We evaluate various sources of errors that occur when attempting to produce a specified coherent change of a two-state quantum system using six popular coherent control techniques: resonant excitation, adiabatic following, composite adiabatic passage, universal composite pulses, shortcut to adiabaticity, and single-shot shaped pulses. As error sources, we consider spatial intensity distribution, transit time variation, inhomogeneous broadening, Doppler broadening, unwanted chirp, and shape errors, as well as errors generated by counter-rotating terms. For the various error types, different techniques emerge as the best performers, but overall we find that universal composite pulses perform most consistently and are most resilient to errors compared to all other procedures.

Electromagnetically induced transparency and absorption in atomic systems have applications such as slow-light generation. Coupled-resonator-induced transparency (CRIT) and absorption (CRIA) are the optical analogy to them. Here we theoretically and experimentally study CRIT and CRIA in two directly coupled whispering-gallery-mode microresonators. The theoretical results give conditions for observing CRIT and CRIA, and predict that a transition between them will happen if we change the coupling strength between the two microresonators or the coupling strength between the fiber taper and the first microresonator. The experimental results demonstrate the transitions between CRIT and CRIA using a microsphere coupled to a sausagelike microresonator. The obtained results give some guidelines to observe CRIT and CRIA.

Weyl photons appear when two three-dimensional photonic bands with linear dispersion are degenerate at a single momentum point, labeled as Weyl point. These points have remarkable properties such as being robust topological monopoles of Berry curvature as well as an associated vanishing density of states. In this work, we report on a systematic theoretical study of the quantum optical consequences of such Weyl photons. First, we analyze the dynamics of a single quantum emitter coupled to a Weyl photonic bath as a function of its detuning with respect to the Weyl point and study the corrresponding emission patterns, using both perturbative and exact treatments. Our calculations show an asymmetric dynamical behavior when the emitter is detuned away from the Weyl frequency, as well as different regimes of highly collimated emission, which ultimately translate in a variety of directional collective decays. Besides, we find that the incorporation of staggered mass and hopping terms in the bath Hamiltonian both enriches the observed phenomenology and increases the tunability of the interaction. Finally, we analyze the competition between the coherent and dissipative components of the dynamics for the case of two emitters and derive the conditions under which an effective interacting spin model description is valid.

Type-I spontaneous parametric down-converted biphotons can be described approximately by a double-Gaussian wave function in configuration space. Using an effective propagator in the Fresnel approximation, the time evolution and transversal spreading of the two-particle biphoton wave function allow us to evaluate the Sorkin parameter $\kappa$, which results from nonclassical path contributions of the kink type and loops to double- and triple-slit interferometry. This simple unidimensional model for the evaluation of $\kappa$ predicts that kinked nonclassical paths may lead to $\kappa \approx {10}^{-5}$ for degenerate biphotons. We show that such a model reproduces well the Sorkin parameter for matter waves found in more involved approaches in the literature. Moreover, we establish a hierarchy of approximations based on the shape of the nonclassical paths for matter waves and compare their size with leading relativistic corrections to the propagator.

A quantum model of the Raman process with the independent Stokes and anti-Stokes nonlinear interactions is developed to study nonclassical correlations between the photons in the Stokes and anti-Stokes fields. The role of the laser pump amplitude, the ratio of the Stokes and anti-Stokes coupling constants, and the population and losses of the vibrational mode in forming the correlations is elucidated. The $g^{\left(2\right)}$ intensity cross-correlation function, noise-reduction factor, two-mode principal squeezing variance, logarithmic negativity, nonclassicality depth, steering parameter, and the Bell parameter are analyzed side by side to shed light to the correlations between the Stokes and anti-Stokes fields. Conditions for having the Stokes and anti-Stokes fields composed of only photon pairs, similarly as it occurs in twin beams in parametric down-conversion, are revealed. They allow for nonzero mean thermal phonon numbers.

Weak measurement as a nonperturbative theory has been shown to be powerful in the fundamentals of quantum mechanics and high-precision metrology, in which the pointer is of great importance to parameter estimation and experimental design. In this work, we find that under the conditions of weak coupling and Gaussian meter, the probability distribution after the postselection follows a bimodal function and the peak contrast ratio (PCR) can be applied as a special pointer, which is different from the shift of mean value. To obtain the PCR, only two values corresponding to the two peaks in the distribution function are required. We theoretically present the relation of the PCR and parameters to be estimated, and then demonstrate it in an experiment. Weak measurement with the PCR pointer has the advantages of reducing the requirements of the apparatus and suppressing noise, which also provides a heuristic approach for studying weak measurement when the weak value is very large.

A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. Here, using the tools of resource theory of superposition, we give the conditions for a class of superposition state transformations. These conditions strictly depend on the scalar products of the basis states and reduce to the well-known majorization condition for quantum coherence in the limit of orthonormal basis. To further superposition-free transformations of $d$-dimensional systems, we provide superposition-free operators for a deterministic transformation of superposition states. The linear independence of a finite number of basis states requires a relation between the scalar products of these states. With this information in hand, we determine the maximal superposition states which are valid over a certain range of scalar products. Notably, we show that, for $d\ge 3$, scalar products of the pure superposition-free states have a greater place in seeking maximally resourceful states. Various explicit examples illustrate our findings.

We present some basic integer arithmetic quantum circuits, such as adders and multiplier-accumulators of various forms, which operate on multilevel qudits. The integers to be processed are represented in an alternative basis after they have been Fourier transformed. Several arithmetic circuits operating on Fourier-transformed integers have appeared in the literature for two-level qubits. Here we extend these techniques to multilevel qudits, as they may offer some advantages relative to qubit implementations. The arithmetic circuits presented here can be used as basic building blocks for higher level algorithms such as quantum phase estimation, quantum simulation, quantum optimization, etc. Detailed decomposition is given down to elementary two-level single- and two-qudit gates as such gates are the most appropriate for physical implementation. A complexity analysis is given after this decomposition step and it is shown that the depth of the circuits is linear in the number of qudits employed and quadratic in the dimension of each qudit while their quantum cost is quadratic in the number of the qudits and quadratic in the dimension.

Restriction to the one-excitation context allows two identical two-level atoms and their common one-mode cavity field to exhibit previously unreported features of three-party entanglement during fully coherent evolution. We find entanglement showing dynamical behavior in the form of nonanalytic slope discontinuities in the time record. Specifically, the entanglements of the system can become abruptly frozen in time, remaining at a constant value, and can subsequently suddenly begin thawing from this value. We calculate the onset timing of such sudden freezings and sudden thawings under several different initial conditions. The conditions producing permanent freezing of entanglement are found. We also identify a nontrivial upper limit for the sum of three individual bipartite entanglements, which exposes the concept of entanglement “volume” and the volume shrinkage that accompanies the entanglement sharing. Further analysis of these freezing and thawing processes reveals quantitative and qualitative constraints on entanglement sharing of three qubits.

Realistic quantum sensors face a trade-off between the number of sensors measured in parallel and the control and readout fidelity $\left(F\right)$ across the ensemble. We investigate how the number of sensors and fidelity affect sensitivity to continuous and intermittent signals. For continuous signals, we find that increasing the number of sensors by $1/F^2$ for $F<1$ always recovers the sensitivity achieved when $F=1$. However, when the signal is intermittent, more sensors are needed to recover the sensitivity achievable with one perfect quantum sensor. We also demonstrate the importance of near-unity control fidelity and readout at the quantum projection noise limit by estimating the frequency components of a stochastic, intermittent signal with a single trapped ion sensor. Quantum sensing has historically focused on large ensembles of sensors operated far from the standard quantum limit. The results presented in this paper show that this is insufficient for quantum sensing of intermittent signals and reemphasizes the importance of the unique scaling of quantum projection noise near an eigenstate.

A simple locally accurate uniform approximation for the nodeless wave function is constructed for a neutral system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the states of positive and negative parity, $\left(1s_0\right)$ and $\left(2p_0\right)$, respectively. It is shown that by keeping the mass and charge of one of the bodies fixed, all systems with different second-body masses are related. This allows one to consider the second body as infinitely massive and to take such a system as basic. Three physical systems are considered in detail: the hydrogen atom with (in)finitely massive proton (deuteron, triton) and the positronium atom $(-e,e)$. We derive the Riccati-Bloch and generalized Bloch equations, which describe the domains of small and large distances, respectively. Based on the interpolation of the small- and large-distance behavior of the logarithm of the wave function, a compact ten-parametric function is proposed. Taken as a variational trial function, it provides accuracy of not less than six significant digits (SDs) ($\lesssim {10}^{-6}$ in relative deviation) for the total energy in the whole domain of considered magnetic fields $[0,{10}^4]$ a.u. and not less than three SDs for the quadrupole moment $Q_{zz}$. To get reference points, the Lagrange mesh method with 16 K mesh points was used to get from ten to six SDs in energy from small to large magnetic fields. Based on the Riccati-Bloch equation, the first 100 perturbative coefficients for the energy, in the form of rational numbers, are calculated and, using the Padé-Borel resummation procedure, the energy is found with not less than ten SDs at magnetic fields $\le 1\mathrm{a}.\mathrm{u}.$

Fragmentation of ${\mathrm{CO}}_2^{4+}$, created by the impact of slow, highly charged ions $(96 \mathrm{keV} {\mathrm{Ar}}^{q+};$ $8\le q\le 14)$ on ${\mathrm{CO}}_2$, has been studied by recoil ion momentum spectrometry. ${\mathrm{CO}}_2^{4+}$ was found to dissociate into three ionic fragments through two channels: ${\mathrm{CO}}_2^{4+}\to {\mathrm{O}}^{+}+{\mathrm{C}}^{2+}+{\mathrm{O}}^{+}$ [the (1,2,1) channel] and ${\mathrm{CO}}_2^{4+}\to {\mathrm{O}}^{2+}+{\mathrm{C}}^{+}+{\mathrm{O}}^{+}$ [the (2,1,1) channel]. The kinetic energy of each fragment ion and the total kinetic energy release (KER) distributions for these channels were derived. Ab initio quantum chemical calculations at the multiconfiguration self-consistent-field configuration-interaction level of theory were carried out to obtain the potential energy curves of ${\mathrm{CO}}_2^{4+}$, from which the expected KER values were derived. A comparison of the experimental KER distributions with the expected KER values for different excited states enabled the estimation of the relative probabilities of accessing different electronic states of ${\mathrm{CO}}_2^{4+}$. These probabilities were found to depend on the projectile charge $q$. The fragmentation was visualized using the Dalitz plots, which revealed that the (1,2,1) channel arises exclusively via concerted fragmentation, while the (2,1,1) channel also has a small contribution from sequential fragmentation.

Ever since the first observation of Bose-Einstein condensation in the 1990s, ultracold quantum gases have been the subject of intense research, providing a unique tool to understand the behavior of matter governed by the laws of quantum mechanics. Ultracold bosonic atoms loaded in an optical lattice are usually described by the Bose-Hubbard model or a variant of it. In addition to the common insulating and superfluid phases, other phases (such as density waves and supersolids) may show up in the presence of a short-range interparticle repulsion and also depending on the geometry of the lattice. We herein explore this possibility, using the graph of a convex polyhedron as a “lattice” and playing with the coordination of nodes to promote the wanted finite-size ordering. To accomplish the job we employ a decoupling approximation, whose efficacy is tested in one case against exact diagonalization. We report zero-temperature results for two Catalan solids, the tetrakis hexahedron and the pentakis dodecahedron, for which a thorough ground-state analysis reveals the existence of insulating “phases” with polyhedral order and a widely extended supersolid region. The key to this outcome is the unbalance in coordination between inequivalent nodes of the graph. The predicted phases can be probed in systems of ultracold atoms using programmable holographic optical tweezers.

We study the properties of singly quantized linear vortices in the supersolid phase of a dipolar Bose-Einstein condensate at zero-temperature modeling ${}^{164}\mathrm{Dy}$ atoms. The system is extended in the $x\text{−}y$ plane and confined by a harmonic trap in the polarization direction $z$. Our study is based on a generalized Gross-Pitaevskii equation. We characterize the ground state of the system in terms of spatial order and superfluid fraction and compare the properties of a single vortex and of a vortex dipole in the superfluid phase (SFP) and in the supersolid phase (SSP). At variance with a vortex in the SFP, which is free to move in the superfluid, a vortex in the SSP is localized at the interstitial sites and does not move freely. We have computed the energy barrier for motion from an equilibrium site to another. The fact that the vortex is submitted to a periodic potential has a dramatic effect on the dynamics of a vortex dipole made of two counter-rotating parallel vortices; instead of rigidly translating as in the SFP, the vortex and antivortex approach each other by a series of jumps from one site to another until they annihilate in a very short time and their energy is transferred to bulk excitations.

It was recently argued that the geometric optics mean path length of rays inside a refractive object under Lambertian illumination is independent of the scattering strength of the medium [Savo et al., Science 358, 765 (2017)]. We here show that it is, in fact, different in the case of zero scattering. We uncover and explain the role of trapped ray trajectories in creating this unexpected discontinuity from zero to low scattering. This allows us to derive alternative analytic results for the zero scattering mean path length of simple refractive shapes. We believe this work provides a fresh perspective on the study of path length inside refractive objects, with possible applications in, for example, the study of scattering by large particles or the design of optical systems.

We extend complete complementarity relations to curved spacetimes by considering a succession of infinitesimal local Lorentz transformations, which implies that complementarity remains valid as the quanton travels through its world line and the complementarity aspects in different points of spacetime are connected. This result allows the study of these different complementary aspects of a quantum system as it travels through spacetime. In particular, we investigate the behavior of these different complementary properties of massive spin-$1/2$ particles in the Schwarzschild spacetime. For geodetic circular orbits, we find that the spin state of one particle oscillates between a separable and an entangled state. For nongeodetic circular orbits, we notice that the frequency of these oscillations gets bigger as the orbit nears the Schwarzschild radius $r_s$.

The search algorithm is one of the most widely studied quantum algorithms, while its complete implementation in experiments is difficult and only a few experimental works have been reported. Based on Grover's algorithm, we propose a scheme of quantum search using nonorthogonal states and experimentally implement the entire scheme in a linear optical system. With this scheme, a large-sized search space can be encoded using only one qubit and the search probability of the target state is $100\%$ in theory. The experimental setup and the operations for implementing this scheme are extremely simple. In our linear optical experiment, different target states are successfully found from a database of nine elements with all fidelities $>0.99$, the state evolution from the initial state to a target state is studied, and the medium states and the final state are shown in a Bloch sphere. The scheme is general and can be easily realized in a wide range of quantum systems. This work may pave an avenue to implement quantum algorithms with nonorthogonal states.

There always exists an entanglement witness for every entangled quantum state. Negativity of the expectation value of an entanglement witness operator guarantees entanglement of the corresponding state, given that the measurement devices involved are perfect, i.e., the performed measurements actually constitute the witness operator for the state under consideration. In a realistic situation, there are two possible ways of measurements to drive the process away from the ideal one. First, wrong measurements may be performed, and, second, while the measurement operators are implemented correctly, the detection process may be noisy. Entanglement witnesses are prone to both of these imperfections. The concept of measurement-device-independent entanglement witnesses was introduced to remove the first problem. We analyze the “detection loophole” in the context of measurement-device-independent entanglement witnesses, which deal with the second problem of imprecise measurements. We obtain an upper bound, a threshold value, on the entanglement witness function in the measurement-device-independent entanglement witness scenario, below which entanglement is guaranteed for given nonideal detector efficiencies, that can involve both lost events and dark counts. We also present a threshold value on the function in the “worst-case scenario” where the threshold of the witness operator for guaranteeing entanglement assumes its maximal negative value.