We study steady-state continuous-variable entanglement in a three-mode optomechanical system consisting of an active optical cavity (gain) coupled to a passive optical cavity (loss) supporting a mechanical mode. For a driving laser which is blue-detuned, we show that coupling between optical and mechanical modes is enhanced in the unbroken-$\mathcal{PT}$-symmetry regime. We analyze the stability and this shows that steady-state solutions are more stable in the gain and loss systems. We use these stable solutions to generate distant entanglement between the mechanical mode and the optical field inside the gain cavity. It results in a giant enhancement of entanglement compared to what is generated in the single lossy cavity. This work offers the prospect of exploring quantum state engineering and quantum information in such systems. Furthermore, such entanglement opens up an interesting possibility to study spatially separated quantum objects.

We study the cooperative optical coupling between regularly spaced atoms in a one-dimensional waveguide using decompositions to subradiant and super-radiant collective excitation eigenmodes, direct numerical solutions, and analytical transfer-matrix methods. We illustrate how the spectrum of transmitted light through the waveguide, including the emergence of narrow Fano resonances, can be understood by the resonance features of the eigenmodes. We describe a method based on super-radiant and subradiant modes to engineer the optical response of the waveguide and to store light. The stopping of light is obtained by transferring an atomic excitation to a subradiant collective mode with the zero radiative resonance linewidth by controlling the level shift of an atom in the waveguide. Moreover, we obtain an exact analytic solution for the transmitted light through the waveguide for the case of a regular lattice of atoms and provide a simple description of how the light transmission may present large resonance shifts when the lattice spacing is close, but not exactly equal, to half of the wavelength of the light. Experimental imperfections such as fluctuations of the positions of the atoms and loss of light from the waveguide are easily quantified in the numerical simulations, which produce the natural result that the optical response of the atomic array tends toward the response of a gas with random atomic positions.

In studying the dynamics of slow light and light storage in a Doppler-broadened electromagnetically-induced-transparency medium, Su et al. [Phys. Rev. A 83, 013827 (2011)] simply included the damping rate of the system into the Schrödinger equation without considering the accompanying quantum jump processes, whose results therefore are prone to be incorrect.

Characterization of nonlocal correlations is one of the most attractive topics in quantum information theory. In this work, we develop the methods of detecting entanglement and steering based on the universal uncertainty relations and fine-grained uncertainty relations. According to the majorization form of the uncertainty relations, the uncertainty quantifier can be constructed by choosing Schur concave functions. Hence a large number of quantifier-independent entanglement and steering criteria are derived, from which many existing criteria based on different quantifiers can be rededuced. Finally, we show that entanglement and steering of pure states and some mixed states such as isotropic states can be always witnessed by some uncertainty quantifier.

The Casimir force between macroscopic bodies is well understood, but not the Casimir force inside bodies. Guided by a physically intuitive picture, we develop the macroscopic theory of the renormalized Casimir stress inside planar materials (where the electromagnetic properties vary in one direction). Our theory may be applied in predicting how inhomogeneous fluids respond to Casimir forces.

Measurement is of central interest in quantum mechanics as it provides the link between the quantum world and the world of everyday experience. One of the features of everyday experience is its robust, objective character, contrasting the delicate nature of quantum systems. Here we analyze in a completely model-independent way the celebrated von Neumann measurement process, using recent techniques of information flow, studied in open quantum systems. We show the generic appearance of objective results in quantum measurements, provided we macroscopically coarse-grain the measuring apparatus and wait long enough. To study genericity, we employ the widely used Gaussian unitary ensemble of random matrices and the Hoeffding inequality. We derive generic objectivization time scales, given solely by the interaction strength and the systems' dimensions. Our results are manifestly universal and are a generic property of von Neumann measurements.

We bring a Bayesian approach to the analysis of clocks. Using exponential distributions as priors for clocks, we analyze how well one can keep time with a single qubit freely precessing under a magnetic field. We find that, at least with a single qubit, quantum mechanics does not allow exact timekeeping, in contrast to classical mechanics, which does. We find the design of the single-qubit clock that leads to maximum accuracy. Further, we find an energy versus accuracy tradeoff—the energy cost is at least $k_{B}T$ times the improvement in accuracy as measured by the entropy reduction in going from the prior distribution to the posterior distribution. We propose a physical realization of the single-qubit clock using charge transport across a capacitively coupled quantum dot.

In most communication scenarios, sending a symbol encoded in a quantum state requires spending resources such as energy, which can be quantified by a cost of communication. A standard approach in this context is to quantify the performance of communication protocol by classical capacity, quantifying the maximal amount of information that can be transmitted through a quantum channel per single use of the channel. However, different figures of merit are also possible and a particularly well-suited one is the classical capacity per unit cost, which quantifies the maximal amount of information that can be transmitted per unit cost. I generalize this concept to account for the quantum nature of the information carriers and communication channels and show that if there exists a state with cost equal to zero, e.g., a vacuum state, the capacity per unit cost can be expressed by a simple formula containing maximization of the relative entropy between two quantum states. This enables me to analyze the behavior of photon information efficiency for general communication tasks and show simple bounds on the capacity per unit cost in terms of quantities familiar from quantum estimation theory. I calculate also the capacity per unit cost for general Gaussian quantum channels.

We present a $\left[\right[7,1,3\left]\right]$ quantum error-correcting code that is able to achieve fault-tolerant syndrome measurement using one ancillary qubit per stabilizer for an error model of independent single-qubit Pauli errors. All single-qubit Pauli errors on the ancillary qubits propagate to form exclusively correctable errors on the data qubits. The situation changes for error models with two-qubit Pauli errors. We compare the level-1 logical error rates under two noise models: the standard Pauli symmetric depolarizing error model and an anisotropic error model. The anisotropic model is motivated by control errors on two-qubit gates commonly applied to trapped ion qubits. We find that one ancillary qubit per syndrome measurement is sufficient for fault-tolerance for the anisotropic error, but is not sufficient for the standard depolarizing errors. We then show how to achieve fault tolerance for the standard depolarizing errors by adding flag qubits to check for errors on select ancillary qubits. Our results on this $\left[\right[7,1,3\left]\right]$ code demonstrates how physically motivated noise models may simplify fault-tolerant protocols.

Precision calculations of the fine and hyperfine structure of muonic atoms are performed in a relativistic approach and results for muonic ${}^{205}\mathrm{Bi}, {}^{147}\mathrm{Sm}$, and ${}^{89}\mathrm{Zr}$ are presented. The hyperfine structure due to magnetic dipole and electric quadrupole splitting is calculated in first-order perturbation theory, using extended nuclear charge and current distributions. The leading correction from quantum electrodynamics, namely vacuum polarization in Uehling approximation, is included as a potential directly in the Dirac equation. Also, an effective screening potential due to the surrounding electrons is calculated, and the leading relativistic recoil correction is estimated.

We propose a scheme to efficiently tune the scattering length of two colliding ground-state atoms by off-resonantly coupling the scattering state to an excited Rydberg molecular state using laser light. For the $s$-wave scattering of two colliding ${}^{87}\mathrm{Rb}$ atoms, we demonstrate that the effective optical length and pole strength of this Rydberg optical Feshbach resonance can be tuned over several orders of magnitude, while incoherent processes and losses are minimized. Given the ubiquity of Rydberg molecular states, this technique should be generally applicable to homonuclear atomic pairs as well as to atomic mixtures with $s$-wave (or even $p$-wave) scattering.

Criteria defining higher-order sub-Poissonian-like fields are given using five different quantities: moments of (I) integrated intensity, (II) photon number, (III) integrated-intensity fluctuation, (IV) photon-number fluctuation, and (V) elements of photocount and photon-number distributions. Relations among the moment criteria are revealed. Performance of the criteria is experimentally investigated using a set of potentially sub-Poissonian fields obtained by post-selection from a twin beam. The criteria based on moments of integrated intensity and photon number and those using the elements of photocount distribution are found as the most powerful. States nonclassical up to the fifth order are experimentally reached in the former case, even the ninth-order nonclassicality is observed in the latter case.

We identify physical scenarios whereby high-peak-power subcycle attosecond field waveforms can be synthesized by coherently combining a multibeam high-order harmonic output generated by a laser driver consisting of a pair of few-cycle pulses with different carrier frequencies. With the relative amplitudes, phases, and group delays of these driver pulses carefully adjusted in each of the driver beams toward confining the recollisions of highest-ponderomotive-energy electrons to an extremely short time gate within a fraction of the driver field cycle, the phase-matched multibeam high-harmonic output can be tailored to yield an intense isolated subgigawatt sub-10-attosecond field waveform. As a general tendency, propagation effects are shown to limit the minimum pulse width of the multibeam high-harmonic output. Still, with appropriate optimization of the gas pressure and the beam geometry, $\approx 10$-as field waveforms can be synthesized at the expense of one to two orders of magnitude of the output radiation energy.

When a few-cycle laser beam nonresonantly propagates through an inversion-symmetric medium, beyond the usual odd-order harmonics in the transmission spectra, a well-defined spectral peak at twice the incident laser central frequency is disclosed [T. Tritschler et al., Phys. Rev. Lett. 90, 217404 (2003)]. Beyond the characterization method via the rf measurement of its carrier-envelope phase dependence, here a more direct mode of characterization is proposed by means of vortex transformation where a few-cycle vortex laser is adopted instead: One can easily clarify its origin as an usual third-order harmonic that appears to be a second-order harmonic, based on the criteria that the topological charge number of harmonics is directly proportional to its harmonic order.

Numerous few-electron atomic systems are considered which can be used effectively for observing a potential variation of the fine-structure constant $\alpha$ and the electron-proton mass ratio $m_e/m_p$. We examine optical magnetic dipole transitions between hyperfine-structure components in heavy highly charged H-like and Li-like ions with observably high sensitivity to a variation of $\alpha$ and $m_e/m_p$. The experimental spectra of the proposed systems consist of a strong single line, which simplifies significantly the data analysis and shortens the necessary measurement time. Furthermore, we propose systems for an experimental test of the variation of quark masses and discuss the expected level of accuracy in assessing its limitations. Finally, we establish which constraints on the variation of these fundamental constants could be provided by measurements with a hyperfine-structure highly-charged-ion clock and some reference clock, showing that a significant improvement of the current limitations can be reached.

Using numerical solutions to the quantum field theoretical Dirac equation, we study the electron-positron pair-creation process from the vacuum due to a spatially localized supercritical electric field. By varying the spatial profile of this external field, we search for optimal field configurations that maximize the pair-creation rate in the steady state. We find that for the class of pulse shapes with a single maximum and fixed total energy, the rate depends nonmonotonically on the field's spatial width and it is insensitive to other characteristics of the pulse shape. It turns out that the Schwinger rate can be corrected such that it can provide analytical estimates for the threshold behavior as well as finite pulse effects.

We provide tools for the quantum simulation of superluminal motion with superconducting circuits. We show that it is possible to simulate the motion of a superconducting qubit at constant velocities that exceed the speed of light in the electromagnetic medium and the subsequent emission of Ginzburg radiation. We also consider possible setups for simulating the superluminal motion of a mirror, finding a link with the super-radiant phase transition of the Dicke model.

Using transversal gates is a straightforward and efficient technique for fault-tolerant quantum computing. Since transversal gates alone cannot be computationally universal, they must be combined with other approaches such as magic state distillation, code switching, or code concatenation to achieve universality. In this paper we propose an alternative approach for universal fault-tolerant quantum computing, mainly based on the code concatenation approach proposed in [T. Jochym-O'Connor and R. Laflamme, Phys. Rev. Lett. 112, 010505 (2014)], but in a nonuniform fashion. The proposed approach is described based on nonuniform concatenation of the 7-qubit Steane code with the 15-qubit Reed-Muller code, as well as the 5-qubit code with the 15-qubit Reed-Muller code, which lead to two 49-qubit and 47-qubit codes, respectively. These codes can correct any arbitrary single physical error with the ability to perform a universal set of fault-tolerant gates, without using magic state distillation.

Current quantum technology is approaching the system sizes and fidelities required for quantum error correction. It is therefore important to determine exactly what is needed for proof-of-principle experiments, which will be a major step towards fault-tolerant quantum computation. Here we propose a surface code based experiment that is the smallest, both in terms of code size and circuit depth, that would allow errors to be detected and corrected for both the $X$ and $Z$ bases of a qubit. This requires 17 physical qubits initially prepared in a product state, on which 16 two-qubit entangling gates are applied before a final measurement of all qubits. A platform agnostic error model is applied to give some idea of the noise levels required for success. It is found that a true demonstration of quantum error correction will require fidelities for the preparation and measurement of qubits and the entangling gates to be above $99\%$.