We investigate the intensity stability of the superradiant laser. Our study focuses on the architecture where a continuous beam of atoms in an electronically excited state crosses the mode of a high-finesse Fabry-Perot cavity, which has been proposed as a new architecture of an active optical clock. We show that such superradiant laser can become unstable and develop chaotic behavior. We derive an analytical criterion for this instability and find that it may only occur when the lifetime of photons in the cavity is significantly shorter than the lifetime of atoms. This criterion allows for refining the necessary parameters to run a superradiant laser as a frequency reference in the optical domain. In particular, we point-out the consequences of the instability on intensity fluctuations and laser linewidth. On the other hand, we also point out that the superradiant laser, when in the unstable regime, can become an interesting playground for studying chaos. At the mean-field level, there is a direct mapping to the Bénard instability associated with fluid turbulence; however quantum fluctuations associated with photon out-coupling and atom re-filling substantially modify the expected behaviors. Finally, we point-out the existence of a regular self-pulsing regime at large atom numbers.

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.

We demonstrate coherent three-photon excitation of the strontium clock transition with a contrast of 51(12)% using a Bose-Einstein condensate. We follow it up with a demonstration of three-photon STIRAP-like transfer, overcoming the typical limitations of this technique to odd-level numbers. We also measure the two-body loss coefficient of ^{84}Sr clock-state atoms. Our work constitutes an essential step towards outcoupling a continuous atom laser beam and provides a fast excitation mechanism for quantum simulation using bosonic alkaline-earth-like atoms.

We recently demonstrated a steady-state Bose-Einstein condensate of strontium atoms. We could turn this into a perpetual atom laser if an efficient outcoupling mechanism is found. Here we show a coherent three-photon excitation of the clock transition in a strontium BEC with contrast of over 50%. We follow it up with a demonstration of three-photon STIRAP-like transfer. In the future, we could use this process to coherently outcouple the atoms from a trap operating at tune-out wavelength.

We present a faster repumping scheme for strontium magneto-optical traps operating on the broad ${\mathrm{5s^2} ^1\mathrm{S}_0} - {\mathrm{5s5p} ^1\mathrm{P}_1}$ laser cooling transition. Contrary to existing repumping schemes, we directly address lost atoms that spontaneously decayed to the ${\mathrm{5s4d} ^1\mathrm{D}_2}$ state, sending them back into the laser cooling cycle by optical pumping on the ${\mathrm{5s4d} ^1\mathrm{D}_2} - {\mathrm{5s8p} ^1\mathrm{P}_1}$ transition. We thus avoid the $\sim 100 \, \mathrm{\mu s}$-slow decay path from ${\mathrm{5s4d} ^1\mathrm{D}_2}$ to the ${\mathrm{5s5p} ^3\mathrm{P}_{1,2}}$ states that is part of other repumping schemes. Using one low-cost external-cavity diode laser emitting at $448 \, \mathrm{nm}$, we show our scheme increases the flux out of a 2D magneto-optical trap by $60 \, \%$ compared to without repumping. Furthermore, we perform spectroscopy on the ${\mathrm{5s4d} ^1\mathrm{D}_2} - {\mathrm{5s8p} ^1\mathrm{P}_1}$ transition and measure its frequency $\nu_{\mathrm{^{88}Sr}} = (668917515.3 \pm 4.0 \pm 25) \, \mathrm{MHz}$. We also measure the frequency shifts between the four stable isotopes of strontium and infer the specific mass and field shift factors, $\delta \nu_\text{SMS} ^{88,86} = -267(45) \, \mathrm{MHz}$ and $\delta \nu_\text{FS} ^{88,86} = 2(42) \, \mathrm{MHz}$. Finally, we measure the hyperfine splitting of the ${\mathrm{5s8p} ^1\mathrm{P}_1}$ state in fermionic strontium, and deduce the magnetic dipole and electric quadrupole coupling coefficients $A = -4(5) \, \mathrm{MHz}$ and $B = 5(35) \, \mathrm{MHz}$. Our experimental demonstration shows that this simple and very fast scheme could improve the laser cooling and imaging performance of cold strontium atom devices, such as quantum computers based on strontium atoms in arrays of optical tweezers.

We propose a minimalistic model to account for the main properties of a continuous superradiant laser, in which a beam of atoms crosses the mode of a high-finesse Fabry-Perot cavity, and collectively emits light into the cavity mode. We focus on the case of weak single atom - cavity cooperativity, and highlight the relevant regime where decoherence due to the finite transit time dominates over spontaneous emission. We propose an original approach where the dynamics of atoms entering and leaving the cavity is described by a Hamiltonian process. This allows deriving the main dynamical equations for the superradiant laser, without the need for a stochastic approach. We derive analytical conditions for a sustained emission and show that the ultimate linewidth is set by the fundamental quantum fluctuations of the collective atomic dipole. We calculate steady-state values of the two-body correlators and show that the continuous superradiant regime is tied to the growth of atom-atom correlations, although these correlations only have a small impact on the laser linewidth.

Bose-Einstein condensates (BECs) are macroscopic coherent matter waves that have revolutionized quantum science and atomic physics. They are important to quantum simulation1 and sensing2,3, for example, underlying atom interferometers in space4 and ambitious tests of Einstein's equivalence principle5,6. A long-standing constraint for quantum gas devices has been the need to execute cooling stages time-sequentially, restricting these devices to pulsed operation. Here we demonstrate continuous Bose-Einstein condensation by creating a continuous-wave (CW) condensate of strontium atoms that lasts indefinitely. The coherent matter wave is sustained by amplification through Bose-stimulated gain of atoms from a thermal bath. By steadily replenishing this bath while achieving 1,000 times higher phase-space densities than previous works7,8, we maintain the conditions for condensation. Our experiment is the matter wave analogue of a CW optical laser with fully reflective cavity mirrors. This proof-of-principle demonstration provides a new, hitherto missing piece of atom optics, enabling the construction of continuous coherent-matter-wave devices.

A steady-state magneto-optical trap (MOT) of fermionic strontium atoms operating on the 7.5 kHz-wide ${^1\mathrm{S}_0} - {^3\mathrm{P}_1}$ transition is demonstrated. This MOT features $8.4 \times 10^{7}$ atoms, a loading rate of $1.3\times 10^{7}$atoms/s, and an average temperature of 12 $\mu$K. These parameters make it well suited to serve as a source of atoms for continuous-wave superradiant lasers operating on strontium's mHz-wide clock transition. Such lasers have only been demonstrated using pulsed Sr sources, limiting their range of applications. Our MOT makes an important step toward continuous operation of these devices, paving the way for continuous-wave active optical clocks.

Quantum degenerate atomic gases are prominent platforms for quantum simulation and high precision sensing. A key challenge for these applications is intrinsic atom loss, which limits quantum gas lifetimes to typically tens of seconds. Here we create a Bose-Einstein condensate of $^{84}\mathrm{Sr}$ atoms that is sustained in steady state for minutes. We achieve this by guiding a continuous stream of Sr gas through a sequence of spatially separated laser cooling stages, until it reaches the condensate's location, which we protect against harmful laser cooling photons. This steady-state quantum degenerate gas paves the way to design and study novel driven-dissipative, non-equilibrium quantum systems, and overcomes a key bottleneck in the realization of a continuous-wave atom laser.

A continuous guided atomic beam of $^{88}\mathrm{Sr}$ with a phase-space density exceeding $10^{-4}$ in the moving frame and a flux of $3 \times 10^{7} \, \mathrm{at \, s^{-1}}$ is demonstrated. This phase-space density is around three orders of magnitude higher than previously reported for steady-state atomic beams. We detail the architecture necessary to produce this ultracold atom source and characterize its output after $\sim 4 \, \mathrm{cm}$ of propagation. With radial temperatures of less than $1 \,\mu \mathrm{K}$ and a velocity of $8.4 \, \mathrm{cm \, s^{-1}}$ this source is ideal for a range of applications. For example, it could be used to replenish the gain medium of an active optical superradiant clock or be employed to overcome the Dick effect that can limit the performance of pulsed-mode atom interferometers, atomic clocks and ultracold atom based sensors in general. Finally, this result represents a significant step towards the development of a steady-state atom laser.

Leading tests of the Standard Model, like measurements of the electron electric dipole moment or of matter-antimatter asymmetry, are built upon our ability to laser-cool atoms and molecules to ultracold temperatures. Unfortunately, laser-cooling remains limited to a minute collection of species with very specific electronic structures. To include more species, such as polyatomic molecules or exotic atoms like antihydrogen, new cooling methods are needed. Here we demonstrate a method based on Sisyphus cooling that was proposed for laser-cooling antihydrogen. In our implementation, atoms are selectively excited to an electronic state whose energy is spatially modulated by an optical lattice, and the ensuing spontaneous decay completes one Sisyphus cycle. We show that this method eliminates many constraints of traditional radiation-pressure-based approaches, while providing similar atom numbers with lower temperatures. This laser-cooling method can be instrumental in bringing new exotic species and molecules to the ultracold regime.

We report on spectroscopic studies of hot and ultracold RbSr molecules, and combine the results in an analysis that allows us to fit a potential energy curve (PEC) for the X(1)2Σ+ ground state bridging the short-to-long-range domains. The ultracold RbSr molecules are created in a μK sample of Rb and Sr atoms and probed by two-colour photoassociation spectroscopy. The data yield the long-range dispersion coefficients C6 and C8, along with the total number of supported bound levels. The hot RbSr molecules are created in a 1000 K gas mixture of Rb and Sr in a heat-pipe oven and probed by thermoluminescence and laser-induced fluorescence spectroscopy. We compare the hot molecule data with spectra we simulated using previously published PECs determined by three different ab initio theoretical methods. We identify several band heads corresponding to radiative decay from the B(2)2Σ+ state to the deepest bound levels of X(1)2Σ+. We determine a mass-scaled high-precision model for X(1)2Σ+ by fitting all data using a single fit procedure. The corresponding PEC is consistent with all data, thus spanning short-to-long internuclear distances and bridging an energy gap of about 75% of the potential well depth, still uncharted by any experiment. We benchmark previous ab initio PECs against our results, and give the PEC fit parameters for both X(1)2Σ+ and B(2)2Σ+ states. As first outcomes of our analysis, we calculate the s-wave scattering properties for all stable isotopic combinations and corroborate the locations of Fano-Feshbach resonances between alkali Rb and closed-shell Sr atoms recently observed [V. Barbéet al., Nat. Phys., 2018, 14, 881]. These results and more generally our strategy should greatly contribute to the generation of ultracold alkali-alkaline-earth dimers, whose applications range from quantum simulation to state-controlled quantum chemistry.

We report on spectroscopic studies of hot and ultracold RbSr molecules, and combine the results in an analysis that allows us to fit a potential energy curve (PEC) for the X(1)$^2\Sigma^+$ ground state bridging the short-to-long-range domains. The ultracold RbSr molecules are created in a $\mu$K sample of Rb and Sr atoms and probed by two-colour photoassociation spectroscopy. The data yield the long-range dispersion coefficients $C_6$ and $C_8$, along with the total number of supported bound levels. The hot RbSr molecules are created in a $1000 \,$K gas mixture of Rb and Sr in a heat-pipe oven and probed by thermoluminescence and laser-induced fluorescence spectroscopy. We compare the hot molecule data with spectra we simulated using previously published PECs determined by three different ab-initio theoretical methods. We identify several band heads corresponding to radiative decay from the B(2)$^2\Sigma^+$ state to the deepest bound levels of X(1)$^2\Sigma^+$. We determine a mass-scaled high-precision model for X(1)$^2\Sigma^+$ by fitting all data using a single fit procedure. The corresponding PEC is consistent with all data, thus spanning short-to-long internuclear distances and bridging an energy gap of about 75% of the potential well depth, still uncharted by any experiment. We benchmark ab-initio PECs against our results, and give the PEC fit parameters for both X(1)$^2\Sigma^+$ and B(2)$^2\Sigma^+$ states. As first outcomes of our analysis, we calculate the $s$-wave scattering properties for all stable isotopic combinations and corroborate the locations of Fano-Feshbach resonances between alkali Rb and closed-shell Sr atoms recently observed [Barbe et al., Nat. Phys., 2018, DOI:10.1038/s41567-018-0169-x]. These results should greatly contribute to the generation of ultracold alkali$-$alkaline-earth dimers, whose applications range from quantum simulation to quantum chemistry.

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.

Magnetic Feshbach resonances allow control of the interactions between ultracold atoms 1 . They are an invaluable tool in studies of few-body and many-body physics 2 , 3 , and can be used to convert pairs of atoms into molecules 4 , 5 by ramping an applied magnetic field across a resonance. Molecules formed from pairs of alkali atoms have been transferred to low-lying states, producing dipolar quantum gases 6 . There is great interest in making molecules formed from an alkali atom and a closed-shell atom such as ground-state Sr or Yb. Such molecules have both a strong electric dipole and an electron spin; they will open up new possibilities for designing quantum many-body systems 7 , 8 , and for tests of fundamental symmetries 9 . The crucial first step is to observe Feshbach resonances in the corresponding atomic mixtures. Very narrow resonances have been predicted theoretically 10 , 11 , 12 , but until now have eluded observation. Here we present the observation of magnetic Feshbach resonances of this type, for an alkali atom, Rb, interacting with ground-state Sr.