Based on a single atom coupled to a fiber-coupled, chip-based microresonator [B. Dayan et al., Science 319, 1062 (2008)], we put forward a scheme to generate optical frequency combs at driving laser powers as low as a few nanowatts. Using state-of-the-art experimental parameters, we investigate in detail the influences of different atomic positions and taper-resonator coupling regimes on optical-frequency-comb generation. In addition to numerical simulations demonstrating this effect, a physical explanation of the underlying mechanism is presented. We find that the combination of the atom and the resonator can induce a large third-order nonlinearity which is significantly stronger than Kerr nonlinearity in Kerr frequency combs. Such enhanced nonlinearity can be used to generate optical frequency combs if driven with two continuous-wave control and probe lasers and significantly reduce the threshold of nonlinear optical processes. The comb spacing can be well tuned by changing the frequency beating between the driving control and probe lasers. The proposed method is versatile and can be adopted to different types of resonators, such as microdisks, microspheres, microtoroids or microrings.

We propose a dissipative scheme to generate a maximally entangled state for two $\Lambda$-type atoms trapped in an optical cavity. Different from the unitary-dynamics-based scheme, our work shows that both atomic spontaneous emission and cavity decay are no longer detrimental, but necessary for entanglement generation. The scheme is independent of initial states and does not require precise time control. A final numerical simulation with two groups of experimental parameters indicates that the present scheme is feasible and the performance could be better than the unitary-dynamics-based scheme.

We investigate the fine-grained uncertainty relations for qubit systems by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective measurements in mutually unbiased bases in $d$-dimensional Hilbert space. All of those uncertainty inequalities can be applied to construct different thermodynamic cycles such that the violation of those inequalities will lead to the violation of the second law of thermodynamics. This reveals the relationship between fine-grained uncertainty and the second law of thermodynamics.

We investigate resource requirements for a fault-tolerant quantum Fourier transform. The quantum Fourier transform is a basic subroutine for quantum algorithms which provide an exponential speedup over known classical ones, such as Shor's algorithm for factoring. To implement single-qubit rotations required for a quantum Fourier transform in a fault-tolerant manner, we consider two types of approaches: gate synthesis and state distillation. While the gate synthesis approximates single-qubit rotations with basic quantum operations, the state distillation allows one to perform single-qubit rotations for a quantum Fourier transform exactly. It is unknown, however, which approach is better for a quantum Fourier transform. Here we develop a state-distillation method optimized for a quantum Fourier transform and compare this performance with those of state-of-the-art techniques for gate synthesis without and with ancillary states (ancillas). The performance is evaluated with the resource requirement for a quantum Fourier transform. The resource is measured by the total number of $\pi /8$ gates denoted by $T$, which is called the $T$ count. Contrary to the expectation, the $T$ count for the state distillation is considerably larger than those for the ancilla-free and ancilla-assisted gate synthesis. Thus, we conclude that the ancilla-assisted gate synthesis is a better approach to a fault-tolerant quantum Fourier transform.

In the postprocessing of quantum key distribution, the raw key bits from the mismatched-basis measurements, where two parties use different bases, are normally discarded. Here, we propose a postprocessing method that exploits measurement statistics from mismatched-basis cases and prove that incorporating these statistics enables uncharacterized qubit sources to be used in the measurement-device-independent quantum key distribution protocol and the Bennett-Brassard 1984 protocol, which is otherwise impossible.

A scheme for suppressing the correlated noise in signals transmitted over the bosonic Gaussian memory channels is proposed. This is a compromise solution rather than removing the noise completely. The scheme is based on linear optical elements, two $N$-port splitters and $N$ number of phase flips. The proposed scheme has the advantages that the correlated noise of the memory channels is greatly suppressed, and the input signal states can be protected excellently when transmitting over the noise channels. We examine the suppressing efficiency of the scheme for the correlated noise, both from quantum information of the states directly transmitted through the noise channel and also from the entanglement teleportation. The operation of phase flips in our scheme is important for the suppression of the correlated noise, which can diminish the effect of noise in quantum communication. Increasing the number of beam splitters also can improve the suppressing efficiency of the scheme in quantum communication.

We derive a hierarchy of separability criteria for multimode continuous-variable systems. They permit one to study in a unified way the $k$-partite entanglement of broad classes of Gaussian and non-Gaussian states. With specific examples we demonstrate the strength of the criteria, and we discuss their assessment based on data obtained from Gaussian measurements.

We show through numerical investigations that the ground-state correlation energies of atomic ions follow an unexpectedly simple scaling relation, $E_c\approx Z^{4/3}{f}_c(Z/N)$, where $N$ is the number of electrons, $Z$ is the atomic number, and $f_c$ is a universal function, for which an analytic expression with a one-parameter fit can be provided. The relation agrees well with several sets of correlation energies obtained from different methods for atomic ions with $N=2,...,18$ and $Z=2,...,28$. Moreover, our relation gives a good agreement with neutral atoms up to $N\approx 90$. Our main result is readily applicable to estimating correlation energies of heavy elements, for which there are no available data in the literature. The simplicity of the relation may also have implications in the development of correlation functionals within density-functional theory.

We consider the theory of multiple-particle fragmentation processes in the light of modern multihit position-sensitive detection. First, we give a formulation of time-independent many-body scattering theory as a direct generalization of standard textbook two-body potential scattering but in such a way as to emphasize position rather than momentum detection. Noteworthy is that classical asymptotic motion of fragments is shown to emerge from this quantum-mechanical time-independent theory and enables the definition of a classical time parameter. This in turn allows a transition to be made to a time-dependent scattering theory, even in the case where all Hamiltonians are time independent. Such a time-dependent description is the basis of the imaging theorem, which connects position detection to momentum detection.

We report elastic integral cross sections for low-energy electron scattering by gas-phase dimethyl sulfide and dimethyl disulfide, obtained with the Schwinger multichannel method with pseudopotentials. Our symmetry-resolved cross sections for dimethyl sulfide reveal that the single broad structure at $3.25\mathrm{eV}$ observed in the electron transmission spectrum (assigned as a ${\sigma }_{\mathrm{CS}}^{*}$ shape resonance) would actually arise from two superimposed anion states in the $B_2$ and $A_1$ symmetry components of the $C_{2v}$ point group. We also obtained two low-lying shape resonances for dimethyl disulfide, in good agreement with the available electron transmission data. In view of the recently reported measurements on dissociative electron attachment to dimethyl disulfide [C. Matias, A. Mauracher, P. Scheier, P. Limão-Vieira, and S. Denifl, Chem. Phys. Lett. 605-606, 71 (2014)], we also calculated cross sections for stretched S–S bond lengths, which indicate a fast stabilization consistent with the experimental data.

Ultrashort nonresonant electromagnetic pulses applied to effective one-electron systems may operate on the electronic state as a position or momentum translation operator. As derived here, extension to many-body correlated systems exposes qualitatively new aspects. For instance, to the lowest order in the electric field intensity the action of the pulse is expressible in terms of the two-body reduced density matrix enabling us to probe various facets of electronic correlations. As an experimental realization we propose a pump-probe scheme in which after a weak, swift “kick” by the nonresonant pulse the survival probability for remaining in the initial state is measured. This probability we correlate to the two-body reduced density matrix. Since the strength of electronic correlation is bond-length sensitive, measuring the survival probability may allow for a direct insight into the bond-dependent two-body correlation in the ground state. As an illustration, full numerical calculations for two molecular systems are provided and different measures of electronic correlations are analyzed.

Recently introduced time-dependent renormalized-natural-orbital theory (TDRNOT) is tested on nonsequential double ionization (NSDI) of a numerically exactly solvable one-dimensional model He atom subject to few-cycle, 800-nm laser pulses. NSDI of atoms in strong laser fields is a prime example of nonperturbative, highly correlated electron dynamics. As such, NSDI is an important “worst-case” benchmark for any time-dependent few and many-body technique beyond linear response. It is found that TDRNOT reproduces the celebrated NSDI “knee,” i.e., a many-order-of-magnitude enhancement of the double-ionization yield (as compared to purely sequential ionization) with only the ten most significant natural orbitals (NOs) per spin. Correlated photoelectron spectra—as “more differential” observables—require more NOs.

We theoretically analyze parametric amplification as a means to produce dichroism based on the orbital angular momentum (OAM) of an incident signal field. The nonlinear interaction is shown to provide differential gain between signal states of differing OAM, the peak gain occurring at half the OAM of the pump field.

We analyze the optical properties of the so-called invisible lenses in the wave-optics regime and show that they are practically invisible for a discrete set of frequencies. For other frequencies, the phase delay of the waves that pass through the lens compared to those that do not disturbs the outgoing waves. The frequencies for which the lens is invisible are influenced by the Gouy phase. This is the only known invisible device made of positive isotropic material at finite frequencies.

We report that nonlocal nonlinear media allow a controlled interaction among coherent solitons with a relative tilt previously imposed, resulting in the generation of rotary self-trapped beams. We demonstrate that two initially separated fundamental solitons can interact, generating stable rotating dipoles for a continuum interval of relative tilt values. Surprisingly, we find that for a higher number of initial solitons launched and after some emission of radiation waves, the initial self-trapped structures can decay into rotating dipole solitons. The normalized orbital angular momentum of these rotating dipoles can be controlled by adjusting the initial tilt.

We go beyond the approximate series expansions used in the dispersion theory of finite-size atoms. We demonstrate that a correct, and nonperturbative, theory dramatically alters the dispersion self-energies of atoms. The nonperturbed theory gives as much as $100\%$ corrections compared to the traditional series-expanded theory for the smaller noble gas atoms.

We study the $XY$ model with infinite-range interactions (Lipkin-Meshkov-Glick model) in the presence of dissipation from spontaneous decay. We show that independent and collective decay lead to qualitatively different phase transitions of the steady state, even though the phase boundary is the same. Independent decay leads to a second-order phase transition to a ferromagnet, while collective decay leads to a first-order transition to a time-dependent oscillatory phase. Then we show that the addition of a drive leads to infinite spin squeezing for collective decay in the thermodynamic limit. Our results can be experimentally seen in trapped-ion and cavity-QED experiments.

We analyze a scheme for generating entanglement between two spinor Bose-Einstein condensates (BECs). The BECs are off-resonantly coupled to a common photon mode and are controlled by external lasers to induce a $S^z{S}^z$ interaction, where $S^z$ is the total spin of the BEC. We directly simulate the scheme numerically for small systems and show the performance of the scheme. The scaling of the entanglement to large-scale systems under realistic conditions of spontaneous emission and cavity photon loss is analyzed. It is shown that both entanglement in the beyond-continuous-variable regime can be generated, where the entanglement is of the order of the maximal entanglement between the systems.

The surface code cannot be used when qubits vanish during computation; instead, a variant known as the topological cluster state is necessary. It has a gate error threshold of $0.75\%$ and requires only nearest-neighbor interactions on a two-dimensional (2D) array of qubits. Previous work on loss tolerance using this code has only considered qubits vanishing during measurement. We begin by also including qubit loss during two-qubit gates and initialization, and then additionally consider interaction errors that occur when neighbors attempt to entangle with a qubit that is not there. In doing so, we show that even our best case scenario requires a loss rate below $1\%$ in order to avoid considerable space-time overhead.

We propose a strategy to improve the performance of the quantum adiabatic algorithm (QAA) on an NP-hard (nondeterministic-polynomial-time-hard) problem exact cover, by increasing the ground-state degeneracy of the problem Hamiltonian. Our strategy is based on the empirical finding that for the QAA the difficulty of random instances decreases with the degeneracy of the ground state. We increase the degeneracy by adding extra qubits to form additional clauses. Our numerical results show that on average our strategy can provide an increase in the minimum gap size along the linear interpolation path of Hamiltonian for both easy and difficult instances. The success probability at fixed total evolution time is thus increased.