Since the development of boson sampling, there has been a quest to construct more efficient and experimentally feasible protocols to test the computational complexity of sampling from photonic states. In this paper, we interpret and extend the results presented previously [Phys. Rev. Lett. 119, 170501 (2017)]. We derive an expression that relates the probability to measure a specific photon output pattern from a Gaussian state to the Hafnian matrix function and use it to design a Gaussian boson sampling protocol. Then, we discuss the advantages that this protocol has relative to other photonic protocols and the experimental requirements for Gaussian boson sampling. Finally, we relate it to the previously most general protocol, scattershot boson sampling [Phys. Rev. Lett. 113, 100502 (2014)].

A $CP$-violating interaction of the nuclear magnetic quadrupole moment (MQM) with electrons in the ytterbium monohydroxide molecule ${}^{173}\mathrm{YbOH}$ is considered. Both the MQM of the ${}^{173}\mathrm{Yb}$ nucleus and the molecular interaction constant $W_M$ are estimated. Electron correlation effects are taken into account within the relativistic Fock-space coupled-cluster method. Results are interpreted in terms of the strength constants of $CP$-violating nuclear forces, neutron dipole moment (EDM), QCD vacuum angle $\theta$, quark EDMs, and chromo-EDMs.

In this paper we present a detailed analysis of the nuclear-spin manifolds associated with the $ns$ Rydberg levels of ${}^{87}\mathrm{Rb}$ atoms that interact with both magnetic and optical lattice fields. Eigenvalues and eigenkets for the Rydberg manifold are obtained and used to study the dynamics of phase-matched emission following illumination of an ensemble of cold atoms with excitation and readout laser pulses. By comparing the measured emission signal to predictions of a model that accounts for the quantized motion of atoms in a one-dimensional optical lattice potential, we are able to extract the Rydberg hyperfine and light shift contributions to the observed modulation frequencies. In this way the hyperfine splitting of Rydberg $ns$ levels is measured for $n$ in the range of 30 to 65. Our results should be relevant for realizations of high-fidelity Rydberg qubits confined in optical potentials.

We study the extended Jaynes-Cummings-Hubbard model on triangular cavity lattices and zigzag ladders. By using density-matrix renormalization-group methods, we observe various types of solids with different density patterns and find evidence for light supersolids, which exist in extended regions of the phase diagram of the zigzag ladder. Furthermore, we observe strong pair correlations in the supersolid phase due to the interplay between the atoms in the cavities and atom-photon interaction. By means of cluster mean-field simulations and a scaling of the cluster size extending our analysis to two-dimensional triangular lattices, we present evidence for the emergence of a light supersolid in this case also.

The spectral and characteristic decompositions of the polarization matrix provide fruitful frameworks for the physical interpretation of three-dimensional (3D) partially polarized light fields. The decompositions are formulated in terms of the three pure eigenstates, which in turn are represented through their associated orthogonal complex 3D Jones vectors. This mathematical orthogonality does not correspond, in general, to orthogonality of the polarization-ellipse planes of the respective eigenstates. Consequently, due to such inherent mathematical complexity, the geometric and physical interpretation of these sets of orthogonal complex vectors, being essential for the best understanding of the structure and properties of partially polarized 3D light, has not been addressed thoroughly. In this work, the geometric and physical features of sets of three orthonormal 3D Jones vectors are identified and analyzed, allowing one to obtain meaningful interpretations of any given mixed (partially polarized) 3D polarization state in terms of either the spectral or the characteristic decompositions. Among other results, it is found that, given a pure polarization state, any plane in space contains the polarization ellipse of a pure state that is orthogonal to it, and the mathematical expressions for the azimuth and ellipticity of such an ellipse are calculated in terms of the angular parameters determining said plane and the ellipticity of the given state. Furthermore, the spin vectors of the three polarization eigenstates are arranged in a peculiar spatial manner, such that they lie in a common plane. Beyond polarization phenomena, the approach presented also has potential applications in areas where 3 × 3 unitary matrices play a key role, like three-level quantum systems and gates for ternary quantum logic circuits.

By analyzing the vectorial Helmholtz equation within the thin-layer approach, we find that light acquires another geometrical phase, in addition to the usual one (the optical Berry phase), during the propagation along a curved path. Unlike the optical Berry phase, the additional geometrical phase is induced by the curvature of the curve and associated with the transverse spin of light. Furthermore, we show an additional Hall effect of light induced by the torsion of the curve and associated with the transverse spin of light, which is different from the usual spin Hall effect of light. Finally, we demonstrate that the usual and transverse-spin-dependent geometrical phase phenomena are described by different geometry-induced U(1) gauge fields in different adiabatic approximations. In the general case, these gauge fields are united in an effective SO(3) gauge field, and the optical Berry phase and transverse-spin-dependent geometrical phase are united in a general geometrical phase of light.

We consider a mixture of spin-1/2 bosons and fermions, where only the bosons are subjected to the spin-orbit coupling induced by Raman beams. The fermions, although not directly coupled to the Raman lasers, acquire an effective spin-orbit coupling through the spin-exchange interaction between the two species. Our calculation shows that this is a promising way of obtaining spin-orbit coupled Fermi gas without Raman-induced heating, where the long-sought topological Fermi superfluids and topological bands can be realized. Conversely, we find that the presence of fermions not only provides a new way to create the supersolid stripe phase of the bosons, but more strikingly it can also greatly increase the spatial period of the bosonic density stripes, and hence makes this phase directly observable in the experiment. This system provides a new and practical platform to explore the physics of spin-orbit coupling, which possesses a dynamic nature through the interaction between the two species.

We develop protocols for high-fidelity single-qubit gates that exploit and extend theoretical ideas for accelerated adiabatic evolution. Our protocols are compatible with qubit architectures where direct transitions between logical states are either vanishingly small or nonexistent; in such systems traditional approaches cannot be implemented. Prime examples are superconducting fluxonium qubits, which have highly localized states, and AMO systems, where there are no dipole allowed transitions between the ground states encoding the logical states. By using an accelerated adiabatic protocol we can enforce the desired adiabatic evolution while having gate times that are comparable to the inverse adiabatic energy gap (a scale that is ultimately set by the amount of power used in the control pulses). By modeling the effects of decoherence, we explore the trade-off between speed and robustness that is inherent to shortcuts-to-adiabaticity approaches.

We derive a quasiclassical expression for the density of states (DOS) of an arbitrary, ultracold, $N$-atom collision complex, for a general potential energy surface (PES). We establish the accuracy of our quasiclassical method by comparing to exact quantum results for the ${\mathrm{K}}_2\text{−}\mathrm{Rb}$ and NaK-NaK systems, with isotropic model PESs. Next, we calculate the DOS for an accurate NaK-NaK PES to be 0.124 $\mu {\mathrm{K}}^{-1}$, with an associated Rice-Ramsperger-Kassel-Marcus sticking time of 6.0 $\mu \mathrm{s}$. We extrapolate the DOS and sticking times to all other polar bialkali-bialkali collision complexes by scaling with atomic masses, equilibrium bond lengths, dissociation energies, and dispersion coefficients. The sticking times calculated here are two to three orders of magnitude shorter than those reported by Mayle et al. [Phys. Rev. A 85, 062712 (2012)]. We estimate dispersion coefficients and collision rates between molecules and complexes. We find that the sticking-amplified three-body loss mechanism is not likely the cause of the losses observed in the experiments.

Dynamic control of atomic dressing to the highly excited Rydberg state in multilevel systems has special appeals owing to the development of flexible and precise measurement. In this study we develop an experimentally accessible proposal to robustly control the dressing probability via a three-step cascaded excitation with double electromagnetically induced transparency (EIT) technique. The system can function as an optical switch where the third addressing laser serving as the control knob can switchably engineer the dressing probability with time. Differing from a conventional two-photon EIT, this scheme facilitates a maximal dressing probability determined by a relative strength between two strong coupling fields, entirely relaxing their absolute values. The collective feature caused by the interactions of a few atoms is also studied leading to an enhanced dressing probability as well as reduced response times. Our work offers the opportunity to a coherent dynamic control of Rydberg excitation and to realize sizable Rydberg-Rydberg interactions in weakly driven multilevel quantum systems.

We establish an objective scheme to determine the macroscopicity of quantum superposition tests with mechanical degrees of freedom. It is based on the Bayesian hypothesis falsification of a class of macrorealist modifications of quantum theory, such as the model of continuous spontaneous localization. The measure uses the raw data gathered in an experiment, taking into account all measurement uncertainties, and can be used to directly assess any conceivable quantum mechanical test. We determine the resulting macroscopicity for three recent tests of quantum physics: double-well interference of Bose-Einstein condensates, Leggett-Garg tests with atomic random walks, and entanglement generation and read-out of nanomechanical oscillators.

We investigate the maximum purity that can be achieved by $k$-uniform mixed states of $N$ parties. Such $N$-party states have the property that all their $k$-party reduced states are maximally mixed. A scheme to construct explicitly $k$-uniform states using a set of specific $N$-qubit Pauli matrices is proposed. We provide several different examples of such states and demonstrate that in some cases the state corresponds to a particular orthogonal array. The obtained states, despite being mixed, reveal strong nonclassical properties such as genuine multipartite entanglement or violation of Bell inequalities.

We present a method to experimentally realize large-scale permutation-symmetric Hamiltonians for continuous-time quantum protocols such as quantum walks and adiabatic quantum computation. In particular, the method can be used to perform an encoded continuous-time quantum search on a hypercube graph with $2^n$ vertices encoded into $2n$ qubits. We provide details for a realistically achievable implementation in Rydberg atomic systems. Although the method is perturbative, the realization is always achieved at second order in perturbation theory, regardless of the size of the mapped system. This highly efficient mapping provides a natural set of problems which are tractable both numerically and analytically, thereby providing a powerful tool for benchmarking quantum hardware and experimentally investigating the physics of continuous-time quantum protocols.

An orthogonal product basis of a composite Hilbert space is genuinely nonlocal if the basis states are locally indistinguishable across every bipartition. From an operational point of view, such a basis corresponds to a separable measurement that cannot be implemented by local operations and classical communication unless all the parties come together in a single location. In this work we classify genuinely nonlocal product bases into different categories. Our classification is based on the state elimination property of the set via orthogonality-preserving measurements when all the parties are spatially separated or different subsets of the parties come together. We then study local state discrimination protocols for several such bases with additional entangled resources shared among the parties. Apart from consuming less entanglement than teleportation-based schemes, our protocols indicate operational significance of the proposed classification and exhibit nontrivial use of genuine entanglement in the local state discrimination problem.

The standard approach to realize a quantum repeater relies upon probabilistic but heralded entangled state manipulations and the storage of quantum states while waiting for successful events. In the literature on this class of repeaters, calculating repeater rates has typically depended on approximations assuming sufficiently small probabilities. Here we propose an exact and systematic approach including an algorithm based on Markov chain theory to compute the average waiting time (and hence the transmission rates) of quantum repeaters with arbitrary numbers of links. For up to four repeater segments, we explicitly give the exact rate formulas for arbitrary entanglement swapping probabilities. Starting with three segments, we explore schemes with arbitrary (not only doubling) and dynamical (not only predetermined) connections. The effect of finite memory times is also considered and the relative influence of the classical communication (of heralded signals) is shown to grow significantly for larger probabilities. Conversely, we demonstrate that for small swapping probabilities the statistical behavior of the waiting time in a quantum repeater cannot be characterized by its average value alone and additional statistical quantifiers are needed. For large repeater systems, we propose a recursive approach based on exactly but still efficiently computable waiting times of sufficiently small subrepeaters. This approach leads to better lower bounds on repeater rates compared to existing schemes.

The three-loop contributions to the Lamb shift of the $1s$ state in the hydrogen atom in order ${\alpha }^3{\left(Z\alpha \right)}^{5}m$, responsible for the second largest contribution to the uncertainty budget, have been known only partially. Here we estimate the remaining three-loop terms of that order. The total three-loop result in order ${\alpha }^3{\left(Z\alpha \right)}^{5}m$ for the $1s$ Lamb shift is found to be $-(3.3\pm 10.5){(\alpha /\pi )}^3{\left(Z\alpha \right)}^{5}m$, which contributes $-0.11\left(34\right)\mathrm{kHz}$ to the energy of the ground state in the hydrogen atom and $-3\left(11\right)\mathrm{kHz}$ in the helium ion. To verify our approach we have also estimated the known contributions in order $\alpha {\left(Z\alpha \right)}^{5}m$ and ${\alpha }^2{\left(Z\alpha \right)}^{5}m$. The obtained estimates are perfectly consistent with the well established results, found previously by other authors.

We report on the investigation of endothermic and nearly thermoneutral atom-exchange collisions in an ultracold atom-dimer mixture. By developing an indirect preparation method based on a molecular bound-bound transition, we are able to directly observe an endothermic collision with a tunable energy threshold and study the state-to-state collision dynamics. The collision rate coefficients show a striking threshold phenomenon. The influence of the reverse process on the collision dynamics is observed for the endothermic and nearly thermoneutral collisions. We carry out zero-range quantum-mechanical scattering calculations to obtain the collision rate coefficients, and the three-body parameter is determined by comparison with the experiments. The observed endothermic and nearly thermoneutral collisions may be employed to implement quantum simulation of the Kondo effect with ultracold molecules.

We have measured and calculated fully differential cross sections (FDCS) for ionization of helium by 75-keV proton impact. Ejected electrons with a speed close to and above the projectile speed were investigated. This range of kinematics represents a largely unexplored regime. A high sensitivity of the FDCS to the details of the description of the few-body dynamics, reported earlier for ionization of ${\mathrm{H}}_2$, was confirmed. A peak structure was found in an electron angular range between the regions where the so-called binary and recoil peaks are usually observed. The need for nonperturbative calculations using a two-center basis set is demonstrated.

We study interaction quenches of the Fermi-Hubbard model initiated from various high-temperature and high-energy states, motivated by cold atom experiments, which currently operate above the ordering temperature(s). We analytically calculate the dynamics for quenches from these initial states, which are often strongly interacting, to the noninteracting limit. Even for high-temperature uncorrelated initial states, transient connected correlations develop. These correlations share many features for all considered initial states. We observe light-cone spreading of intertwined spin and density correlations. The character of these correlations is quite different from their low-temperature equilibrium counterparts: for example, the spin correlations can be ferromagnetic. We also show that an initially localized hole defect affects spin correlations near the hole, suppressing their magnitude and changing their sign.

We demonstrate the existence of a type of spatially localized excitations in the unitary Fermi gas: spin-polarized droplets with a peculiar internal structure involving an abrupt change in the pairing phase at the surface of the droplet. It resembles the structure of the Josephson-$\pi$ junction occurring when a slice of a ferromagnet is sandwiched between two superconductors. The stability of the impurity is enhanced by the mutual interplay between the polarization effects and the pairing field, resulting in an exceptionally long-lived state. The prospects for its realization in experiments are discussed.