Low-frequency fluctuations (LFFs) represent a dynamical instability that occurs in semiconductor lasers when they are operated near the lasing threshold and subject to moderate optical feedback. LFFs consist of sudden power dropouts followed by gradual, stepwise recoveries. We analyze experimental time series of intensity dropouts and quantify the complexity of the underlying dynamics employing two tools from information theory, namely, Shannon’s entropy and the Martín, Plastino, and Rosso statistical complexity measure. These measures are computed using a method based on ordinal patterns, by which the relative length and ordering of consecutive interdropout intervals (i.e., the time intervals between consecutive intensity dropouts) are analyzed, disregarding the precise timing of the dropouts and the absolute durations of the interdropout intervals. We show that this methodology is suitable for quantifying subtle characteristics of the LFFs, and in particular the transition to fully developed chaos that takes place when the laser’s pump current is increased. Our method shows that the statistical complexity of the laser does not increase continuously with the pump current, but levels off before reaching the coherence collapse regime. This behavior coincides with that of the first- and second-order correlations of the interdropout intervals, suggesting that these correlations, and not the chaotic behavior, are what determine the level of complexity of the laser’s dynamics. These results hold for two different dynamical regimes, namely, sustained LFFs and coexistence between LFFs and steady-state emission.

We calculate the four-wave-mixing signal of excitons generated at ${\mathit{k}}_4={\mathit{k}}_1+{\mathit{k}}_2-{\mathit{k}}_3$ by two pulsed entangled photon pairs (${\mathit{k}}_1$, ${\mathit{k}}_2$) and (${\mathit{k}}_3$, ${\mathit{k}}_4$), where all four modes are chronologically ordered. Entangled photons offer an unusual combination of bandwidths and temporal resolution not possible by classical beams. Contributions from different resonances can be selected by varying the parameters of the photon wave function. The signal scales linearly rather than quadratically with the laser field intensity, which allows performance of the measurements at low powers.

Profiles of spectral lines due to the thermal motion of light-emitting particles are formulated based on the classical and the relativistic Doppler effects, respectively. For the classical case, the well-known Doppler-broadened line profile is reproduced. For the relativistic case, the line profile obtained is asymmetrically broadened with increasing temperature. However, the peak frequency remains unshifted, in contrast to blueshifted, as has been predicted in the current literature. Reasoning is given as to why the relativistic Doppler-broadened line profile currently accepted is probably invalid.

Considering a system of ultracold atoms in an optical lattice, we propose a simple and robust implementation of a quantum simulator for the homogeneous $t$-$J$ model with a well-controlled fraction of holes $x$. The proposed experiment can provide valuable insight into the physics of cuprate superconductors. A similar scheme applied to bosons, moreover, allows one to investigate experimentally the subtle role of inhomogeneity when a system passes from one quantum phase to another.

We show that a laser beam can be diffracted by a more concentrated light pulse due to quantum vacuum effects. We compute analytically the intensity pattern in a realistic experimental configuration, and discuss how it can be used to measure the parameters describing photon-photon scattering in vacuum. In particular, we show that the quantum electrodynamics prediction can be detected in a single-shot experiment at future 100-PW lasers such as ELI or HIPER. On the other hand, if carried out at one of the present high-power facilities, such as OMEGA EP, this proposal can lead either to the discovery of nonstandard physics or to substantial improvement in the current limits by PVLAS collaboration on the photon-photon cross section at optical wavelengths. This example of manipulation of light by light is simpler to realize and more sensitive than existing, alternative proposals, and can also be used to test Born-Infeld theory or to search for axionlike or minicharged particles.

We consider the problem of approximating ground states of one-dimensional quantum systems within the two most common variational ansatzes, namely, the mean-field ansatz and matrix product states. We show that both for mean field and for matrix product states of fixed bond dimension, the optimal solutions can be found in a way which is provably efficient (i.e., scales polynomially). This implies that the corresponding variational methods can be in principle recast in a way which scales provably polynomially. Moreover, our findings imply that ground states of one-dimensional commuting Hamiltonians can be found efficiently.

The density-matrix renormalization-group method is very effective at finding ground states of one-dimensional (1D) quantum systems in practice, but it is a heuristic method, and there is no known proof for when it works. In this article we describe an efficient classical algorithm which provably finds a good approximation of the ground state of 1D systems under well-defined conditions. More precisely, our algorithm finds a matrix product state of bond dimension $D$ whose energy approximates the minimal energy such states can achieve. The running time is exponential in $D$, and so the algorithm can be considered tractable even for $D$, which is logarithmic in the size of the chain. The result also implies trivially that the ground state of any local commuting Hamiltonian in 1D can be approximated efficiently; we improve this to an exact algorithm.

We discuss a quantum counting algorithm which transforms a physical particle-number state (and superpositions thereof) into a binary number. The algorithm involves two quantum Fourier transformations. One transformation is in physical space, where a stream of $n<N=2^K$ (charged) particles is coupled to $K$ qubits, rotating their states by prescribed angles. The second transformation is within the Hilbert space of qubits and serves to read out the particle number in a binary form. Applications include a divisibility check characterizing the size of a finite train of particles in a quantum wire and a scheme allowing one to entangle multiparticle wave functions in a Mach-Zehnder interferometer, generating Bell, Greenberger-Horne-Zeilinger, or Dicke states.

The variation or “scaling” of the quantum capacitances is explored for 45 diatomic molecules as a function of their dimensions. Scaling trends in the capacitances of these diatomic molecules dictate an “atoms-in-molecules” view of their valence energetics. That is, experimentally derived quantum capacitances for both homonuclear and heteronuclear diatomic molecules scale linearly with the average of the mean radii for the outermost orbitals of their component atoms. This is in accord with Maxwell’s law for classical capacitors formed from two conducting atom-sized spheres in tangential contact. However, the scaling behavior for the molecules has some nonclassical features. Notably, the quantum capacitances extrapolate to nonzero values at zero dimensions. Radius-capacitance points of the homonuclear diatomics lie primarily along five scaling lines, with each determined by points for molecules composed of atoms with the same atomic symmetry (i.e., atoms from the same column in the periodic table). Five scaling lines for heteronuclear diatomics each are determined by points for molecules of the same or similar molecular symmetries. The molecules’ quantum capacitances are calculated from their ionization potentials (IPs) and electron affinities (EAs). Thus, equations or laws for the scaling lines impose mutual consistency conditions among these electron detachment energies for different diatomics of similar symmetries. By taking advantage of this, the linear quantum capacitance scaling laws and ab initio atomic mean radii are used to predict IPs for two diatomics with known EAs (Ga${}_2$ and SeO), but for which there is no standard value of the IP. Similarly, the laws are used to predict EAs that were unknown or uncertain for several diatomics (Li${}_2$, LiF, CSe, PN, BF, BCl, SiO, GeO, NCl, CaO, SrO, and BaO) with known IPs.

Electrostatic velocity filtering is a technique for the production of continuous guided beams of slow polar molecules from a thermal gas. We extended this technique to produce pulses of slow molecules with a narrow velocity distribution around a tunable velocity. The pulses are generated by sequentially switching the voltages on adjacent segments of an electric quadrupole guide synchronously with the molecules propagating at the desired velocity. This technique is demonstrated for deuterated ammonia (ND${}_3$), delivering pulses with a velocity in the range of $20-100$ m/s and a relative velocity spread of $(16\pm 2)\%$ at full width at half maximum. At velocities around $60$ m/s, the pulses contain up to ${10}^6$ molecules each. The data are well reproduced by Monte Carlo simulations, which provide useful insight into the mechanisms of velocity selection.

A method to compensate for Earth’s gravity tide over an extended axial region is reported. Flattening acceleration is important in experiments where the coupling of the dynamics of free-falling probes to the gravity gradient generates stochastic noise on the measurement. Optimized cylindrically symmetric mass distributions lower Earth’s tidal effect over $10$ cm by a factor $10$${}^3$. A multimass compensation system with comparable performance is devised for tall atom interferometers. Reducing the gravity gradient is essential in terrestrial experiments based on atom fountain configurations being developed to precisely test general relativity or the neutrality of matter.

We explore quantitatively the fundamental connection between the entropy and local uncertainty product as an entanglement measure within the lowest energy eigenstate of a class of two-coupled anharmonic oscillator systems. We find that these two quantum aspects approach a unique relation as the entanglement between the oscillators becomes large if the potential of the first collective mode displays a generic single-well potential structure. This implies that the uncertainty product can be a good choice for the characterization of entanglement when the entropy is sufficiently large. Interestingly, although this relation is robust against the anharmonic perturbation, we find that it can be altered effectively by a quantum catastrophe.

We theoretically present a method to realize a deterministic photon-photon $\sqrt{\text{SWAP}}$ gate using a three-level $\Lambda$ system interacting with single photons in reflection geometry. The $\Lambda$ system is used completely passively as a temporary memory for a photonic qubit; the initial state of the $\Lambda$ system may be arbitrary, and active control by auxiliary fields is unnecessary throughout the gate operations. These distinct merits make this entangling gate suitable for deterministic and scalable quantum computation.

We have studied the interaction of molecular hydrogen with metal surfaces under fast-grazing-incidence conditions, by means of classical dynamics calculations based on density functional theory six-dimensional potential energy surfaces. We have performed calculations on two activated systems, ${\mathrm{H}}_2$/NiAl(110) and ${\mathrm{H}}_2$/Cu(111), and on two nonactivated systems, ${\mathrm{H}}_2$/Pd(111) and ${\mathrm{H}}_2$/Pd(110). We show that for rather open surfaces the computed $1-R$ probabilities (where $R$ represents the reflectivity) as a function of the normal collision energy at grazing incidence (along low-Miller-index directions) mimic reasonably well the dissociative adsorption probabilities obtained at normal incidence and thermal energies from the dissociation threshold up to the saturation limit. Our results indicate that fast grazing incidence experiments could be used as complement to traditional sticking experiments at thermal energies to determine dissociative adsorption saturation limits, which are usually unreachable due to limitations in traditional molecular beam experiments

We study theoretically the electron wave packet generated by an attosecond pulse train (APT) which is probed with a time-delayed infrared (IR) laser pulse. The APT creates an excited state and a continuum electron wave packet. By ionizing the excited state with an IR, a delayed new continuum electron wave packet is created. The interference of the wave packets from the two paths, as reflected in angle-resolved photoelectron spectra, is analyzed analytically. Using the analytical expressions, we examine the possibility of retrieving information on the electron wave packet generated by the APT.

The quantum dynamics of one-dimensional bosonic Josephson junctions with attractive and repulsive interparticle interactions is studied by using the Bose-Hubbard model and by numerically exact computations of the full many-body Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an equivalence between the evolution in time of the survival probability and the fragmentation of attractive and repulsive Josephson junctions with attractive and repulsive interactions of equal magnitude. The full many-body Hamiltonian does not possess this symmetry and, consequently, the dynamics of the attractive and repulsive junctions are different.

The coherence properties of degenerate Bose gases have usually been expressed in terms of spatial correlation functions, neglecting the rich information encoded in their temporal behavior. In this article we show, using a Hamiltonian classical-field formalism, that temporal correlations can be used to characterize familiar properties of a finite-temperature degenerate Bose gas. The temporal coherence of a Bose-Einstein condensate is limited only by the slow diffusion of its phase, and thus the presence of a condensate is indicated by a sharp feature in the temporal power spectrum of the field. We show that the condensate mode can be obtained by averaging the field for a short time in an appropriate phase-rotating frame, and that for a wide range of temperatures, the condensate obtained in this approach agrees well with that defined by the Penrose-Onsager criterion based on one-body (spatial) correlations. For time periods long compared to the phase diffusion time, the field will average to zero, as we would expect from the overall $\mathrm{U}(1)$ symmetry of the Hamiltonian. We identify the emergence of the first moment on short time scales with the concept of $\mathrm{U}(1)$ symmetry breaking that is central to traditional mean-field theories of Bose condensation. We demonstrate that the short-time averaging procedure constitutes a general analog of the “anomalous” averaging operation of symmetry-broken theories by calculating the anomalous thermal density of the field, which we find to have form and temperature dependence consistent with the results of mean-field theories.

We present a scheme to obtain the coherently enhanced Raman scattering in atomic vapor which is induced by a spin wave initially written by a weak write laser. The enhancement of Raman scattering is dependent on the number and the spatial distribution of the flipped atoms generated by the weak write laser. Such an enhanced Raman scattering may have practical applications in quantum information, nonlinear optics, and laser spectroscopy because of its simplicity.

We present a theoretical study of an experiment designed to detect radiation-pressure shot noise in an optomechanical system. Our model consists of a coherently driven optical cavity mode that is coupled to a mechanical oscillator. We examine the cross-correlation between two quadratures of the output field from the cavity. We determine under which circumstances radiation-pressure shot noise can be detected by a measurement of this cross-correlation. This is done in the general case of nonzero detuning between the frequency of the drive and the cavity resonance frequency. We study the qualitative features of the different contributions to the cross-correlator and provide quantitative figures of merit for the relative importance of the radiation-pressure shot noise contribution to other contributions. We also propose a modified setup of this experiment relevant to the “membrane-in-the-middle” geometry, which potentially can avoid the problems of static bistability and classical noise in the drive.

We consider two identical and noninteracting harmonic oscillators coupled to either two independent bosonic baths or to a common bosonic bath. Under the only assumption, weak coupling, we analyze in detail the non-Markovian short-time-scale evolution of intensity correlations, entanglement, and quantum discord for initial two-mode squeezed-thermal vacuum states. In the independent reservoirs case, we observe the detrimental effect of the environment for all these quantities and we establish a hierarchy for their robustness against the environmental noise. In the common reservoir case, for initial uncorrelated states, we find that only quantum discord can be created via interaction with the bath, while entanglement and subshot noise intensity correlations remain absent.