to the growth of entanglement entropy.

We have measured the effect of dipole-dipole interactions on the frequency of a collective mode of a Bose-Einstein condensate. At relatively large numbers of atoms, the experimental measurements are in good agreement with zero temperature theoretical predictions based on the Thomas Fermi approach. Experimental results obtained for the dipolar shift of a collective mode show a larger dependency to both the trap geometry and the atom number than the ones obtained when measuring the modification of the condensate aspect ratio due to dipolar forces. These findings are in good agreement with simulations based on a gaussian ansatz.

The high chemical reactivity of strontium, which can opacify a viewport exposed to a strontium atomic source, is a concern for some atomic physics experiments where it is sometimes necessary to send a laser beam counter-propagating relative to the atomic beam. While a number of experiments use heated sapphire windows to reduce strontium deposition and increase the viewport lifetime, here we study another possibility, consisting of sending the laser beam into the atomic flux by reflecting it off a mirror at 45$^{\circ}$ exposed to the strontium flux. We present our attempt to find a substrate that can be exposed to strontium and maintain high reflectivity. We first present the formation of a strontium metallic mirror under high flux ($> 10^{13}$ at/s/cm$^2$) on a sapphire substrate, and measure its reflectivity at 45$^\circ$ to be 0.65 (S) and 0.51 (P). On two other substrates, initially reflective metallic mirrors, we show for slightly lower fluxes (i.e., a factor of 3) that some reaction - most probably oxidation - is able to prevent the formation of the metallic layer even in high vacuum conditions. Instead, we observe the growth of a dielectric transparent medium. Despite the continuous deposition of strontium, the back surface reflectivity continues to dominate. We show the unusual evolution of reflectivity on these substrates, and emphasize two observations: i) a sharp threshold in the strontium flux separating transparent material growth from lossy material growth; ii) strontium's highly efficient capture of oxygen, even from rarefied sources: here mostly the residual high vacuum pressure (10$^{-7}$mbar full pressure) and possibly a protective SiO$_2$ surface on one of the substrates.

We report on the observation of a collective spin mode in a spinor Bose-Einstein condensate. Initially, all spins point perpendicular to the external magnetic field. The lowest energy mode consists of a sinusoidal oscillation of the local spin around its original axis, with an oscillation amplitude that linearly depends on the spatial coordinates. The frequency of the oscillation is set by the zero-point kinetic energy of the BEC. The observations are in excellent agreement with hydrodynamic equations. The observed spin mode has a universal character, independent of the atomic spin and spin-dependent contact interactions.

We study the impact of spin-exchange collisions on the dynamics of Bose-Einstein condensation by rapidly cooling a chromium multicomponent Bose gas. Despite relatively strong spin-dependent interactions, the critical temperature for Bose-Einstein condensation is reached before the spin degrees of freedom fully thermalize. The increase in density due to Bose-Einstein condensation then triggers spin dynamics, hampering the formation of condensates in spin-excited states. Small metastable spinor condensates are, nevertheless, produced, and they manifest in strong spin fluctuations.

We analyze the spin dynamics of an out-of-equilibrium large spin dipolar atomic Bose gas in an optical lattice. We observe a smooth crossover from a complex oscillatory behavior to an exponential behavior throughout the Mott-to-superfluid transition. While both of these regimes are well described by our theoretical models, we provide data in the intermediate regime where dipolar interactions, contact interactions, and superexchange mechanisms compete. In this strongly correlated regime, spin dynamics and transport are coupled, which challenges theoretical models for quantum magnetism.

We report on the production of a degenerate Fermi gas of Cr-53 atoms, polarized in the state F = 9/2, m(F) = -9/2, by sympathetic cooling with bosonic S = 3, m(S) = -3 Cr-52 atoms. We load in an optical dipole trap 3 x 10(453)Cr atoms with 10(6) Cr-52 atoms. Despite the initial small number of fermionic atoms, we reach a final temperature of T similar or equal to 0.6 x T-f (Fermi temperature), with up to 10(3) Cr-53 atoms. This surprisingly efficient evaporation stems from an interisotope scattering length vertical bar a(BF)vertical bar = 80(+/- 10)a(B) (Bohr radius) which is small enough to reduce evaporative losses of the fermionic isotope, but large enough to assure thermalization.

We propose and experimentally demonstrate a new cooling mechanism leading to purification of a Bose-Einstein condensate (BEC). Our scheme starts with a BEC polarized in the lowest energy spin state. Spin excited states are thermally populated by lowering the single particle energy gap set by the magnetic field. Then, these spin-excited thermal components are filtered out, which leads to an increase of the BEC fraction. We experimentally demonstrate such cooling for a spin 3 ^{52}Cr dipolar BEC. Our scheme should be applicable to Na or Rb, with the perspective to reach temperatures below 1 nK.

We experimentally study the spin dynamics of mesoscopic ensembles of ultracold magnetic spin-3 atoms located in two separated wells of an optical dipole trap. We use a radio-frequency sweep to selectively flip the spin of the atoms in one of the wells, which produces two separated spin domains of opposite polarization. We observe that these engineered spin domains are metastable with respect to the long-range magnetic dipolar interactions between the two ensembles. The absence of inter-cloud dipolar spin-exchange processes reveals a classical behavior, in contrast to previous results with atoms loaded in an optical lattice. When we merge the two subsystems, we observe spin-exchange dynamics due to contact interactions which enable the first determination of the s-wave scattering length of 52Cr atoms in the S=0 molecular channel a_0=13.5^{+11}_{-10.5}a_B (where a_B is the Bohr radius).

We study dipolar relaxation of a chromium Bose-Einstein condensate loaded into a three-dimensional (3D) optical lattice. We observe dipolar relaxation resonances when the magnetic energy released during the inelastic collision matches an excitation towards higher-energy bands. Spectroscopy of these resonances for two orientations of the magnetic field provides a 3D band spectroscopy of the lattice. The narrowest resonance is registered for the lowest excitation energy. Its line shape is sensitive to the on-site interaction energy. We use such sensitivity to probe number squeezing in a Mott insulator.

We report on the realization of quantum magnetism using a degenerate dipolar gas in an optical lattice. Our system implements a lattice model resembling the celebrated t-J model. It is characterized by a nonequilibrium spinor dynamics resulting from intersite Heisenberg-like spin-spin interactions provided by nonlocal dipole-dipole interactions. Moreover, due to its large spin, our chromium lattice gases constitute an excellent environment for the study of quantum magnetism of high-spin systems, as illustrated by the complex spin dynamics observed for doubly occupied sites.

Magnetic dipole-dipole interactions (MDDIs) are long-ranged and anisotropic. They induce a coupling between spin and angular momentum degrees of freedom paving the way for new interesting physics in the fields of quantum gases and magnetism. This paper thoroughly studies dipolar relaxation (DR) processes in a chromium BEC. Atoms are transferred from the absolute ground state with m = -3 to the excited m = +3 Zeeman state and are loaded in a 3D optical lattice; the magnetic state distribution of this system under various conditions is monitored. In a previous publication, it was demonstrated how the confinement of a quantum gas in 1D and 2D optical lattices deeply modifies the DR processes. In particular, it was shown that DR is inhibited at low magnetic fields when the released energy becomes smaller than the vibrational quantum of energy at the bottom of the lattice wells. In the present work, instability (or decay) of the “excited state BEC” appears as a resonant process as the released energy matches band excitation. Analyzing these resonances as a function of the magnetic field orientation reveals a new manifestation of the anisotropy of MDDIs. The spectroscopy of these resonances as a function of the field intensity is found to be sensitive to the lattice site number occupancy as demonstrated by performing it after various system preparation schemes including number-squeezed Mott states. Decays from sites housing three atoms produce entangled spin and orbital states.

We measure the excitation spectrum of a dipolar chromium Bose-Einstein condensate with Raman-Bragg spectroscopy. The energy spectrum depends on the orientation of the dipoles with respect to the excitation momentum, demonstrating an anisotropy that originates from the dipole-dipole interactions between the atoms. We compare our results with the Bogoliubov theory based on the local density approximation and, at large excitation wavelengths, with the numerical simulations of the time-dependent Gross-Pitaevskii equation. Our results show an anisotropy of the speed of sound.