In a recent work, Y. D. Chong et al. [Phys. Rev. Lett. 105, 053901 (2010)] proposed the idea of a coherent perfect absorber (CPA) as the time-reversed counterpart of a laser, in which a purely incoming radiation pattern is completely absorbed by a lossy medium. The optical medium that realizes CPA is obtained by reversing the gain with absorption, and thus it generally differs from the lasing medium. Here it is shown that a laser with an optical medium that satisfies the parity-time $(\mathcal{PT})$ symmetry condition $\epsilon (-\mathbf{r})={\epsilon }^{*}(\mathbf{r})$ for the dielectric constant behaves simultaneously as a laser oscillator (i.e., it can emit outgoing coherent waves) and as a CPA (i.e., it can fully absorb incoming coherent waves with appropriate amplitudes and phases). Such a device can thus be referred to as a $\mathcal{PT}$-symmetric CPA laser. The general amplification or absorption features of the $\mathcal{PT}$ CPA laser below lasing threshold driven by two fields are determined.

We describe a general framework based on modal expansion for the study of optical-frequency combs generated with monolithic whispering-gallery-mode resonators. We obtain a set of time-domain rate equations describing the dynamics of each mode as a function of the main characteristics of the cavity, namely, Kerr nonlinearity, absorption, coupling losses, and cavity dispersion (geometrical and material). A stability analysis of the various side modes is performed, which finds analytically the threshold power needed for comb generation. We show that the various whispering gallery modes are excited in a nontrivial way, strongly dependent on the value of the overall cavity dispersion. We demonstrate that the combs are not simply generated through a direct transfer of energy from the pumped mode to all their neighbors but rather through complex intermediate interactions. Anomalous cavity dispersion is also demonstrated to be critical for these cascading processes, and comb generation is thereby unambiguously linked to modulational instability. This theory accurately describes the emergence of spectral modulation and free spectral-range tunability in the comb. It also enables a clear understanding of the various phenomena responsible for the spectral span limitation. Our theoretical predictions are in excellent agreement with the numerical simulations, and they successfully explain the internal mechanisms responsible for the generation of hundreds of Kerr modes in monolithic whispering-gallery-mode resonators.

We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) $P$ on a graph with a set of unknown marked vertices, one can define a related absorbing walk $P^{\text{'}}$ where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian $H(s)$ from the interpolated Markov chain $P(s)=(1-s)P+{\mathit{sP}}^{\text{'}}$ and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.

Three fermions with strongly repulsive interactions in a spherical harmonic trap constitute the simplest nontrivial system that can exhibit the onset of itinerant ferromagnetism. Here, we present exact solutions for three trapped, attractively interacting fermions near a Feshbach resonance. We analyze energy levels on the upper branch of the resonance where the atomic interaction is effectively repulsive. When the $s$-wave scattering length $a$ is sufficiently positive, three fully polarized fermions are energetically stable against a single spin-flip, indicating the possibility of itinerant ferromagnetism, as inferred in the recent experiment. We also investigate the high-temperature thermodynamics of a strongly repulsive or attractive Fermi gas using a quantum virial expansion. The second and third virial coefficients are calculated. The resulting equations of state can be tested in future quantitative experimental measurements at high temperatures and can provide a useful benchmark for quantum Monte Carlo simulations.

We theoretically present a method to realize a deterministic photon-photon $\sqrt{\text{SWAP}}$ gate using a three-level $\Lambda$ system interacting with single photons in reflection geometry. The $\Lambda$ system is used completely passively as a temporary memory for a photonic qubit; the initial state of the $\Lambda$ system may be arbitrary, and active control by auxiliary fields is unnecessary throughout the gate operations. These distinct merits make this entangling gate suitable for deterministic and scalable quantum computation.

We investigate a two-species Fermi gas in which one species is confined in two parallel layers and interacts with the other species in the three-dimensional space by a tunable short-range interaction. Based on the controlled weak coupling analysis and the exact three-body calculation, we show that the system has a rich phase diagram in the plane of the effective scattering length and the layer separation. Resulting phases include an interlayer $s$-wave pairing, an intralayer $p$-wave pairing, a dimer Bose-Einstein condensation, and a Fermi gas of stable Efimov-like trimers. Our system provides a widely applicable scheme to induce long-range interlayer correlations in ultracold atoms.

A method is proposed to directly measure the temperature of a gas of weakly interacting fermionic atoms loaded into an optical lattice. This technique relies on Raman spectroscopy and is applicable to experimentally relevant temperature regimes. Additionally, a similar spectroscopy scheme can be used to obtain information on the quasiparticle properties and Hubbard bands of the metallic and Mott-insulating states of interacting fermionic spin mixtures. These two methods provide experimentalists with probes to accurately characterize fermionic quantum gases confined to optical lattices.

We design magnetic traps for atoms based on the average magnetic field of vortices induced in a type-II superconducting thin film. This magnetic field is the critical ingredient of the demonstrated vortex-based atom traps, which operate without transport current. We use Bean’s critical-state method to model the vortex field through mesoscopic supercurrents induced in the thin strip. The resulting inhomogeneous magnetic fields are studied in detail and compared to those generated by multiple normally conducting wires with transport currents. Various vortex patterns can be obtained by programing different loading-field and transport-current sequences. These variable magnetic fields are employed to make versatile trapping potentials.

We study the translational motion of an atom in the vicinity of a weakly driven nanofiber with two fiber-Bragg-grating mirrors. We calculate numerically and analytically the force, the friction coefficients, and the momentum diffusion. We find that the spatial dependences of the force, the friction coefficients, and the momentum diffusion are very complicated due to the evanescent-wave nature of the atom-field coupling as well as the effect of the van der Waals potential. We show that the time development of the mean number of photons in the cavity closely follows the translational motion of the atom through the nodes and antinodes of the fiber-guided cavity standing-wave field even though the cavity finesse is moderate, the cavity is long, and the probe field is weak.

We perform a numeric study (Worm algorithm Monte Carlo simulations) of ultracold two-component bosons in two- and three-dimensional optical lattices. At strong enough interactions and low enough temperatures the system features magnetic ordering. We compute critical temperatures and entropies for the disappearance of the Ising antiferromagnetic and the $\mathit{xy}$-ferromagnetic order and find that the largest possible entropies per particle are $~0.5k_B$. We also estimate (optimistically) the experimental hold times required to reach equilibrium magnetic states to be on a scale of seconds. Low critical entropies and long hold times render the experimental observations of magnetic phases challenging and call for increased control over heating sources.

We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped ${}^{87}\mathrm{Rb}$ atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.

The propagation of polarization-entangled states of light through fluctuating loss channels in the turbulent atmosphere is studied, including the situation of strong losses. We consider violations of Bell inequalities by light, emitted by a parametric down-conversion source, after transmission through the turbulent atmosphere. It is shown by analytical calculations that, in the presence of background radiation and dark counts, fluctuating loss channels may preserve entanglement properties of light even better than standard loss channels, when postselected measurements are applied.

The collective excitation of a gas of highly excited atoms confined to a large spacing ring lattice is studied, where the ground and the excited states are resonantly coupled via a laser field. Attention is focused on the regime where the interaction between the highly excited atoms is very weak in comparison to the Rabi frequency of the laser. In this case, the many-body excitations of the system can be expressed in terms of free spinless fermions. The complex many-particle states arising in this regime are characterized and their properties, for example their correlation functions, are studied. Additional investigation into how some of these many-particle states can actually be experimentally accessed by a temporal variation of the laser parameters is performed.

The conjunction of atom-cavity physics and photonic structures (“solid light” systems) offers new opportunities in terms of more device functionality and the probing of designed emulators of condensed-matter systems. By analogy to the canonical one-electron approximation of solid-state physics, we propose a one-polariton approximation to study these systems. Using this approximation, we apply Bloch states to the uniformly tuned Jaynes-Cummings-Hubbard model to analytically determine the energy-band structure. By analyzing the response of the band structure to local atom-cavity control, we explore its application as a quantum simulator and show phase-transition features absent in mean-field theory. Using this approach for solid light systems, we extend the analysis to include detuning impurities to show the solid light analogy of the semiconductor. This investigation also shows features with no semiconductor analog.

We demonstrate that the characteristics of the high-order harmonic spectra generated by few-cycle carrier-envelope phase-stabilized pulses can be finely adjusted by controlling the time-dependent ellipticity. The experimental measurements show evidence for the generation of single, pairs, and trains of attosecond pulses by controlling the time window of linear polarization of the driving pulses. The influence of the carrier-envelope phase on the generation process in different confinement configurations is interpreted and analyzed using a nonadiabatic stationary phase model. We show that the xuv emission depends critically on particular aspects of the fundamental electric field that allows us to steer the electron trajectories on the time scale of tens of attoseconds.

Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great detail the optical lattice generated by the coherent superposition of three coplanar running laser waves with respective angles $2\pi /3$. The corresponding band structure displays Dirac cones located at the corners of the Brillouin zone and close to half-filling this system is well described by massless Dirac fermions. We characterize their properties by accurately deriving the nearest-neighbor hopping parameter $t_0$ as a function of the optical lattice parameters. Our semiclassical instanton method proves in excellent agreement with an exact numerical diagonalization of the full Hamilton operator in the tight-binding regime. We conclude that the temperature range needed to access the Dirac fermions regime is within experimental reach. We also analyze imperfections in the laser configuration as they lead to optical lattice distortions which affect the Dirac fermions. We show that the Dirac cones do survive up to some critical intensity or angle mismatches which are easily controlled in actual experiments. In the tight-binding regime, we predict, and numerically confirm, that these critical mismatches are inversely proportional to the square root of the optical potential strength. We also briefly discuss the interesting possibility of fine tuning the mass of the Dirac fermions by controlling the laser phase in an optical lattice generated by the incoherent superposition of three coplanar independent standing waves with respective angles $2\pi /3$.

We propose initial conditions that could facilitate the excitation of rogue waves. Understanding the initial conditions that foster rogue waves could be useful both in attempts to avoid them by seafarers and in generating highly energetic pulses in optical fibers.

Invariant entangled states remain unchanged under simultaneous identical unitary transformations of all their subsystems. We experimentally generate and characterize such invariant two-, four-, and six-photon polarization entangled states. This is done only with a suitable filtering procedure of multiple emissions of entangled photon pairs from a single source without any interferometric overlaps. We get the desired states utilizing bosonic emission enhancement due to indistinguishability. The setup is very stable and gives high interference contrasts. Thus, the process is a very likely candidate for various photonic demonstrations of quantum information protocols.

In this paper, we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order $a^3$, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.

We present theoretical and experimental studies on quantum path interferences in high-order harmonic generation. Simulations of the single-atom response allow us to calculate the different quantum paths contributions; their relative phases and the resulting interferences can be finely controlled through the laser intensity that provides an efficient means for controlling the electron trajectories with an accuracy on the ten attoseconds time scale. Simulations of the macroscopic response demonstrate the need of spatial and spectral filtering of the harmonic beam in order to observe the interferences between the two shortest quantum paths. Our numerical results are in very good agreement with experimental data. These investigations represent a step toward the full characterization and control of the atomic harmonic dipole.