We describe a methodology and standard of proof for experimental claims of quantum random-number generation (QRNG), analogous to well-established methods from precision measurement. For appropriately constructed physical implementations, lower bounds on the quantum contribution to the average min-entropy can be derived from measurements on the QRNG output. Given these bounds, randomness extractors allow generation of nearly perfect “$\epsilon$-random” bit streams. An analysis of experimental uncertainties then gives experimentally derived confidence levels on the $\epsilon$ randomness of these sequences. We demonstrate the methodology by application to phase-diffusion QRNG, driven by spontaneous emission as a trusted randomness source. All other factors, including classical phase noise, amplitude fluctuations, digitization errors, and correlations due to finite detection bandwidth, are treated with paranoid caution, i.e., assuming the worst possible behaviors consistent with observations. A data-constrained numerical optimization of the distribution of untrusted parameters is used to lower bound the average min-entropy. Under this paranoid analysis, the QRNG remains efficient, generating at least 2.3 quantum random bits per symbol with 8-bit digitization and at least 0.83 quantum random bits per symbol with binary digitization at a confidence level of 0.999 93. The result demonstrates ultrafast QRNG with strong experimental guarantees.

Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental systems are typically limited to restricted forms of two-body interactions. Therefore, universal adiabatic quantum computation requires a method for approximating quantum many-body Hamiltonians up to arbitrary spectral error using at most two-body interactions. Hamiltonian gadgets, introduced around a decade ago, offer the only current means to address this requirement. Although the applications of Hamiltonian gadgets have steadily grown since their introduction, little progress has been made in overcoming the limitations of the gadgets themselves. In this experimentally motivated theoretical study, we introduce several gadgets which require significantly more realistic control parameters than similar gadgets in the literature. We employ analytical techniques which result in a reduction of the resource scaling as a function of spectral error for the commonly used subdivision, three- to two-body and $k$-body gadgets. Accordingly, our improvements reduce the resource requirements of all proofs and experimental proposals making use of these common gadgets. Next, we numerically optimize these gadgets to illustrate the tightness of our analytical bounds. Finally, we introduce a gadget that simulates a $YY$ interaction term using Hamiltonians containing only $\{X,Z,XX,ZZ\}$ terms. Apart from possible implications in a theoretical context, this work could also be useful for a first experimental implementation of these key building blocks by requiring less control precision without introducing extra ancillary qubits.

Bound and resonance states of the dipole-bound anion of hydrogen cyanide ${\mathrm{HCN}}^{-}$ are studied using a nonadiabatic pseudopotential method and the Berggren expansion technique involving bound states, decaying resonant states, and nonresonant scattering continuum. We devise an algorithm to identify the resonant states in the complex energy plane. To characterize spatial distributions of electronic wave functions, we introduce the body-fixed density and use it to assign families of resonant states into collective rotational bands. We find that the nonadiabatic coupling of electronic motion to molecular rotation results in a transition from the strong-coupling to weak-coupling regime. In the strong-coupling limit, the electron moving in a subthreshold, spatially extended halo state follows the rotational motion of the molecule. Above the ionization threshold, the electron's motion in a resonance state becomes largely decoupled from molecular rotation. The widths of resonance-band members depend primarily on the electron orbital angular momentum.

We study a hybrid quantum system composed of an ion and an electric dipole. We show how a trapped ion can be used to measure the small electric field generated by a classical dipole. We discuss the application of this scheme to measure the electric dipole moment of cold polar molecules, whose internal state can be controlled with ultrafast laser pulses, by trapping them in the vicinity of a trapped ion.

The triple differential cross section for ionization of the inert gases He, Ne, Ar, Kr, and Xe in energy-sharing perpendicular plane geometry is investigated. Encouraging agreement with recent experiments is found using the distorted-wave Born approximation (DWBA). Mechanisms are discussed which explain the He and Ne data but which seem to be masked by the greater distortion effects in the heavier targets. The inclusion of postcollisional interaction is explored using Gamow, $N_{ee}$, and Ward-Macek, $M_{ee}$, factors. While both help to improve the shape of the cross section for He and Ne at the lower energies, they are not successful for the other targets, and both factors prove to be too strong for all the inert gases with increasing impact energy. It is well known that $N_{ee}$ destroys normalization. Comparing DWBA $+M_{ee}$ results with some absolute experimental points at 1 and 2 eV indicates that it is also not to be trusted on normalization. An interesting situation with Ar is highlighted near 25 eV, where the cross section may be tending towards a strong interference minimum or zero.

Supersolid is a long-sought exotic phase of matter, which is characterized by the coexistence of a diagonal long-range order of solid and an off-diagonal long-range order of superfluid. Possible candidates to realize such a phase have been previously considered, including hard-core bosons with long-range interaction and soft-core bosons. Here we demonstrate that an ultracold atomic condensate of hard-core bosons with contact interaction can establish a supersolid phase when simultaneously subjected to spin-orbit coupling and a spin-dependent periodic potential. This supersolid phase is accompanied by topologically nontrivial spin textures, and is signaled by the separation of momentum distribution peaks, which can be detected via time-of-flight measurements. We also discuss possibilities to produce and observe the supersolid phase for realistic experimental situations.

We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice in a Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low-energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight, and effective impurity mass. The divergence of the effective mass in the low-energy limit gives rise to a power-law singularity in the impurity spectral function and provides an example of an emergent orthogonality catastrophe in a bosonic system.

In Bose-Einstein condensates with an attractive contact interaction the stable ground state and an unstable excited state emerge in a tangent bifurcation at a critical value of the scattering length. At the bifurcation point both the energies and the wave functions of the two states coalesce, which is the characteristic of an exceptional point. In numerical simulations signatures of the exceptional point can be observed by encircling the bifurcation point in the complex extended space of the scattering length, however, this method cannot be applied in an experiment. Here we show in which way the exceptional point effects the collapse dynamics of the Bose-Einstein condensate. The harmonic inversion analysis of the time signal given as the spatial extension of the collapsing condensate wave function can provide clear evidence for the existence of an exceptional point. This method can be used for an experimental verification of exceptional points in Bose-Einstein condensates.

We investigate the phase structure of spin-imbalanced unitary Fermi gases beyond mean-field theory by means of the functional renormalization group. In this approach, quantum and thermal fluctuations are resolved in a systematic manner. The discretization of the effective potential on a grid allows us to accurately account for both first- and second-order phase transitions that are present on the mean-field level. We compute the full phase diagram in the plane of temperature and spin imbalance and discuss the existence of other conjectured phases such as the Sarma phase and a precondensation region. In addition, we explain on a qualitative level how we expect that in situ density images are affected by our findings and which experimental signatures may potentially be used to probe the phase structure.

We introduce a detector that selectively probes the phononic excitations of a cold Bose gas. The detector is composed of a single impurity atom confined by a double-well potential, where the two lowest eigenstates of the impurity form an effective probe qubit that is coupled to the phonons via density-density interactions with the bosons. The system is analogous to a two-level atom coupled to photons of the radiation field. We demonstrate that tracking the evolution of the qubit populations allows probing both thermal and coherent excitations in targeted phonon modes. The targeted modes are selected in both energy and momentum by adjusting the impurity's potential. We show how to use the detector to observe coherent density waves and to measure temperatures of the Bose gas down to the nanokelvin regime. We analyze how our scheme could be realized experimentally, including the possibility of using an array of multiple impurities to achieve greater precision from a single experimental run.

We propose an all-optical antiwaveguide mechanism for steering, splitting, and cloning of an optical beam without diffraction. We use a spatially inhomogeneous pump beam to create an antiwaveguide structure in a Doppler broadened $\mathcal{N}$-type four-level Raman gain medium for a copropagating weak probe beam. We show that a transverse modulated index of refraction and gain due to the spatially dependent pump beam hold the keys to steering, splitting, and cloning of an optical beam. We have also shown that an additional control field permits the propagation of an optical beam through an otherwise gain medium without diffraction and instability. We further discuss how finesse of the cloned images can be increased by changing the detuning of the control field. We arrive at similar results by using homogeneously broadened gain media at higher density.

Wigner's argument inferring a Bell-type inequality for the Einstein–Podolsky–Rosen–Bohm entangled state is generalized here for any $N$-partite state. This is based on assuming for the relevant dichotomic observables the existence of the overall joint probability distributions, satisfying the locality condition, which would yield the measurable marginal probabilities. For any $N$, such a generalized Wigner inequality (GWI) is violated by quantum mechanics for all pure entangled states. The efficacy of GWI is probed, comparing with the Seevinck–Svetlichny multipartite Bell-type inequality, by calculating threshold visibilities for the quadripartite Greenberger–Horne–Zeilinger, Cluster, and $W$ states that determine their respective robustness with respect to the quantum-mechanical violation of GWI in the presence of white noise.

We propose an implementation scheme of a frequency-domain quantum computation (FDQC) to avoid major gate errors accompanying the computation. The FDQC is a way to implement many solid-state qubits defined in a frequency domain without distinction of their positions. The FDQC has some gate errors due to unwanted effects of operation lights on qubits. We investigate conditions to perform gates suppressing the errors using a model of the FDQC with the unwanted interactions. Consequently, we find a scheme to selectively manipulate many qubits using the FDQC.

We study maximally entangled states and fully entangled fraction in general $d^{\prime }\otimes d$ ($d^{\prime }\ge d$) systems. Necessary and sufficient conditions for maximally entangled pure and mixed states are presented. As a natural generalization of the usual fully entangled fraction for $d\otimes d$ systems, we define the maximal overlap between a given quantum state and the maximally entangled states as the fully entangled fraction in $d^{\prime }\otimes d$ systems. The properties of this fully entangled fraction and its relations to quantum teleportation have been analyzed. The witness for detecting maximally entangled states and quantum states that are useful for quantum teleportation is provided.

In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground-state eigenvalue problems known as the Feynman-Kitaev clock Hamiltonian. A prominent family of methods for the study of quantum ground states is quantum Monte Carlo methods, and recently the full configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated great promise for practical systems. We combine the Feynman-Kitaev clock Hamiltonian with FCIQMC to formulate a technique for the study of quantum dynamics problems. Numerical examples using quantum circuits are provided as well as a technique to further mitigate the sign problem through time-dependent basis rotations. Moreover, this method allows one to combine the parallelism of Monte Carlo techniques with the locality of time to yield an effective parallel-in-time simulation technique.

Based on the measurement of quantum correlation functions, the quantum statistical properties of spectral measurements are studied for broadband radiation fields. The spectral filtering of light before its detection is compared with the direct detection followed by the spectral analysis of the recorded photocurrents. As an example, the squeezing spectra of the atomic resonance fluorescence are studied for both types of filtering procedures. The conditions for which the detection of the nonclassical signatures of the radiation is possible are analyzed. For the considered example, photocurrent filtering appears to be the superior option to detect nonclassicality due to the vacuum-noise effects in the optical filtering.

It is widely believed that surface plasmon polaritons (SPPs) at flat metal surfaces cannot be directly excited by free-space lights due to momentum mismatch. Here we propose a way to resonantly excite SPPs by lights without using any coupler and propose a kind of surface-plasmon-resonance (SPR) system which can be simply composed by a metal film and a bottom medium whose real part of permittivity is less than unity. A light, which is incident from vacuum or air to the upper surface of the metal film, can directly excite a SPP at the lower surface of the metal film. Some special media can be selected as the bottom medium, including atomic vapor of electromagnetically induced transparency (EIT) and some special solid media. In the atomic EIT case, the steep dispersion at the transparent window can lead to interesting phenomena; e.g., very slow directional moving of the EIT atoms can lead to unidirectional SPPs (reverse-propagating SPP modes do not exist) and therefore lead to a highly asymmetric SPR angle spectrum which is very sensitive to the velocity of the atoms. We also present feasible and simple designs of all-solid-state coupler-free SPR systems, which are simply composed by a titanium film and a substrate of amorphous aluminum oxide or silicon oxide.

Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts toward realizing nonlinear behavior at the single-photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new figure of merit for realizing strong nonlinearity which scales with the single-photon optomechanical coupling and the sideband resolution of the mechanical mode with respect to the cavity linewidth. We find that current devices based on optomechanical crystals, thought to be in the weak-coupling regime, may be able to achieve strong quantum nonlinearity, enabling deterministic interactions between single photons.