We study the photon transfer along a linear array of three coupled cavities where the central one contains an interacting two-level system in the strong- and ultrastrong-coupling regimes. We find that an inhomogeneously coupled array forbids a complete single-photon transfer between the external cavities when the central one performs a Jaynes-Cummings dynamics. This is not the case in the ultrastrong-coupling regime, where the system exhibits singularities in the photon transfer time as a function of the cavity-qubit coupling strength. Our model can be implemented within the state-of-the-art circuit quantum electrodynamics technology and it represents a building block for studying photon state transfer through scalable cavity arrays.

We present a scheme for tuning and controlling nanomechanical resonators by subjecting them to electrostatic gradient fields, provided by nearby tip electrodes. We show that this approach enables access to a regime of optomechanics where the intrinsic nonlinearity of the nanoresonator can be explored. In this regime, one or several laser-driven cavity modes coupled to the nanoresonator and suitably adjusted gradient fields make it possible to control the motional state of the nanoresonator at the single-phonon level. Some applications of this platform have been presented previously [S. Rips, M. Kiffner, I. Wilson-Rae, and M. J. Hartmann, New J. Phys. 14, 023042 (2012); S. Rips and M. J. Hartmann, Phys. Rev. Lett. 110, 120503 (2013)]. Here we provide a detailed description of the corresponding setup and its optomechanical coupling mechanisms together with an in-depth analysis of possible sources of damping or decoherence and a discussion of the readout of the nanoresonator state.

We present an approach for calculating the nonlinear propagation of surface plasmon polaritons in one-dimensional planar waveguides consisting of a metal slab or a semi-infinite metal bounded by linear dielectrics, starting with an assumed third-order nonlinearity that characterizes the nonlinear response of the metal. With this approach we model the self-phase-modulation of surface plasmon polaritons. Expressions relating the complex nonlinear parameter of these surface waves with the third-order nonlinear susceptibility of the metal are provided. We present and discuss results pertaining to the self-phase-modulation of the symmetric and antisymmetric surface plasmon polaritons supported by a thin gold slab in vacuum and of the surface plasmon polariton supported by the single gold-vacuum interface.

It is not always justified to model the environment of a realistic quantum system as a collection of harmonic oscillators or two-level systems. To explore interesting physics associated with a composite environment, here we study the dynamics of a qubit coupled to a second two-level system, which is in turn coupled to a harmonic-oscillator bath. That is, the qubit of interest is in the presence of a composite environment consisting of the second two-level system and a conventional harmonic-oscillator bath. We investigate the issue of pointer states of decoherence for the qubit for different coupling strengths between the qubit and such a composite environment. It is shown that for weak-, intermediate-, or strong-coupling strengths, the qubit's reduced density matrix has a coupling-strength-dependent diagonal representation, thus yielding coupling-strength-dependent computational pointer states. Interestingly, the associated decoherence rate can decrease as the coupling strength increases.

We show a procedure to classically simulate the Majorana equation in $1+1$ dimensions via two one-dimensional photonic crystals. We use a decomposition of the Majorana equation into two Dirac equations and propose an approach that uses a bichromatic refractive index distribution and nearest-neighbor couplings of the type found in Glauber-Fock lattices. This allows us to escape the restriction of staying near the Brillouin zone imposed by the classical simulation of Dirac dynamics with bichromatic lattices. Furthermore, it is possible to simulate the evolution of Gaussian wave packets under the Majorana-Dirac equation with light impinging only into the first waveguide of our bichromatic-Glauber-Fock lattice.

We derive necessary and sufficient conditions for arbitrary multimode (pure or mixed) Gaussian states to be equivalent under Gaussian local unitary operations. To do so, we introduce a standard form for Gaussian states, which has the properties that (i) every state can be transformed into its standard form via Gaussian local unitaries and (ii) it is unique and (iii) it can be easily computed. Thus, two states are equivalent under Gaussian local unitaries if and only if their standard forms coincide. We explicitly derive the standard form for two- and three-mode Gaussian pure states. We then investigate transformations between these classes by means of Gaussian local operations assisted by classical communication. For three-mode pure states, we identify a global property that cannot be created but only destroyed by local operations. This implies that the highly entangled family of symmetric three-mode Gaussian states is not sufficient to generate all three-mode Gaussian states by local Gaussian operations.

We establish tight upper and lower bounds for the entanglement of formation of an arbitrary two-mode Gaussian state employing the necessary properties of Gaussian channels. Both bounds are strictly given by the entanglement of formation of symmetric Gaussian states, which are simply constructed from the reduced states obtained by partial trace of the original one.

The $N$-representability problem is the problem of determining whether there exists $N$-particle states with some prescribed property. Here we report an affirmative solution to the fermion $N$-representability problem when both the density and the paramagnetic current density are prescribed. This problem arises in current-density functional theory and is a generalization of the well-studied corresponding problem (only the density prescribed) in density functional theory. Given any density and paramagnetic current density satisfying a minimal regularity condition (essentially that a von Weizäcker–like canonical kinetic energy density is locally integrable), we prove that there exists a corresponding $N$-particle state. We prove this by constructing an explicit one-particle reduced density matrix in the form of a position-space kernel, i.e., a function of two continuous-position variables. In order to make minimal assumptions, we also address mathematical subtleties regarding the diagonal of, and how to rigorously extract paramagnetic current densities from, one-particle reduced density matrices in kernel form.

In a recent contribution our group proposed a perturbative approach to deal with the open problem of double ionization of helium by electron impact. The goal of this work is to delve into the physics of the scattering function, and provide evidence of the nature of the single-ionization channels present in the three-body wave function. We show that the fast oscillating parts of the wave function are indeed the single-ionization channels, which appear coupled with the double continuum ones. We found a particular type of basis set within the Generalized Sturmian method that is better suited to isolate single from double-ionization channels.

Rydberg atoms excited by cold blackbody radiation are shown to display long-lived quantum coherences on time scales of tens of picoseconds. By solving non-Markovian equations of motion with no free parameters we obtain the time evolution of the density matrix and demonstrate that the blackbody-induced temporal coherences manifest as slowly decaying (100 ps) quantum beats in time-resolved fluorescence. An analytic model shows the dependence of the coherent dynamics on the energy splitting between atomic eigenstates, transition dipole moments, and coherence time of the radiation. Experimental detection of the fluorescence signal from a trapped ensemble of ${10}^8$ Rydberg atoms is discussed, but shown to be technically challenging at present, requiring cosmic-microwave-background amplification somewhat beyond current practice.

Using worm-type quantum Monte Carlo simulations, we investigate bosonic mixtures on a triangular lattice of two species of bosons, which interact via nearest-neighbor intraspecies ($V$) and on-site interspecies ($U$) repulsions. For the case of symmetric hopping amplitude ($t_A/V=t_B/V$) and $U/V=1$, we determine a rich ground-state phase diagram that contains double-solid, double-superfluid, supersolid (SS), solid-superfluid (solid-SF), and counterflow supersolid (CSS) states. The SS, solid-SF, and CSS states exhibit spontaneous symmetry breaking among the three sublattices of the triangular lattice and between the two species, which leads to a nonzero crystalline density wave order in each species. We, furthermore, show that the CSS and the SS states are present for $t_A/V\ne t_B/V$, and the latter even survives up to the $t_A/V\to \infty$ or $t_B/V\to \infty$ limit. The effects induced by the variation of $U/V$ and by the imbalance of particle numbers of the two species are also explored.

We consider light propagation through a pair of nonlinear optical waveguides with absorption, placed in a medium with power gain. The active medium boosts the in-phase component of the overlapping evanescent fields of the guides, while the nonlinearity of the guides couples it to the damped out-of-phase component creating a feedback loop. As a result, the structure exhibits stable stationary and oscillatory regimes in a wide range of gain-loss ratios. We show that the pair of actively coupled ($\mathcal{AC}$) waveguides can act as a stationary or integrate-and-fire comparator sensitive to tiny differences in their input powers.

In this paper, we address the propagation of a near resonant laser inside an atomic vapor in the case when, due to the Kerr effect, the laser beam would either self-focus or self-defocus. We show, both theoretically and experimentally, how to get rid of such an alteration in the transverse beam profile without changing any of the characteristics of the laser light under consideration (wavelength, intensity, etc.), nor of the atomic vapor. Moreover, our proposed method offers a lot of control on the beam profile, whose transverse size after propagation may be chosen at will by making use of a second, copropagating laser, whose required wavelength and intensity may be derived analytically.

The collision of the two surface plasmon polariton pulses at the interface between a metal and a dielectric with cubic nonlinearity is investigated. We reveal the possibility of the reflection of a weak signal surface plasmon from the strong pump plasmon pulse resulting in the time delay and spectral shift in the signal plasmon pulse. Using such an interaction, one can control the propagation dynamics of the signal pulse via the modulation of the intensity of the pump pulse.

The solutions to the free Schrödinger equation discussed by P. Strange (arXiv:1309.6753) and A. Aiello (arXiv:1309.7899) are analyzed. It is shown that their properties can be explained with the help of Niederer's transformation.

We propose a way to detect the fractal energy spectrum of the Hofstadter model from the density distributions of ultracold fermions in an external trap. At low temperature, the local compressibility is proportional to the density of states of the system, which reveals the fractal energy spectrum. However, thermal broadening and noises in the real experimental situation inevitably smear out fine features in the density distribution. To overcome this difficulty, we use the maximum entropy method to extract the density of states directly from the noisy thermal density distributions. Simulations show that one is able to restore the core feature of the Hofstadter's butterfly spectrum with current experimental techniques. By further reducing the noise or the temperature, one can refine the resolution and observe fine structures of the butterfly spectrum.

We generally study whether or not the information of open quantum systems would be totally erased by their surrounding environments in thermalization processes. A complex system composed of a harmonic oscillator and its environment is studied. When the interaction spectral density contains zero-value regions, there is a threshold of system-bath coupling, ${\eta }_c$, above which the initial information of the system partially remains. We estimated this threshold by the properties of the system and its bath, i.e., the density of the environment states. Thus, its long-time stabilization deviates from the usual thermalization. This nonthermal stabilization happens as a non-Markovian effect.

When a harmonic oscillator is under the influence of a Gaussian process such as linear damping, parametric gain, and linear coupling to a thermal environment, its coherent states are transformed into states with Gaussian Wigner function. Qubit states can be encoded in the $|0\rangle$ and $|1\rangle$ Fock states of a quantum harmonic oscillator, and it is relevant to know the fidelity of the output qubit state after a Gaussian process on the oscillator. In this paper we present a general expression for the average qubit fidelity in terms of the first and second moments of the output from input coherent states subjected to Gaussian processes.

We present an algorithm to approximate partition functions of three-body classical Ising models on two-dimensional lattices of arbitrary genus, in the real-temperature regime. Even though our algorithm is purely classical, it is designed by exploiting a connection to topological quantum systems, namely, the color codes. The algorithm performance (in achievable accuracy) is exponentially better than other approaches that employ mappings between partition functions and quantum state overlaps. In addition, our approach gives rise to a protocol for quantum simulation of such Ising models by simply measuring local observables on color codes.

The dual-kinetic-balance (DKB) technique was previously developed to eliminate spurious states in the finite-basis-set-based solution of the Dirac equation in central fields. In the present paper, it is extended to the Dirac equation for systems with axial symmetry. The efficiency of the method is demonstrated by the calculation of the energy spectra of hydrogenlike ions in the presence of static uniform electric or magnetic fields. In addition, the DKB basis set is implemented to solve the time-dependent Dirac equation making use of the split-operator technique. The excitation and ionization probabilities for the hydrogenlike argon and tin ions exposed to laser pulses are evaluated.