The one- and two-photon scattering matrix $S$ is obtained analytically for a one-dimensional waveguide and a pointlike scatterer with $N$ excited levels (generalized $\mathsf{\text{V}}\text{-type}$ atom). We argue that the two-photon scattering matrix contains sufficient information to distinguish between different level structures which are equivalent for single-photon scattering, such as a $\mathsf{\text{V}}$ atom with $N=2$ excited levels and two two-level systems. In particular, we show that the scattering with the $\mathsf{\text{V}}\text{-type}$ atom exhibits a destructive interference effect leading to two-photon coupled-resonator-induced transparency, where the nonlinear part of the two-photon scattering matrix vanishes when each incident photon fulfills a single-photon condition for transparency.

Single-photon devices at microwave frequencies are important for applications in quantum information processing and communication in the microwave regime. In this work we describe a proposal of a multioutput single-photon device. We consider two superconducting resonators coupled to a gap-tunable qubit via both its longitudinal and transverse degrees of freedom. Thus, this qubit-resonator coupling differs from the coupling in standard circuit quantum-electrodynamic systems described by the Jaynes-Cummings model. We demonstrate that an effective quadratic coupling between one of the normal modes and the qubit can be induced and this induced second-order nonlinearity is much larger than that for conventional Kerr-type systems exhibiting photon blockade. Assuming that a coupled normal mode is resonantly driven, we observe that the output fields from the resonators exhibit strong sub-Poissonian photon-number statistics and photon antibunching. Contrary to previous studies on resonant photon blockade, the first-excited state of our device is a pure single-photon Fock state rather than a polariton state, i.e., a highly hybridized qubit-photon state. In addition, it is found that the optical state truncation caused by the strong qubit-induced nonlinearity can lead to an entanglement between the two resonators, even in their steady state under the Markov approximation.

We describe how electromagnetically induced transparency may be used to construct a nontraditional near-ideal quantum heat engine as constrained by the second law. The engine is pumped by a thermal reservoir that may be either hotter or colder than that of an exhaust reservoir, and also by a monochromatic laser. As output, it produces a bright narrow emission at line center of an otherwise absorbing transition.

Wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix $\rho \left(t\right)$ with only diagonal elements in a given basis $\left\{\right|n\rangle \}$, it may be treated as a classical mixture, i.e., a system which randomly occupies the basis states $|n\rangle$ with probabilities ${\rho }_{nn}\left(t\right)$. Equivalent to so-called smoothing in classical probability theory, subsequent probing of the occupation of the states $|n\rangle$ may improve our ability to retrodict what was the outcome of a projective state measurement at time $t$. Here, we show with experiments on a superconducting qubit that the smoothed probabilities do not, in the same way as the diagonal elements of $\rho \left(t\right)$, permit a classical mixture interpretation of the state of the system at the past time $t$.

Gapless many-body quantum systems in one spatial dimension are universally described by the Luttinger liquid effective theory at low energies. Essentially, only two parameters enter the effective low-energy description, namely, the speed of sound and the Luttinger parameter. These are highly system dependent and their calculation requires accurate nonperturbative solutions of the many-body problem. Here we present a simple theoretical method that only uses collisional information to extract the low-energy properties of spinless one-dimensional systems. Our results are in remarkable agreement with available results for integrable models and from large-scale Monte Carlo simulations of one-dimensional helium and hydrogen isotopes. Moreover, we estimate theoretically the critical point for spinodal decomposition in one-dimensional ${}^4\mathrm{He}$ and show that the exponent governing the divergence of the Luttinger parameter near the critical point is exactly 1/2, in excellent agreement with Monte Carlo simulations.

It is well known that a state with complex energy cannot be the eigenstate of a self-adjoint operator, such as the Hamiltonian. Resonances, i.e., states with exponentially decaying observables, are not vectors belonging to the conventional Hilbert space. One can describe these resonances in an unusual mathematical formalism based on the so-called rigged Hilbert space (RHS). In the RHS, the states with complex energy are denoted as Gamow vectors (GVs), and they model decay processes. We study the GVs of the reversed harmonic oscillator, and we analytically and numerically investigate the unstable evolution of wave packets. We introduce the background function to study initial data that are not composed only by a summation of GVs, and we analyze different wave packets belonging to specific function spaces. Our work furnishes support for the idea that irreversible wave propagation can be investigated using rigged-Hilbert-space quantum mechanics and provides insight for the experimental investigation of irreversible dynamics.

Quantum noise is ubiquitous to quantum systems as they incessantly interact with their surroundings and results in degrading useful resources such as coherence for single quantum systems and quantum correlations for multipartite systems. Given the importance of these resources in various quantum information processing protocols, it is of the utmost importance to characterize how deteriorating a particular noise scenario (quantum channel) is in reference to a certain resource. Here we develop a theory of coherence-breaking channels for single quantum systems. Any quantum channel on a single quantum system will be called a coherence-breaking channel if it is an incoherent channel and maps any state to an incoherent state. We explicitly and exhaustively characterize these coherence-breaking channels. Moreover, we define the coherence-breaking indices for incoherent quantum channels and present various examples to elucidate this concept. We further introduce the concept of coherence sudden death under noisy evolutions and make an explicit connection of the phenomenon of coherence sudden death with the coherence-breaking channels and the coherence-breaking indices together with various suggestive examples. Furthermore, for higher-dimensional Hilbert spaces, we establish the typicality of the dynamics of coherence under any incoherent quantum channel exploiting the concentration of measure phenomenon.

We determine the frequency of the Yb I ${}^{1}S_0\text{−}{}^{1}P_1$ transition at 399 nm using an optical frequency comb. Although this transition was measured previously using an optical transfer cavity [D. Das et al., Phys. Rev. A 72, 032506 (2005)], recent work has uncovered significant errors in that method. We compare our result of 751 526 533.49 $\pm$ 0.33 MHz for the ${}^{174}\mathrm{Yb}$ isotope with those from the literature and discuss observed differences. We verify the correctness of our method by measuring the frequencies of well-known transitions in Rb and Cs, and by demonstrating proper control of systematic errors in both laser metrology and atomic spectroscopy. We also demonstrate the effect of quantum interference due to hyperfine structure in a divalent atomic system and present isotope shift measurements for all stable isotopes.

We report direct laser spectroscopy of the ${}^1{S}_0$ to ${}^3{D}_1$ highly-forbidden M1 clock transition in ${}^{175}{\mathrm{Lu}}^{+}$. Clock operation is demonstrated on three pairs of Zeeman transitions, one pair from each hyperfine manifold of the ${}^3{D}_1$ term. We measure the hyperfine intervals of the ${}^3{D}_1$ to 10 ppb uncertainty and infer the optical frequency averaged over the three hyperfine transitions to be $353.6399159522\left(6\right)$ THz. The lifetime of the ${}^3{D}_1$ state is inferred to be ${174}_{-32}^{+23}$ hours from the M1 coupling strength.

The effects of the lattice constant and electron affinity on the negative-ion conversion of a neutral atom undergoing grazing scattering on an ionic-crystal surface over the complete velocity range were investigated. Here, a comparison of negative-ion conversion of neutral ${\mathrm{O}}^0\text{−}\mathrm{KCl}\left(100\right),{\mathrm{F}}^0\text{−}\mathrm{KCl}\left(100\right)$, and ${\mathrm{O}}^0\text{−}\mathrm{KI}\left(100\right)$ surface systems shows that the pronounced difference in the efficiency of negative-ion formation between ${\mathrm{F}}^0\text{−}\mathrm{KCl}\left(100\right)$ and ${\mathrm{O}}^0\text{−}\mathrm{KCl}\left(100\right)$ is caused by the large difference in their projectile electron affinities, whereas the difference between ${\mathrm{O}}^0\text{−}\mathrm{KI}\left(100\right)$ and ${\mathrm{O}}^0\text{−}\mathrm{KCl}\left(100\right)$ is caused by the difference in their lattice constants.

The theoretical $\gamma$-ray spectra from positron-electron annihilation process in a wide variety of atoms and molecules are studied. The theoretical Doppler broadened $\gamma$-ray spectra for core, inner valence, and outer valence electrons of these molecules are studied systematically. The present results show that the experimental $\gamma$-ray spectra agree well with inner valence electrons, especially the lowest occupied valence orbital electrons rather than the outer valence electrons. These inner valence electrons show a strong correlation with the corresponding available experimental measurements. These findings are interesting because the outer valence electrons have been supposed to have larger probability annihilating with positrons rather than the inner valence electrons. The present work also suggests that the accurate positron wave functions must be involved to identify the dominance of the bound electrons clearly in positron-electron annihilation process.

Double ionization of a model helium system by intense extreme ultraviolet laser pulses is investigated by solving the time-dependent Schrödinger equation and extracting the photoelectron spectra. Considering a frequency regime where the nonsequential two-photon double ionization is expected to dominate the double ionization process according to the perturbation theory, we identify the sequential and nonsequential mechanisms from the joint energy spectra of two electrons in the strong-field regime. In the nonperturbative regime, we find that sequential multiphoton double ionization shows remarkable peaks in the joint energy spectra and these peaks spread their widths with increasing laser field strength, which is caused by the ac Stark effect. Thus in the strong-field regime, the ac Stark shifts of different ionic states can be observed from the sequential multiphoton features in the joint energy spectra and the signs of the ac Stark shifts can be controlled by the laser frequency. We also find that the nonsequential mechanism dominates double ionization only at low field strengths while the sequential multiphoton mechanism contributes substantially at high field strengths, in accordance with estimates from rate equations.

We calculate the reflection and transmission probabilities in a one-dimensional Fermi gas with an equal mixing of the Rashba and Dresselhaus spin-orbit coupling (RD-SOC) produced by an external Raman laser field. These probabilities are computed over multiple relevant energy ranges within the pseudopotential approximation. Strong scattering resonances are found whenever the incident energy approaches either a scattering threshold or a quasibound state attached to one of the energetically closed higher dispersion branches. A striking difference is demonstrated between two very different regimes set by the Raman laser intensity, namely, between scattering for the single-minimum dispersion versus the double-minimum dispersion at the lowest threshold. The presence of RD-SOC together with the Raman field fundamentally changes the scattering behavior and enables the realization of very different one-dimensional theoretical models in a single experimental setup when combined with a confinement-induced resonance.

Tightly confined modes of light, as in optical nanofibers or photonic crystal waveguides, can lead to large optical coupling in atomic systems, which mediates long-range interactions between atoms. These one-dimensional systems can naturally possess couplings that are asymmetric between modes propagating in different directions. Strong long-range interaction among atoms via these modes can drive them to a self-organized periodic distribution. In this paper, we examine the self-organizing behavior of atoms in one dimension coupled to a chiral reservoir. We determine the solution to the equations of motion in different parameter regimes, relative to both the detuning of the pump laser that initializes the atomic dipole-dipole interactions and the degree of reservoir chirality. In addition, we calculate possible experimental signatures such as reflectivity from self-organized atoms and motional sidebands.

An additive and semidefinite programming (SDP) computable entanglement measure is introduced to upper bound the amount of distillable entanglement in bipartite quantum states by operations completely preserving the positivity of partial transpose (PPT). This quantity is always smaller than or equal to the logarithmic negativity, the previously best known SDP bound on distillable entanglement, and the inequality is strict in general. Furthermore, a succinct SDP characterization of the one-copy PPT deterministic distillable entanglement for any given state is also obtained, which provides a simple but useful lower bound on the PPT distillable entanglement. Remarkably, there is a genuinely mixed state of which both bounds coincide with the distillable entanglement, while being strictly less than the logarithmic negativity.

Efimov physics is renowned for the self-similar spectrum featuring the universal ratio of one eigenenergy to its neighbor. Even more esoteric is the numerically unveiled fact that every Efimov trimer is accompanied by a pair of tetramers. Here we demonstrate that this hierarchy of universal few-body clusters has a topological origin by identifying the numbers of universal three- and four-body bound states with the winding numbers of the renormalization-group limit cycle in theory space. The finding suggests a topological phase transition in mass-imbalanced few-body systems which should be tested experimentally.

We develop a theory of optomechanical cooling with a squeezed input light field. We show that Stokes heating transitions can be fully suppressed when the driving field is squeezed below the vacuum noise level at an appropriately selected squeezing phase and for a finite amount of squeezing. The quantum backaction limit to laser cooling can be therefore moved down to zero and the resulting final temperature is then solely determined by the ratio between the thermal phonon number and the optomechanical cooperativity parameter, independently of the actual values of the cavity linewidth and mechanical frequency. Therefore, driving with a squeezed input field allows us to prepare nanomechanical resonators, even with low resonance frequency, in their quantum ground state with a fidelity very close to one.

Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor-oscillating neutral mesons for the two most promising collapse models, the QMUPL (quantum mechanics with universal position localization) model and the mass-proportional CSL (continuous spontaneous localization) model. Our results are showing (i) a strong sensitivity to the very assumptions of the noise field underlying those two collapse models and (ii) under particular assumptions the CSL case allows one even to recover the decay dynamics. This in turn allows one to predict the effective collapse rates solely based on the measured values for the oscillation (mass differences) and the measured values of the decay constants. The four types of neutral mesons ($K$ meson, $D$ meson, $B_d$ meson, and $B_s$ meson) lead surprisingly to ranges comparable to those put forward by Adler [J. Phys. A: Math. Theor. 40, 2935 (2007)] and Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986)]. Our results show that these systems at high energies are very sensitive to possible modifications of the standard quantum theory, making them a very powerful laboratory to rule out certain collapse scenarios and study the detailed physical processes solving the measurement problem.