Phonon Laser in the Quantum Regime.

We demonstrate a trapped-ion system with two competing dissipation channels, implemented independently on two ion species cotrapped in a Paul trap. By controlling coherent spin-oscillator couplings and optical pumping rates we explore the phase diagram of this system, which exhibits a regime analogous to that of a (phonon) laser but operates close to the quantum ground state with an average phonon number of n[over ¯]<10. We demonstrate phase locking of the oscillator to an additional resonant drive, and also observe the phase diffusion of the resulting state under dissipation by reconstructing the quantum state from a measurement of the characteristic function.

Optical Control of a Single Nuclear Spin in the Solid State.

We demonstrate a novel method for coherent optical manipulation of individual nuclear spins in the solid state, mediated by the electronic states of a proximal quantum emitter. Specifically, using the nitrogen-vacancy (NV) color center in diamond, we demonstrate control of a proximal ^{14}N nuclear spin via an all-optical Raman technique. We evaluate the extent to which the intrinsic physical properties of the NV center limit the performance of coherent control, and we find that it is ultimately constrained by the relative rates of transverse hyperfine coupling and radiative decay in the NV center's excited state. Possible extensions and applications to other color centers are discussed.

Topological Quantum Optics Using Atomlike Emitter Arrays Coupled to Photonic Crystals.

We propose an experimentally feasible nanophotonic platform for exploring many-body physics in topological quantum optics. Our system is composed of a two-dimensional lattice of nonlinear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact through the guided modes of the photonic crystal, and a uniform magnetic field gives rise to large topological band gaps, robust edge states, and a nearly flat band with a nonzero Chern number. The presence of a topologically nontrivial nearly flat band paves the way for the realization of fractional quantum Hall states and fractional topological insulators in a topological quantum optical setting.

Topological Quantum Optics in Two-Dimensional Atomic Arrays.

We demonstrate that two-dimensional atomic emitter arrays with subwavelength spacing constitute topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space emission are strongly suppressed. Breaking time-reversal symmetry with a magnetic field results in gapped photonic bands with nontrivial Chern numbers and topologically protected, long-lived edge states. Due to the inherent nonlinearity of constituent emitters, such systems provide a platform for exploring quantum optical analogs of interacting topological systems.

Certifying separability in symmetric mixed states of N qubits, and superradiance.

Separability criteria are typically of the necessary, but not sufficient, variety, in that satisfying some separability criterion, such as positivity of eigenvalues under partial transpose, does not strictly imply separability. Certifying separability amounts to proving the existence of a decomposition of a target mixed state into some convex combination of separable states; determining the existence of such a decomposition is "hard." We show that it is effective to ask, instead, if the target mixed state "fits" some preconstructed separable form, in that one can generate a sufficient separability criterion relevant to all target states in some family by ensuring enough degrees of freedom in the preconstructed separable form. We demonstrate this technique by inducing a sufficient criterion for "diagonally symmetric" states of N qubits. A sufficient separability criterion opens the door to study precisely how entanglement is (not) formed; we use ours to prove that, counterintuitively, entanglement is not generated in idealized Dicke model superradiance despite its exemplification of many-body effects. We introduce a quantification of the extent to which a given preconstructed parametrization comprises the set of all separable states; for "diagonally symmetric" states our preconstruction is shown to be fully complete. This implies that our criterion is necessary in addition to sufficient, among other ramifications which we explore.

Quantum phases of quadrupolar Fermi gases in optical lattices.

We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.

All-optical Fresnel lens in coherent media: controlling image with image.

We theoretically explore an all-optical method for generating tunable diffractive Fresnel lenses in coherent media based on electromagnetically induced transparency. In this method, intensity-modulated images in coupling light fields can pattern the coherent media to induce the desired modulo-2π quadratic phase profiles for the lenses to diffract probe light fields. We characterize the focusing and imaging properties of the induced lenses. In particular, we show that the images in coupling fields can flexibly control the images in probe fields by diffraction, where large focal length tunability from 1 m to infinity and high output (∼ 88% diffraction efficiency) can be achieved. Additionally, we also find that the induced Fresnel lenses can be rapidly modulated with megahertz refresh rates using image-bearing square pulse trains in coupling fields. Our proposed lenses may find a wide range of applications for multimode all-optical signal processing in both the classical and quantum regimes.

Ion crystal transducer for strong coupling between single ions and single photons.

A new approach for the realization of a quantum interface between single photons and single ions in an ion crystal is proposed and analyzed. In our approach the coupling between a single photon and a single ion is enhanced via the collective degrees of freedom of the ion crystal. Applications including single-photon generation, a memory for a quantum repeater, and a deterministic photon-photon, photon-phonon, or photon-ion entangler are discussed.

Collective atomic scattering and motional effects in a dense coherent medium.

We investigate collective emission from coherently driven ultracold (88)Sr atoms. We perform two sets of experiments using a strong and weak transition that are insensitive and sensitive, respectively, to atomic motion at 1 µK. We observe highly directional forward emission with a peak intensity that is enhanced, for the strong transition, by >10(3) compared with that in the transverse direction. This is accompanied by substantial broadening of spectral lines. For the weak transition, the forward enhancement is substantially reduced due to motion. Meanwhile, a density-dependent frequency shift of the weak transition (∼10% of the natural linewidth) is observed. In contrast, this shift is suppressed to <1% of the natural linewidth for the strong transition. Along the transverse direction, we observe strong polarization dependences of the fluorescence intensity and line broadening for both transitions. The measurements are reproduced with a theoretical model treating the atoms as coherent, interacting radiating dipoles.

Two-dimensional all-optical spatial light modulation with high speed in coherent media.

We show theoretical evidence that coherent systems based on electromagnetically induced transparency (EIT) can function as optically addressed spatial light modulators with megahertz modulation rates. The transverse spatial properties of cw probe fields can be modulated fast using two-dimensional optical patterns. To exemplify our proposal, we study real-time generation and manipulation of Laguerre-Gaussian beams by means of phase or amplitude modulation using flat-top image-bearing pulse trains as coupling fields in low-cost hot vapor EIT systems.