Within the Bogoliubov–de Gennes linearization theory of quantum or classical perturbations around a background solution to the one-dimensional nonlinear Schrödinger equation, we study the back-reaction of wave-packet perturbations on a gray-soliton background. From our recently published exact solutions, we determine that a wave packet effectively jumps ahead as it passes through a soliton, emerging with a wavelength-dependent forward translation in comparison to its motion in absence of the soliton. From this and from the full theory's exact momentum conservation, we deduce that post-Bogoliubov back-reaction must include a commensurate forward advance by the soliton itself. We quantify this effect with a simple theory, and confirm that it agrees with full numerical solution of the classical nonlinear Schrödinger equation. We briefly discuss the implications of this effect for quantum behavior of solitons in quasicondensed dilute gases at finite temperature.

We report on the two-photon superbunching effect of thermal light via constructive multiple two-photon path interference, showing the possibility of controlling the bunching property of thermal light in a linear optical system. By inserting $n$ pairs of mutually first-order incoherent optical channels as a cascade into the traditional Hanbury Brown and Twiss (HBT) interferometer, the two-photon bunching peak-to-background ratio of thermal light can be increased by up to $2\times 1.5^n$, surpassing the theoretical upper limit of 2 for a traditional HBT interferometer. Experimentally, the ratio was measured to be $2.4\pm 0.1$ when one pair of optical channels was inserted. Such a scheme can be viewed as a prototype of a two-photon grating.

We consider nonlinear analogs of parity-time- ($\mathcal{PT}$-) symmetric linear systems exhibiting defocusing nonlinearities. We study the ground state and odd excited states (dark solitons and vortices) of the system and report the following remarkable features. For relatively weak values of the parameter $\varepsilon$ controlling the strength of the $\mathcal{PT}$-symmetric potential, excited states undergo (analytically tractable) spontaneous symmetry breaking; as $\varepsilon$ is further increased, the ground state and first excited state, as well as branches of higher multisoliton (multivortex) states, collide in pairs and disappear in blue-sky bifurcations, in a way which is strongly reminiscent of the linear $\mathcal{PT}$ phase transition—thus termed the nonlinear $\mathcal{PT}$ phase transition. Past this critical point, initialization of, e.g., the former ground state, leads to spontaneously emerging solitons and vortices.

We investigate the nature of the three-mode interaction inside an optomechanically active microtoroid with a sizable ${\chi }^{\left(2\right)}$ coefficient. Experimental techniques are quickly advancing to the point where structures with the necessary properties can be made, and we argue that these provide a natural setting in which to observe rich dynamics leading, for instance, to genuine tripartite steady-state entanglement. We also show that this approach lends itself to a full characterization of the three-mode state of the system.

In this Brief Report, we study phase structure of a system of hard-core bosons with a nearest-neighbor (NN) repulsive interaction in a stacked triangular lattice. The Hamiltonian of the system contains two parameters, one of which is the hopping amplitude $t$ between NN sites and the other is the NN repulsion $V$. We investigate the system by means of the Monte Carlo simulations and clarify the low- and high-temperature phase diagrams. Phase diagrams contain various phases, e.g., solid, superfluid, supersolid, and phase-separated states. The result is compared with the phase diagram of the two-dimensional system in a triangular lattice at vanishing temperature.

In many quantum computer architectures, the qubits are in close proximity to metallic device elements. Metals have a high density of photon modes, and the fields spill out of the bulk metal because of the evanescent-wave component. Thus thermal and quantum electromagnetic Johnson-type noise from metallic device elements can decohere nearby qubits. In this Rapid Communication we use quantum electrodynamics to compute the strength of this evanescent-wave Johnson noise as a function of distance $z$ from a metallic half space. Previous treatments have shown unphysical divergences at $z=0$. We remedy this by using a proper nonlocal dielectric function. Decoherence rates of local qubits are proportional to the magnitude of electric or magnetic correlation functions evaluated at the qubit position. We present formulas for the decoherence rates. These formulas serve as an important constraint on future device architectures. Comparison with single-electron spin relaxation measurements shows that evanescent-wave Johnson noise may constitute the dominant relaxation mechanism in experiments performed at low magnetic field.

We report on an experimental demonstration of four-photon quantum interference using telecom-wavelength photons. The realization of multiphoton quantum interference is essential to linear optics quantum information processing and measurement-based quantum computing. We have developed a source that efficiently emits photon pairs in a pure spectrotemporal mode at a telecom-wavelength region, and have demonstrated quantum interference exhibiting reduced fringe intervals that correspond to a reduced de Broglie wavelength of up to the four-photon NOON state. Our result should open a path to practical quantum information processing using telecom-wavelength photons.

For a dynamical map $\Lambda (t,0)$, which sends a state $\rho \left(0\right)$ of a quantum open system to a state $\rho \left(t\right)=\Lambda (t,0)\rho \left(0\right)$, the decomposition law $\Lambda (t,0)=\Lambda (t,t_c)\Lambda (t_c,0)$ may break down at a specific time $t_c$. In this paper, we present a method to find the singular points $t_c$ and propose a measure for the singularity of the dynamical map. Two examples are portrayed to illustrate the method, and the measure of singularity for these singular points is calculated and discussed. An extension to a high-dimensional system is presented.

We introduce a scheme based on adiabatic passage that allows for long-range quantum communication through tight-binding chain with always-on interaction. By adiabatically varying the external gate voltage applied on the system, the electron can be transported from the sender's dot to the aim one. We numerically solve the Schrödinger equation for a system with a given number of quantum dots. It is shown that this scheme is a simple and efficient protocol to coherently manipulate the population transfer under suitable gate pulses. The dependence of the energy gap and the transfer time on system parameters is analyzed and shown numerically. Our method provides a guidance for future realization of adiabatic quantum state transfer in experiments.

We consider quantum correlations in a spin-1/2 open chain of $N$ nodes with the $XY$ Hamiltonian using different bases for the density-matrix representation and the initial state with a single polarized node. These bases of our choice are the following: (i) the basis of eigenvectors of the fermion operators which appears naturally through the Jordan-Wigner transformation (this representation of the density matrix is referred to as the $\beta$ representation); (ii) its Fourier representation ($c$ representation of the density matrix); and (iii) the basis of eigenvectors of the operators $I_{jz}$ (the $z$ projection of the $j$th spin, $j=1,\cdots ,N$). Although for the short chains (a few nodes) the qualitative behavior of the entanglement and the discord are very similar (the difference is quantitative), this is not valid for longer chains ($N\gtrsim 10$). In this case, there are qualitative and quantitative distinctions between the entanglement and the discord in all three cases. We underline the three most important features: (i) the quantum discord is static in the $\beta$ representation, where the entanglement is identical to zero; (ii) in the $c$ representation, the concurrence may be nonzero only between the nearest neighbors (with a single exception), while the discord is nonzero between any two nodes; and (iii) there is so-called “echo” in the evolution of the discord, which is not observed in the evolution of the concurrence. Using different bases, we may choose the preferable behavior of quantum correlations which allows a given quantum system to be more flexible in applications.

We develop a general technique to analyze the quantum effects of acceleration on realistic spatially localized electromagnetic field states entangled in the polarization degree of freedom. We show that for this setting, quantum entanglement may build up as the acceleration increases, providing a clear signature of phenomena related to the Unruh and Hawking effects.

The phase-coding quantum cryptographic scheme using the homodyne detection and weak coherent state [Hirano et al., Phys. Rev. A 68, 042331 (2003)] provides the simplest continuous-variable quantum key distribution scheme from the experimental side. However, the inherent loss of the practical system will not only increase the bit error rate (BER) but also affect the security of the final key. In this paper, we propose a single-photon-detection attack, and then the security of the final key will be compromised in some parameter regimes. Our results show that the BER induced by Eve can be lower than the inherent BER induced by the loss of the system in some parameter regimes. Furthermore, our attack gives the maximal communication distance of this scheme for given experimental parameters.

The physics of coherent beams of photons carrying axial orbital angular momentum (OAM) is well understood, and such beams, sometimes known as vortex beams, have found applications in optics and microscopy. Recently electron beams carrying very large values of axial OAM have been generated. In the absence of coupling to an external electromagnetic field, the propagation of such vortex electron beams is virtually identical mathematically to that of vortex photon beams propagating in a medium with a homogeneous index of refraction. But when coupled to an external electromagnetic field, the propagation of vortex electron beams is distinctly different from photons. Here we use the exact path integral solution to Schrodinger's equation to examine the time evolution of an electron wave function carrying axial OAM. Interestingly we find that the nonzero OAM wave function can be obtained from the zero OAM wave function, in the case considered here, simply by multipling it by an appropriate time and position dependent prefactor. Hence adding OAM and propagating it can in this case be replaced by first propagating then adding OAM. Also, the results shown provide an explicit illustration of the fact that the gyromagnetic ratio for OAM is unity. We also propose a novel version of the Bohm-Aharonov effect using vortex electron beams.

A general method to measure the energy distribution function of molecular fragments using a pulsed electron beam with time-delayed extraction coupled to a time-of-flight spectrometer is presented. The energy distributions of the homoisotopic species ${}^{14,15}$N${}^{+}$ and ${}^{14,15}$N${{}_2}^{2+}$, with the same mass-to-charge ratio, produced by 35–400 eV electron impact ionization of N${}_2$, are disentangled, showing two independent fragmentation routes for N${}^{+}$ ions with kinetic energies smaller than 1.0 eV. No measurable isotopic effect was found, indicating that predissociation does not play a role in this region of impact energies.

We consider the tunneling ionization of an electron, bound by a zero-range potential and a constant magnetic field, under the influence of a monochromatic laser beam with elliptical polarization. The exact solution of the Schrödinger equation and the Green's function for an electron moving in an arbitrary electromagnetic wave and crossed constant electric and magnetic fields are obtained. The exact expressions are found for the level shift and width of the electron in a zero-range force field, a constant magnetic field, and a monochromatic electromagnetic field. In the case of ionization of neutral atoms and positive ions, we also take into consideration the Coulomb interaction of the emerging electron with the atomic or ionic core. The first-order contributions from the Stark and Zeeman effects to the ionization rate are taken into account as well. The paper generalizes the results earlier obtained by V. M. Rylyuk and J. Ortner [Phys. Rev. A 67, 013414 (2003)].

We present our proposals for generating a total-hyperfine-spin-zero state for two $f=1$ or two $f=2$ particles, starting from initial unentangled states. We show that our goal can be achieved by exploiting spin-changing dynamics and quadratic Zeeman shifts with realistic choices of external magnetic fields and evolution time intervals.

We present an extension of the time-dependent density matrix renormalization group, also known as the time evolving block decimation algorithm, allowing for the computation of dynamically important excited states of one-dimensional many-body systems. We show its practical use for analyzing the dynamical properties and excitations of the Bose-Hubbard model describing ultracold atoms loaded in an optical lattice from a Bose-Einstein condensate. This allows for a deeper understanding of nonadiabaticity in experimental realizations of insulating phases.

We derive the Josephson relation for a dilute Bose gas in the framework of an auxiliary-field (AF) resummation of the theory in terms of the normal- and anomalous-density condensates. In the leading order of the AF loop expansion (LOAF) we find two critical temperatures in the phase diagram: the critical temperature $T_c$, where the atom Bose-Einstein condensate (BEC) appears first, and the temperature $T^{☆}>T_c$, which indicates the onset of superfluidity and the appearance of a diatom condensate in the system. In this context, the Josephson relation shows that the superfluid density is related to the square of a second-order parameter, the anomalous density, $\langle A\rangle \langle \phi \phi \rangle$, which can be thought of as a diatom condensate analogous to the Cooper-pair condensate discussed in the BCS approach to dilute Fermi gases. This is in contrast with the corresponding result in the Bose gas theory without a diatom condensate, which predicts that the superfluid density is proportional to the square of the usual atom BEC condensate, $\langle \phi \rangle$. In the region between $T_c$ and $T^{☆}$ the anomalous-density Green's function contains a zero energy-momentum state corresponding to a Goldstone state. This is a two-particle state with U(1) charge two. Our findings are consistent with the prediction that in the temperature range between $T_c$ and $T^{☆}$ a fraction of the system is in the superfluid state in the absence of the usual atom BEC condensate. This situation is similar to the case of dilute Fermi gases, where the superfluid density is proportional to the square of the gap parameter. The Josephson relation relies on the existence of zero energy and momentum excitations showing the intimate relationship between superfluidity and the Goldstone theorem.

In this work I apply a recently proposed improvement procedure, originally conceived to reduce finite lattice-spacing effects in transfer matrices for dilute Fermi systems, to tuning operators for the calculation of observables. I construct, in particular, highly improved representations for the energy and the contact as a first step in an improvement program for finite-temperature calculations. I illustrate the effects of improvement on those quantities with a ground-state lattice calculation at unitarity.

We derive a set of equations that describes the shape and behavior of a single perturbed vortex line in a Bose-Einstein condensate. Through the use of a matched asymptotic expansion and a unique coordinate transform, a relation for a vortex's velocity, anywhere along the line, is found in terms of the trapping, rotation, and distortion of the line at that location. This relation is then used to find a set of differential equations that give the line's specific shape and motion. This work extends a previous similar derivation by Svidzinsky and Fetter [Phys. Rev. A 62, 063617 (2000)], and enables a comparison with recent numerical results.