We present a method for accurate measurements of both the gravity acceleration and its vertical gradient using a dual-atom interferometer, in principle, free from any uncertainty related to the absolute or relative positions of the two atomic samples. The method relies on the use of a dual-lock technique, which simultaneously stirs the chirp rate applied to the frequency difference between the interferometer lasers to compensate the gravity acceleration and the frequency jump applied to the lasers at the mid pulse of the interferometer to compensate for the gravity gradient. This allows one, in the end, to determine the two inertial quantities of interest in terms of frequencies.

A main objective of topological photonics is the design of disorder-resilient optical devices. Many prospective applications would benefit from nonlinear effects, which not only are naturally present in real systems but also are needed for switching in computational processes, while the underlying particle interactions are a key ingredient for the manifestation of genuine quantum effects. A particularly attractive switching mechanism of dynamical systems are infinite-period bifurcations into limit cycles, as these set on with a finite amplitude. Here we describe how to realize this switching mechanism by combining attractive and repulsive particle interactions in a driven-dissipative Su-Schrieffer-Heeger model, such as realized in excitonic lasers and condensates so that the system displays a non-Hermitian combination of parity and charge-conjugation ($\mathcal{PC}$) symmetry. We show that this symmetry survives in the nonlinear case and induces infinite-period and limit-cycle bifurcations (distinct from a Hopf bifurcation) where the system switches from a symmetry-breaking stationary state into a symmetry-protected power-oscillating state of finite amplitude. These protected dynamical solutions display a number of characteristic features, among which are their finite amplitude at onset, their arbitrary long oscillation period close to threshold, and the symmetry of their frequency spectrum which provides a tuneable frequency comb. Phases with different transition scenarios are separated by exceptional points in the stability spectrum, involving nonhermitian degeneracies of symmetry-protected excitations.

We study the dynamics of two ensembles of atoms (or equivalently, atomic clocks) coupled to a bad cavity and pumped incoherently by a Raman laser. Our main result is the nonequilibrium phase diagram for this experimental setup in terms of two parameters: detuning between the clocks and the repump rate. There are three main phases: a trivial steady state (phase I), where all atoms are maximally pumped, a nontrivial steady state corresponding to monochromatic superradiance (phase II), and amplitude-modulated superradiance (phase III). Phases I and II are fixed points of the mean-field dynamics, while in most of phase III stable attractors are limit cycles. Equations of motion possess an axial symmetry and a ${\mathbb{Z}}_2$ symmetry with respect to the interchange of the two clocks. Either one or both of these symmetries are spontaneously broken in various phases. The trivial steady state loses stability via a supercritical Hopf bifurcation bringing about a ${\mathbb{Z}}_2$-symmetric limit cycle. The nontrivial steady state goes through a subcritical Hopf bifurcation responsible for coexistence of monochromatic and amplitude-modulated superradiance. Using Floquet analysis, we show that the ${\mathbb{Z}}_2$-symmetric limit cycle eventually becomes unstable and gives rise to two ${\mathbb{Z}}_2$-asymmetric limit cycles via a supercritical pitchfork bifurcation. Each of the above attractors has its own unique fingerprint in the power spectrum of the light radiated from the cavity. In particular, limit cycles in phase III emit frequency combs—series of equidistant peaks, where the symmetry of the frequency comb reflects the symmetry of the underlying limit cycle. For typical experimental parameters, the spacing between the peaks is several orders of magnitude smaller than the monochromatic superradiance frequency, making the lasing frequency highly tunable.

We investigate the absorption spectra for the $F_g=1\to F_e=0$ transition of the $D_2$ line of ${}^{87}\mathrm{Rb}$ excited by a linearly polarized light in the presence of a transverse magnetic field (TMF) in different directions. Using the theoretical methods in quantum optics, we obtain the analytical expressions for the atomic density-matrix elements and the absorption spectrum. We analyze the splitting proportional to the magnitude of the TMF in the coherent population trapping absorption spectrum and explain its physical origin. Then, the sensitivity of the resonance signal to the phase (in our case, to the angle between the TMF and the light polarization) is investigated. We show and explain the splitting of the bright resonance and find the simple dependence of the separation of this splitting on the magnitude and the direction of the TMF. Therefore, this system may provide a possible method for the measurement of the magnetic field vector. In addition, we study the coherence of the system based on an observable coherence measure, namely, robustness of coherence (ROC). We find that in the case where the absorption signal becomes difficult to detect, the change of the ROC spectrum becomes more obvious and the extreme points are well maintained. Therefore, this may provide a scheme for the measurement of the magnetic field which is complementary to that based on the absorption signal of the laser.

The effect of finite boundaries in the propagation of spatial nonlocal solitons in media with cylindrical symmetry is analyzed. Using Ehrenfest's theorem together with the Green's function of the nonlinear refractive index equation, we derive an analytical expression for the force exerted on the soliton by the boundaries, verifying its validity by full numerical propagation. We show that the dynamics of the soliton are determined not only by the degree of nonlocality, but also by the boundary conditions for the refractive index. In particular, we report that a supercritical pitchfork bifurcation appears when the boundary condition exceed a certain threshold value.

The power and efficiency of many-body heat engines can be boosted by performing cooperative nonadiabatic operations in contrast to the commonly used adiabatic implementations. Here the key property relies on the fact that nonadiabaticity is required in order to allow for cooperative effects that can use the thermodynamic resources only present in the collective nonpassive state of a many-body system. In particular, we consider the efficiency of an Otto cycle, which increases with the number of copies used and reaches a many-body bound, which we discuss analytically.

A system of linearly coupled quantum harmonic oscillators can be diagonalized when the system is dynamically stable using a Bogoliubov canonical transformation. However, this is just a particular case of more general canonical transformations that can be performed even when the system is dynamically unstable. Specific canonical transformations can transform a quadratic Hamiltonian into a normal form, which greatly helps to elucidate the underlying physics of the system. Here, we provide a self-contained review of the normal form of a quadratic Hamiltonian as well as step-by-step instructions to construct the corresponding canonical transformation for the most general case. Among other examples, we show how the standard two-mode Hamiltonian with a quadratic position coupling presents, in the stability diagram, all the possible normal forms corresponding to different types of dynamical instabilities.

Entanglement monotone is defined as a convex measure of entanglement that does not increase on average under local operations and classical communication (LOCC). Here we call an entanglement monotone a strict entanglement monotone (SEM) if it decreases strictly on average under LOCC. We show that, for any convex roof extended entanglement monotone that on pure states is given by a function of the reduced states, if the function is strictly concave, then it is a SEM. Moreover, we prove that the negativity and the relative entropy of entanglement, which are not defined by the convex roof structure, are also SEMs. In addition, if the squashed entanglement could be obtained by some optimal extension, then it is a SEM as well. Our results imply that entanglement is strictly decreasing on average under LOCC.

Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near term. Adiabatic quantum computing, quantum annealing, computation by a continuous-time quantum walk, and special purpose quantum simulators all use this strategy. In this work, we carry out a detailed examination of adiabatic and quantum-walk implementation of the quantum search algorithm, using the more physically realistic hypercube connectivity, rather than the complete graph, for our base Hamiltonian. We calculate optimal adiabatic schedules both analytically and numerically for the hypercube and then interpolate between adiabatic and quantum-walk searching, obtaining a family of hybrid algorithms. We show that all of these hybrid algorithms provide the quadratic quantum speedup when run with optimal parameter settings, which we determine and discuss in detail. We incorporate the effects of multiple runs of the same algorithm, noise applied to the qubits, and two types of problem misspecification, determining the optimal hybrid algorithm for each case. Our results reveal a rich structure of how these different computational mechanisms operate and should be balanced in different scenarios. For large systems with low noise and good control, a quantum walk is the best choice, while hybrid strategies can mitigate the effects of many shortcomings in hardware and problem misspecification.

We introduce a measure of coherence which is extended from the coherence rank via the standard convex roof construction; we call it the logarithmic coherence number. This approach is parallel to the Schmidt measure in entanglement theory. We study some interesting properties of the logarithmic coherence number and show that this quantifier can be considered as a proper coherence measure. We find that the logarithmic coherence number can be calculated exactly for a large class of mixed states. We also discuss the relationships between the logarithmic coherence number and other coherence quantifiers, e.g., the relative entropy of coherence, the $l_1$-norm coherence, and average fidelity coherence. We give the relationship between coherence and entanglement in a bipartite system, and our results can be generalized to multipartite settings. Finally, we give that the creation of entanglement with bipartite incoherent operations is bounded by the logarithmic coherence number of the initial system during the process.

We propose a method for decomposing continuous-variable operations into a universal gate set, without the use of any approximations. We fully characterize a set of transformations admitting exact decompositions and describe a process for obtaining them systematically. Gates admitting these decompositions can be synthesized exactly, using circuits that are several orders of magnitude smaller than those achievable with previous methods. Our method relies on strategically using unitary conjugation and a lemma to the Baker-Campbell-Hausdorff formula to derive new exact decompositions from previously known ones, leading to exact decompositions for a large class of gates. We demonstrate the wide applicability of these exact gate decompositions by identifying several quantum algorithms and simulations of bosonic systems that can be implemented with higher precision and shorter circuit depths using our techniques.

We introduce a high-dimensional quantum encoding based on coherent mode-dependent single-photon subtraction from multimode squeezed states. This encoding can be seen as a generalization to the case of nonzero squeezing of the standard single-photon multirail encoding. The advantage is that the presence of squeezing enables the use of common tools in continuous-variable quantum processing, which in turn allows us to show that arbitrary $d$-level quantum states can be generated and detected by simply tuning the classical fields that gate the photon-subtraction scheme. Therefore, the scheme is suitable for mapping arbitrary classical data in quantum mechanical form. Regardless of the dimension of the data-set alphabet, the mapping is conditioned on the subtraction of a single photon only, making it nearly unconditional. We prove that this encoding can be used to calculate vector distances, a pivotal primitive in various quantum machine-learning algorithms.

The $B$-spline $R$-matrix method is used to investigate the photoionization of neutral iron from the ground and excited states in the energy region from the ionization thresholds to 2 Ry. The multiconfiguration Hartree-Fock method in connection with adjustable configuration expansions and term-dependent orbitals is employed for an accurate representation of the initial states of Fe i and the target wave functions of Fe ii. The close-coupling expansion contains 261 $LS$ states of Fe ii and includes all levels of the $3d^{6}4s,3d^{5}4s^2,3d^7,3d^{6}4p$, and $3d^{5}4s4p$ configurations. Full inclusion of all terms from the principal configurations considerably changes both the low-energy resonance structure and the energy dependence of the background cross sections. Partial cross sections are analyzed in detail to clarify the most important scattering channels. Comparison with other calculations is used to place uncertainty bounds on our final photoionization cross sections and to assess the likely uncertainties in the existing data sets.

We analyze the dynamics of Bose-Einstein condensates loaded in rotating ring lattices made of a few sites, and show how rotation maps the states found in this finite system onto those belonging to a static infinite lattice. Ring currents and soliton states in the absence of a lattice find their continuation in the presence of the lattice as nonlinear Bloch waves and soliton-like states connecting them. Both bright gap solitons and dark-soliton trains are shown to connect continuously to linear solutions. The existence of adiabatic paths upon varying rotation frequency between states with quantized supercurrents suggests highly controllable methods for the experimental generation of persistent currents.

We present an elegant application of matter-wave interferometry to the velocimetry of cold atoms whereby, in analogy to Fourier transform spectroscopy, the one-dimensional velocity distribution is manifest in the frequency domain of the interferometer output. By using stimulated Raman transitions between hyperfine ground states to perform a three-pulse interferometer sequence, we have measured the velocity distributions of clouds of freely expanding ${}^{85}\mathrm{Rb}$ atoms with temperatures of 34 and $18\mu \mathrm{K}$. Quadrature measurement of the interferometer output as a function of the temporal asymmetry yields velocity distributions with excellent fidelity. Our technique, which is particularly suited to ultracold samples, compares favorably with conventional Doppler and time-of-flight techniques, and it reveals artefacts in standard Raman Doppler methods. The technique is related to, and provides a conceptual foundation of, interferometric matter-wave accelerometry, gravimetry, and rotation sensing.

In the paper, we employ a wave-function approach to investigate the evolution of a two-photon wave packet propagating in a one-dimensional waveguide coupled to the Jaynes-Cummings (JC) system. We derive and solve, both analytically and numerically, a set of equations of motion governing the quantum state of the system. That allows us to provide real-time analysis of the evolution of the wave packet two-photon joint spectrum (2PJS) and the excitation dynamics of the JC system in the course of its interaction with the two-photon pulse. We demonstrate that the 2PJS and the spectrum of the wave packet scattered from the JC system experience transformation for nonzero atom-cavity couplings. Moreover, using Schmidt decomposition, we show that the scattered photons feature frequency entanglement contrary to the incident ones which are not entangled.

We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is driven below its resonance, providing optical damping of the mechanical oscillations. We study the nonlinear coherent response of the mechanical oscillator in this setup. For large mechanical amplitudes, we find that the system can display dynamical multistability if the optomechanical cooperativity exceeds a critical value. This analysis relates standard optomechanical damping to the dynamical attractors known from the theory of optomechanical self-sustained oscillations. We also investigate the effect of thermal and quantum noise and estimate the noise-induced switching rate between the stable states of the system. We then consider applications of this system and primarily focus on how it can be used as bifurcation amplifiers for the detection of small mechanical or optical signals. Finally, we show that in a related but more complicated setup featuring resonant optomechanical interactions, the same effects can be realized with a relaxed requirement on the size of the mechanical oscillations.

We generalize the concept of radially self-accelerating beams to the domain of optical pulses. In particular, we show how radially self-accelerating optical pulses (RSAPs) can be constructed by suitable superpositions of X-waves, which are a natural extension of Bessel beams in the pulsed domain. Moreover, we show that while field-rotating RSAPs preserve their self-acceleration character, intensity-rotating RSAPs only possess pseudo-self-acceleration, as their transverse intensity distribution is deformed during propagation due to their propagation-dependent angular velocity.

We examine the electron-positron pair-creation process from the vacuum for general time-dependent external fields. By applying the framework of optimal control theory, we determine those temporal pulse shapes, which can maximize the final number of created positrons for a given set of momenta. In the perturbative regime of sufficiently small pulse energies or short interaction times, we obtain analytical forms that match the computational data of the optimal fields for the chosen sets of positronic momenta.

The no-cloning property of quantum mechanics allows unforgeability of quantum banknotes and credit cards. Quantum credit card protocols involve a bank, a client, and a payment terminal and their practical implementation typically relies on encoding information on weak coherent states of light. Here, we provide a security proof in this practical setting for semi-device-independent quantum money with classical verification, involving an honest bank, a dishonest client, and a potentially untrusted terminal. Our analysis uses semidefinite programming in the coherent state framework and aims at simultaneously optimizing over the noise and losses introduced by a dishonest party. We discuss secure regimes of operation in both fixed and randomized phase settings, taking into account experimental imperfections. Finally, we study the evolution of protocol security in the presence of a decohering optical quantum memory and identify secure credit card lifetimes for a specific configuration.