Collimated directional emission is essentially required for an asymmetric resonant cavity. In this paper, we theoretically investigate a type of peanut-shaped microcavity which can support highly directional emission with a beam divergence as small as 2.5°. The mechanism of the collimated emission of this type of peanut-shaped microcavity is explained with a short-term ray trajectory. Moreover, the explanations are also confirmed by a numerical wave simulation. This extremely narrow divergence of the emission holds great potential in highly collimated lasing from on-chip microcavities.

Nanoscale lasers sustain a few optical modes so that the fraction of spontaneous emission $\beta$ funnelled into the useful (lasing) mode is high (of the order of 10${}^{-1}$) and the threshold, which traditionally corresponds to an abrupt kink in the light-in–light-out curve, becomes ill defined. We propose an alternative definition of the threshold that is based on the dynamical response of the laser and is valid even for $\beta =1$ lasers. The laser dynamics is analyzed through a reconstruction of its phase-space trajectory for pulsed excitations. Crossing the threshold, brings about a change in the shape of the trajectory and in the area contained in it. An unambiguous determination of the threshold in terms of this change is shown theoretically and illustrated experimentally in a photonic-crystal laser.

It is shown that the method of using excited-state wave functions in constructing exactly solvable potentials as suggested by Berger and Ussembayev [Phys. Rev. A 82, 022121 (2010)] can be generalized further. Using this method, exactly solvable potentials related to the harmonic oscillator and some other potentials are obtained. The nonlinear symmetry algebras underlying the harmonic-oscillator models are also obtained explicitly.

Unanyan, Otterbach, and Fleischhauer [Phys. Rev. A 79, 044101 (2009)] found that the confinement limit of a one-dimensional Dirac particle in a symmetric potential is half its corresponding Compton length and can be derived from the Dirac equation. Then, Toyama and Nogami [Phys. Rev. A 81, 044106 (2010)] conjectured that a more stringent limit holds for any symmetric potential. I would like to show, in this Brief Report, that the confinement limit conjectured by Toyama and Nogami can be derived from the Dirac equation.

We propose an efficient scheme for the realization of quantum information transfer and entanglement with nitrogen-vacancy (N-$V$) centers coupled to a high-$Q$ whispering-gallery mode (WGM) microresonator. We show that based on the effective dipole-dipole interaction between the N-$V$ centers mediated by the WGM, quantum information can be transferred between the N-$V$ centers through Raman transitions combined with laser fields. This protocol may open up promising possibilities for quantum communications with the solid-state quantum electrodynamic cavity system.

It has been recently shown that the placement of a three-level $\mathsf{V}$-type quantum emitter in the proximity of metallic nanostructures can create dynamics similar to that of quantum interference in spontaneous emission. Here we continue this work and present results on the population dynamics of a three-level V-type quantum emitter for various initial conditions in the presence of a two-dimensional array of metal-coated dielectric nanospheres.

We derive the density functional for the ground-state energy of a two-dimensional, spin-polarized gas of neutral fermionic atoms with magnetic-dipole interaction, in the Thomas-Fermi-Dirac approximation. For many atoms in a harmonic trap, we give analytical solutions for the single-particle spatial density and the ground-state energy, in dependence on the interaction strength, and we discuss the weak-interaction limit that is relevant for experiments. We then lift the restriction of full spin polarization and account for a time-independent inhomogeneous external magnetic field. The field strength necessary to ensure full spin polarization is derived.

In this paper a scheme is proposed for measuring nuclear-spin-dependent parity-nonconservation effects in highly charged ions. The idea is to employ circularly polarized laser light for inducing the transition between the level $(1s2s){}^1{S}_0$ and the hyperfine sublevels of $(1s2s){}^3{S}_1$ in He-like ions with nonzero nuclear spin. We argue that an interference between the allowed magnetic dipole $M1$ and the parity-violating electric dipole $E1$ decay channel leads to an observable asymmetry of order ${10}^{-7}$ in the transition cross section, in the atomic range $28⩽Z⩽35$. Experimental requirements for asymmetry measurements are discussed in the case of He-like ${}_{34}^{77}$Se.

We investigate the dynamical properties of a trapped finite-temperature normal Fermi gas with dipole-dipole interaction. For the free-expansion dynamics, we show that the expanded gas always becomes stretched along the direction of the dipole moment. In addition, we present the temperature and interaction dependences of the asymptotic aspect ratio. We further study the collapse dynamics of the system by suddenly increasing the dipolar interaction strength. We show that, in contrast to the anisotropic collapse of a dipolar Bose-Einstein condensate, a dipolar Fermi gas always collapses isotropically when the system becomes globally unstable. We also explore the interaction and temperature dependences for the frequencies of the low-lying collective excitations.

We study a system of ultracold fermionic polar molecules in a two-dimensional square lattice interacting via both the long-range dipole-dipole interaction and a short-range on-site attractive interaction. Singlet-superfluid, change density wave, and supersolid phases are found to exist in the system. We map out the zero-temperature phase diagram and find that the supersolid phase is considerably stabilized by the dipole-dipole interaction and thus can exist over a large region of filling factors. We study the melting of the supersolid phase with increasing temperature, map out a finite-temperature phase diagram of the system at fixed filling, and determine the parameter region where the supersolid phase can possibly be observed in experiments.

We consider the density response of a spin-imbalanced ultracold Fermi gas in an optical lattice in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We calculate the collective mode spectrum of the system in the generalized random-phase approximation and find that, although the collective modes are damped even at zero temperature, the damping is weak enough to have well-defined collective modes. We calculate the speed of sound in the gas and show that it is anisotropic due to the anisotropy of the FFLO pairing, which implies an experimental signature for the FFLO state.

We compute the geometric phase for a spin-1/2 particle under the presence of a composite environment, composed of an external bath (modeled by an infinite set of harmonic oscillators) and another spin-1/2 particle. We consider both cases: an initial entanglement between the spin-1/2 particles and an initial product state in order to see if the initial entanglement has an enhancement effect on the geometric phase of one of the spins. We follow the nonunitary evolution of the reduced density matrix and evaluate the geometric phase for a single two-level system. We also show that the initial entanglement enhances the sturdiness of the geometric phase under the presence of an external composite environment.

Measurements with a one-electron quantum cyclotron determine the electron magnetic moment, given by $g/2=1.001\hspace{0.5em}159\hspace{0.5em}652\hspace{0.5em}180\hspace{0.5em}73(28)[0.28\mathrm{ppt}]$, and the fine structure constant, $\alpha {}^{-1}=137.035\hspace{0.5em}999\hspace{0.5em}084(51)[0.37\mathrm{ppb}]$. Announcements of these measurements [Phys. Rev. Lett. 97, 030801 (2006); 100, 120801 (2008)] are supplemented here with a more complete description of the one-electron quantum cyclotron and the measurement methods, a discussion of the cavity control of the radiation field, a summary of the analysis of the measurements, and a fuller discussion of the uncertainties.

We study the sensitivity of the microwave and submillimeter transitions of the isotopologues of hydronium to the variation of the electron-to-proton mass ratio $\mu$. These sensitivities are enhanced for the low-frequency mixed inversion-rotational transitions. The lowest frequency transition (6.6 GHz) takes place for isotopologue ${\mathrm{H}}_2$DO${}^{+}$ and the respective sensitivity to $\mu$ variation is close to 200. This is about two orders of magnitude larger than the sensitivity of the inversion transition in ammonia, which is currently used for the search of $\mu$ variation in astrophysics.

Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the multidimensional variance-based uncertainty principle. The article concludes with an open conjecture.

We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the process of time evolution, using a single-layered tensor network structure. This significantly reduces the computational costs and allows simulations in a larger submanifold of the Hilbert space as bounded by the bond dimension of the tensor network. We present numerical evidence for stability of the method on an antiferromagnetic isotropic Heisenberg model where good agreement is found with the available accurate results.

A detailed derivation of the master equation of the cavity radiation of a coherently prepared Y-shaped four-level correlated emission laser is presented. The outline of the procedures that can be employed in analytically solving the stochastic differential equations and the rate equations of various correlations are also provided. It is shown that coherently preparing the atoms in the upper two energy levels and the lower level initially can lead to a genuine continuous-variable tripartite entanglement. Moreover, preparing the atoms in the coherent superposition, other than the possible maximum or minimum, of the upper two energy levels, leaving the lower level unpopulated, may lead to a similar observation. With the possibility of the atom at the intermediate energy level to take three different transition roots guided by the induced coherence, this system, in general, is found to encompass versatile options for practical utilization. In particular, coupling at least one of the dipole forbidden transitions by an external radiation is expected to enhance the degree of detectable entanglement.

Pairwise quantum discord (QD) and classical correlation (CC) are studied in the $\mathit{XY}$ spin chain with three-spin interaction. We analyze their capability in detecting quantum phase transitions (QPTs) at both zero and finite temperatures and find that the pairwise QD of two neighboring spins is more reliable than that of any other distances in identifying QPTs. Both the QD and CC detect quantum critical points associated with first- and higher-order QPTs caused by field and three-spin interactions at finite temperatures. In addition, we find a different finite-size scaling behavior for QD from previous reports for the transverse field Ising case and show some interesting phenomena of QD and entanglement of formation for finite temperatures.