Fidelity is a figure of merit widely employed in quantum technology in order to quantify similarity between quantum states and, in turn, to assess quantum resources or reconstruction techniques. Fidelities higher than, say, 0.9 or 0.99, are usually considered as a piece of evidence to say that two states are very close in the Hilbert space. On the other hand, on the basis of several examples for qubits and continuous variable systems, we show that such high fidelities may be achieved by pairs of states with considerably different physical properties, including separable and entangled states or classical and nonclassical ones. We conclude that fidelity as a tool to assess quantum resources should be employed with caution, possibly combined with additional constraints restricting the pool of achievable states, or only as a mere summary of a full tomographic reconstruction.

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

We consider a Dirac one-electron atom placed in a weak, static, uniform electric field. We show that, to the first order in the strength of the perturbing field, the only magnetic multipole moment induced in the ground state of the atom is the quadrupole one. The tensorial structure of that moment is resolved. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997); Szmytkowski, J. Phys. B 30, 2747(E) (1997)], we derive a closed-form expression for an $E1\to M2$ cross-susceptibility of the atom in the ground state.

We perform calculations of $s$-$d_{5/2}$ nuclear-spin-dependent parity nonconservation amplitudes for Rb, Cs, Ba${}^{+}$, Yb${}^{+}$, Fr, Ra${}^{+}$, and Ac${}^{2+}$. These systems prove to be good candidates for use in atomic experiments to extract the so-called anapole moment, a $P$-odd $T$-even nuclear moment important for the study of parity-violating nuclear forces. We also extend our previous works by calculating the missed spin-dependent amplitudes for the $s$-$d_{3/2}$ transitions in the above systems.

We investigate the cooling dynamics of a trapped $\Lambda$-configuration atom coupling to a high-finesse cavity. We find that the heating effects due to diffusion and heating transitions can be simultaneously suppressed by the cavity-induced transparency and the electromagnetically induced transparency effects, respectively. Compared to the current cavity cooling schemes, the trapped atom in our scheme can be cooled to a relatively lower final temperature.

The triangular Bose-Hubbard trimer is topologically the minimal model for a BEC superfluid circuit. As a dynamical system of two coupled freedoms it has mixed phase space with chaotic dynamics. We employ a semiclassical perspective to study triangular trimer physics beyond the conventional picture of the superfluid-to-insulator transition. From the analysis of the Peierls-Nabarro energy landscape, we deduce the various regimes in the $(\Omega ,u)$ parameter space, where $u$ is the interaction and $\Omega$ is the superfluid rotation-velocity. We thus characterize the superfluid stability and chaoticity of the many-body eigenstates throughout the Hilbert space.

We study collective excitations of a trapped Fermi gas at finite temperature using the Bogoliubov–de Gennes mean-field theory in conjunction with the generalized random-phase approximation. The collective excitations are analyzed through the density response of a monopole excitation. We show the appearance of several modes at the normal-fluid–superfluid phase-transition temperature: Higgs mode–like pairing amplitude modulations, analogues of the second sound in the trapped gas, and an edge mode that is also the strongest mode in the response.

We theoretically investigate the high-temperature thermodynamics of a harmonically trapped Fermi gas across a narrow Feshbach resonance by using the second-order quantum virial expansion, and point out some new features compared to the broad resonance. The interatomic interaction is modeled by the pseudopotential with an additional parameter, i.e., the effective range, to characterize the narrow-resonance width. Deep inside the width of a narrow Feshbach resonance, we find the second virial coefficient evolves with the effective range from the well-known universal value $1/4$ in the broad-resonance limit to one another value $1/2$ in the narrow-resonance limit. This means the Fermi gas interacts more strongly at the narrow resonance. In addition, far beyond the resonance width, we find the harmonically trapped Fermi gas still manifests an appreciable interaction effect across a narrow Feshbach resonance, which is contrary to our knowledge of the broad Feshbach resonance. All our results can be directly tested in current narrow Feshbach resonance experiments, which are generally carried out in a harmonic trap.

Following the recent proposal to create quadrupolar gases [Bhongale et al., Phys. Rev. Lett. 110, 155301 (2013)], we investigate what quantum phases can be created in these systems in one dimension. We consider a geometry of two coupled one-dimensional (1D) systems, and derive the quantum phase diagram of ultracold fermionic atoms interacting via quadrupole-quadrupole interactions within a Tomonaga-Luttinger-liquid framework. We map out the phase diagram as a function of the distance between the two tubes and the angle between the direction of the tubes and the quadrupolar moments. The latter can be controlled by an external field. We show that there are two magic angles ${\theta }_{B,1}^c$ and ${\theta }_{B,2}^c$ between 0 and $\pi /2$, where the intratube quadrupolar interactions vanish and change signs. Adopting a pseudospin language with regard to the two 1D systems, the system undergoes a spin-gap transition and displays a zigzag density pattern, above ${\theta }_{B,2}^c$ and below ${\theta }_{B,1}^c$. Between the two magic angles, we show that polarized triplet superfluidity and a planar spin-density-wave order compete with each other. The latter corresponds to a bond-order solid in higher dimensions. We demonstrate that this order can be further stabilized by applying a commensurate periodic potential along the tubes.

We investigate the transport through a few-level quantum system described by a Markovian master equation with temperature- and particle-density-dependent chemical potentials. From the corresponding Onsager relations we extract linear response transport coefficients in analogy to the electronic conductance, thermal conductance, and thermopower. Considering ideal Fermi and Bose gas reservoirs, we observe steady-state currents against the thermal bias as a result of the nonlinearities introduced by the constraint of a constant particle density in the reservoirs. Most importantly, we find signatures of the onset of Bose-Einstein condensation in the transport coefficients.

The interactions between light and matter are strongly enhanced when atoms are placed in high-finesse quantum cavities, offering tantalizing opportunities for generating exotic new quantum phases. In this work we show that both spin-orbit interactions and strong synthetic magnetic fields result when a neutral atom is confined within a ring cavity, whenever the internal atomic states are coupled to two off-resonant counter-propagating modes. We diagonalize the resulting cavity polariton Hamiltonian and find characteristic spin-orbit dispersion relations for a wide range of parameters. An adjustable uniform gauge potential is also generated, which can be converted into a synthetic magnetic field for neutral atoms by applying an external magnetic field gradient. Very large synthetic magnetic fields are possible, as the strength is proportional to the (average) number of photons in each of the cavity modes. The results suggest that strong-coupling cavity quantum electrodynamics can be a useful environment for the formation of topological states in atomic systems.

We investigate, through simulation, the polarization state evolution of high-power, ultrashort laser pulses during atmospheric propagation. A dielectric response model for the molecular rotation handling arbitrary, transverse polarization couples both the amplitude and phase of the polarization states. We find that, while circularly and linearly polarized pulses maintain their polarization, elliptically polarized pulses become depolarized due to energy equilibration between left and right circularly polarized states. The depolarization can be detrimental to remote radiation generation schemes and obscures time-integrated polarization measurements.

In a recent paper, Bamba and Ogawa [Phys. Rev. A 88, 013814 (2013)] developed a microscopic model describing a photonic cavity coupled to an excitonlike resonance. One of the results they obtained studying such a model is that, in the ultrastrong coupling regime, dissipation rates calculated applying the rotating-wave approximation on the system-environment coupling qualitatively differ from the ones calculated using a microscopic theory based on the quantum electrodynamics for dielectric media. Here I show that this result is an artifact, caused by an inconsistent application of the rotating-wave approximation and by an unphysical parameter choice.

As mentioned by De Liberato [Phys. Rev. A 89, 017801 (2014)], when we suppose the metallic thin mirror and perform the renormalization to the approach starting from the frequently used system-environment-coupling Hamiltonian, we can certainly resolve the discrepancy of its result from that obtained by the reliable approach in the main discussion of our paper [Phys. Rev. A 88, 013814 (2013)]. Although the suggested approach is currently applicable to the specific situation after checking its validity by our reliable but cumbersome approach, we instead propose to start from the system-environment-coupling Hamiltonian determined properly by the mechanism of the confinement and loss of the cavity fields. This approach is applicable to any cavity structure, in principle, and we do not face the renormalization problem appearing in the Comment.

We show that for two-qubit chained Bell inequalities with an arbitrary number of measurement settings, nonlocality and entanglement are not only different properties but are inversely related. Specifically, we analytically prove that in absence of noise, robustness of nonlocality, defined as the maximum fraction of detection events that can be lost such that the remaining ones still do not admit a local model, and concurrence are inversely related for any chained Bell inequality with an arbitrary number of settings. The closer quantum states are to product states, the harder it is to reproduce quantum correlations with local models. We also show that, in presence of noise, nonlocality and entanglement are simultaneously maximized only when the noise level is equal to the maximum level tolerated by the inequality; in any other case, a more nonlocal state is always obtained by reducing the entanglement. In addition, we observed that robustness of nonlocality and concurrence are also inversely related for the Bell scenarios defined by the tight two-qubit three-setting $I_{3322}$ inequality, and the tight two-qutrit inequality $I_3$.

In this paper, we consider fermionic systems in discrete space-time evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete space-time can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete space-time that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields, and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete space-time can be efficiently simulated on a quantum computer.

Quantum repeaters represent one possible way to achieve long-distance quantum key distribution. Collins et al. [O. A. Collins, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, Phys. Rev. Lett. 98, 060502 (2007)] proposed multiplexing as a method to increase the repeater rate and to decrease the requirement of memory coherence time. Motivated by the experimental fact that long-range connections are practically demanding, in this paper we extend the original quantum repeater multiplexing protocol to the case of short-range connection. We derive analytical formulas for the repeater rate and we show that for short connection lengths it is possible to have most of the benefits of a full-range multiplexing protocol. Then we incorporate decoherence of quantum memories and we study the optimal matching for the Bell-state measurement protocol permitting us to minimize the memory requirements. Finally, we calculate the secret key rate and we show that the improvement via finite-range multiplexing is of the same order of magnitude as that via full-range multiplexing.

Rate coefficients (α${}_{\mathrm{D}}$) for the dissociative recombination of ${\mathrm{Ar}}_2$${}^{+}$ and N${}_4$${}^{+}$ in low-temperature plasmas have been determined by multiphoton ionization of the parent gas (Ar or N${}_2$) at 248 nm, in combination with microwave interferometry at 9.2 GHz. A subpicosecond, Ti:Al${}_2$O${}_3$-KrF hybrid laser system generating 40 mJ pulses at 248 nm serves as a photoionization source within one arm of an interferometer having a bandwidth of ∼800 MHz, thereby providing an ultrafast (δ-function) plasma channel generator and a noninvasive, microwave probe of the plasma that together decouple the ionization mechanism (and source) from the electron detection process. Comparisons of measurements of the temporally resolved electron density with numerical simulations find α${}_{\mathrm{D}}$ to be $(1.2-6.0)\times {10}^{-6}$ cm${}^3$ s${}^{-1}$ for ${\mathrm{Ar}}_2$${}^{+}$ and $(2\pm 1)\times {10}^{-6}$ cm${}^3$ s${}^{-1}$ for N${}_4$${}^{+}$ for background pressures in the 150–600 Torr Ar and 10–400 Torr N${}_2$ intervals, respectively. Both sets of constants are consistent with values reported previously in other ranges of gas pressure. The data and simulations indicate the cross section for four-photon ionization of Ar at 248 nm to be $(5\pm 3)\times {10}^{-118}$ cm${}^8$ s${}^3$, or approximately 1.4 orders of magnitude lower than the single value in the literature [Uiterwaal et al., Phys. Rev. A 57, 392 (1998)]. Sub-50-ns transients observed in the electron density temporal profile for N${}_2$ pressures above ∼100 Torr suggest that the rate constant for N${}_2\left(B\right)$-N${}_2\left(B\right)$ associative ionization is almost an order of magnitude larger than the currently accepted value.

A universal programmable discriminator can perform discrimination between two unknown states, and the optimal solution can be approached via discrimination between the two averages over the uniformly distributed unknown input pure states, as has been widely discussed in previous works. In this paper, we consider the success probabilities of the optimal universal programmable unambiguous discriminators when applied to the pure input states. More precisely, the analytic results of the success probabilities are derived with the expressions of the optimal measurement operators for the universal discriminators, and we find that the success probabilities are independent of the dimension $d$ while the amount of copies in the two program registers is equal. The success probability of the programmable unambiguous discriminator can asymptotically approach that of the usual unambiguous discrimination (state comparison) as the number of copies in the program registers (data register) goes to infinity.