We theoretically propose an efficient way to generate and detect squeezed light by a single qubit in circuit QED. By tuning the qubit energy splitting close to the fundamental frequency of the first harmonic mode (FHM) in a transmission line resonator and placing the qubit at the nodal point of the third harmonic mode, one can generate the resonantly enhanced squeezing of the FHM upon pumping with the second harmonic mode. In order to investigate the photon number splitting for the squeezed FHM, we have numerically calculated the qubit absorption spectrum, which exhibits regularly spaced peaks at frequencies separated by twice the effective dispersive shift. It is also shown that adding a small pump field for the FHM makes additional peaks develop in between the dominant ones as well.

We present results on the dynamics of split-ring dimers having both gain and loss in one-dimensional nonlinear parity-time- ($\mathcal{PT}$-)symmetric magnetic metamaterials. For the long-wave (continuum) limit approximation and in the weakly nonlinear limit, we show analytic results on the existence of gap soliton solutions and on symmetry-breaking phenomenon at a critical value of the gain or loss term.

We investigate the performance of entangled coherent states for quantum-enhanced phase estimation. An exact analytical expression of quantum Fisher information is derived to show the role of photon losses on the ultimate phase sensitivity. We find a transition of the sensitivity from the Heisenberg scaling to the classical scaling due to quantum decoherence of the photon state. This quantum-classical transition is uniquely determined by the number of photons being lost, instead of the number of incident photons or the photon loss rate alone. Our results also reveal that a crossover of the sensitivity between the entangled coherent state and the NOON state can occur even for very small photon loss rate.

We analyze tunneling from vortex states in elliptically shaped traps. Using the hydrodynamic representation of the Gross-Pitaevskii (nonlinear Schrödinger) equation, we derive analytically and demonstrate numerically an interesting type of quantum fluid flow: a jetlike singularity formed by the interaction between the vortex and the asymmetric trap. For strongly elongated traps and high enough vorticity, the ellipticity overwhelms the circular rotation, resulting in the ejection of jets in narrow, well-defined directions. These jets are formed due to a convergence of trajectories starting from the top of the potential barrier and meeting at a certain point on the exit line. Under proper conditions they will appear in any coherent wave system with angular momentum and noncircular symmetry, such as superfluids, Bose-Einstein condensates, and light.

Negative-ion fractions depending on incident energies and angles have been measured for keV-energy fluorine negative ions scattering on a graphite surface at a scattering angle of 38°. For specular scattering, the fraction increases monotonously with increasing incident energy. A specific feature is the nonmonotonic angular dependence of the fraction with the variation of incident angles. It strongly indicates the interaction-time-dependent electron transfer process. The incident-velocity effect has been taken into account to analyze the experimental results, in which an exponential scaling is found.

We investigate the stability of $N$-soliton molecules in dispersion-managed optical fibers with focus on the recently realized 2- and 3-soliton molecules. We calculate their binding energy using an averaged nonlinear Schr$\ddot{\mathrm{o}}$dinger equation. A combination of variational and numerical solutions to this equation shows that it describes well the intensity profiles and relative separations of the experimental molecules. Extending the calculation to larger values of $N$, the binding energy per soliton is found to saturate at $N\ge 7$.

The electron shakeoff of ${}^{35}$Cl atoms resulting from the $\beta$${}^{+}$ decay of ${}^{35}$Ar${}^{+}$ ions has been investigated using a Paul trap coupled to a recoil-ion spectrometer. The charge-state distribution of the recoiling daughter nuclei is compared to theoretical calculations accounting for shakeoff and Auger processes. The calculations are in excellent agreement with the experimental results and enable one to identify the ionization reaction routes leading to the formation of all charge states.

Precise measurements of tiny forces and displacements play an important role in science and technology. The precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is necessarily spoiled by the unavoidable influence of noise. Here we obtain a quantum limit for the uncertainty in the estimation of the amplitude of a classical force with arbitrary time dependence, acting on a noisy quantum-mechanical oscillator. We determine the best initial state of the oscillator and the best measurement procedure, thus getting a rigorous and useful benchmark for experiments aiming to detect extremely small forces.

We use the entanglement negativity, a measure of entanglement for mixed states, to probe the structure of entanglement in the ground state of a topologically ordered system. Through analytical calculations of the negativity in the ground state(s) of the toric code model, we explicitly show that the pure-state entanglement of a region $A$ and its complement $B$ is the sum of two types of contributions: boundary entanglement and long-range entanglement. Boundary entanglement is seen to be insensitive to tracing out the degrees of freedom in the interior of regions $A$ and $B$, and therefore it entangles only degrees of freedom in $A$ and $B$ that are close to their common boundary. We recover the well-known result that boundary entanglement is proportional to the size of each boundary separating $A$ and $B$ and it includes an additive, universal correction. The second, long-range, contribution to pure-state entanglement appears only when $A$ and $B$ are noncontractible regions (e.g., on a torus) and it is seen to be destroyed when tracing out a noncontractible region in the interior of $A$ or $B$. In the toric code, only the long-range contribution to the entanglement depends on the specific ground state under consideration.

In this paper we study the behavior of the entanglement measure dubbed negativity in the context of the toric code model. Using a replica method introduced recently by Calabrese, Cardy, and Tonni [Phys. Rev. Lett. 109, 130502 (2012)], we obtain an exact expression which illustrates how the nonlocal correlations present in a topologically ordered state reflect in the behavior of the negativity of the system. We find that the negativity has a leading area-law contribution if the subsystems are in direct contact with one another (as expected in a zero-range correlated model). We also find a topological contribution directly related to the topological entropy, provided that the partitions are topologically nontrivial in both directions on a torus. We further confirm by explicit calculation that the negativity captures only quantum contributions to the entanglement. Indeed, we show that the negativity vanishes identically for the classical topologically ordered eight-vertex model, which on the contrary exhibits a finite von Neumann entropy, inclusive of topological correction.

We demonstrate the relation between a global phase of the quantum gate and the layout of energy levels of its effective Hamiltonian required for implementing the gate for minimum time. By an example of the quantum Fourier transform gate for a qudit represented by a quadrupole nucleus with the spin $I$ $=$ 1, the effective Hamiltonians and minimum implementation times for different global phases are found. Using numerical optimal control methods, the problem of the global phase in searching for the optimal pulse shape is considered in detail for the quantum Fourier transform gate at $I$ $=$ 1, 3/2, 2, and 5/2. It is shown that at the constrained control time the gradient algorithms can converge to the solutions corresponding to different global phases or the same global phase with different minimum times of the gate implementation.

In this paper, we show that the quantum Zeno effect can occur for generalized quantum measurements or operations. As a consequence of frequently performing nonselective measurements (or trace-preserving completely positive maps), the evolution of a certain measurement-invariant state is governed by an effective Hamiltonian defined by the measurement (or map) and the free-evolution Hamiltonian. For selective measurements, the state may change randomly with time according to measurement outcomes, but some physical quantities (operators) still evolve according to the effective Hamiltonian.

The Pauli matrices are a set of three $2\times 2$ complex Hermitian unitary matrices. In this article, we investigate the relationships between certain roots of the Pauli matrices and how gates implementing those roots are used in quantum circuits. Techniques for simplifying such circuits are given. In particular, we show how those techniques can be used to find a circuit of $\text{Clifford}+T$ gates starting from a circuit composed of gates from the well-studied NOT, CNOT, V library.

We present a detailed study of the effect of double core polarization (the polarization of core electrons due to the simultaneous action of the electric dipole and parity-violating weak fields) for amplitudes of the $ss$ and $sd$ parity-nonconserving transitions in Rb, Cs, Ba${}^{+}$, La${}^{2+}$, Tl, Fr, Ra${}^{+}$, Ac${}^{2+}$, and Th${}^{3+}$ as well as electron electric-dipole-moment enhancement factors for the ground states of the above neutral atoms and Au. This effect is quite large and has the potential to resolve some disagreement between calculations in the literature. It also has significant consequences for the use of experimental data in the accuracy analysis.

Theoretical doubly differential and total cross sections for electron-induced double ionization of oriented water molecules are reported here. The calculations are performed within the first Born approximation by describing the initial molecular state by means of single-center wave functions. Furthermore, the incident (scattered) electron is described by a plane wave while a Coulomb wave function is used for modeling the two secondary ejected electrons. The contribution of each final state to the double-ionization process is analyzed, namely, in considering target electrons ejected either from similar or from different molecular subshells. Thus, secondary electron energetic distributions as well as total cross sections are reported for particular target configurations, pointing out orientation effects in the double-ionization process.

Stimulated optical forces offer a simple and efficient method for providing optical forces far in excess of the saturated radiative force. The bichromatic force, using a counterpropagating pair of two-color beams, has so far been the most effective of these stimulated forces for deflecting and slowing atomic beams. We have numerically studied the evolution of a two-level system under several different bichromatic and polychromatic light fields, while retaining the overall geometry of the bichromatic force. New insights are gained by studying the time-dependent trajectory of the Bloch vector, including a better understanding of the remarkable robustness of bi- and polychromatic forces with imbalanced beam intensities. We show that a four-color polychromatic force exhibits great promise. By adding new frequency components at the third harmonic of the original bichromatic detuning, the force is increased by nearly 50$\%$ and its velocity range is extended by a factor of 3, while the required laser power is increased by only 33$\%$. The excited-state fraction, crucial to possible application to molecules, is reduced from 41$\%$ to 24$\%$. We also discuss some important differences between polychromatic forces and pulse trains from a high-repetition-rate laser.

Dynamics of the autoionizing states in O${}_2$ was investigated using the method of laser-field-assisted extreme-ultraviolet photoionization. Harmonics, ranging from 9th to 21st orders generated in Kr with 25 fs laser pulses at 820 nm, were employed to carry out photoionization of O${}_2$. Distinct autoionization features in the photoelectron spectrum, stemming from the resonant excitation of superexcited states of O${}_2$ by the 11th harmonic, were observed. The superexcited states, referred to as autoionizing states, were identified to be the ${\nu }^{\prime }$ $=$ 0, $n$ $=$ 5 Rydberg states converging to the $b$ ${}^4$Σ${}_g$${}^{-}$ state of O${}_2$${}^{+}$. Infrared laser pulses were utilized as the probe to monitor time-varying characteristics of photoionization and autoionization of O${}_2$. A decay time of 21 fs was obtained for the autoionizing states of O${}_2$ by deconvoluting the pump-probe results in O${}_2$ and Ar.

We study the ground-state properties of one-dimensional mixtures of bosonic and fermionic atoms resonantly coupled to fermionic Feshbach molecules. When the particle densities of fermionic atoms and Feshbach molecules differ, the system undergoes various depletion transitions between binary and ternary mixtures as a function of the detuning parameter. However, when the particle densities of fermionic atoms and Feshbach molecules are identical, the molecular conversion and disassociation processes induce a gap in a sector of low-energy excitations, and the remaining system can be described by a two-component Tomonaga-Luttinger liquid. Using a bosonization scheme, we derive the effective low-energy Hamiltonian for the system, which has a similar form as that of the two-chain problem of coupled Tomonaga-Luttinger liquids. With the help of improved perturbative renormalization group analysis of the latter problem, we determine the ground-state phase diagram and find that it contains a phase dominated by composite superfluid or pairing correlations between the open and closed resonant channels.

The resonant scattering of gap solitons (GSs) of the periodic nonlinear Schrödinger equation, with a localized defect which is symmetric under the parity and the time-reversal ($\mathcal{PT}$) symmetry, is investigated. It is shown that for suitable amplitudes ratios of the real and imaginary parts of the defect potential the resonant transmission of the GS through the defect becomes possible. The resonances occur for potential parameters which allow the existence of localized defect modes with the same energy and norm of the incoming GS. Scattering properties of gap solitons of different band gaps with effective masses of opposite sign are investigated. The possibility of unidirectional transmission and blockage of gap solitons by $\mathcal{PT}$ defect, as well as, amplification and destruction induced by multiple reflections from two $\mathcal{PT}$ defects, are also discussed.

In Phys. Rev. A 69, 012102 (2004), Schreecharan, Panigrahi, and Banerji present a general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials, e.g., Morse and Poschl-Teller. I have examined coherent states of the Morse oscillator presented by the authors and have found them to have incorrect mathematical substitutions. As such, this Comment looks at the correctness of two important equations that have led to their Morse oscillator coherent states.