The application of quantum estimation theory to the problem of imaging two incoherent point sources has recently led to new insights and better measurements for incoherent imaging and spectroscopy. To establish a more general limit beyond the case of two sources, here I evaluate a quantum bound on the Fisher information that can be extracted by any far-field optical measurement about the moments of a subdiffraction object. The bound matches the performance of a spatial-mode-demultiplexing (SPADE) measurement scheme in terms of its scaling with the object size, indicating that SPADE is close to quantum-optimal. Coincidentally, the result is also applicable to the estimation of diffusion parameters with a quantum probe subject to random displacements.

Rayleigh's criterion states that it becomes essentially difficult to resolve two incoherent optical point sources separated by a distance below the width of point spread functions (PSFs), namely, in the subdiffraction limit. Recently, researchers have achieved superresolution for two incoherent point sources with equal strengths, surpassing Rayleigh's criterion. However, situations where more than two point sources needed to be resolved have not been fully investigated. Here we prove that for any incoherent sources with arbitrary strengths, a one- or two-dimensional (1D or 2D) image can be precisely resolved up to its second moment in the subdiffraction limit, i.e., the Fisher information (FI) is nonzero. But the FI with respect to higher order moments always tends to zero polynomially as the size of the image decreases, for any type of nonadaptive measurement. We call this phenomenon a modern description of Rayleigh's criterion. For PSFs under certain constraints, the optimal measurement basis estimating all moments in the subdiffraction limit for 1D weak-source imaging is constructed. Such a basis also generates the optimal-scaling FI with respect to the size of the image for 2D or strong-source imaging, which achieves an overall quadratic improvement compared to direct imaging.

We consider a weakly interacting uniform atomic Bose gas with a time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov treatment we investigate the time evolution of several observables, including the momentum distribution, the degree of coherence in the system, and their dependence on dimensionality and temperature. We rigorously prove that the low-momentum Bogoliubov modes remain frozen during the whole evolution, while the high-momentum ones adiabatically follow the change in time of the interaction strength. At intermediate momenta we point out the occurrence of oscillations, which are analogous to Sakharov oscillations. We identify two wide classes of time-dependent behaviors of the coupling for which an exact solution of the problem can be found, allowing for an analytic computation of all the relevant observables. A special emphasis is put on the study of the coherence property of the system in one spatial dimension. We show that the system exhibits a smooth “light-cone effect,” with typically no prethermalization.

We use tensor network methods—matrix product states, tree tensor networks, and locally purified tensor networks—to simulate the one-dimensional Bose-Hubbard model for zero and finite temperatures in experimentally accessible regimes. First we explore the effect of thermal fluctuations on the system ground state by characterizing its Mott and superfluid features. Then we study the behavior of the out-of-equilibrium dynamics induced by quenches of the hopping parameter. We confirm a Kibble-Zurek scaling for zero temperature and characterize the finite-temperature behavior, which we explain by means of a simple argument.

We present the experimental control of non-Markovian dynamics of open quantum systems simulated with photonic entities. The polarization of light is used as the system, whereas the surrounding environment is represented by light's spatial structure. The control of the dynamics is achieved by the engineering of the environment via spatial interference. Using the behavior of the trace distance, we are able to identify each dynamics and characterize the position of maximum revival of information.

We present two-photon photoassociation to the least-bound vibrational level of the $X{}^1\mathrm{\Sigma }_g^{+}$ electronic ground state of the ${}^{86}\mathrm{Sr}_2$ dimer and measure a binding energy of $E_b=-83.00\left(7\right)\left(20\right)\mathrm{kHz}$. Because of the very small binding energy, this is a halo state corresponding to the scattering resonance for two ${}^{86}\mathrm{Sr}$ atoms at low temperature. The measured binding energy, combined with universal theory for a very weakly bound state on a potential that asymptotes to a van der Waals form, is used to determine an $s$-wave scattering length $a=810.6\left(3\right)\left(9\right)a_0$, which is consistent with, but substantially more accurate than, the previously determined $a=798\left(12\right)a_0$ found from mass scaling and precision spectroscopy of other Sr isotopes. For the intermediate state, we use a bound level on the metastable ${}^{1}S_0\text{−}{}^{3}P_1$ potential. Large sensitivity of the dimer binding energy to light near resonant with the bound-bound transition to the intermediate state suggests that ${}^{86}\mathrm{Sr}$ has great promise for manipulating atom interactions optically and probing naturally occurring Efimov states.

We report on the experimental realization of ultracold ${}^{174}\mathrm{Yb}-{}^7\mathrm{Li}$ (boson-boson) and ${}^{173}\mathrm{Yb}-{}^7\mathrm{Li}$ (fermion-boson) mixtures. They are loaded into three-dimensional (3D) or one-dimensional (1D) optical lattices that are species-selectively deep for the heavy ytterbium (Yb) and shallow for the light bosonic lithium (Li) component, realizing novel mixed dimensional systems. In the 1D optical lattice the band structure of ${}^{173}\mathrm{Yb}$ is reconstructed in the presence of ${}^7\mathrm{Li}$. Spectroscopic measurements of the ${}^{174}\mathrm{Yb}-{}^7\mathrm{Li}$ mixture in the 3D lattice give access to the ${}^{174}\mathrm{Yb}$ Mott-insulator structure. Ground-state interspecies scattering lengths are determined to be $|a_{\mathrm{bg}}({}^{174}\mathrm{Yb}-{}^7\mathrm{Li})|=(1.11\pm 0.17)\mathrm{nm}$ and $|a_{\mathrm{bg}}({}^{173}\mathrm{Yb}-{}^7\mathrm{Li})|=(1.16\pm 0.18)\mathrm{nm}$. The formation and characterization of an ultracold ${}^{173}\mathrm{Yb}-{}^7\mathrm{Li}$ mixture is a first step toward a possible realization of a topological $p_x+i{p}_y$ superfluid in this system.

Almost 10 years ago, energetic neutral hydrogen atoms were detected after a strong-field double ionization of ${\mathrm{H}}_2$. This process, called “frustrated tunneling ionization,” occurs when an ionized electron is recaptured after being driven back to its parent ion by the electric field of a femtosecond laser. In the present study we demonstrate that a related process naturally occurs in clusters without the need of an external field: we observe a charge hopping that occurs during a Coulomb explosion of a small helium cluster, which leads to an energetic neutral helium atom. This claim is supported by theoretical evidence. As an analog to frustrated tunneling ionization, we term this process “frustrated Coulomb explosion.”

Multipartite quantum entanglement serves as a resource for spatially separated parties performing distributed quantum information processing. Any multipartite entangled state can be generated from appropriately distributed bipartite entangled states by local operations and classical communication (LOCC), and in this sense, any distributed process based on shared multipartite entanglement and LOCC is simulatable by using only bipartite entangled states and LOCC. We show here that this reduction scenario does not hold when there exists a limitation on the size of the local quantum system of each party. Under such a limitation, we prove that there exists a set of multipartite quantum states such that these states in the set cannot be prepared from any distribution of bipartite entanglement, while the states can be prepared from a common resource state exhibiting multipartite entanglement. We also show that temporal uses of bipartite quantum communication resources within a limitation of local system sizes are sufficient for preparing this common resource state exhibiting multipartite entanglement, yet there also exist other states exhibiting multipartite entanglement which cannot be prepared even in this setting. Hence, when the local quantum system sizes are limited, multipartite entanglement is an indispensable resource without which certain processes still cannot be accomplished.

We propose a method for the detection and characterization of nuclear decay processes. Specifically, we describe how nuclear decay recoil can be observed within small particles levitated in an optical trap with high positional resolution. Precise measurements of the magnitude of each recoil as well as their rate of occurrence can provide accurate information about the isotopic composition of a radioactive sample. We expect that this technique for nuclear material characterization will be especially useful in the area of nuclear forensic analysis.

Stationary solitary waves are studied in an array of $M$ linearly coupled one-dimensional Bose-Einstein condensates (BECs) by means of the Gross-Pitaevskii equation. Solitary wave solutions with the character of overlapping dark solitons, Josephson vortex-antivortex arrays, and arrays of half-dark solitons are constructed for $M>2$ from known solutions for two coupled BECs. Additional solutions resembling vortex dipoles and rarefaction pulses are found numerically. Stability analysis of the solitary waves reveals that overlapping dark solitons can become unstable and susceptible to decay into arrays of Josephson vortices. The Josephson vortex arrays have mixed stability but for all parameters we find at least one stationary solitary wave configuration that is dynamically stable. The different families of nonlinear standing waves bifurcate from one another. In particular we demonstrate that Josephson-vortex arrays bifurcate from dark soliton solutions at instability thresholds. The stability thresholds for dark soliton and Josephson-vortex type solutions are provided, suggesting the feasibility of realization with optical lattice experiments.

A quantum emitter coupled to an optical bimodal cavity in the solid-state implementation has recently proven to be an excellent platform for coherent generation of nonclassical light on a chip. However, the impacts of the structural couplings between the photonic modes via different arrangements of optical cavity and waveguide are rarely considered. Here, we explore in detail the characteristics of the photon antibunching in bimodal cavity quantum electrodynamics (QED) via taking into account two different cavity-waveguide arrangements: (i) an inline geometry and (ii) a side-coupled geometry. In our scheme, both cavity modes are simultaneously coupled to a two-level emitter but are not directly coupled to each other, owing to their orthogonal polarizations. It is clearly shown that the quality of the photon antibunching in the bimodal cavity QED, namely, the smallness of the second-order intensity correlation function at zero time, is closely related to the cavity-waveguide arrangements. The optimal photon antibunching can be achieved in the side-coupled geometry and the antibunching quality is about two orders of magnitude lower than that in the inline geometry. This enhancement of the photon antibunching is ascribed to the combination of two kinds of quantum interference effects in the waveguide-cavity QED system. We also find that the side-coupled architecture can make the device robust against the frequency mismatch between the two cavity modes, as compared to the inline geometry. In addition, we find that this mismatch can be used to generate better antibunching. The realization of our proposal with existing cavity-waveguide QED architectures is also discussed.

The 100-year-long problem concerning the correct form of the electromagnetic energy-momentum tensor in continuous media (usually called the Abraham-Minkowski problem) continues to attract interest. Here we provide a critical analysis of interpretations presented in the literature on this topic recently, in two cases—one real experiment on radiation pressure A. Kundu et al., Sci. Rep. 7, 42538 (2017), and one computer experiment M. Partanen et al., Phys. Rev. A 95, 063850 (2017).

We have investigated rovibronic levels of the strongly mixed $b{}^3\mathrm{\Pi }_1–c{}^3\mathrm{\Sigma }_1^{+}–B{}^1\mathrm{\Pi }_1$ states [the 2(1), 3(1), and 4(1) states in Hund's case (c) notation] of ${}^{85}\mathrm{Rb}{}^{133}\mathrm{Cs}$ in the energy range of 13 950–14 200 ${\mathrm{cm}}^{-1}$ using short-range photoassociation (PA). For selected PA states, vibrational and rotational branching in the $X{}^1{\mathrm{\Sigma }}^{+}$ state have been investigated using resonance-enhanced multiphoton ionization and depletion spectroscopy. Efficient production of ${}^{85}\mathrm{Rb}{}^{133}\mathrm{Cs}$ molecules in the rovibronic-ground-state $X{}^1{\mathrm{\Sigma }}^{+}$ ($v=0, J=0$), at up to $\sim 1\times {10}^4$ molecules/s, has been achieved.

Quantum computing allows for the potential of significant advancements in both the speed and the capacity of widely used machine learning techniques. Here we employ quantum algorithms for the Hopfield network, which can be used for pattern recognition, reconstruction, and optimization as a realization of a content-addressable memory system. We show that an exponentially large network can be stored in a polynomial number of quantum bits by encoding the network into the amplitudes of quantum states. By introducing a classical technique for operating the Hopfield network, we can leverage quantum algorithms to obtain a quantum computational complexity that is logarithmic in the dimension of the data. We also present an application of our method as a genetic sequence recognizer.

We show that the contact parameter of $N$ harmonically trapped interacting one-dimensional bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that $N$-body effects can be almost factorized. The small deviations observed between our analytical results and density matrix renormalization group (DMRG) calculations are more pronounced when the interaction energy is maximal (i.e., at intermediate interaction strengths) but they remain bounded by the large-$N$ local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe ansatz. The rescaled two-body solution is so close to the exact ones, that is possible, within a simple expression interpolating the rescaled two-boson result to the local density, to obtain $N$-boson contact and ground-state energy functions in very good agreement with DMRG calculations. Our results suggest a change of paradigm in the study of interacting quantum systems, giving to the contact parameter a more fundamental role than energy.

At ultralow energies, atoms and molecules undergo collisions and reactions that are best described in terms of quantum-mechanical wave functions. In contrast, at higher energies these processes can be understood quasiclassically. Here, we investigate the crossover from the quantum-mechanical to the quasiclassical regime both experimentally and theoretically for photodissociation of ultracold diatomic strontium molecules. This basic reaction is carried out with a full control of quantum states for the molecules and their photofragments. The photofragment angular distributions are imaged and calculated by using a quantum-mechanical model as well as the Wenzel–Kramers–Brillouin approximation and a semiclassical approximation that are explicitly compared across a range of photofragment energies. The reaction process is shown to converge to its high-energy (axial-recoil) limit when the energy exceeds the height of any reaction barriers. This phenomenon is quantitatively investigated for two-channel photodissociation by using intuitive parameters for the channel amplitude and phase. While the axial-recoil limit is generally found to be well described by a commonly used quasiclassical model, we find that when the photofragments are identical particles, their bosonic or fermionic quantum statistics can cause this model to fail, requiring a quantum-mechanical treatment even at high energies.

Because molecules can have their orientation locked when embedded into a solid rare-gas matrix, their hyperfine structure is strongly perturbed relative to the freely rotating molecule. The addition of an electric field further perturbs the structure, and we have found an interesting effect: the Stark shift of the hyperfine states in these molecules depends on the molecular orientation. These shifts enable the selective detection of molecules with different orientations relative to the axes of a rare-gas crystal, which will be an important ingredient of an improved electron electric dipole moment measurement using large ensembles of polar molecules trapped in rare-gas matrices. We outline an experimental procedure exploiting the orientation-dependent detection, which could be used for a significantly improved measurement of the electron electric dipole moment.

For light-intensity-correlation measurements, different methods are used in the high-photon-number or high-intensity regime and in the single- and two-photon regime. Hence, there is an unfortunate measurement “gap” primarily for multiphoton, quantum states. These states, for example, multiphoton Fock states, will be increasingly important in the realization of quantum technologies and in exploring the boundaries between quantum and classical optics. We show that a naïve approach based on attenuation, state splitting, and two-detector correlation can give the correct two-time intensity correlation for any state. We analyze how added losses decrease the measurement systematic error. The price to be paid is that the losses increase the measurement statistical error or, alternatively, increase the acquisition time for a given tolerable level of statistical error. We have experimentally demonstrated the feasibility of the method for a coherent state and a quasithermal state. The method is easy to implement in any laboratory and will simplify characterization of medium and highly excited nonclassical states as they become experimentally available.

With this work we start a project calculating the QED contribution of order ${\alpha }^{7}m$ to the $2{}^{3}P–2{}^{3}S$ transition energy in helium, aiming for an accurate determination of the nuclear charge radius $r_E$ from measurements of the corresponding transition frequency. Together with the complementary determination of $r_E$ from muonic helium, this project will provide a stringent test of universality of electromagnetic interactions of leptons in the Standard Model. We report a calculation of the relativistic corrections to the Bethe logarithm for the $2{}^{3}S$ and $2{}^{3}P$ states, which is the most numerically demanding part of the project.