We analyze theoretically and numerically the nonlinear process of pulse formation in mode-locked lasers, starting from a perturbation of a continuous wave. Focusing on weak-to-moderate dispersion systems, we show that pulse growth is initially slow, dominated by a cascade of energy from low to high axial modes, followed by fast strongly nonlinear growth, and finally relaxation to the stable pulse wave form. The pulse grows initially by condensing a fixed amount of energy into a decreasing time interval, with peak power growing toward a finite-time singularity that is checked when the gain bandwidth is saturated by the pulse.

We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic certification relies on a bound for the coherent information of a quantum channel that can be applied with arbitrary bipartite mixed input states and generalized output measurements.

The discrete Efimov scaling behavior, well known in the low-energy spectrum of three-body bound systems for large scattering lengths (unitary limit), is identified in the energy dependence of an atom-molecule elastic cross section in mass-imbalanced systems. That happens in the collision of a heavy atom with mass $m_H$ with a weakly bound dimer formed by the heavy atom and a lighter one with mass $m_L\ll m_H$. Approaching the heavy-light unitary limit, the $s$-wave elastic cross section $\sigma$ will present a sequence of zeros or minima at collision energies following closely the Efimov geometrical law. Our results, obtained with Faddeev calculations and supplemented by a Born-Oppenheimer analysis, open a perspective to detecting the discrete scaling behavior from low-energy scattering data, which is timely in view of the ongoing experiments with ultracold binary mixtures having strong mass asymmetries, such as lithium and cesium or lithium and ytterbium.

Calculation of the entropy of an ideal Bose-Einstein condensate (BEC) in a three-dimensional trap reveals unusual, previously unrecognized, features of the canonical ensemble. It is found that, for any temperature, the entropy of the Bose gas is equal to the entropy of the excited particles although the entropy of the particles in the ground state is nonzero. We explain this by considering the correlations between the ground-state particles and particles in the excited states. These correlations lead to a correlation entropy which is exactly equal to the contribution from the ground state. The correlations themselves arise from the fact that we have a fixed number of particles obeying quantum statistics. We present results for correlation functions between the ground and excited states in a Bose gas, so as to clarify the role of fluctuations in the system. We also report the sub-Poissonian nature of the ground-state fluctuations.

A dynamic procedure is established within the generalized Tavis–Cummings model to generate light states with discrete point symmetries, given by the cyclic group ${\mathcal{C}}_n$. We consider arbitrary dipolar coupling strengths of the atoms with a one-mode electromagnetic field in a cavity. The method uses mainly the matter-field entanglement properties of the system, which can be extended to any number of three-level atoms. An initial state constituted by the superposition of two states with definite total excitation numbers, ${|\psi \rangle }_{M_1}$, and ${|\psi \rangle }_{M_2}$, is considered. It can be generated by the proper selection of the time of flight of an atom passing through the cavity. We demonstrate that the resulting Husimi function of the light is invariant under cyclic point transformations of order $n=|M_1-M_2|$.

We derive the quantum mechanical description of light-matter interactions in optical cavities characterized solely by radiative decay. Unique to radiative decay is the conservation of photon number and coherence, in stark contrast to absorptive losses. This prohibits the description of such cavities by traditional means, e.g., coupling it to a bath of harmonic oscillators into which energy is dissipated. Here, we propose a description of cavities with radiative decay by introducing cavity and noise operators in terms of scattering modes. A multimode input-output formalism to predict measurable far field quantities arises naturally. We apply our general model to the special case of the single excitation regime. We find dynamics reminiscent of the dissipative Jaynes-Cummings model, but with vanishing backaction and a rich temporal and spectral structure of the output modes.

Diffusing-wave spectroscopy is a powerful technique which consists in measuring the temporal correlation function of the intensity of light multiply scattered by a medium. In this paper, we apply this technique to cold atoms under purely ballistic motion and we investigate the transition between the single and the multiple-scattering regime. The intensity correlation function changes from a simple Gaussian function, whose width reveals the sample temperature, to a more complex decay shortened by the frequency redistribution in the thick cloud. These features are quantitatively compared to simulations with a phase-coherent and an incoherent model. Both show a very good agreement with the experiments.

To guarantee the security of uniform random numbers generated by a quantum random-number generator, we study secure extraction of uniform random numbers when the environment of a given quantum state is controlled by the third party, the eavesdropper. Here we restrict our operations to incoherent strategies that are composed of the measurement on the computational basis and incoherent operations (or incoherence-preserving operations). We show that the maximum secure extraction rate is equal to the relative entropy of coherence. By contrast, the coherence of formation gives the extraction rate when a certain constraint is imposed on the eavesdropper's operations. The condition under which the two extraction rates coincide is then determined. Furthermore, we find that the exponential decreasing rate of the leaked information is characterized by Rényi relative entropies of coherence. These results clarify the power of incoherent strategies in random-number generation, and can be applied to guarantee the quality of random numbers generated by a quantum random-number generator.

We report on photoassociation (PA) spectroscopy of a degenerate Fermi gas of ${}^{173}\mathrm{Yb}$ atoms near the dissociation limit of the spin-forbidden ${}^{1}S_0$–${}^{3}P_1$ intercombination transition. An atom-loss spectrum is measured from a trapped sample for a spectral range down to $-1$ GHz with respect to the $f=5/2\to f^{\prime }=7/2$ atomic resonance. The spectrum shows 80 PA resonances, revealing the high nuclear spin nature of the system. To obtain additional information on the excited molecular states, we investigate the Zeeman effect on the spectrum near a detuning of $-0.8$ GHz and examine the quantum numbers of the Zeeman levels using various two-component spin mixture samples. Finally, we measure the atom-loss rate under PA light for several pronounced PA resonances.

We propose to study the transition from a nodal-loop to nodal-chain phase in a tunable two-dimensional $\pi$-flux lattice with periodical modulation potential. The Hamiltonian describes a periodically modulated optical lattice system under artificial magnetic fluxes and the tunable modulation phase factor provides additionally an artificial dimension of external parameter space. We demonstrate that this lattice system is able to describe a semimetal with either a nodal-loop or a nodal-chain Fermi surface in the extended three-dimensional Brillouin zone. By changing the strength of modulation potential $V$, we realize the transformation between the nodal-loop and nodal-chain semimetal.

Phase-changing materials (PCMs) are widely used for optical data recording, sensing, all-optical switching, and optical limiting. Our focus here is on the case when the change in transmission characteristics of the optical material is caused by the input light itself. Specifically, the light-induced heating triggers the phase transition in the PCM. In this paper, using a numerical example, we demonstrate that the incorporation of the PCM in a photonic structure can lead to a dramatic modification of the effects of light-induced phase transition, as compared to a stand-alone sample of the same PCM. Our focus is on short pulses. We discuss some possible applications of such phase-changing photonic structures for optical sensing and limiting.

We explore an electromagnetic field coupled to a mechanical resonator via quadratic optomechanical interaction in the reversed dissipation regime where the mechanical damping rate is much higher than the cavity-field dissipation rate. It is shown that in this regime, the cavity field effectively acquires an additional reservoir which is conditioned by the temperature of the mechanical bath as well as the mechanical damping rate. We analytically find the steady-state mean photon number and the critical temperature of the mechanical oscillator to cool or heat the coupled electromagnetic field. We also show that in the case of quadratic coupling, the temperature of the mechanical oscillator can be estimated in the quantum regime by observing the noise spectrum of the cavity field.

The interference of single photons from independent sources is an essential tool in quantum information processing. However, the interfering of photons with long temporal states in a time-resolved manner has rarely been studied. This is because without transmitting spectral filters or coupling to a cavity mode single photons generated in traditional nonlinear crystals suffer from a short temporal profile below 1 ns. With spectral correlation maintained in the biphotons generated from spontaneous four-wave mixing process in cold atom clouds, here we demonstrate the temporal interference of two frequency-tunable long photons from two independent cold atomic sources. We observe and analyze the interference of frequency-mismatched photons, where the phenomenon of the quantum beat at megahertz separation is displayed. Our paper provides more details for the quantum beat of two independent narrow-band single photons, which may find potential application in frequency-encoded photonic qubits in quantum information processing.

By combining analytical and numerical approaches, we study resonantly enhanced second-harmonic generation by individual high-index dielectric nanoparticles made of centrosymmetric materials. Considering both bulk and surface nonlinearities, we describe second-harmonic nonlinear scattering from a silicon nanoparticle optically excited in the vicinity of the magnetic and electric dipolar resonances. We discuss the contributions of different nonlinear sources and the effect of the low-order optical Mie modes on the characteristics of the generated far field. We demonstrate that the multipolar expansion of the radiated field is dominated by dipolar and quadrupolar modes (two axially symmetric electric quadrupoles, an electric dipole, and a magnetic quadrupole) and the interference of these modes can ensure directivity of the nonlinear scattering. The developed multipolar analysis can be instructive for interpreting the far-field measurements of the nonlinear scattering and it provides prospective insights into a design of complementary metal-oxide-semiconductor compatible nonlinear nanoantennas fully integrated with silicon-based photonic circuits, as well as methods of nonlinear diagnostics.

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed error tolerance $\delta$. The lower bound is given on the basis of the Cramér-Rao inequality, where the quantum Fisher information is bounded by the squared evolution time. The upper bound is obtained by an explicit construction of estimation procedures. By comparing the cases with different numbers of Hamiltonian channels, we also find that the few-channel procedure with adaptive feedback and the many-channel procedure with entanglement are equivalent in the sense that they require the same amount of time resource up to a constant factor.

Entanglement is a unique feature of quantum theory and has tremendous potential for application. Nevertheless, the complexity of quantum entanglement grows exponentially with an increase in the number of entangled particles. Here we introduce a quantum state concentration scheme which decomposes the multipartite entangled state into a set of bipartite and tripartite entangled states. It is shown that the complexity of the entanglement induced by the large number of particles is transformed into the high dimensions of bipartite and tripartite entangled states for pure quantum systems. The results not only simplify the tedious work of verifying the (in)equivalence of multipartite entangled states, but also are instructive in the quantum many-body problem involving multipartite entanglement.

Precision spectroscopy of molecular Rydberg states of high principal quantum number ($n\ge 50$) followed by Rydberg series extrapolation currently represents the most accurate method of determining the ionization energies of neutral molecules. Until recently, such determinations relied on the use of pulsed laser radiation and supersonic molecular beams, which limited the spectral linewidths and induced ac Stark shifts, thus causing undesirable statistical and systematic uncertainties. We report on the combination of single-mode continuous-wave laser radiation, calibrated with a frequency comb, with slow supersonic beams expanding from low-temperature reservoirs, to record transitions to high-$n$ molecular Rydberg states with unprecedented accuracy. As illustration, we present the result of a measurement, with a relative frequency accuracy of $\mathrm{\Delta }\nu /\nu =2\times {10}^{-10}$ and an absolute accuracy of 64 kHz, of the transition from the $GK$ ${}^1\mathrm{\Sigma }_g^{+}(v=0,N=2)$ state of ${\mathrm{H}}_2$ to the $n=50$ $f$ Rydberg state belonging to a series converging on the $X^{+}{}^2\mathrm{\Sigma }_g^{+}(v^{+}=0,N^{+}=0)$ ground state of ${{\mathrm{H}}_2}^{+}$. The accuracy of the result $[{\nu }_{\text{NIR}}=380132832.236{\left(0.035\right)}_{\text{stat}}{\left(0.054\right)}_{\text{sys}}\text{MHz}]$ approaches the accuracy that can be achieved in similar measurements on ultracold alkali-metal-atom samples, although the dominant sources of uncertainties are different. The implications of our result for precision measurements of the adiabatic ionization energy of ${\mathrm{H}}_2$ and of the energy-level structure of ${{\mathrm{H}}_2}^{+}$ are discussed.

Energy levels, wavelengths, magnetic-dipole and electric-quadrupole transition rates between the low-lying states are evaluated for ${\mathrm{W}}^{51+}$ to ${\mathrm{W}}^{54+}$ ions with $3d^n$ ($n=2$ to 5) electronic configurations by using an approach combining configuration interaction with the linearized coupled-cluster single-double method. The QED corrections are directly incorporated into the calculations and their effect is studied in detail. Uncertainties of the calculations are discussed. This study of such highly charged ions with the present method opens the way for future applications allowing an accurate prediction of properties for a very wide range of highly charged ions aimed at providing precision benchmarks for various applications.

We propose a theoretical idea to use an ultracold Fermi gas as a quantum simulator for the study of the low-density region of a neutron-star interior. Our idea is different from the standard quantum simulator that heads for perfect replication of another system, such as the Hubbard model discussed in high-$T_{\mathrm{c}}$ cuprates. Instead, we use the similarity between two systems and theoretically make up for the difference between them. That is, (1) we first show that the strong-coupling theory developed by Nozières and Schmitt–Rink (NSR) can quantitatively explain the recent experiment on the equation of state (EoS) in a ${}^6\mathrm{Li}$ superfluid Fermi gas in the BCS (Bardeen–Cooper–Schrieffer) unitary limit far below the superfluid phase-transition temperature $T_{\mathrm{c}}$. This region is considered to be very similar to the low-density region (crust regime) of a neutron star (where a nearly unitary $s$-wave neutron superfluid is expected). (2) We then theoretically compensate the difference that, while the effective range $r_{\mathrm{eff}}$ is negligibly small in a superfluid ${}^6\mathrm{Li}$ Fermi gas, it cannot be ignored ($r_{\mathrm{eff}}=2.7$ fm) in a neutron star, by extending the NSR theory to include effects of $r_{\mathrm{eff}}$. The calculated EoS when $r_{\mathrm{eff}}=2.7$ fm is shown to agree well with the previous neutron-star EoS in the low-density region predicted in nuclear physics. Our idea indicates that an ultracold atomic gas may more flexibly be used as a quantum simulator for the study of other complicated quantum many-body systems, when we use not only the experimental high tunability, but also the recent theoretical development in this field. Since it is difficult to directly observe a neutron-star interior, our idea would provide a useful approach to the exploration for this mysterious astronomical object.