An atomic boson sampler.

A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non-interacting dynamics1. An efficient exact classical simulation of boson sampling is not believed to exist, which has motivated ground-breaking boson sampling experiments in photonics with increasingly many photons2-12. However, it is difficult to generate and reliably evolve specific numbers of photons with low loss, and thus probabilistic techniques for postselection7 or marked changes to standard boson sampling10-12 are generally used. Here, we address the above challenges by implementing boson sampling using ultracold atoms13,14 in a two-dimensional, tunnel-coupled optical lattice. This demonstration is enabled by a previously unrealized combination of tools involving high-fidelity optical cooling and imaging of atoms in a lattice, as well as programmable control of those atoms using optical tweezers. When extended to interacting systems, our work demonstrates the core abilities required to directly assemble ground and excited states in simulations of various Hubbard models15,16.

Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice.

Quantum walks provide a framework for designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. We do this by combining the fast, programmable control provided by optical tweezers with the scalable, homogeneous environment of an optical lattice. With these tools we study continuous-time quantum walks of single atoms on a square lattice and perform proof-of-principle demonstrations of spatial search with these walks. When scaled to more particles, the capabilities demonstrated can be extended to study a variety of problems in quantum information science, including performing more effective versions of spatial search using a larger graph with increased connectivity.

High-power, fiber-laser-based source for magic-wavelength trapping in neutral-atom optical clocks.

We present a continuous-wave, 810 nm laser with watt-level powers. Our system is based on difference-frequency generation of 532 and 1550 nm fiber lasers in a single pass through periodically poled lithium niobate. We measure the broadband spectral noise and relative intensity noise to be compatible with off-resonant dipole trapping of ultracold atoms. Given the large bandwidth of the fiber amplifiers, the output can be optimized for a range of wavelengths, including the strontium clock-magic-wavelength of 813 nm. Furthermore, with the exploration of more appropriate nonlinear crystals, we believe that there is a path toward scaling this proof-of-principle design to many watts of power and that this approach could provide a robust, rack-mountable trapping laser for future use in strontium-based optical clocks.

Half-minute-scale atomic coherence and high relative stability in a tweezer clock.

The preparation of large, low-entropy, highly coherent ensembles of identical quantum systems is fundamental for many studies in quantum metrology1, simulation2 and information3. However, the simultaneous realization of these properties remains a central challenge in quantum science across atomic and condensed-matter systems2,4-7. Here we leverage the favourable properties of tweezer-trapped alkaline-earth (strontium-88) atoms8-10, and introduce a hybrid approach to tailoring optical potentials that balances scalability, high-fidelity state preparation, site-resolved readout and preservation of atomic coherence. With this approach, we achieve trapping and optical-clock excited-state lifetimes exceeding 40 seconds in ensembles of approximately 150 atoms. This leads to half-minute-scale atomic coherence on an optical-clock transition, corresponding to quality factors well in excess of 1016. These coherence times and atom numbers reduce the effect of quantum projection noise to a level that is comparable with that of leading atomic systems, which use optical lattices to interrogate many thousands of atoms in parallel11,12. The result is a relative fractional frequency stability of 5.2(3) × 10-17τ-1/2 (where τ is the averaging time in seconds) for synchronous clock comparisons between sub-ensembles within the tweezer array. When further combined with the microscopic control and readout that are available in this system, these results pave the way towards long-lived engineered entanglement on an optical-clock transition13 in tailored atom arrays.

Observation of Laughlin states made of light.

Much of the richness in nature emerges because simple constituents form an endless variety of ordered states1. Whereas many such states are fully characterized by symmetries2, interacting quantum systems can exhibit topological order and are instead characterized by intricate patterns of entanglement3,4. A paradigmatic example of topological order is the Laughlin state5, which minimizes the interaction energy of charged particles in a magnetic field and underlies the fractional quantum Hall effect6. Efforts have been made to enhance our understanding of topological order by forming Laughlin states in synthetic systems of ultracold atoms7,8 or photons9-11. Nonetheless, electron gases remain the only systems in which such topological states have been definitively observed6,12-14. Here we create Laughlin-ordered photon pairs using a gas of strongly interacting, lowest-Landau-level polaritons as a photon collider. Initially uncorrelated photons enter a cavity and hybridize with atomic Rydberg excitations to form polaritons15-17, quasiparticles that here behave like electrons in the lowest Landau level owing to a synthetic magnetic field created by Floquet engineering18 a twisted cavity11,19 and by Rydberg-mediated interactions between them16,17,20,21. Polariton pairs collide and self-organize to avoid each other while conserving angular momentum. Our finite-lifetime polaritons only weakly prefer such organization. Therefore, we harness the unique tunability of Floquet polaritons to distil high-fidelity Laughlin states of photons outside the cavity. Particle-resolved measurements show that these photons avoid each other and exhibit angular momentum correlations, the hallmarks of Laughlin physics. This work provides broad prospects for the study of topological quantum light22.

Interacting Floquet polaritons.

Ordinarily, photons do not interact with one another. However, atoms can be used to mediate photonic interactions1,2, raising the prospect of forming synthetic materials3 and quantum information systems4-7 from photons. One promising approach combines highly excited Rydberg atoms8-12 with the enhanced light-matter coupling of an optical cavity to convert photons into strongly interacting polaritons13-15. However, quantum materials made of optical photons have not yet been realized, because the experimental challenge of coupling a suitable atomic sample with a degenerate cavity has constrained cavity polaritons to a single spatial mode that is resonant with an atomic transition. Here we use Floquet engineering16,17-the periodic modulation of a quantum system-to enable strongly interacting polaritons to access multiple spatial modes of an optical cavity. First, we show that periodically modulating an excited state of rubidium splits its spectral weight to generate new lines-beyond those that are ordinarily characteristic of the atom-separated by multiples of the modulation frequency. Second, we use this capability to simultaneously generate spectral lines that are resonant with two chosen spatial modes of a non-degenerate optical cavity, enabling what we name 'Floquet polaritons' to exist in both modes. Because both spectral lines correspond to the same Floquet-engineered atomic state, adding a single-frequency field is sufficient to couple both modes to a Rydberg excitation. We demonstrate that the resulting polaritons interact strongly in both cavity modes simultaneously. The production of Floquet polaritons provides a promising new route to the realization of ordered states of strongly correlated photons, including crystals and topological fluids, as well as quantum information technologies such as multimode photon-by-photon switching.

Electromagnetic and gravitational responses of photonic Landau levels.

Topology has recently become a focus in condensed matter physics, arising in the context of the quantum Hall effect and topological insulators. In both of these cases, the topology of the system is defined through bulk properties ('topological invariants') but detected through surface properties. Here we measure three topological invariants of a quantum Hall material-photonic Landau levels in curved space-through local electromagnetic and gravitational responses of the bulk material. Viewing the material as a many-port circulator, the Chern number (a topological invariant) manifests as spatial winding of the phase of the circulator. The accumulation of particles near points of high spatial curvature and the moment of inertia of the resultant particle density distribution quantify two additional topological invariants-the mean orbital spin and the chiral central charge. We find that these invariants converge to their global values when probed over increasing length scales (several magnetic lengths), consistent with the intuition that the bulk and edges of a system are distinguishable only for sufficiently large samples (larger than roughly one magnetic length). Our experiments are enabled by applying quantum optics tools to synthetic topological matter (here twisted optical resonators). Combined with advances in Rydberg-mediated photon collisions, our work will enable precision characterization of topological matter in photon fluids.

Synthetic Landau levels for photons.

Synthetic photonic materials are an emerging platform for exploring the interface between microscopic quantum dynamics and macroscopic material properties. Photons experiencing a Lorentz force develop handedness, providing opportunities to study quantum Hall physics and topological quantum science. Here we present an experimental realization of a magnetic field for continuum photons. We trap optical photons in a multimode ring resonator to make a two-dimensional gas of massive bosons, and then employ a non-planar geometry to induce an image rotation on each round-trip. This results in photonic Coriolis/Lorentz and centrifugal forces and so realizes the Fock­Darwin Hamiltonian for photons in a magnetic field and harmonic trap. Using spatial- and energy-resolved spectroscopy, we track the resulting photonic eigenstates as radial trapping is reduced, finally observing a photonic Landau level at degeneracy. To circumvent the challenge of trap instability at the centrifugal limit, we constrain the photons to move on a cone. Spectroscopic probes demonstrate flat space (zero curvature) away from the cone tip. At the cone tip, we observe that spatial curvature increases the local density of states, and we measure fractional state number excess consistent with the Wen­Zee theory, providing an experimental test of this theory of electrons in both a magnetic field and curved space. This work opens the door to exploration of the interplay of geometry and topology, and in conjunction with Rydberg electromagnetically induced transparency, enables studies of photonic fractional quantum Hall fluids and direct detection of anyons.