We demonstrate machine learning assisted design of a two-qubit gate in a Rydberg tweezer system. Two low-energy hyperfine states in each of the atoms represent the logical qubit and a Rydberg state acts as an auxiliary state to induce qubit interaction. Utilizing a hybrid quantum-classical optimizer, we generate optimal pulse sequences that implement a CNOT gate with high fidelity, for experimentally realistic parameters and protocols, as well as realistic limitations. We show that local control of single qubit operations is sufficient for performing quantum computation on a large array of atoms. We generate optimized strategies that are robust for both the strong-coupling, blockade regime of the Rydberg states, but also for the weak-coupling limit. Thus, we show that Rydberg-based quantum information processing in the weak-coupling limit is a desirable approach, being robust and optimal, with current technology.

We characterize interisotope interorbital interactions between atoms in the S-1(0) ground state and the P-3(0) metastable state in interacting Fermi-Fermi mixtures of Yb-171 and Yb-173. We perform high-precision clock spectroscopy to measure interaction-induced energy shifts in a deep three-dimensional optical lattice and determine the corresponding scattering lengths. We find the elastic interaction of the interisotope mixtures Yb-173(e)-Yb-171(g) and Yb-173(g)-Yb-171(e) to be weakly attractive and very similar, while the corresponding two-body decay coefficients differ by more than two orders of magnitude. By comparing different spin mixtures we experimentally demonstrate the SU(2) circle times SU( 6) symmetry of the elastic interactions. Furthermore, we measure the interorbital spin-exchange interaction in Yb-171 and confirm its previously observed antiferromagnetic nature.

We present a novel locking scheme for active length-stabilization and frequency detuning of a cavity optomechanical device based on the optical spring effect. The error signal is generated by utilizing the position measurement of a thermally driven intra-cavity nanomechanical device and employing its detuning-dependent frequency shift caused by the dispersive coupling to the cavity field. The scheme neither requires external modulation of the laser or the cavity nor does it demand for additional error signal readout, rendering its technical implementation rather simple for a large variety of existing optomechanical devices. Specifically, for large-linewidth microcavities or in situations where other locking schemes appear unfavorable conceptually or are hard to realize technically, the optical spring lock represents a potential alternative for stabilizing the cavity length. We explain the functional principle of the lock and characterize its performance in terms of bandwidth and gain profile.

We present the design of an extreme ultraviolet (XUV) pulse shaper relying on reflective optics. The instrument will allow tailoring of the time-frequency spectrum of femtosecond pulses generated by seeded free-electron lasers (FEL) and high-harmonic generation (HHG) sources down to a central wavelength of ~15 nm. The device is based on the geometry of a 4f grating compressor that is a standard concept in ultrafast laser science and technology. We apply it to shorter wavelengths using grazing-incidence optics operated under ultra-high vacuum conditions. The design blaze angle and the line density of the gratings allow the manipulation of all different harmonics typical for seeded FEL and HHG photon sources without the need of realignment of the instrument and even simultaneously in multi-color experiments. A proof-of-principle pulse shaping experiment using 266 nm laser light has been performed, demonstrating relative phase-control of femtosecond UV pulses.

We employ metastable ultracold 173Yb atoms to study dynamics in the 1D dissipative Fermi–Hubbard model experimentally and theoretically, and observe a complete inhibition of two-body losses after initial fast transient dynamics. We attribute the suppression of particle loss to the dynamical generation of a highly entangled Dicke state. For several lattice depths and for two- and six-spin component mixtures we find very similar dynamics, showing that the creation of strongly correlated states is a robust and universal phenomenon. This offers interesting opportunities for precision measurements.

Machine-learning techniques such as artificial neural networks are currently revolutionizing many technological areas and have also proven successful in quantum physics applications1–4. Here, we employ an artificial neural network and deep-learning techniques to identify quantum phase transitions from single-shot experimental momentum-space density images of ultracold quantum gases and obtain results that were not feasible with conventional methods. We map out the complete two-dimensional topological phase diagram of the Haldane model5–7 and provide an improved characterization of the superfluid-to-Mott-insulator transition in an inhomogeneous Bose–Hubbard system8–10. Our work points the way to unravel complex phase diagrams of general experimental systems, where the Hamiltonian and the order parameters might not be known. Machine learning can help to identify quantum phase transitions. Here a trained neural network is applied to single-shot density images from a quantum gas experiment, realizing the Haldane model and the Bose–Hubbard model.

A promising route to novel quantum technologies are hybrid quantum systems, which combine the advantages of several individual quantum systems. We have realized a hybrid atomic-mechanical experiment consisting of a Si3N4 membrane oscillator cryogenically precooled to 500 mK and optically coupled to a cloud of laser cooled 87Rb atoms. Here, we demonstrate active feedback cooling of the oscillator to a minimum mode occupation of n ¯ m = 16 ± 1 corresponding to a mode temperature of Tmin ≈ 200 μK. Furthermore, we characterize in detail the coupling of the membrane to the atoms by means of sympathetic cooling. By simultaneously applying both cooling methods we demonstrate the possibility of preparing the oscillator near the motional ground state while it is coupled to the atoms. Realistic modifications of our setup will enable the creation of a ground state hybrid quantum system, which opens the door for coherent quantum state transfer, teleportation and entanglement as well as quantum enhanced sensing applications.

Magnetically-tunable Feshbach resonances are an indispensable tool for experiments with atomic quantum gases. We report on twenty thus far unpublished Feshbach resonances and twenty one further probable Feshbach resonances in spin mixtures of ultracold fermionic 40 K with temperatures well below 100 nK. In particular, we locate a broad resonance at B=389.6 G with a magnetic width of 26.4 G. Here 1 G=10^-4 T. Furthermore, by exciting low-energy spin waves, we demonstrate a novel means to precisely determine the zero crossing of the scattering length for this broad Feshbach resonance. Our findings allow for further tunability in experiments with ultracold 40 K quantum gases.

In this work we present a reflective split-and-delay unit (SDU) developed for interferometric time-resolved experiments utilizing an (extreme ultraviolet) XUV pump–XUV probe scheme with focused free-electron laser beams. The developed SDU overcomes limitations for phase-resolved measurements inherent to conventional two-element split mirrors by a special design using two reflective lamellar gratings. The gratings produce a high-contrast interference signal controlled by the grating displacement in every diffraction order. The orders are separated in the focal plane of the focusing optics, which enables one to avoid phase averaging by spatially selective detection of a single interference state of the two light fields. Interferometry requires a precise relative phase control of the light fields, which presents a challenge at short wavelengths. In our setup the phase delay is determined by an in-vacuum white light interferometer (WLI) that monitors the surface profile of the SDU in real time and thus measures the delay for each laser shot. The precision of the WLI is 1 nm as determined by optical laser interferometry. In the presented experimental geometry it corresponds to a time delay accuracy of 3 as, which enables phase-resolved XUV pump–XUV probe experiments at free-electron laser (FEL) repetition rates up to 60 Hz.

We describe the construction of an apparatus designed to realize a hybrid quantum system comprised of a cryogenically cooled mechanical oscillator and ultra-cold 87Rb atoms coupled via light. The outstanding feature of our instrument is an in situ adjustable asymmetric all-fiber membrane-in-the-middle cavity located inside an ultra-high vacuum dilution refrigerator based cryostat. We show that Bose-Einstein condensates of N=2×106 atoms can be produced in less than 20 s and demonstrate a single photon optomechanical coupling strength of g0=2π×9 kHz employing a high-stress Si3N4 membrane with a mechanical quality factor Qm>107 at a cavity setup temperature of TMiM = 480 mK.

We study and realize asymmetric fiber-based cavities with optimized mode match to achieve high reflectivity on resonance. This is especially important for mutually coupling two physical systems via light fields, e.g., in quantum hybrid systems. Our detailed theoretical and experimental analysis reveals that on resonance, the interference effect between the directly reflected non-modematched light and the light leaking back out of the cavity can lead to large unexpected losses due to the mode filtering of the incoupling fiber. Strong restrictions for the cavity design result out of this effect and we show that planar-concave cavities are clearly best suited. We validate our analytical model using numerical calculations and demonstrate an experimental realization of an asymmetric fiber Fabry-Pérot cavity with optimized parameters.

Collective behavior in many-body systems is the origin of many fascinating phenomena in nature, ranging from the formation of clouds to magnetic properties of solids. We report on the observation of collective spin dynamics in an ultracold Fermi sea with large spin. As a key result, we observed long-lived and large-amplitude coherent spin oscillations driven by local spin interactions. At ultralow temperatures, Pauli blocking stabilizes the collective behavior, and the Fermi sea behaves as a single entity in spin space. With increasing temperature, we observed a stronger damping associated with particle-hole excitations. Unexpectedly, we found a high-density regime where excited spin configurations are collisionally stabilized. Our results reveal the intriguing interplay between microscopic processes either stimulating or suppressing collective effects in a fermionic many-body system.

A fundamental question in many-body physics is how closed quantum systems reach equilibrium. We address this question experimentally and theoretically in an ultracold large-spin Fermi gas where we find a complex interplay between internal and motional degrees of freedom. The fermions are initially prepared far from equilibrium with only a few spin states occupied. The subsequent dynamics leading to redistribution among all spin states is observed experimentally and simulated theoretically using a kinetic Boltzmann equation with full spin coherence. The latter is derived microscopically and provides good agreement with experimental data without any free parameters. We identify several collisional processes, which occur on different time scales. By varying density and magnetic field, we control the relaxation dynamics and are able to continuously tune the character of a subset of spin states from an open to a closed system.

We propose to detect quadrupole interactions of neutral ultra-cold atoms via their induced mean-field shift. We consider a Mott insulator state of spin-polarized atoms in a two-dimensional optical square lattice. The quadrupole moments of the atoms are aligned by an external magnetic field. As the alignment angle is varied, the mean-field shift shows a characteristic angular dependence, which constitutes the defining signature of the quadrupole interaction. For the $^{3}P_{2}$ states of Yb and Sr atoms, we find a frequency shift of the order of tens of Hertz, which can be realistically detected in experiment with current technology. We compare our results to the mean-field shift of a spin-polarized quasi-2D Fermi gas in continuum.

A breakthrough in cold atom quantum technology is hindered by a bottleneck in the supporting technologies. We discuss a cold atom technology platform developed within the European iSense project, aiming at a gravimeter as demonstrator.

In 1834, the Scottish engineer John Scott Russell made a fascinating discovery. He observed a solitary water wave that travelled along a narrow canal for several miles without any significant change in its shape or amplitude. Ever since, such solitary waves, known as solitons, have been thought to have a key role in fundamental transport processes in myriad nonlinear systems — ranging from fibre-optic and meteorological systems to biological and astrophysical ones. On page 426 of this issue, Yefsah et al.1 demonstrate the first experimental realization of 'dark solitons' in an ultracold quantum gas of strongly interacting fermionic atoms. Strikingly, they observe that the dynamics of a soliton in such a gas is slowed down by almost a factor of 20 compared with state-of-the-art theoretical predictions.* Dark solitons are localized dips in the density distribution of a background medium. Like their bright analogues, they are particle-like entities because they retain their shape while they propagate or interact with other solitons2. This behaviour is the result of a delicate balance of the medium's dispersion and nonlinear properties, and is in strong contrast to that of an ordinary wave packet (a superposition of plane waves) propagating in a linear medium, in which the packet will continuously spread and ultimately disappear. Although the appearance of solitons is quite a robust phenomenon and is not crucially dependent on the exact properties of the medium, the dynamics of solitons changes depending on the medium. In particular, for quantum-mechanical systems, thermal as well as quantum fluctuations perturb solitons significantly, which makes solitons excellent probes of the system. Dark solitons entered the world of ultracold quantum gases about a decade ago, when they were first observed3 in Bose–Einstein condensates (BECs). If a gas of bosons (particles with integer spin) is cooled to very low temperatures, the bosons tend to collectively condense into the lowest available quantum-mechanical state, giving rise to a BEC. One feature of a BEC is the emergence of frictionless flow, or superfluidity, which in turn can lead to the appearance of dark solitons. By exploiting the exceptional control attainable in BEC experiments, researchers have achieved several breakthroughs, including confirming the particle-like nature of solitons and the elasticity of soliton collisions4, 5, 6. The situation changes drastically for a gas of fermions — particles with half-integer spin. Unlike bosons, fermions are subject to the Pauli exclusion principle, according to which no two identical fermions may occupy the same quantum state simultaneously. To condense into a common quantum state with a macroscopic number of particles and form a superfluid, fermions first have to turn into bosons, and they can do so by forming pairs that have a resulting integer spin. The size of a pair crucially depends on the interaction between the particles, and determines the underlying physics. If the size is small compared with the inter-particle spacing, tightly bound molecules form and the system condenses into a BEC. If the size is much larger than the inter-particle distance, weakly bound pairs form and superfluidity ensues — much like the formation of Cooper pairs of electrons in superconductors. This second regime is known as the Bardeen–Cooper–Schrieffer (BCS) regime. Theory can conveniently describe these two regimes, and the existence of solitons naturally arises from the existence of superfluidity in these interacting fermionic systems7, 8, 9. In the crossover between the BEC and BCS regimes, the pair size is comparable to the inter-particle spacing and the gas is difficult to describe10. However, this regime is particularly appealing because its physics is the same for all different types of fermions — such a Fermi gas is said to be universal or unitary. Lacking any satisfactory theoretical description, researchers have conducted several experiments in this regime using ultracold quantum gases of fermions, and fundamental equilibrium and a few dynamical properties have been observed. One striking example was the observation of vortices, quantized units of angular momentum, which unambiguously confirmed the existence of robust superfluidity also in the unitary Fermi gas11. In their experiments, Yefsah et al. used the dynamical evolution of dark solitons across the BEC–BCS transition as a probe of the underlying Fermi gas. They continuously varied the pair size in an ultracold gas of lithium-6 fermionic atoms over the complete BEC–BCS crossover (Fig. 1) using a tool known as magnetic Feshbach resonance. They created dark solitons and allowed them to oscillate in the 'harmonic trap' they used to confine the atoms. Unexpectedly, they found that, whereas soliton oscillations deep in the BEC regime behaved quite as expected from theory, their motion was slowed down by almost a factor of 20 in the unitary and BCS regimes. The authors observed that, as these regimes are approached, the density dip that makes up a dark soliton gets significantly more filled with non-condensed-gas atoms than expected from calculations. This filling makes the soliton heavier and thus slows down its motion7, 8, 9. Thermal and quantum fluctuations could both be responsible for these non-condensed atoms and thus for the existence of such heavy solitons. Yefsah et al. have carefully analysed soliton oscillations at different temperatures and showed that the observed increase in the effective mass of the solitons is not caused by thermal fluctuations. On the other hand, existing theories underestimate the effect of quantum fluctuations, so Yefsah and colleagues' study should be regarded as a benchmark quantum simulation to test future theories of strongly interacting Fermi gases. Regardless of whether exotic states inside the solitons, such as Andreev bound states, or completely different and as yet unknown mechanisms can generate the slow motion of the dark solitons, shedding light on this problem might turn out to be beneficial for our general understanding of strongly interacting fermions. Download references