We describe and expand upon the scalable randomized benchmarking protocol proposed in Phys. Rev. Lett. 106, 180504 (2011) which provides a method for benchmarking quantum gates and estimating the gate dependence of the noise. The protocol allows the noise to have weak time and gate dependence, and we provide a sufficient condition for the applicability of the protocol in terms of the average variation of the noise. We discuss how state-preparation and measurement errors are taken into account and provide a complete proof of the scalability of the protocol. We establish a connection in special cases between the error rate provided by this protocol and the error strength measured using the diamond norm distance.

We demonstrate high accuracy calculations for the HeH${}^{+}$ molecule using analytic formulas for two-center two-electron integrals with exponential functions. The Born-Oppenheimer potential for the ground electronic ${}^1{\Sigma }^{+}$ state is obtained in the range of 0.1–60 a.u. with precision of about ${10}^{-12}$ a.u. As an example, at the equilibrium distance between nuclei $r_{\mathrm{e}}=1.463283$ a.u., the Born-Oppenheimer potential amounts to $-2.978708310771\left(1\right)$ a.u. Obtained results lay the ground for theoretical predictions in HeH${}^{+}$ with spectroscopic precision.

Associative and Penning ionization cross sections are calculated for collisions between metastable hydrogen $2s$ atoms at thermal energies. Cross sections for deuterium $2s$ collisions are also reported. The associative ionization cross sections behave as $E^{-1}$ for collision energy $E$, in agreement with an existing experiment. The Penning ionization cross sections dominate for all energies and are found to follow the $E^{-2/3}$ behavior that was predicted in previous work for the total ionization cross section. The magnitudes of our theoretical associative ionization cross sections for $\text{H}\left(2s\right)+\text{H}\left(2s\right)$ collisions are between two and four times larger than the experimental data.

We study the short-range correlation strength of three-dimensional spin-half dilute atomic Fermi gases with spin-orbit coupling. The interatomic interaction is modeled by the contact pseudopotential. In the high-temperature limit, we derive the expression for the second-order virial expansion of the thermodynamic potential via the ladder diagrams. We further evaluate the second-order virial expansion in the limit that the spin-orbit coupling constants are small and find that the correlation strength between the fermions increases as the fourth power of the spin-orbit coupling constants. At zero temperature, we consider the cases in which there are symmetric spin-orbit couplings in two or three directions. In such cases, there is always a two-body bound state of zero net momentum. In the limit that the average interparticle distance is much larger than the dimension of the two-body bound state, the system primarily consists of condensed bosonic molecules that fermions pair to form; we find that the correlation strength also becomes bigger compared to that in the absence of spin-orbit coupling. Our results indicate that generic spin-orbit coupling enhances the short-range correlations of the Fermi gases. Measurement of such enhancement by photoassociation experiment is also discussed.

Absolute photoionization cross sections of Ar${}^{+}$, Ar${}^{2+}$, and Ar${}^{3+}$ ions have been measured in the 250–280 eV photon energy range. These results are compared to theoretical cross sections extracted from two new calculations we performed. They reproduce well the general behavior of the experimental spectra and the magnitude of the direct photoionization cross sections. However, the oscillator strength of the resonant structure in the spectra, dominated by $2p\to 3d$ transitions, is overestimated up to 80$\%$ by our calculations.

We study the field dependency of the Berezinskii-Kosterlitz-Thouless transition temperature $T_c\left(H\right)$ of Bose gases in a two-dimensional optical lattice in the synthetic magnetic field using the Metropolis Monte Carlo method. The system is described by the frustrated $XY$ model and the critical temperature is determined through observing the disappearance of the central peak of the momentum distribution of the gas, which can be directly measured by the time-of-flight absorbing imaging in cold-atom experiments. $T_c\left(H\right)$ is found to exhibit a largest peak at the fraction of a flux quantum $f=\phi /{\phi }_0=1/2$ and a second-largest one at $f=1/3$, in agreement with former studies on superconducting Josephson arrays. We also indicate that the synthetic magnetic field experiment can produce strong enough frustration for exploring the physics of the frustrated $XY$ model.

We investigate the quantum dynamics of an experimentally realized spin-orbit-coupled Bose-Einstein condensate in a double-well potential. The spin-orbit coupling can significantly enhance the atomic interwell tunneling. We find the coexistence of internal and external Josephson effects in the system, which are moreover inherently coupled in a complicated form even in the absence of interatomic interactions. Moreover, we show that the spin-dependent tunneling between two wells can induce a net atomic spin current referred as spin Josephson effects. Such spin Josephson effects can be observable under realistic conditions.

We describe the generic effects of loss or gain on pulse propagation in photonic-crystal and plasmonic waveguides that support “frozen” or “in-band” slow light at dispersion inflection points in the absence of loss (or gain). Using an analytical perturbation theory, we find that propagating and evanescent modes hybridize when loss exceeds a certain threshold, resulting in a reduced attenuation rate and switching from slow to superluminal velocity. Numerical simulations for photonic-crystal waveguides reveal the dynamic nature of this transition with forward-backward pulse velocity oscillations for loss above the threshold. Importantly, we show that the light intensity is enhanced close to the input end of the waveguide even under strong material losses, indicating the potential for slow-light enhancement of optical effects, even in such lossy waveguides.

In this work, we present integral cross sections for elastic scattering of low-energy electrons by the nitro compounds nitroethylene, nitroethane, and 1-nitropropane, for energies up to 8 eV. We calculated the scattering cross sections using the Schwinger multichannel method with pseudopotentials in the static-exchange plus polarization approximation and compared our results with our previous calculations for the nitromethane molecule. Our integral cross sections show ${\pi }^{*}$ and ${\sigma }^{*}$ shape resonances for all compounds, which are important in the understanding of dissociation processes.

We consider the interaction between a ZnO nanorod and a SiO${}_2$ nanorod in bromobenzene. Using optical data for the interacting objects and ambient we calculate the force (from short-range attractive van der Waals force to intermediate-range repulsive Casimir-Lifshitz force to long-range entropically driven attraction). The nonretarded van der Waals interaction is attractive at all separations. We demonstrate a retardation-driven repulsion at intermediate separations. At short separations (in the nonretarded limit) and at large separations (in the classical limit) the interaction is attractive. These effects can be understood from an analysis of multiple crossings of the dielectric functions of the three media as functions of imaginary frequencies.

Using the microcanonical picture of transport—a framework ideally suited to describe the dynamics of closed quantum systems such as ultracold atom experiments—we show that the exact dynamics of noninteracting fermions and bosons exhibits very different transport properties when the system is set out of equilibrium by removing the particles from half of the lattice. We find that fermions rapidly develop a finite quasisteady-state current reminiscent of electronic transport in nanoscale systems. This result is robust—it occurs with or without a harmonic confining potential and at zero or finite temperature. The zero-temperature bosonic current instead exhibits strong oscillatory behavior that decays into a steady-state of zero current only in the thermodynamic limit. These differences appear most strikingly in the different particle number fluctuations on half of the lattice as a consequence of the spin statistics. These predictions can be readily verified experimentally.

We present a detailed error analysis of a Rydberg blockade mediated controlled-not quantum gate between two neutral atoms as demonstrated recently in Isenhower et al. [Phys. Rev. Lett. 104, 010503 (2010)] and Zhang et al. [Phys. Rev. A 82, 030306 (2010)]. Numerical solutions of a master equation for the gate dynamics, including all known sources of technical error, are shown to be in good agreement with experiments. The primary sources of gate error are identified and suggestions given for future improvements. We also present numerical simulations of quantum process tomography to find the intrinsic fidelity, neglecting technical errors, of a Rydberg blockade controlled phase gate. The gate fidelity is characterized using trace overlap and trace distance measures. We show that the trace distance is linearly sensitive to errors arising from the finite Rydberg blockade shift and introduce a modified pulse sequence which corrects the linear errors. Our analysis shows that the intrinsic gate error extracted from simulated quantum process tomography can be under 0.002 for specific states of ${}^{87}$Rb or Cs atoms. The relation between the process fidelity and the gate error probability used in calculations of fault tolerance thresholds is discussed.

We present a theoretical description of the formation of weakly bound ($E_b\sim 0.1\text{--}10$ meV) negative ions in collisions of Rydberg atoms with neutral atoms or molecules. Using the adiabatic approximation for the collision, we obtain an analytical expression for the formation cross section. It is shown that the cross section has a sharp peak in its dependence on the principal quantum number of the Rydberg electron. This result is in agreement with the experimental studies. We obtain a simple analytical expression that relates the peak position and the binding energy of the negative ion. This expression generalizes the empirical law previously established by Desfrançois [Phys. Rev. A 51, 3667 (1995)]. Comparison of our calculations with the experimental data on dipole-bound anion formation shows that the obtained formula can be used for determination of binding energies of weakly bound negative ions from Rydberg electron transfer reactions with good accuracy.

We show that the perturbative nonlinearity associated with three-atom interactions, competing with standard two-body repulsive interactions, can change dramatically the evolution of one-dimensional (1D) dispersive shock waves in a Bose-Einstein condensate. In particular, we prove the existence of a rich crossover dynamics, ranging from the formation of multiple shocks regularized by nonlinear oscillations culminating in coexisting dark and antidark matter waves to 1D-soliton collapse. For a given scattering length, all these different regimes can be accessed by varying the density of atoms in the condensate.

The Tavis-Cummings model for more than one qubit interacting with a common oscillator mode is extended beyond the rotating wave approximation (RWA). We explore the parameter regime in which the frequencies of the qubits are much smaller than the oscillator frequency and the coupling strength is allowed to be ultrastrong. The application of the adiabatic approximation introduced by Irish et al. [Phys. Rev. B 72, 195410 (2005)] for a single-qubit system is extended to the multiqubit case. For a two-qubit system, we identify three-state manifolds of close-lying dressed energy levels and obtain results for the dynamics of intramanifold transitions that are incompatible with results from the familiar regime of the RWA. We exhibit features of two-qubit dynamics that are different from the single-qubit case, including calculations of qubit-qubit entanglement. Both number state and coherent state preparations are considered, and we derive analytical formulas that simplify the interpretation of numerical calculations. Expressions for individual collapse and revival signals of both population and entanglement are derived.

We propose an experimental scheme to implement a second-order nonlocal superposition operation ${\widehat{a}}^{†2}+e^{i\phi }{\widehat{b}}^{†2}$ and its variants by way of Hong-Ou-Mandel interference. The second-order coherent operations enable us to generate a NOON state with high particle number in a heralded fashion and also can be used to enhance the entanglement properties of continuous variable states. We discuss the feasibility of our proposed scheme considering realistic experimental conditions such as on-off photodetectors with nonideal efficiency and imperfect single-photon sources.

Phase diffusion represents a crucial obstacle toward the implementation of high-precision interferometric measurements and phase-shift-based communication channels. Here we present a nearly optimal interferometric scheme based on homodyne detection and coherent signals for the detection of a phase shift in the presence of large phase diffusion. In our scheme the ultimate bound to interferometric sensitivity is achieved already for a small number of measurements, of the order of hundreds, without using nonclassical light.

Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems—they are at least enough for the calculation of the ground-state and excited-state energies. Moreover, for a nondegenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine $>k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for nondegenerate excited states. In fact, for fermionic systems, it has been conjectured that any nondegenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any nondegenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. We further show that any nondegenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix). These results set up a solid framework for the study of excited-state properties of many-body systems.

We show that the time-dependent Schrödinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of suitably chosen internal clock variables, thereby unifying the conditional probability interpretation (CPI) and the semiclassical approach for the problem of time in quantum theory. Our formalism stems from an exact factorization of the Hamiltonian eigenfunction of the clock plus system composite, where the clock and system factors play the role of marginal and conditional probability amplitudes, respectively. Application of the Variation Principle leads to a pair of exact coupled pseudoeigenvalue equations for these amplitudes, whose solution requires an iterative self-consistent procedure. The equation for the conditional amplitude constitutes an effective “equation of motion” for the quantum state of the system with respect to the clock variables. These coupled equations also provide a convenient framework for treating the back-reaction of the system on the clock at various levels of approximation. At the lowest level, when the WKB approximation for the marginal amplitude is appropriate, in the classical limit of the clock variables the TDSE for the system emerges as a matter of course from the conditional equation. In this connection, we provide a discussion of the characteristics required by physical systems to serve as good clocks. This development is seen to be advantageous over the original CPI and semiclassical approach since it maintains the essence of the conventional formalism of quantum mechanics, admits a transparent interpretation, avoids the use of the Born-Oppenheimer approximation, and resolves various objections raised about them.

A scheme is presented for generating steady three-atom singlet states via three V-type atoms interacting with a strongly dissipative two-mode cavity. The local quantum feedback control is applied based on quantum-jump detection to make the target state fidelity as high as possible. This scheme is insensitive to detection inefficiencies since it only delays the time at which stationarity is achieved. Nevertheless, the spontaneous emission plays a negative role in the current system.