We provide detailed proofs of triangle inequalities in coherence measures and entanglement concurrence. If a rank-2 state $\varrho$ can be expressed as a convex combination of two pure states, i.e., $\varrho =p_1|{\psi }_1\rangle \langle {\psi }_1|+p_2|{\psi }_2\rangle \langle {\psi }_2|$, a triangle inequality can be established as $|E\left(\right|{\mathrm{\Psi }}_1\rangle )-E\left(\right|{\mathrm{\Psi }}_2\rangle \left)\right|\le E\left(\varrho \right)\le E\left(\right|{\mathrm{\Psi }}_1\rangle )+E\left(\right|{\mathrm{\Psi }}_2\rangle )$, where $|{\mathrm{\Psi }}_1\rangle =\sqrt{p_1}|{\psi }_1\rangle$ and $|{\mathrm{\Psi }}_2\rangle =\sqrt{p_2}|{\psi }_2\rangle$; $E$ can be considered either coherence measures or entanglement concurrence. This inequality displays mathematical beauty for its similarity to the triangle inequality in plane geometry. An illustrative example is given after the proof.

We theoretically investigate the resonant Auger process via multiple core-excited states. The presence of multiple core-excited states sets off interference into the common final continuum, and we show that the degree of interference depends on the various parameters such as the intensity of the employed x-ray pulse and the lifetimes of the core-excited states. For the specific examples we employ the double ($1s^{-1}3p$ and $1s^{-1}4p$) core-excited states of Ne atom and numerically solve the time-dependent Schrödinger equation to demonstrate that the energy-resolved electron spectra clearly exhibit the signature of interference.

Superfluid vortex dynamics on an infinite cylinder differs significantly from that on a plane. The requirement that a condensate wave function be single valued upon once encircling the cylinder means that such a single vortex cannot remain stationary. Instead, it acquires one of a series of quantized translational velocities around the circumference, the simplest being $\pm \hslash /\left(2MR\right)$, with $M$ the mass of the superfluid particles and $R$ the radius of the cylinder. A generalization to a finite cylinder automatically includes these quantum-mechanical effects through the pairing of the single vortex and its image in either the top or bottom end of the surface. The dynamics of a single vortex on this surface provides a hydrodynamic analog of Laughlin pumping. The interaction energy for two vortices on an infinite cylinder is proportional to the classical stream function $\chi \left({\mathit{r}}_{12}\right)$, and it crosses over from logarithmic to linear when the intervortex separation ${\mathit{r}}_{12}$ becomes larger than the cylinder radius. An appendix summarizes the connection to an earlier study of Ho and Huang for one or more vortices on an infinite cylinder. A second appendix reviews the topologically equivalent planar annulus, where such quantized vortex motion has no offset, but Laughlin pumping may be more accessible to experimental observation.

In this paper, we study the stochastic resonance (SR) effect in a driven dissipative Jaynes-Cummings model. The SR effect is systematically investigated in the semiclassical and full quantum frameworks, and in both cases we find that SRs simultaneously occur for optical and atomic degrees of freedom. In particular, at zero temperature, quantum SR can be induced merely by vacuum fluctuations. Although the qualitative features of semiclassical SR and quantum SR are similar, their mechanisms are completely different: semiclassical SR is induced by thermal activation while quantum SR is induced by quantum-tunneling-assisted transitions. Our results provide a theoretical basis for experimentally observing and studying the SR phenomenon of the Jaynes-Cummings model in the quantum regime.

We present the concept of a realization of three-photon interference based on the procedure of light storage and release. Three probe photons are stored in an atomic medium in the tetrapod configuration. The medium irradiated by three control fields is shown to act as a flexible tritter. By changing the control fields applied at three stages of the photons' release, one can regulate the probabilities of obtaining various numbers of photons at each stage. Some of the signal coincidence probabilities can be made equal to zero, which is a generalization of the Hong-Ou-Mandel effect. The interference is demonstrated to gradually disappear for an increasing degree of the photons' distinguishability.

Quantum Darwinism extends the traditional formalism of decoherence to explain the emergence of classicality in a quantum universe. A classical description emerges when the environment tends to redundantly acquire information about the pointer states of an open system. In light of recent interest, we apply the theoretical tools of the framework to a qubit coupled with many bosonic subenvironments. We examine the degree to which the same classical information is encoded across collections of (i) complete subenvironments and (ii) residual “pseudomode” components of each subenvironment, the conception of which provides a dynamic representation of the reservoir memory. Overall, significant redundancy of information is found as a typical result of the decoherence process. However, by examining its decomposition in terms of classical and quantum correlations, we discover classical information to be nonredundant in both cases i and ii. Moreover, with the full collection of pseudomodes, certain dynamical regimes realize opposite effects, where either the total classical or quantum correlations predominantly decay over time. Finally, when the dynamics are non-Markovian, we find that redundant information is suppressed in line with information backflow to the qubit. By quantifying redundancy, we concretely show it to act as a witness to non-Markovianity in the same way as the trace distance does for nondivisible dynamical maps.

We introduce a family of quantum circuits in continuous variables and we show that, relying on the widely accepted conjecture that the polynomial hierarchy of complexity classes does not collapse, their output probability distribution cannot be efficiently simulated by a classical computer. These circuits are composed of input photon-subtracted (or photon-added) squeezed states, passive linear optics evolution, and eight-port homodyne detection. We address the proof of hardness for the exact probability distribution of these quantum circuits by exploiting mappings onto different architectures of subuniversal quantum computers. We obtain both a worst-case and an average-case hardness result. Hardness of boson sampling with eight-port homodyne detection is obtained as the zero squeezing limit of our model. We conclude with a discussion on the relevance and interest of the present model in connection to experimental applications and classical simulations.

We study the small frequency behavior of the bulk viscosity spectral function using stochastic fluid dynamics. We obtain a number of model independent results, including the long-time tail of the bulk stress correlation function and the leading nonanalyticity of the spectral function at small frequency. We also establish a lower bound on the bulk viscosity which is weakly dependent on assumptions regarding the range of applicability of fluid dynamics. The bound on the bulk viscosity $\zeta$ scales as ${\zeta }_{\min }\sim {(P-\frac{2}{3}\mathcal{E})}^2{\sum }_i{D}_i^{-2}$, where $D_i$ are the diffusion constants for energy and momentum and $P-\frac{2}{3}\mathcal{E}$, where $P$ is the pressure and $\mathcal{E}$ is the energy density, is a measure of scale breaking. Applied to the cold Fermi gas near unitarity, $|\lambda /a_s|\gtrsim 1$, where $\lambda$ is the thermal de Broglie wavelength and $a_s$ is the $s$-wave scattering length, this bound implies that the ratio of bulk viscosity to entropy density satisfies $\zeta /s\gtrsim 0.1\hslash /k_B$. Here, $\hslash$ is Planck's constant and $k_B$ is Boltzmann's constant.

A system of two-level noninteracting atoms driven by superposition of two Glauber coherent photonic states (a cat state) is studied. The field state is continuously restored by a source explicitly incorporated into the model. Due to its nature, the cat state changes phase by $\pi$ upon stimulated excitation of any atom, a peculiar kind of coherent quantum feedback. That results in correlations between photonic and atomic subsystems. In the limit of a strong field, the ansatz for the system's density matrix is proposed and an approximate analytical solution to the master equation is obtained in the case of a large number of atoms and slow spontaneous emission. Based on this solution, the steady-state second-order correlation function of atomic photoemissions is evaluated and investigated. The results demonstrate a remarkable difference from the case of the classical field (i.e., the field in a Glauber coherent state).

We study the statistics of the lasing output from a single-atom quantum heat engine, which was originally proposed by Scovil and Schulz-DuBois [H. E. D. Scovil and E. O. Schulz-DuBois, Phys. Rev. Lett. 2, 262 (1959)]. In this heat engine model, a single three-level atom is coupled with an optical cavity and is in contact with a hot and a cold heat bath together. We derive a fully quantum laser equation for this heat engine model and obtain the photon number distribution both below and above the lasing threshold. With the increase of the hot bath temperature, the population is inverted and lasing light comes out. However, we notice that if the hot bath temperature keeps increasing, the atomic decay rate is also enhanced, which weakens the lasing gain. As a result, another critical point appears at a very high temperature of the hot bath, after which the output light become thermal radiation again. To avoid this double-threshold behavior, we introduce a four-level heat engine model, where the atomic decay rate does not depend on the hot bath temperature. In this case, the lasing threshold is much easier to achieve and the double-threshold behavior disappears.

In this paper we studied the shaping and evolution of singular beams bearing optical vortices with fractional topological charges both in uniform and nonuniform anisotropic media. Starting from representation of the fractional-order vortex states as a superposition of an infinite number of integer-order vortices with certain energy distributions (the vortex spectra) we showed that the smooth wave front of the fractional vortex beam can either decay into an asymmetric array of integer-order vortices or, vice versa, the array of optical vortices can form a smooth helicoid-shaped wave front. We showed that by superimposing a finite number of the fractional-order vortex beams one can shape symmetric singular beams with arbitrary valued topological charges. We demonstrated that in biaxial crystals under the condition of the conical diffraction the fractional-order vortices are unstable. We also demonstrated that the circular fiber array with a space-variant birefringence is an appropriate medium for fractional-order vortex beams. In such arrays the supermodes may bear the half-integer-order vortices in circular components. Forming such supermodes plays a decisive role in evanescent-coupling assisted phase locking of individual fiber modes combined with tunneling of polarization states between anisotropic fibers in the array. We showed that the integer-charge phase increment in a fractional-order supermode consists of two half-integer-charge phase contributions. The explicit phase contribution is connected with the Pancharatnam-Berry phase that arises due to the phenomenon of nonadiabatic following. The implicit half-integer-charge phase contribution (or the “hidden phase”) happens due to the sign alteration of the amplitude factors in the field components that corresponds to the wave-front cuts. We have also made the comparison of the hidden and hydrodynamic phases in superfluidic fractional-charge vortices with analogous phases in fractional-order supermodes. We have established that in the optical case the hidden phase corresponds to the hydrodynamic phase in superfluids, whereas the hidden superfluidic phase is the analog of the optical Pancharatnam-Berry phase in supermodes.

Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi gas from first principles. Applying state-of-the-art analytic continuation techniques, we obtain the spectral function and the density and spin structure factors providing unique tools to visualize the BEC-BCS crossover. These quantities will allow for a direct comparison with experiments.

We consider the problem of estimating the temperature $T$ of a very cold equilibrium sample. The temperature estimates are drawn from measurements performed on a quantum Brownian probe strongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their nonperturbative interaction. We argue that this is advantageous for low-temperature thermometry, as we show in our model that (i) the thermometric precision at low $T$ can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures—a regime which is particularly relevant to quantum technologies.

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and $\gamma$ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.