The repulsive Lieb-Liniger model can be obtained as the nonrelativistic limit of the sinh-Gordon model: all physical quantities of the latter model ($S$-matrix, Lagrangian, and operators) can be put in correspondence with those of the former. We use this mapping, together with the thermodynamical Bethe ansatz equations and the exact form factors of the sinh-Gordon model, to set up a compact and general formalism for computing the expectation values of the Lieb-Liniger model both at zero and finite temperatures. The computation of one-point correlators is thoroughly detailed and when possible compared with known results in the literature.

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a hard-wall trap or a harmonic oscillator trap with a tunable $\delta$-function barrier at the trap center. The mixture consists of a 1D Bose gas with repulsive interactions and of a 1D noninteracting spin-aligned Fermi gas, with both species interacting through hard-core interactions. Using a generalized Bose-Fermi mapping, we calculate the reduced single-particle density matrix and the momentum distribution of the gas as a function of barrier strength and the parity of particle number. The secondary peaks in the momentum distribution show remarkable correlation between particles on the two sides of the split.

We consider the stimulated Raman transition between two long-lived states via multiple intermediate states, such as between hyperfine ground states in the alkali-metal atoms. We present a concise treatment of the general, multilevel, off-resonant case, and we show how the lightshift emerges naturally in this approach. We illustrate our results by application to alkali-metal atoms and we make specific reference to cesium. We comment on some artifacts, due solely to the geometrical overlap of states, which are relevant to existing experiments.

Pulse shaping in a narrowband single-photon source based on cavity-enhanced spontaneous parametric down-conversion is analyzed. The scheme for pulse shaping is developed such that the wave form (both amplitude and phase) of heralded photons can be fully controlled by that of the pump pulse. It is shown that the developed scheme allows one to avoid additional losses introduced by amplitude modulators, thereby achieving the highest possible heralding efficiency.

Closed expressions are derived for the quantum measurement statistics of pre- and postselected Gaussian particle beams. The weakness of the preselection step is shown to compete with the nonorthogonality of postselection in a transparent way. The approach is shown to be useful in analyzing postselection-based signal amplification, allowing measurements to be extended far beyond the range of validity of the well-known Aharonov-Albert-Vaidman limit. Additionally, the present treatment connects postselected weak measurement to the topic of phase-contrast microscopy.

In this work we show that the distillation protocol proposed by P. Chen et al. [Phys. Rev. A 54, 3824 (1996)] allows one to distill Bell states at any time for a system evolving in vacuum and prepared in an initial singlet. It is also shown that the same protocol, applied in nonzero temperature thermal baths, yields a considerable recovering of entanglement.

We demonstrate ionic-type photonic lattices consisting of alternating positive and negative lattice potentials akin to those of ionic crystals in solids. A modified geometrical structure factor is developed for describing Bragg scattering in these non-Bravais photonic lattices. We show that lattice reconfiguration leads to incomplete Brillouin zone spectra due to selective band-gap closures. Experimentally, incomplete Brillouin zone spectra and associated Bragg-reflection suppression are observed in such ionic-type lattices optically induced in a bulk nonlinear crystal. Our experimental results agree well with our theoretical analysis.

We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state, as well as its usefulness as a quantum channel for teleportation. We find interesting relationships among the amplitude of the coherent states constituting the CTECSs, the number of subsystems forming the logical qubits (redundancy), and the extent to which amplitude damping affects the entanglement of the channel. For instance, in the sense of sudden death of entanglement, given a fixed value of the initial coherent state amplitude, the entanglement life span is shortened if redundancy is increased.

A nonrelativistic classification of charged molecular hydrogenic, helium, and mixed helium-hydrogenic chains with one or two electrons which can exist in a strong magnetic field $B\lesssim {10}^{16}$ G is given. It is shown that for both $1e-2e$ cases at the strongest studied magnetic fields the longest hydrogenic chain contains at most five protons, indicating the existence of ${\mathrm{H}}_5{}^{4+}$ and ${\mathrm{H}}_5{}^{3+}$ ions, respectively. In the case of the helium chains, the longest chains can exist at the strongest studied magnetic fields with three and four $\alpha$ particles for $1e-2e$ cases with the possible existence of ${\mathrm{He}}_3{}^{5+}$ and ${\mathrm{He}}_4{}^{6+}$, respectively. For mixed helium-hydrogenic chains, the number of heavy centers can reach five for the highest magnetic fields studied. In general, for a fixed magnetic field, two-electron chains are more bound than one-electron chains.

Recently Song et al. [Phys. Rev. A 80, 012331 (2009)] discovered that certain two-qutrit entangled states interacting with multilocal dephasing undergo distillability sudden death (DSD). We generalized their studies for quantum states under global, collective, and multilocal dephasing. We found that for a specific family of quantum states DSD and entanglement sudden death may happen under global dephasing as well as under multilocal dephasing. Moreover, for these states simple local unitary transformations may not avoid DSD under the current dynamics. As there is no definitive criterion for separability or entanglement of density matrices with dimensions greater than six, therefore we believe that the results obtained in this article are restricted to the specific family of states considered here.

We theoretically study how to control transport, bound states, and resonant states of a single photon in a one-dimensional coupled-cavity array. We find that the transport of a single photon in the cavity array can be controlled by tuning the frequency of either one or two cavities. If one of the cavities in the array has a tunable frequency, and its frequency is tuned to be larger (or smaller) than those of other cavities, then there is a photon bound state above (or below) the energy band of the coupled-cavity array. However, if two cavities in the array have tunable frequencies, then there exist both bound states and resonant states. If the frequencies of the two cavities are chosen to be much larger than those of other cavities, and the hopping couplings between any two nearest-neighbor cavities are weak, then a single photon with a resonant wave vector can be trapped in the region between the two frequency-tunable cavities. In this case, a quantum supercavity can be formed by these two frequency-tunable cavities. We also study how to apply this photon transport control to an array of coupled superconducting transmission line resonators.

We investigate the strong-field double ionization using a semiclassical model, in which the recollision-induced excitation-tunneling (RIET) effect has been taken into account with the Wentzel-Kramers-Brillouin (WKB) approach. When the laser intensity is below the recollision threshold, we find that both RIET and multiple recollisions become significant and can produce the anticorrelated (back-to-back) electron pair. Distinct footprints left by these two mechanisms on the correlated momentum spectra have been identified. As another signature of the transition to below the recollision threshold regime, we find that the V-shaped (or fingerlike) structure in the correlated momentum spectra fades away. Our model calculations have been compared with a recent experiment on argon atoms.

We present a theoretical study of the BEC-BCS crossover in the Bose-Einstein-condensate (BEC) regime in the case of an unequal number of fermions of two species. We take full account of the composite nature of the dimers made of fermions. In the limit of low densities, we calculate the ground-state energy of the system, or equivalently the chemical potentials of each species, as well as the one-particle gap and the energy of an “impurity” immersed in a Fermi sea. For the chemical potentials we go up to order $(\mathrm{density}){}^{4/3}$. The results found involve the exact atom-dimer $a_{\mathrm{AD}}$ and dimer-dimer $a_{\mathrm{DD}}$ scattering lengths and therefore include the three- and four-body problems in the many-body problem. We briefly comment on the importance of the different mean-field corrections for recent experiments.

The behaviors of a rapidly rotating Bose-Einstein condensate under extreme elongation in a two-dimensional anisotropic harmonic plus quartic trap are investigated. Due to the quartic trap, the system remains stable at high rotating velocity, $\Omega ⩾{\omega }_{\perp }$ (${\omega }_{\perp }$ is the radial harmonic trap frequency), and vortex lattices form even in the absence of the repulsive $s$-wave interaction ($g$). When $g$ is present, the interplay between $g$ and the quartic trap potential can lead to rich vortex lattice transition states as a function of $\Omega$, to which vortex lattices vanish eventually at some higher $\Omega$.

The resolution of current cryoelectron microscopy of radiation-sensitive specimens is ultimately limited by statistical noise because of the necessarily small number of electrons. To bypass this resolution barrier, we propose an extended in-focus phase-contrast microscopy scheme. The scheme incorporates a pixelwise deformable electrostatic mirror at a plane conjugate to the back focal plane of the objective lens. This setup would extract structural information more efficiently than otherwise and naturally enable generation of phase contrast. We present key concepts regarding microscope operations and estimate the degree of electron dose reduction that should in turn enable a resolution improvement.

We study a relation between the concurrence of assistance and the Mermin inequality on three-qubit pure states and claim that if a three-qubit pure state has a minimal concurrence of assistance greater than $1/2$ then the state violates some Mermin inequality. In this work, we analytically show that our claim holds for several classes and also find that it can be generalized to the set of all three-qubit pure states by exploiting previous numerical work [C. Emary and C. W. J. Beenakker, Phys. Rev. A 69, 032317 (2004)].

We study the exact solution of the two-body problem on a tight-binding one-dimensional lattice, with pairwise interaction potentials which have an arbitrary but finite range. We show how to obtain the full spectrum, the bound and scattering states, and the “low-energy” solutions by very efficient and easy-to-implement numerical means. All bound states are proven to be characterized by roots of a polynomial whose degree depends linearly on the range of the potential, and we discuss the connections between the number of bound states and the scattering lengths. “Low-energy” resonances can be located with great precision with the methods we introduce. Further generalizations to include more exotic interactions are also discussed.

Exact master equations describing the decay of a two-state system into a structured reservoir are constructed. By employing the exact solution for the model, analytical expressions are determined for the memory kernel of the Nakajima-Zwanzig master equation and for the generator of the corresponding time-convolutionless master equation. This approach allows an explicit comparison of the convergence behavior of the corresponding perturbation expansions. Moreover, the structure of widely used phenomenological master equations with a memory kernel may be incompatible with a nonperturbative treatment of the underlying microscopic model. Several physical implications of the results on the microscopic analysis and the phenomenological modeling of non-Markovian quantum dynamics of open systems are discussed.

We study and experimentally implement a double-slit quantum eraser in the presence of a controlled decoherence mechanism. A two-photon state, produced in a spontaneous parametric down-conversion process, is prepared in a maximally entangled polarization state. A birefringent double slit is illuminated by one of the down-converted photons, and it acts as a single-photon two-qubits controlled-not gate that couples the polarization with the transversal momentum of these photons. The other photon, which acts as a which-path marker, is sent through a Mach-Zehnder-like interferometer. When the interferometer is partially unbalanced, it behaves as a controlled source of decoherence for polarization states of down-converted photons. We show the transition from wavelike to particle-like behavior of the signal photons crossing the double slit as a function of the decoherence parameter, which depends on the length path difference at the interferometer.