We study continuous-variable graph states with regular and complex network shapes, and we report their cost as a global measure of squeezing and the number of squeezed modes that are necessary to build the network. We provide an analytical formula to compute the experimental resources required to implement the graph states, and we use it to show that the scaling of the squeezing cost with the size of the network strictly depends on its topology. We show that homodyne measurements along parallel paths between two nodes allow one to increase the final entanglement in these nodes, and we use this effect to boost the efficiency of an entanglement routing protocol. The devised routing protocol is particularly efficient in running time for complex sparse networks.

We consider entanglement-assisted frequency estimation by Ramsey interferometry in the presence of dephasing noise from general spatiotemporally correlated environments. By working in the widely employed local estimation regime, we show that even for infinite measurement statistics, noise renders standard estimators biased or ill defined. We introduce ratio estimators which, at the cost of doubling the required resources, are insensitive to noise and retain the asymptotic precision scaling of standard ones. While ratio estimators are applicable also in the limit of Markovian noise, we focus on non-Markovian dephasing from a bosonic bath and show how knowledge about the noise spectrum may be used to maximize metrological advantage by tailoring the sensor's geometry. Notably, Heisenberg scaling is attained up to a logarithmic prefactor by maximally entangled states, while optimal Zeno scaling is afforded by one-axis twisted spin-squeezed states.

Light is a precious tool to probe matter, as it captures microscopic and macroscopic information on the system. However, the measurement will be limited by the coherence of the light, both spatial and temporal, which itself reveals certain properties of the emitters. We here report on the transition from a thermal (classical) to a spontaneous emission (SE) (quantum) mechanism for the loss of light temporal coherence from a macroscopic atomic cloud. The coherence is probed by intensity-intensity correlation measurements realized on the light scattered by the atomic sample, and the transition is explored by tuning the balance between thermal coherence loss and SE via the pump strength. The transition occurs only at low temperatures, which illustrates the potential of cold atom setups to investigate the classical-to-quantum transition in macroscopic systems.

Continuous-variable (CV) quantum computing has shown great potential for building neural network models. These neural networks can have different levels of quantum-classical hybridization depending on the complexity of the problem. Previous work on CV neural network protocols required the implementation of non-Gaussian operators in the network. These operators were used to introduce nonlinearity, an essential feature of neural networks. However, these protocols are hard to execute experimentally. We built a CV hybrid quantum-classical neural network protocol that can be realized experimentally with current photonic quantum hardware. Our protocol uses Gaussian gates only with the addition of ancillary qumodes. We implemented nonlinearity through repeat-until-success measurements on ancillary qumodes. To test our neural network, we studied canonical machine-learning and quantum computer problems in a supervised learning setting—state preparation, curve fitting, and classification problems. We achieved high fidelity in state preparation of single-photon (99.9%), cat (99.8%), and Gottesman-Kitaev-Preskill (93.9%) states, a well-fitted curve in the presence of noise at a cost of less than 1%, and more than 95% accuracy in classification problems. These results bode well for real-world applications of CV quantum neural networks.

The determination of ultra-long-range molecular potential curves has been reformulated using the Coulomb Green's function to give a solution in terms of the roots of an analytical determinantal equation. For a system consisting of one Rydberg atom with a fine structure and a neutral perturbing ground state atom with hyperfine structure, the solution yields potential energy curves and wave functions in terms of the quantum defects of the Rydberg atom and the electron-perturber scattering phase shifts and hyperfine splittings. This method provides a promising alternative to the standard currently utilized method of diagonalization, which suffers from problematic convergence issues and nonuniqueness, and can potentially yield a more quantitative relationship between Rydberg molecule spectroscopy and electron-atom scattering phase shifts.

The realization of photonic crystal waveguides with high topological protection enables robust light propagation against defect-induced scattering. It should allow the design of very compact devices by exploiting guiding through sharp bends with low losses and backreflection. In this work we use valley topological triangular resonators coupled to an input waveguide to evaluate the conversion between helical topological edge modes with opposite helicity at sharp bends or routing elements like splitters. To that purpose, we first analyze via numerical simulations the existence of backward scattering at cavity corners or transmission with helicity conversion at the splitter between the input waveguide and the cavity. We show evidence that such processes take place, in particular at sharp corners, which results in transmission minima and split resonances, otherwise nonexistent. In order to evaluate the small coupling coefficients associated with this effect, a phenomenological model based on an exact parametrization of scattering matrices at splitters and corners of the resonators is then introduced. By comparison with the numerical simulations, we are able to quantify the helicity conversion at sharp bends and splitters. Finally, we use the obtained set of phenomenological parameters to compare the predictions of the model with full numerical simulations for fractal-inspired cavities based on the Sierpiński triangle construction. We show that the agreement is overall good but shows more differences for the cavity composed of the smallest triangles. Our results suggest that even in a system exempt from geometrical and structural defects, helicity conversion is not negligible at corners, sharp bends, and splitters. However, simpler but predictive calculations can be realized with a phenomenological approach, allowing simulations of very large devices beyond the reach of standard numerical methods, which is crucial to the design of photonic devices which gather compactness and low losses through topological conduction of electromagnetic waves.

We show the possibility of implementing a deep dissipative optical lattice for neutral atoms with a macroscopic period. The depth of the lattice can reach magnitudes comparable to the depth of the magnetooptical traps (MOT), while the presence of dissipative friction forces allows for the trapping and cooling of atoms. The area of localization of trapped atoms reaches submillimeter size, and the number of atoms is comparable to the number trapped in MOT. As an example, we study lithium atoms for which the macroscopic period of the lattice $\mathrm{\Lambda }=1.5$ cm. Such deep optical lattices with a macroscopic period open up the possibility for developing effective methods for cooling and trapping neutral atoms without the use of magnetic field as an alternative to MOT. This is important for developing compact systems based on cold atoms.

We give theoretical insight into the critical problem of a modified cavity mode of an open resonator that is subject to a perturbation outside its cavity region. We utilize the framework of quasinormal modes (QNMs), which are the natural mode solutions to the open boundary problem with complex eigenfrequencies. This requires a non-Hermitian mode theory, typically using just a few dominant QNMs for resonant cavities, which are important for solving a wide range of problems in classical and quantum optics, including cavity quantum electrodynamics. We first highlight a fundamental problem with currently adopted formulas using QNM perturbation theory, when perturbations are added outside the resonator structure and present a potential step for solving this problem, connected to a regularization of the QNMs. We show several calculations of the QNMs and regularized QNM theory for simple one-dimensional cavities as well as a practical three-dimensional cavity structure. We first concentrate on the illustrative case of a one-dimensional dielectric barrier, where analytical QNM solutions are possible. We study the change of the mode frequency as a function of distance between the cavity and another smaller barrier structure (forming the outside perturbation). The results obtained from a few QNM expansion are also compared with exact analytical solutions from a transfer matrix approach. We show explicitly how regularization prevents a problematic spatial divergence for QNM perturbations in the far-field region, though eventually higher-order effects and multimodes can also play a role in the full scattering solution, and retaining a pure discrete QNM picture becomes questionable in such situations since the input-output coupling ultimately involves reservoir modes. To investigate a more practical cavity example, we also show results for a full three-dimensional plasmonic resonator of arbitrary shape and complex dispersion and loss, which again displays the divergent nature of the first-order mode change predicted from regular QNM perturbation theory, and an exponentially damped behavior from our regularized QNM theory.

We examine spectral signatures of Rydberg atoms driven with near-resonant dual-tone radio-frequency (rf) fields in the regime of strong driving. We experimentally demonstrate and theoretically model a variety of nonlinear and multiphoton phenomena in the atomic Rydberg response that manifest in the electromagnetically-induced-transparency spectra. Our results echo previous studies of two-level atoms driven with bichromatic optical fields. In comparison to optical studies, the rf-driven Rydberg system utilizes a more complex excitation pathway and electromagnetic fields from two different spectral regimes: a two-photon optical excitation continuously creates highly excited Rydberg atoms, while rf fields drive resonant coupling between the Rydberg levels and generate strong mixing. However, our spectra reflect nearly identical effects of the dual-tone rf fields on the atomic Rydberg observables, showing detuning-dependent splittings and Rabi-frequency-dependent peak numbers and relative strengths, and avoided crossings at subharmonic resonances. We thus validate previous two-state models in this more complex physical system. In the context of Rydberg electrometry, we use these investigations to explore a technique in which we tune a known rf field to observe spectra which give the frequency and power of an unknown rf field using the complex dual-tone spectra.

We show that the loss of nonclassicality (including quantum entanglement) cannot be compensated by the (incoherent) amplification of $\mathcal{PT}$-symmetric systems. We address this problem by manipulating the quantum fluctuating forces in the Heisenberg-Langevin approach. Specifically, we analyze the dynamics of two nonlinearly coupled oscillator modes in a $\mathcal{PT}$-symmetric system. An analytical solution allows us to separate the contribution of reservoir fluctuations from the evolution of quantum statistical properties of the modes. In general, as reservoir fluctuations act constantly, the complete loss of nonclassicality and entanglement is observed for long times. To elucidate the role of reservoir fluctuations in a long-time evolution of nonclassicality and entanglement, we consider and compare the predictions from two alternative models in which no fatal long-time detrimental effects on the nonclassicality and entanglement are observed. This is so as, in the first semiclassical model, no reservoir fluctuations are considered at all. This, however, violates the fluctuation-dissipation theorem. The second, more elaborated, model obeys the fluctuation-dissipation relations as it partly involves reservoir fluctuations. However, to prevent the above long-time detrimental effects, the reservoir fluctuations have to be endowed with the nonphysical properties of a sink model. In both models, additional incorporation of the omitted reservoir fluctuations results in their physically consistent behavior. This behavior, however, predicts the gradual loss of the nonclassicality and entanglement. Thus the effects of reservoir fluctuations related to damping cannot be compensated by those related to amplification. This qualitatively differs from the influence of damping and amplification to a direct coherent dynamics of $\mathcal{PT}$-symmetric systems in which their mutual interference results in a periodic behavior allowing for nonclassicality and entanglement at arbitrary times.

Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem from the viewpoint of quantum metrology, we are able to find optimal measurements under the assumption of good prior knowledge. We implement these measurements on a superconducting quantum computer. Our demonstration produces sufficiently low error to allow the saturation of the theoretical limits, given by the Nagaoka-Hayashi bound. We also present simulations of adaptive measurement schemes utilizing the proposed method. The results of the simulations show the robustness of the method in characterizing arbitrary qubit states with different amounts of prior knowledge.

Solving optimization problems on near term quantum devices requires developing error mitigation techniques to cope with hardware decoherence and dephasing processes. We propose a mitigation technique based on parity encoding. This method uses a redundant encoding of logical variables to solve optimization problems on fully programmable planar quantum chips. We discuss how this redundancy can be exploited to mitigate errors in quantum optimization algorithms. In the specific context of the quantum approximate optimization algorithm, we show that errors can be significantly mitigated by appropriately modifying the objective cost function.

We simulate the capture process of MgF molecules into a frequency-chirped molecular magneto-optical trap (MOT). Our calculations show that by chirping the frequency, the MOT capture velocity is increased by about a factor of 4 to 80 m/s, allowing for direct loading from a two-stage cryogenic buffer gas beam source. Moreover, we simulate the effect of this frequency chirp for molecules already present in the MOT. We find that the MOT should be stable with little to no molecule loss. The chirped MOT should thus allow loading of multiple molecule pulses to increase the number of trapped molecules

Microwave spectroscopy is used to measure the relative energy separations between strontium $n{}^{1}S_0, n{}^{1}P_1, n{}^{1}D_2$, and $n{}^{1}F_3$ Rydberg levels for $50\lesssim n\lesssim 70$ with uncertainties, limited by possible stray electric fields, of a few tens of kilohertz. These microwave results are used to develop a revised set of Rydberg-Ritz quantum defect parameters that can be used to predict level separations between the singlet $S, P, D$, and $F$ states over a broad range of $n$ with much higher precision, typically $\sim 20$ kHz, than is possible using earlier published parameter sets. The determination of accurate transition frequencies is central to the planning of quantum simulation experiments that involve microwave-coupled Rydberg levels, such as in the creation of Rydberg-atom synthetic dimensions.

Non-Abelian gauge field plays a central role in understanding the geometrical and topological phenomena in physics. Here we experimentally induce a non-Abelian gauge field in the degenerate eigensubspace of a double-$\mathrm{\Lambda }$ four-level atomic system. The non-Abelian nature of the gauge field is detected through the measurement of the noncommutativity of two successive evolution loops. Then we theoretically propose and experimentally demonstrate a scheme to measure the non-Abelian gauge field through multiloop evolution and robust holonomic quantum gates. The demonstrated scheme offers the advantage of detecting the non-Abelian gauge field with amplification through multiloop evolution. Our results pave the way for an experimentally feasible approach to achieving high-resolution and high-precision measurements of the gauge fields.

The quantum interference of two wavelength-entangled photons overlapping at a beamsplitter results in an oscillating interference pattern. The frequency of the beat note is dependent on the wavelength separation of the entangled photons but is robust to wavelength scale perturbations that can limit the practicality of standard interferometry. Here we use two-color entanglement interferometry to evaluate the variation in thickness of a semi-transparent sample in combination with two-dimensional raster scanning. The axial precision and the dynamic range of the microscope are actively controlled by adjusting the wavelength separation of the entangled photon pairs. Sub-$\mu \text{m}$ precision is reported using up to $12.3\text{nm}$ of detuning and $\sim {10}^4$ detected photon pairs.

Interference phenomena are often claimed to resist classical explanation. However, such claims are undermined by the fact that the specific aspects of the phenomenology upon which they are based can in fact be reproduced in a noncontextual ontological model [Catani et al., arXiv:2111.13727]. This raises the question of what other aspects of the phenomenology of interference $\mathit{do}$ in fact resist classical explanation. We answer this question by demonstrating that the most basic quantum wave-particle duality relation, which expresses the precise tradeoff between path distinguishability and fringe visibility, cannot be reproduced in any noncontextual model. We do this by showing that it is a specific type of uncertainty relation and then leveraging a recent result establishing that noncontextuality restricts the functional form of this uncertainty relation [Catani et al., Phys. Rev. Lett. 129, 240401 (2022)]. Finally, we discuss what sorts of interferometric experiment can demonstrate contextuality via the wave-particle duality relation.

We demonstrate reduction of the dc polarizability of cesium atom Rydberg states in a 77-K environment utilizing microwave field dressing. In particular we reduce the polarizability of $52P_{3/2}$ states which have resonances at 5.35 GHz to $51D_{5/2}$, suitable for interfacing Rydberg atoms to superconducting resonators in a cryogenic environment. We measure the polarizability of the Rydberg states using magneto-optical-trap loss spectroscopy. Using an off-resonant microwave-frequency dressing field coupling $52P_{3/2}$ and $51D_{5/2}$ we demonstrate a reduction in dc polarizability of the $52P_{3/2}$ states over $80\%$. Experimental findings are in good agreement with a numerical model of the atom-dressing field system developed using the Shirley-Floquet formalism. We also demonstrate that the dc polarizability reduction is highly anisotropic, with near total nulling possible when the dc and dressing fields are aligned, but only a factor of 2 reduction in polarizability when the fields are orthogonal. These results may aid in stabilizing Rydberg resonances against varying dc fields present near surfaces, enabling advancement in the development of hybrid Rydberg-atom–superconducting-resonator quantum gates.

It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is discussed, with the quantum contribution specified by a measure of the noncommutativity of a given set of operators relative to the quantum state, and the classical contribution generated by the mixedness of the state. Suitable measures of noncommutativity or “quantumness” include quantum Fisher information, and the asymmetry of a given set, group, or algebra of operators, and are generalized to nonprojective observables and quantum channels. Strong entropic uncertainty relations and lower bounds for Rényi entropies are obtained, valid for arbitrary discrete observables, that take the mixedness of the state into account via a classical contribution to the lower bound. These relations can also be interpreted without reference to quantum-classical decompositions, as tradeoff relations that bound the asymmetry of one observable in terms of the entropy of another.

We present a general framework that computes the two-photon spontaneous emission rate of a quantum emitter close to an arbitrary photonic structure beyond the dipolar approximation. This is relevant for strongly confined light fields, such as in plasmonic nano- and picocavities, which are currently being explored to enhance higher-order light-matter interactions. In our framework, the emitter contribution to this process is calculated analytically, while the influence of the photonic environment is determined via the computation of Purcell factors with conventional electromagnetic simulations, which avoids tedious analytic calculations for the environment. Also, our framework efficiently handles asymmetric structures that were not treated before. We show that placing a hydrogen-like emitter close to a silver nanodisk enhances the transition rate between two spherically symmetric states by 5 and 11 orders of magnitude via electric dipole and quadrupole two-photon transitions, respectively. In the future, controlling this process promises efficient entangled two-photon sources for quantum applications, new platforms in spectroscopy, as well as broadband absorbers and emitters.