Realizing strong interactions between individual photons, mediated by matter, is a cornerstone for advancing photonic quantum computing and quantum nonlinear optics. In such systems, the interaction range is typically limited by the narrow bandwidth of the material excitation, resulting in a trade-off between interaction strength and pulse duration. Here, we address this limitation by exploring interactions between counter-propagating photons mediated by Rydberg polaritons. We experimentally demonstrate strong photon-photon interactions, achieving a record-long anti-correlation range exceeding 1 & micro;s. This extended range enables photon pulses that are long enough to fit within the polariton bandwidth, yet short enough to remain within the interaction range. Under these conditions, we observe complete photon blockade of entire pulses, tunable via their relative timing. Extending to the three-photon regime, we observe enhanced interactions when a photon encounters a counter-propagating pair. These results, supported by analytical theory and numerical simulations, establish counter-propagating Rydberg polaritons as a powerful platform for engineering interactions in quantum light fields, enabling deterministic photonic operations and opening new directions in few-photon quantum dynamics. (c) 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Strong atom-photon interactions on scalable photonic platforms hold significant potential for both atomic and photonic quantum information platforms. In particular, trapping of a single atom on a planar photonic integrated resonator at the subwavelength distances required for strong coupling to the guided modes has remained an outstanding challenge. Here we demonstrate efficient trapping of a single ultracold rubidium atom within the evanescent field of an integrated silicon-nitride microring resonator, at distances of 150-200 nm from the chip surface. Efficient, single-stroke loading process is achieved using an evanescent-field mechanism related to Sisyphus cooling, in which a single scattering event dissipates the atom's kinetic energy and transfers it into a near-surface trap. We observe logarithmic scaling of trapping durations spanning from sub-millisecond timescales up to 1 second, without continuous cooling. The trapped atom couples efficiently to the resonator, enabling on-chip photon collection, photon antibunching, and Purcell-enhanced spontaneous emission with single-atom cooperativity exceeding unity. Our results establish the potential of CMOS-compatible chip-based atom-photon interfaces for scalable quantum photonic circuits.

We develop a theory of the transverse spatial dynamics of two interacting photons in a Rydberg nonlinear medium. Extending the well-studied one-dimensional case, we explore both longitudinal and transverse correlations of photons propagating as Rydberg polaritons. We identify distinct behaviors and scaling laws for these correlations, arising from fundamentally different mechanisms in the two directions: diffraction for transverse correlations and diffusion for longitudinal correlations. We develop a model incorporating a Gaussian optical beam and an inhomogeneous atomic density distribution, from which we derive quantitative predictions for correlation functions in both directions. We further show that the propagation equations can be reduced to a single Schrödinger-like equation, allowing approximate solutions that are supported by full numerical results. Our findings indicate that the transverse correlation length is determined primarily by the blockade radius, whereas the longitudinal correlation length is limited by bandwidth. These results establish transverse Rydberg blockade as a distinct and measurable correlation mechanism and show that spatial photon correlations provide a direct means of measuring the blockade radius.

We introduce and study coherent polarization self-rotation (CPSR), a two-photon light-matter interaction in dense alkali-metal vapors that enables both narrowband optical spectroscopy of magnetic transitions and coherent coupling between light and collective atomic spins. Unlike conventional polarization self-rotation, CPSR requires initial spin polarization and a predominantly linearly polarized probe. It operates efficiently even in optically thick vapors with high buffer-gas pressure, rapid spin-exchange collisions, and optically-unresolved hyperfine structure. We demonstrate CPSR with near-unity contrast in rubidium and achieve an exceptionally narrow two-photon linewidth of 10 Hz in potassium. CPSR realizes a coherent interface between one optical quadrature and the long-lived collective electronic spin, offering a robust and scalable light-spin coupling in optically thick platforms. This opens new opportunities for quantum optics, including coherent transduction between light and ultra-long-lived noble-gas spins via alkali spins.

We investigate the generation of deterministic and heralded non-Gaussian states of light, using a single two-level system coupled to a chiral waveguide. We study the case of a single two level system driven by pulsed coherent and squeezed drive in a chiral waveguide. For coherent input pulses, we show that the emitter can deterministically generate Wigner-negative states, albeit of limited rank. Going beyond, using squeezed-vacuum inputs, we show that the interaction produces bimodal non-Gaussian states from which higher-stellar-rank states, including large squeezed cat states, can be experimentally extracted with a substantial success rate. Motivated by experimental implementations, we further analyze the effect of imperfect coupling and of the intrinsic 50% collection limit of symmetric, non-chiral waveguides. Finally, we propose a simple interferometric scheme that recovers an effectively chiral interaction in an otherwise bidirectional waveguide.

We present a practical approach for interfacing light with a two-dimensional atomic tweezer array. Typical paraxial fields are poorly matched to the array's multi-diffraction-order radiation pattern, thus severely limiting the interface coupling efficiency. Instead, we propose to design a field mode that naturally couples to the array: it consists of a unique superposition of multiple beams corresponding to the array's diffraction orders. This composite mode can be generated from a single Gaussian beam using standard free-space optics, including spatial light modulators and a single objective lens. For a triangular array with lattice spacing about twice the wavelength, all diffraction angles remain below 35 degrees, making the scheme compatible with standard objectives of numerical aperture NA <= 0.7. Our analytical theory and scattering simulations reveal that the interface efficiency r(0) for quantum information tasks scales favorably with the array atom number N: reaching > 0.99 (> 0.9999) for N = 149 (N similar to 1000) and scaling as 1 - r(0) similar to 1/N for large N. The scheme is robust to optical imperfections and atomic-position errors, offering a viable path for quantum light-matter applications in current tweezer-array platforms.

Rydberg entangling gates in optical-tweezer arrays are commonly executed with the trapping light switched off, so every gate contains a release–and–recapture cycle that heats the atomic motion and can ultimately limit circuit depth. We develop a motional refocusing protocol that exactly removes this heating in the harmonic approximation using only programmable intensity switching of the trapping light. The protocol closes the release–and–recapture cycle for every matched harmonic mode, returning arbitrary motional populations and coherences exactly up to ordinary evolution under the static trap. We derive the recovery sequence in closed form for arbitrary catch depth and prove that, within the experimentally relevant regime, it is the unique globally time-optimal solution under bounded trap intensity. The harmonic theory is then extended in two directions. First, we construct exact common-intensity recovery sequences that simultaneously refocus several nondegenerate harmonic modes, including radial–axial and fully anisotropic three-dimensional traps. Second, we derive a composite sequence that suppresses the leading anharmonic correction of weakly anharmonic traps by canceling all first-order motional transitions induced by the quartic anharmonicity, changing the residual heating law from U_0^-2 to U_0^-4. Wave-packet simulations in realistic Gaussian tweezers validate the analytic theory and quantify the residual effects of anharmonicity, finite switching ramps, trap ellipticity, and control errors. Applied to representative cesium Rydberg gates, the protocol suppresses the dominant recapture heating to the anharmonic floor and prevents the associated motional Doppler contribution from increasing with circuit depth. The resulting framework provides a practical route toward heating-free trap-off neutral-atom gates using only trap-intensity modulation.

We study quantum light-matter interfaces based on bilayer atomic arrays in free space, considering interlayer spacings a_z that may deviate from the Bragg-symmetric condition, a_z∈integer× λ/2 with λ the light wavelength. Mapping the problem to a one-dimensional model, we show that the interface efficiency is fully determined by simple scattering observables - reflection and transmission - providing a direct, experimentally accessible characterization. This reveals new opportunities for optimizing light-matter coupling by operating beyond the Bragg symmetry. In particular, we identify configurations that suppress diffraction losses via destructive interference, enabling substantially improved interface efficiencies compared to Bragg-constrained designs. In addition, we introduce a new quantum memory scheme based on a collective dark state whose coupling to light is continuously controlled by tuning the interlayer spacing. More broadly, our results establish non-symmetric atomic arrays as a flexible platform for efficient quantum interfaces in free space.

Measurement time represents a critical bottleneck limiting the operational speed of neutral atom quantum computers, as it cannot be accelerated through parallelization like other quantum operations. We present a protocol for fast measurement of neutral atoms based on a new, fast multi-atom Rydberg gate that significantly reduces the measurement integration time and improves the measurement fidelity. Our approach employs a multi-qubit register of N ancilla atoms within a single Rydberg blockade region to measure a single data qubit. This enables an N-fold enhancement in photon emission collections, while reducing the measurement's sensitivity to loss. The scheme requires spectral separation between the data qubit and the ancillae, achievable through either a dual-species architecture or a targeted light shift. Beyond this, the scheme is straightforward to implement: it relies only on global pulses, global photon collection, and avoids both atom shuttling and numerically optimized pulses. Simulations of a Cs–Rb platform demonstrate that with only five ancillae (N=5), measurement infidelity below 10^-3 within 6 μs is achievable.

Nuclear spins of noble gases exhibit exceptionally long coherence times and can potentially serve as a long-lived storage medium for quantum information. We analyze and compare the performance of two mechanisms for mapping the quantum state of light onto the collective spin state of noble gases. The first mechanism utilizes collisional exchange with the electronic spin state of metastable noble-gas atoms, while the second relies on spin-exchange collisions with ground-state alkali-metal atoms. We describe the operation of an optical quantum memory relying on these two mechanisms using a compact model and study strategies that optimize the memory storage efficiency. Through numerical simulations, we identify optimal sequences for storing optical signals with different signal bandwidths and electronic spin relaxation rates. This work highlights the qualitative difference between the two approaches for using noble gases as long-lived quantum memories at non-cryogenic conditions and outlines the regimes in which they are expected to be efficient.

Controlling the synchronization of photons from probabilistic quantum sources plays a pivotal role in advancing efficient quantum information processing. We report the realization of a probabilistic entangling gate operating on actively synchronized photon pairs, using a quantum memory based on warm atomic vapor. We achieve a truth-table fidelity exceeding 85% and demonstrate Bell-inequality violation for all four Bell states. The reduction in visibility of the Hong-Ou-Mandel interference introduced by the storage process is identified as a primary factor limiting the gate fidelity. We derive an exact quantitative relation between Hong-Ou-Mandel visibility and gate fidelity for pure single photons, which applies to all photonic gates relying on interference, regardless of the physical platform.

We present a theoretical study of quantum correlations between interacting photons realized through co-propagating Rydberg polaritons. We show that the spatial evolution of the n-photon wavefunction is governed by a multiband dispersion featuring one massive mode and multiple massless modes with degenerate Dirac points and n-fold rotational symmetry. The resulting band structure is warped, departing from the single-band, parabolic approximation commonly assumed for interacting polaritons. Our analytical results are supported by rigorous numerical modeling that fully accounts for photon propagation inside the finite atomic medium. These findings advance the understanding of multi-photon interactions and support the development of future multi-photon control tools.

We consider quantum light-matter interfaces comprised of multiple layers of two-dimensional tweezer atomic arrays, wherein the lattice spacings exceed the wavelength of light. While the coupling of light to a single layer of such a "superwavelength" lattice is considerably reduced due to scattering losses to high diffraction orders, we show that the addition of layers can suppress these losses through destructive interference between the layers. Mapping the problem to a 1D model of a quantum interface wherein the coupling efficiency is characterized by a reflectivity, we analyze the latter by developing a geometrical optics formulation, accounting for realistic finite-size arrays. We find that optimized efficiency favors small diffraction-order angles and small interlayer separations, and that the coupling inefficiency for two layers universally scales as N^{-1} with the atom number per layer N. We validate our predictions using direct numerical calculations of the scattering reflectivity and the performance of a quantum memory protocol, demonstrating high atom-photon coupling efficiency. This opens the way for various applications in tweezer atomic-array platforms.

We consider the coupling of light, via an optical cavity, to two-dimensional atomic arrays whose lattice spacing exceeds the wavelength of the light. Such “superwavelength” spacing is typical of optical tweezer arrays. While subwavelength arrays exhibit strong atom-photon coupling, characterized by high optical reflectivity in free space, the coupling efficiency of superwavelength arrays is reduced due to collective scattering losses to high diffraction orders. We show how a moderate-finesse cavity can overcome these losses. As the scattering losses peak at certain discrete values of the lattice spacing, the spacing can be optimized to achieve efficient atom-photon coupling in the cavity. Our cavity-QED theory properly accounts for collective dipolar interactions mediated by the lossy, non-cavity-confined photon modes and for finite-size effects of both the array and the light field. These findings pave the way to harnessing the versatility of tweezer arrays for efficient atom-photon interfaces in applications of quantum computing, networking, and nonlinear optics.

Estimation of the phase delay between interferometer arms is the core of transmission phase microscopy. Such phase estimation may exhibit an error below the standard quantum (shot-noise) limit, if the input is an entangled two-mode state, e.g., a N00N state. We show, by contrast, that such supersensitive phase estimation (SSPE) is achievable by incoherent, e.g., thermal, light that is injected into a Mach-Zehnder interferometer via a Kerr-nonlinear two-mode coupler. Phase error is shown to be reduced below 1/n, n being the mean photon number, by thermal input in such interferometric setups, even for small nonlinear phase shifts per photon pair or for significant photon loss. Remarkably, the phase accuracy achievable in such setups by thermal input surpasses that of coherent light with the same n. Available mode couplers with giant Kerr nonlinearity that stem either from dipole-dipole interactions of Rydberg polaritons in a cold atomic gas, or from cavity-enhanced dispersive atom-field interactions, may exploit such effects to substantially advance interferometric phase microscopy using incoherent, faint light sources.

This tutorial introduces the theoretical and experimental basics of electromagnetically induced transparency (EIT) in thermal alkali vapors. We first give a brief phenomenological description of EIT in simple three-level systems of stationary atoms and derive analytical expressions for optical absorption and dispersion under EIT conditions. Then we focus on how the thermal motion of atoms affects various parameters of the EIT system. Specifically, we analyze the Doppler broadening of optical transitions, ballistic versus diffusive atomic motion in a limited-volume interaction region, and collisional depopulation and decoherence. Finally, we discuss the common trade-offs important for optimizing an EIT experiment and give a brief ‘walk-through’ of a typical EIT experimental setup. We conclude with a brief overview of current and potential EIT applications.

We propose heat machines that are nonlinear, coherent, and closed systems composed of few field (oscillator) modes. Their thermal-state input is transformed by nonlinear Kerr interactions into nonthermal (non-Gaussian) output with controlled quantum fluctuations and the capacity to deliver work in a chosen mode. These machines can provide an output with strongly reduced phase and amplitude uncertainty that may be useful for sensing or communications in the quantum domain. They are experimentally realizable in optomechanical cavities where photonic and phononic modes are coupled by a Josephson qubit or in cold gases where interactions between photons are transformed into dipole-dipole interacting Rydberg atom polaritons. This proposed approach is a step toward the bridging of quantum and classical coherent and thermodynamic descriptions.

Efficient synchronization of single photons that are compatible with narrow band atomic transitions is an outstanding challenge, which could prove essential for photonic quantum information processing. Here we report on the synchronization of independently generated single photons using a room-temperature atomic quantum memory. The photon source and the memory are interconnected by fibers and employ the same ladder-level atomic scheme. We store and retrieve the heralded single photons with end-to-end efficiency of η_{e2e}=25% and final antibunching of g_{h}^{(2)}=0.023. Our synchronization process results in an over tenfold increase in the photon-pair coincidence rate, reaching a rate of more than 1000 detected synchronized photon pairs per second. The indistinguishability of the synchronized photons is verified by a Hong-Ou-Mandel interference measurement.

We present general guidelines for finding solid-state systems that could serve as coherent electron spin-photon interfaces even at relatively high temperatures, where phonons are abundant but cooling is easier, and show that transition metal ions in various crystals could comply with these guidelines. As an illustrative example, we focus on divalent nickel ions in magnesium oxide. We perform electron spin resonance spectroscopy and polarization-sensitive magneto-optical fluorescence spectroscopy of a dense ensemble of these ions and find that (i) the ground-state electron spin stays coherent at liquid-helium temperatures for several microseconds, and (ii) there exists energetically well-isolated excited states which can couple to two ground state spin sub-levels via optical transitions of orthogonal polarizations. The latter implies that fast, coherent optical control over the electron spin is possible. We then propose schemes for optical initialization and control of the ground-state electron spin using polarized optical pulses, as well as two schemes for implementing a noise-free, broadband quantum-optical memory at near-telecom wavelengths in this material system.