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A fundamental challenge in modern physics is bridging the gap between an exact description of few-body microscopic systems and the emergent description of many-body macroscopic systems. This gap may be bridged by tracing the properties of well-controlled intermediate-size mesoscopic systems. Here, we study mesoscopic signatures of a spatial self-organization phase transition in deterministically prepared arrays of between 10 and 22 atoms inside an optical cavity. Through precise engineering of the atom-cavity interactions, we reveal how critical behavior depends on atom number. We identify characteristic dynamical behaviors related to symmetry breaking and system size in the self-organized regime, and observe a finite optomechanical susceptibility at the critical point. This work opens the door to probing particle-number- and time-resolved properties of phase transitions in mesoscopic systems., Comment: 21 pages, 9 figures

We propose the use of collective states of matter as a resource for the deterministic generation of quantum states of light, which are fundamental for quantum information technologies. Our minimal model consists of three emitters coupled to a half-waveguide, i.e., a one-dimensional waveguide terminated by a mirror. Photon-mediated interactions between the emitters result in the emergence of bright and dark states. The dark states form a decoherence-free subspace, protected from dissipation. Local driving of the emitters and control of their resonance frequencies allows to perform arbitrary quantum gates within the decoherence-free subspace. Coupling to bright states facilitates photon emission, thereby enabling the realization of quantum gates between light and matter. We demonstrate that sequential application of these gates leads to the generation of photonic entangled states, such as Greenberger-Horne-Zeilinger and one- and two-dimensional cluster states.

We present a theoretical framework for 'collective transition quenching', a quantum many-body dissipative phenomenon that occurs in systems with multiple collective decay channels. Despite the competition, interactions suppress all but the dominant decay transition, leading to a 'winner takes all' dynamic where the system primarily settles into the dominant ground state. We prove that, in the presence of permutation symmetry, this problem is exactly solvable for any number of competing channels. Additionally, we develop an approximate model for the dynamics by mapping the evolution into a continuity equation for a fluid, and show analytically that the dominant transition ratio converges to unity with increasing system size as a power-law, for any branching ratio. This near-deterministic preparation of the dominant ground state has broad applicability. As an example we discuss a protocol for molecular photoassociation where collective dynamics effectively acts as a catalyst, amplifying the yield in a particular final state. Our results open new avenues for many-body strategies in the preparation and control of quantum systems., Comment: 5 pages, 3 figures

Quantum systems are open, continually exchanging energy and information with the surrounding environment. This interaction leads to decoherence and decay of quantum states. In complex systems, formed by many particles, decay can become correlated and enhanced. A fundamental question then arises: what is the maximal decay rate of a large quantum system, and how does it scale with its size? In this work, we address these issues by reformulating the problem into finding the ground state energy of a generic spin Hamiltonian. Inspired by recent work in Hamiltonian complexity theory, we establish rigorous and general upper and lower bounds on the maximal decay rate. These bounds are universal, as they hold for a broad class of Markovian many-body quantum systems. For many physically-relevant systems, the bounds are asymptotically tight, resulting in exact scaling laws with system size. Specifically, for large atomic arrays in free space, these scalings depend only on the arrays' dimensionality and are insensitive to details at short length-scales. The scaling laws establish fundamental limits on the decay rates of quantum states and offer valuable insights for research in many-body quantum dynamics, metrology, and fault tolerant quantum computation.

Subwavelength atomic arrays in free space are becoming a leading platform for exploring emergent many-body quantum phenomena. These arrays feature strong light-induced dipole-dipole interactions, resulting in subradiant collective resonances characterized by narrowed linewidths. In this work, we present a sideband cooling scheme for atoms trapped in subwavelength arrays that utilizes these narrow collective resonances. We derive an effective master equation for the atomic motion by adiabatically eliminating the internal degrees of freedom of the atoms, and validate its prediction with numerical simulations of the full system. Our results demonstrate that subradiant resonances enable the cooling of ensembles of atoms to temperatures lower than those achievable without dipole interactions, provided the atoms have different trap frequencies. Remarkably, narrow collective resonances can be sideband-resolved even when the individual atomic transition is not. In such scenarios, ground state cooling becomes feasible solely due to light-induced dipole-dipole interactions. This approach could be utilized for future quantum technologies based on dense ensembles of emitters, and paves the way towards harnessing many-body cooperative decay for enhanced motional control., Comment: 10 pages of main text and appendix, with 4 figures. 9 pages of Supplemental Material, with 4 figures

Optical networks are the leading platform for the transfer of information due to their low loss and ability to scale to many information channels using optical frequency modes. To fully leverage the quantum properties of light in this platform, it is desired to manipulate higher-dimensional superpositions by orchestrating linear, beamsplitter-type interactions between several channels simultaneously. We propose a method of achieving simultaneous, all-to-all coupling between N optical frequency modes via N-way Bragg-scattering four-wave mixing. By exploiting the frequency degree of freedom, additional modes can be multiplexed in an interaction medium of fixed volume and loss, avoiding the introduction of excess noise. We generalize the theory of the frequency-encoded two-mode interaction to N modes under this four-wave mixing approach and experimentally verify the quantum nature of this scheme by demonstrating three-way multiphoton interference. The two input photons are shared among three frequency modes and display interference differing from that of two classical (coherent-state) inputs. These results show the potential of our approach for the scalability of photonic quantum information processing to general N-mode systems in the frequency domain.

Atoms are not two-level systems, and their rich internal structure often leads to complex phenomena in the presence of light. Here, we analyze off-resonant light scattering including the full hyperfine and magnetic structure. We find a set of frequency detunings where the induced atomic dipole is the same irrespective of the Zeeman state, and where two-photon transitions that alter the atomic state turn off. For alkali atoms and alkaline-earth ions, if the hyperfine splitting is dominated by the magnetic dipole moment contribution, these detunings approximately coincide. Therefore, at a given ``magical'' detuning, all Zeeman states in a hyperfine manifold behave almost identically, and can be traced out to good approximation. This feature prevents state decoherence due to light scattering, which impacts quantum optics experiments and quantum information applications., Comment: 12+9 pages, 4+1 figures, 2 tables. This version is in line with the published version

We realize collective enhancement and suppression of light scattered by an array of tweezer-trapped $^{87}$Rb atoms positioned within a strongly coupled Fabry-P\'{e}rot optical cavity. We illuminate the array with light directed transverse to the cavity axis, in the low saturation regime, and detect photons scattered into the cavity. For an array with integer-optical-wavelength spacing each atom scatters light into the cavity with nearly identical scattering amplitude, leading to an observed $N^2$ scaling of cavity photon number as the atom number increases stepwise from $N=1$ to $N=8$. By contrast, for an array with half-integer-wavelength spacing, destructive interference of scattering amplitudes yields a non-monotonic, sub-radiant cavity intensity versus $N$. By analyzing the polarization of light emitted from the cavity, we find that Rayleigh scattering can be collectively enhanced or suppressed with respect to Raman scattering. We observe also that atom-induced shifts and broadenings of the cavity resonance are precisely tuned by varying the atom number and positions. Altogether, tweezer arrays provide exquisite control of atomic cavity QED spanning from the single- to the many-body regime.

We study temporal oscillations, known as dynamical beats, developed by a propagating pulse due to its interaction with a near-resonant collective medium of $^{133}$Cs atoms randomly captured by a nanofiber-based optical lattice. A phenomenological theory provides an intuitive explanation and quantitative predictions, which are improved by an input-output theory considering multiple-scattering between the atoms. The results deepen our understanding of light propagation in waveguide QED, essential in time-frequency analysis and light engineering for probing, manipulating, and exploiting many-body quantum systems.

In inverted atomic ensembles, photon-mediated interactions give rise to Dicke superradiance, a form of many-body decay that results in a rapid release of energy as a photon burst. While originally studied in pointlike ensembles, this phenomenon persists in extended ordered systems if the inter-particle distance is below a certain bound. Here, we investigate Dicke superradiance in a realistic experimental setting using ordered arrays of alkaline-earth(-like) atoms, such as strontium and ytterbium. Such atoms offer exciting new opportunities for light-matter interactions as their internal structure allows for trapping at short interatomic distances compared to their long-wavelength transitions, providing the potential for collectively enhanced dissipative interactions. Despite their intricate electronic structure, we show that two-dimensional arrays of these atomic species should exhibit many-body superradiance for achievable lattice constants. Moreover, superradiance effectively ``closes'' transitions, such that multilevel atoms become more two-level like. This occurs because the avalanchelike decay funnels the emission of most photons into the dominant transition, overcoming the single-atom decay ratios dictated by their fine structure and Zeeman branching. Our work represents an important step in harnessing alkaline-earth atoms as quantum optical sources and as platforms to explore many-body dissipative dynamics., Comment: 10 + 9 pages, 7 + 3 figures, 2 tables. This version is in line with the published version

Photon-mediated interactions within an excited ensemble of emitters can result in Dicke superradiance, where the emission rate is greatly enhanced, manifesting as a high-intensity burst at short times. The superradiant burst is most commonly observed in systems with long-range interactions between the emitters, although the minimal interaction range remains unknown. Here, we put forward a new theoretical method to bound the maximum emission rate by upper bounding the spectral radius of an auxiliary Hamiltonian. We harness this tool to prove that for an arbitrary ordered array with only nearest-neighbor interactions in all dimensions, a superradiant burst is not physically observable. We show that Dicke superradiance requires minimally the inclusion of next-nearest-neighbor interactions. For exponentially decaying interactions, the critical coupling is found to be asymptotically independent of the number of emitters in all dimensions, thereby defining the threshold interaction range where the collective enhancement balances out the decoherence effects. Our findings provide key physical insights to the understanding of collective decay in many-body quantum systems, and the designing of superradiant emission in physical systems for applications such as energy harvesting and quantum sensing., Comment: 5 pages, 4 figures

We propose metasurface holograms as a novel platform to generate optical trap arrays for cold atoms with high fidelity, efficiency, and thermal stability. We developed design and fabrication methodologies to create dielectric, phase-only metasurface holograms based on titanium dioxide. We experimentally demonstrated optical trap arrays of various geometries, including periodic and aperiodic configurations with dimensions ranging from 1D to 3D and the number of trap sites up to a few hundred. We characterized the performance of the holographic metasurfaces in terms of the positioning accuracy, size and intensity uniformity of the generated traps, and power handling capability of the dielectric metasurfaces. Our proposed platform has great potential for enabling fundamental studies of quantum many-body physics, and quantum simulation and computation tasks. The compact form factor, passive nature, good power handling capability, and scalability of generating high-quality, large-scale arrays also make the metasurface platform uniquely suitable for realizing field-deployable devices and systems based on cold atoms.

The many-body decay of extended collections of two-level systems remains an open problem. Here, we investigate whether an array of emitters coupled to a one-dimensional bath undergoes Dicke superradiance. This is a process whereby a completely inverted system becomes correlated via dissipation, leading to the release of all the energy in the form of a rapid photon burst. We derive the minimal conditions for the burst to happen as a function of the number of emitters, the chirality of the waveguide, and the single-emitter optical depth, both for ordered and disordered ensembles. Many-body superradiance occurs because the initial fluctuation that triggers the emission is amplified throughout the decay process. In one-dimensional baths, this avalanchelike behavior leads to a spontaneous mirror symmetry breaking, with large shot-to-shot fluctuations in the number of photons emitted to the left and right. Superradiant bursts may thus be a smoking gun for the generation of correlated photon states of exotic quantum statistics., Comment: 16 pages, 9 figures

Subradiant excited states in finite chains of two-level quantum emitters coupled to a one-dimensional reservoir are a resource for superior photon storage and controlled photon manipulation. Typically, states storing multiple excitations exhibit fermionic correlations and are thus characterized by an anti-symmetric wavefunction, which makes them hard to prepare experimentally. Here we identify a class of quasi-localized dark states with up to half of the qubits excited, which appear for lattice constants that are an integer multiple of the guided-mode wavelength. They allow for a high-fidelity preparation and minimally invasive read out in state-of-the-art setups. In particular, we suggest an experimental implementation using a coplanar wave-guide coupled to superconducting transmon qubits on a chip. As free space and intrinsic losses are minimal, virtually perfect dark states can be achieved even for a low number of qubits, enabling fast preparation and manipulation with high fidelity., Comment: 11 pages, 6 figures

When a broadband signal propagates through a dispersive medium, some frequency components move faster than the center of the pulse. This leads to the appearance of precursors, transient signals that emerge from the medium earlier than the main part of the pulse and seem to propagate superluminally. Here, we investigate the microscopic origin of precursors in a minimal setup: an array of qubits coupled to a waveguide. The linear transmission function only converges to that of a continuous medium for large qubit numbers. Nevertheless, the dispersion produced by only two qubits is enough to produce oscillatory transients. Precursors are best observed under conditions of electromagnetically-induced transparency, as the center of the pulse is significantly delayed. Under these conditions, just a single qutrit is enough to generate a precursor. Our results pave the way towards dispersion engineering of light with just a few qubits, and can be realized with superconducting qubits coupled to transmission lines or atoms coupled to optical waveguides., Comment: 10 pages, 6 figures