We develop a method for executing robust and selective transfer of populations between a single level and preselected superpositions of energy eigenstates. Viewed in the frequency domain, our method amounts to executing a series of simultaneous adiabatic passages into each component of the target superposition state. Viewed in the time domain, the method works by accumulating the wave function of the target wave packet as it revisits the transition region, in what amounts to an extension of the piecewise adiabatic passage technique [E. A. Shapiro et al., Phys. Rev. Lett. 99, 033002 (2007)] to the multistate regime. The viability of the method is verified by performing numerical tests for the ${\text{Na}}_2$ molecule.

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{-4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions “fermionize” under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

Nowadays it is experimentally feasible to create artificial, and in particular, non-Abelian gauge potentials for ultracold atoms trapped in optical lattices. Motivated by this fact, we investigate the fundamental properties of an ultracold Fermi gas in a non-Abelian U(2) gauge potential characterized by a constant Wilson loop. Under this specific condition, the energy spectrum exhibits a robust band structure with large gaps and reveals a new fractal figure. The transverse conductivity is related to topological invariants and is shown to be quantized when the Fermi energy lies inside a gap of the spectrum. We demonstrate that the analog of the integer quantum Hall effect for neutral atoms survives the non-Abelian coupling and leads to a striking fractal phase diagram. Moreover, this coupling induces an anomalous Hall effect as observed in graphene.

Effects of multiplicative noise on optical bistability in a three-level atomic medium in a ring cavity are investigated experimentally and theoretically. Steady-state intensity distributions as well as switching and dwell times have been measured as functions of noise strength. System response to an external periodic signal is also explored. It is found that the probability for the system to stay in the upper state increases with increasing noise strength. When a small periodic signal is added to the input field, the probability for the upper state has a maximum as a function of multiplicative noise strength. A simple theoretical model based on nonlinear atomic susceptibility is presented to interpret the experimental observations.

We show the transition from a fully quantized interaction to a semiclassical one in entangled small-number quantum systems using the quantum trajectories approach. In particular, we simulate the microwave Ramsey zones used in Rydberg-atom interferometry, filling in the gap between the strongly entangling Jaynes-Cummings evolution and the semiclassical rotation of the atomic internal states. We also correlate the information flowing with leaking photons to the entanglement generation between cavity field and flying atom and detail the roles played by the strong dissipation and the external driving force in preserving atomic coherence through the interaction.

The single-photon transport in a single-mode waveguide, coupled to a cavity embedded with a two-level atom, is analyzed. The single-photon transmission and reflection amplitudes, as well as the cavity and the atom excitation amplitudes, are solved exactly via a real-space approach. It is shown that the dissipations of the cavity and of the atom, respectively, affect distinctively on the transport properties of the photons and on the relative phase between the excitation amplitudes of the cavity mode and the atom.

We analyze the single-photon transport in a single-mode waveguide coupled to a whispering-gallery-type resonator interacting with a two-level atom. The single-photon transport properties such as the transmission and reflection amplitudes, as well as the resonator and the atom responses, are solved exactly via a real-space approach. The treatment includes the intermode backscattering between the two degenerate whispering-gallery modes of the resonator, and the dissipations of the resonator and the atom. We also show that a generalized critical coupling condition, that the single-photon transmission at the output of the waveguide goes to zero on resonance for a matched system, holds for the full coupled waveguide-ring resonator-atom system.

Materials that exhibit loss or gain have a complex-valued refractive index $n$. Nevertheless, when considering the propagation of optical pulses, using a complex $n$ is generally inconvenient—hence the standard choice of real-valued refractive index, i.e., $n_s=\text{Re}\left(\sqrt{n^2}\right)$. However, an analysis of pulse propagation based on the second-order wave equation shows that use of $n_s$ results in a wave vector different to that actually exhibited by the propagating pulse. In contrast, an alternative definition $n_c=\sqrt{\text{Re}\left(n^2\right)}$, always correctly provides the wave vector of the pulse. Although for small loss the difference between the two is negligible, in other cases it is significant; it follows that phase and group velocities are also altered. This result has implications for the description of pulse propagation in near resonant situations, such as those typical of metamaterials with negative (or otherwise exotic) refractive indices.

Four-photon scattering in nonlinear waveguides is an important physical process that allows photon-pair generation in well-defined guided modes, with high rate and reasonably low noise. Most of the experiments to date used the scalar four-photon scattering process in which the pump photons and the scattered photons have the same polarization. In birefringent waveguides, vectorial four-photon scatterings are also allowed: these vectorial scattering processes involve photons with different polarizations. In this paper, the theory of four-photon scattering in nonlinear, birefringent, and dispersive fibers is developed in the framework of the quantum theory of light. The work focuses on the spectral properties and quantum correlations (including entanglement) of photon pairs generated in high-birefringence and low-birefringence fibers.

Cold atoms provide a unique arena to study many-body systems far from equilibrium. Furthermore, phases in cold atom systems are conveniently investigated by dynamical probes pushing the system out of equilibrium. Here, we discuss the pumping of doubly occupied sites in a fermionic Mott insulator by a periodic modulation of the hopping amplitude. We show that deep in the insulating phase the many-body system can be mapped onto an effective two-level system which performs coherent Rabi oscillations due to the driving. Coupling of the two-level system to the remaining degrees of freedom renders the Rabi oscillations damped. We compare this scheme to an alternative description where the particles are incoherently pumped into a broad continuum.

The effect of feedback on a two-level dissipative system is studied in this paper. The results show that it is possible to control the phase in the open system even if its state cannot be manipulated from an arbitrary initial one to an arbitrary final one. The dependence of the geometric phase on the control parameters is calculated and discussed.

We theoretically demonstrate that a photonic crystal microcavity coupled to waveguides works as an optical beam splitter. Numerical simulations illustrate that spatially separated two output modes have a relative phase close to $\pi /2$ and tunable transmission coefficients. The general transformation of this beam splitter gives a single-qubit rotation operator about the $x$ axis. Using such beam splitters, we show single-photon interference via the Mach-Zehnder interferometer and two-photon entanglement via Hong-Ou-Mandel effect. This system may have great applications in constructing interferometers and integrated circuits for optical quantum information processing with solid-state materials.

The signal-to-noise ratios (SNRs) of three Gaussian-state ghost-imaging configurations—distinguished by the nature of their light sources—are derived. Two use classical-state light, specifically a joint signal-reference field state that has either the maximum phase-insensitive or the maximum phase-sensitive cross correlation consistent with having a proper $P$ representation. The third uses nonclassical light, in particular an entangled signal-reference field state with the maximum phase-sensitive cross correlation permitted by quantum mechanics. Analytic SNR expressions are developed for the near-field and far-field regimes, within which simple asymptotic approximations are presented for low-brightness and high-brightness sources. A high-brightness thermal-state (classical phase-insensitive state) source will typically achieve a higher SNR than a biphoton-state (low-brightness, low-flux limit of the entangled-state) source, when all other system parameters are equal for the two systems. With high efficiency photon-number-resolving detectors, a low-brightness, high-flux entangled-state source may achieve a higher SNR than that obtained with a high-brightness thermal-state source.

A detailed experimental study of antiphase dynamics in a two-mode semiconductor laser with optical injection is presented. The device is a specially designed Fabry-Pérot laser that supports two primary modes with a terahertz frequency spacing. Injection in one of the primary modes of the device leads to a rich variety of single and two-mode dynamical scenarios, which are reproduced with remarkable accuracy by a four-dimensional rate equation model. Numerical bifurcation analysis reveals the importance of torus bifurcations in mediating transitions to antiphase dynamics and of saddle node of limit-cycle bifurcations in switching of the dynamics between single- and two-mode regimes.

We address a number of issues regarding solid-state electron electric-dipole moment (EDM) experiments, focusing on gadolinium-iron garnet [(GdIG) chemical formula ${\text{Gd}}_3{\text{Fe}}_5{\text{O}}_{12}$] as a possible sample material. GdIG maintains its high magnetic susceptibility down to 4.2 K, which enhances the EDM-induced magnetization of a sample placed in an electric field. We estimate that lattice polarizability gives rise to an EDM enhancement factor of approximately 20. We also calculate the effect of the demagnetizing field for various sample geometries and permeabilities. Measurements of intrinsic GdIG magnetization noise are presented, and the fluctuation-dissipation theorem is used to compare our data with the measurements of the imaginary part of GdIG permeability at 4.2 K, showing good agreement above frequencies of a few hertz. We also observe how the demagnetizing field suppresses the noise-induced magnetic flux, confirming our calculations. The statistical sensitivity of an EDM search based on a solid GdIG sample is estimated to be on the same level as the present experimental limit. Such a measurement would be valuable given the completely different methods and systematics involved. The most significant systematics in such an experiment are the magnetic hysteresis and the magnetoelectric effect. Our analysis shows that it should be possible to control these at the level of statistical sensitivity.

Intensive light pulse interaction with a dense resonant medium is considered. The possibilities of optical switching and pulse compression at realistic parameters of the medium are analyzed. Pulse-shape transformation in different photonic-band-gap structures containing a dense resonant medium is studied. In particular, the effect of dispersion compensation due to nonlinear interaction with a medium is reported. The possibility of pulse control with another pulse is considered in the schemes of copropagating and counterpropagating pulses. It is shown that a photonic crystal makes controlling more effective, at least in the case of copropagating pulses.

The influence of a phase-modulated control field on the phenomenon of electromagnetically induced transparency (EIT) is investigated theoretically. We show that the phase modulation changes the dispersive properties of the medium considerably since it results in temporal oscillations of the transparency window in frequency space. This is in marked contrast to the standard EIT setup, where the transparency window is fixed and determined by the two-photon resonance condition. In particular, we find that the phase modulation enables the propagation of probe pulses with disjoint frequency spectra at different times and allows the shifting of the central frequency of a probe pulse almost without distortion of its shape. We employ the time-dependent susceptibility of the medium to explain and analyze our results and demonstrate that this concept yields qualitative as well as quantitative agreement with the numerical integration of Maxwell-Bloch equations. Our theoretical model can be applied to other media with time-dependent susceptibilities.

Faraday rotation is one way to realize quantum nondemolition measurement of electron spin in quantum dots. To describe Faraday rotation, semiclassical models are typically used based on quantized electron-spin states and classical electromagnetic fields. Such treatments neglect the entanglement between electronic and photonic degrees of freedom that produce intrinsic quantum noise, limiting the ultimate sensitivity of this technique. We present a fully quantum-mechanical description of Faraday rotation and quantify this intrinsic noise. A method for measuring the purity of a given spin state is suggested based on this analysis.

We analyze the creation of spin squeezed atomic ensembles by simultaneous dispersive interactions with several optical frequencies. A judicious choice of optical parameters enables optimization of an interferometric detection scheme that suppresses inhomogeneous light shifts and keeps the interferometer operating in a balanced mode that minimizes technical noise. We show that when the atoms interact with two-frequency light tuned to cycling transitions the degree of spin squeezing ${\xi }^2$ scales as ${\xi }^2\sim 1/d$, where $d$ is the resonant optical depth of the ensemble. In real alkali metal atoms there are loss channels and the scaling may be closer to ${\xi }^2\sim 1/\sqrt{d}$. Nevertheless the use of two frequencies provides a significant improvement in the degree of squeezing attainable as we show by quantitative analysis of nonresonant probing on the Cs $D_1$ line. Two alternative configurations are analyzed: a Mach-Zehnder interferometer that uses spatial interference and an interaction with multifrequency amplitude modulated light that does not require a spatial interferometer.

We investigate a generalized many-body model of Feshbach molecule formation that includes the atom-atom, atom-molecule, and molecule-molecule interactions. We show that the picture of two-body molecule production depicted by the Landau-Zener model is significantly altered by the particle interactions. In the adiabatic limit, we work out a formula for the ceiling of conversion efficiency when the interaction strength is larger than a critical value. In the sudden limit, we derive a closed equation for the conversion efficiency using stationary phase approximation. Our theory predicts a significant role of the particle interactions in atom-molecule conversion when the atom density is high and the Feshbach resonance width is narrow.