We present an entirely linear all-optical method of cavity scale factor enhancement that relies on mode coupling between the orthogonal polarization modes of a single optical cavity, eliminating the necessity of using an atomic medium to produce the required anomalous dispersion, which decreases the dependence of the scale factor on temperature and increases signal-to-noise ratio by reducing absorption and nonlinear effects. The use of a single cavity results in common mode rejection of the noise and drift that would be present in a system of two coupled cavities. We show that the scale-factor-to-mode-width ratio is increased above unity for this system, and demonstrate tuning of the scale factor by (i) directly varying the polarization mode coupling via rotation of an intracavity half-wave plate, and (ii) coherent control of the cavity reflectance which is achieved simply by varying the incident polarization superposition. These tuning methods allow us to closely approach the critical anomalous dispersion condition and achieve unprecedented enhancements in scale factor and in the scale-factor-to-mode-width ratio. Based on these findings, we propose an adaptation of the traditional optical cavity gyroscope that takes advantage of polarization mode coupling to enhance the gyro scale factor, and demonstrate how the bandwidth of the scale factor enhancement for this gyroscope can be effectively broadened in comparison with fast-light gyroscopes based on atomic media.

Surface-enhanced coherent nonlinear optical signals can dramatically improve detection sensitivity of spectroscopic imaging techniques. Large enhancement factors (EFs) of many orders of magnitude are expected for coherent Raman scattering of molecules in local fields of plasmonic nanostructures. However, only small EFs, several orders of magnitude less than the predicted values, were experimentally observed. To understand this discrepancy we measured the spatial variation of the shape of surface-enhanced coherent anti-Stokes Raman scattering (SECARS) spectra of pyridazine on randomly aggregated gold nanoparticles. We developed a model to simulate the dependence of SECARS spectra on the position and linewidth of the surface plasmon resonance, and attribute small (and even negative) EFs to local destructive interference. We report measurements of nanoscale phase effects in SECARS, and propose strategies to increase experimental EFs towards theoretical predictions.

We propose an interferometric method to measure ${\mathbb{Z}}_2$ topological invariants of time-reversal invariant topological insulators realized with optical lattices in two and three dimensions. We suggest two schemes which both rely on a combination of Bloch oscillations with Ramsey interferometry and can be implemented using standard tools of atomic physics. In contrast to topological Zak phase and Chern number, defined for individual one-dimensional and two-dimensional Bloch bands, the formulation of the ${\mathbb{Z}}_2$ invariant involves at least two Bloch bands related by time-reversal symmetry which one must keep track of in measurements. In one of our schemes this can be achieved by the measurement of Wilson loops, which are non-Abelian generalizations of Zak phases. The winding of their eigenvalues is related to the ${\mathbb{Z}}_2$ invariant. We thereby demonstrate that Wilson loops are not just theoretical concepts but can be measured experimentally. For the second scheme we introduce a generalization of time-reversal polarization which is continuous throughout the Brillouin zone. We show that its winding over half the Brillouin zone yields the ${\mathbb{Z}}_2$ invariant. To measure this winding, our protocol only requires Bloch oscillations within a single band, supplemented by coherent transitions to a second band which can be realized by lattice shaking.

We demonstrate sub-Doppler laser cooling and magneto-optical trapping of the rare-earth element holmium. Atoms are loaded from an atomic beam source and captured in six-beam ${\sigma }_{+}-{\sigma }_{-}$ molasses using a strong $J=15/2\leftrightarrow J=17/2$ cycling transition at $\lambda =410.5$ nm. Due to the small difference in hyperfine splittings and Landé $g$ factors in the lower and upper levels of the cooling transition the MOT is self-repumped without additional repump light, and deep sub-Doppler cooling is achieved with the magnetic trap turned on. We measure the leakage out of the cycling transition to metastable states and find a branching ratio $<$${10}^{-5}$, which is adequate for state-resolved measurements on hyperfine encoded qubits.

Studies of cold atom collisions and few-body interactions often require the energy dependence of the scattering phase shift, which is usually expressed in terms of an effective-range expansion. We use accurate coupled-channel calculations on ${}^6$Li, ${}^{39}$K, and ${}^{133}$Cs to explore the behavior of the effective range in the vicinity of both broad and narrow Feshbach resonances. We show that commonly used expressions for the effective range break down dramatically for narrow resonances and near the zero crossings of broad resonances. We present an alternative parametrization of the effective range that is accurate through both the pole and the zero crossing for both broad and narrow resonances. However, the effective-range expansion can still fail at quite low collision energies, particularly around narrow resonances. We demonstrate that an analytical form of an energy and magnetic-field-dependent phase shift, based on multichannel quantum defect theory, gives accurate results for the energy-dependent scattering length.

For the one-dimensional repulsive Bose gas (Lieb-Liniger model), we study a special class of highly excited states obtained by giving a finite momentum to subgroups of particles. These states, which correspond to “splitting” the ground-state Fermi-sea-like quantum number configuration, are zero-entropy states which display interesting properties more normally associated with ground states. Using a numerically exact method based on integrability, we study these states' excitation spectrum, density correlations, and momentum distribution functions. These correlations display power-law asymptotics and are shown to be accurately described by an effective multicomponent Tomonaga-Luttinger liquid theory whose parameters are obtained from the Bethe ansatz. The nonuniversal correlation prefactors are moreover obtained from integrability, yielding a completely parameter-free fit of the correlator asymptotics.

We investigate experimentally the backscattering properties of an array of atoms that is evanescently coupled to an optical nanofiber in the strongly nonparaxial regime. We observe that the power and the polarization of the backscattered light depend on the nanofiber-guided excitation field in a way that significantly deviates from the predictions of a simple model based on two-level atoms and a scalar waveguide. Even though it has been widely used in previous experimental and theoretical studies of waveguide-coupled quantum emitters, this simple model is thus in general not adequate even for a qualitative description of such systems. We develop an ab initio model that includes the multilevel structure of the atoms and the full vectorial properties of the guided field and find very good agreement with our data.

We study the three-dimensional nature of the quantum interface between an ensemble of cold, trapped atomic spins and a paraxial laser beam, coupled through a dispersive interaction. To achieve strong entanglement between the collective atomic spin and the photons, one must match the spatial mode of the collective radiation of the ensemble with the mode of the laser beam while minimizing the effects of decoherence due to optical pumping. For ensembles coupling to a probe field that varies over the extent of the cloud, the set of atoms that indistinguishably radiates into a desired mode of the field defines an inhomogeneous spin wave. Strong coupling of a spin wave to the probe mode is not characterized by a single parameter, the optical density, but by a collection of different effective atom numbers that characterize the coherence and decoherence of the system. To model the dynamics of the system, we develop a full stochastic master equation, including coherent collective scattering into paraxial modes, decoherence by local inhomogeneous diffuse scattering, and backaction due to continuous measurement of the light entangled with the spin waves. This formalism is used to study the squeezing of a spin wave via continuous quantum nondemolition measurement. We find that the greatest squeezing occurs in parameter regimes where spatial inhomogeneities are significant, far from the limit in which the interface is well approximated by a one-dimensional, homogeneous model.

We present an experimental and theoretical study of modal nonlinear dynamics in a specially designed dual-mode semiconductor Fabry-Pérot laser with a saturable absorber. At zero bias applied to the absorber section, we have found that with increasing device current, single-mode self-pulsations evolve into a complex dynamical state where the total intensity experiences regular bursts of pulsations on a constant background. Spectrally resolved measurements reveal that in this state the individual modes of the device can follow highly symmetric but oppositely directed spiraling orbits. Using a generalization of the rate equation description of a semiconductor laser with saturable absorption to the multimode case, we show that these orbits appear as a consequence of the interplay between the material dispersion in the gain and absorber sections of the laser. Our results provide insights into the factors that determine the stability of multimode states in these systems, and they can inform the development of semiconductor mode-locked lasers with tailored spectra.

A transparent material exhibits ultrafast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, such as optical manipulation, biophysics, cavity optomechanics, quantum optics, and optical tractors, and is relevant in fundamental problems such as the Abraham-Minkoswky dilemma or the Casimir effect. Here, we show that an ultrafast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order-of-magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.

The superadiabatic quantum driving, producing a perfect adiabatic transfer on a given Hamiltonian by introducing an additional Hamiltonian, is theoretically analyzed for transfers within a three-level system. Our starting point is the stimulated Raman adiabatic passage, realized through different schemes of laser pulses. We determine the superadiabatic correction for each scheme. The fidelity, robustness, and transfer time of all the superadiabatic transfer schemes are discussed. We derive that all superadiabatic corrections are based on a $\pi$- (or near-$\pi$)-area pulse coupling between the initial and final states. The benefits in the protocol robustness overcome the difficulties associated to the actual implementation of the three-level superadiabatic transfer.

We present improved theoretical calculations of transition frequencies for the fundamental transitions $(L=0,v=1)\to (L^{\prime }=0,v^{\prime }=0)$ in the hydrogen molecular ions $H_2^{+}$ and HD${}^{+}$ with a relative uncertainty $4\times {10}^{-11}$ and for the two-photon transitions in the antiprotonic helium atom with a relative uncertainty ${10}^{-10}$. To do that, the one-loop self-energy correction of order $\alpha {\left(Z\alpha \right)}^6$ is derived in the two Coulomb center approximation, and numerically evaluated in the case of the aforementioned transitions. The final results also include a complete set of other spin-independent corrections of order $m{\alpha }^7$. The leading order corrections of ${\alpha }^2{ln}^3{\left(Z\alpha \right)}^{-2}{\left(Z\alpha \right)}^6$ are also considered that allows one to estimate a magnitude of yet uncalculated contributions.

Relativistic and QED corrections are calculated for the hyperfine splitting (hfs) in the $2S_{1/2}$ ground state of ${}^9\mathrm{Be}$${}^{+}$ ions with an exact account for electronic correlations. The achieved accuracy is sufficient to determine the finite nuclear size effects from the comparison to the experimental hfs value. The obtained results establish the ground to determine the neutron halo in ${}^{11}\mathrm{Be}$.

We address an open question about the existence of entangled continuous-variable (CV) Werner states with positive partial transpose (PPT). We prove that no such state exists by showing that all PPT CV Werner states are separable. The separability follows by observing that these CV Werner states can be approximated by truncating the states into a finite-dimensional convex mixture of product states. In addition, the constituents of the product states comprise a generalized non-Gaussian measurement which gives, rather surprisingly, a strictly tighter upper bound on quantum discord than photon counting. These results uncover the presence of only negative partial transpose entanglement and illustrate the complexity of more general nonclassical correlations in this paradigmatic class of genuine non-Gaussian quantum states.

We perform resolved optical sideband spectroscopy on a single ${}^{40}$Ca${}^{+}$ ion in a Penning trap. We probe the electric quadrupole allowed $S_{1/2}\leftrightarrow D_{5/2}$ transition at 729 nm and observe equally spaced sidebands for the three motional modes. The axial mode, parallel to the trap axis, is a one-dimensional harmonic oscillator, whereas the radial cyclotron and magnetron modes are circular motions perpendicular to the magnetic field. The total energy associated with the magnetron motion is negative, but here we probe only the (positive) kinetic energy. From the equivalent Doppler widths of the sideband spectra corresponding to the three motions we find effective temperatures of $1.1\pm 0.2$ mK, $7\pm 3$ mK, and $42\pm 8$ $\mu$K for the axial, modified cyclotron, and magnetron modes, respectively. These should be compared to the cooling limits, estimated using optimal laser parameters, of 0.38 mK, 0.8 mK, and $\sim$10 $\mu$K. In future work we aim to perform resolved-sideband cooling of the ion on the 729-nm transition.

When two chains of quantum systems are driven at their ends by a two-mode squeezed reservoir, they approach a steady state characterized by the formation of many entangled pairs. Each pair is made of one element of the first and one of the second chain. This effect has been already predicted under the assumption of broadband squeezing. Here we investigate the situation of finite-bandwidth reservoirs. This is done by modeling the driving bath as the output field of a nondegenerate parametric oscillator. The resulting non-Markovian dynamics is studied within the theoretical framework of cascade open quantum systems. It is shown that the formation of pair-entangled structures occurs as long as the normal-mode splitting of the arrays does not overcome the squeezing bandwidth of the reservoir.

The so-called remarkable formula [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. Lett. 55, 2273 (1985)] for the Helmholtz free energy is applied to the problem of determining the interaction potential to all orders in the coupling strength of a pair of oscillator dipoles interacting through the familiar dipole-dipole interaction of electrodynamics. Simple, straightforward calculations lead to expressions for (1) the London short-range potential, (2) the Casimir-Polder long-range potential, and (3) the potential at high temperature. Explicit results are shown for both the temperature dependence of the interaction potential and its deviation from the weak-coupling limit. It is stressed that the interaction potential is a change in free energy, not the energy; in particular, in the high temperature case, the change of energy is zero.

The impulsive alignment of the noble-gas dimers ${\mathrm{Ne}}_2$, ${\mathrm{Ar}}_2$, ${\mathrm{Kr}}_2$, and ${\mathrm{Xe}}_2$ is experimentally investigated by determining the alignment through Coulomb explosion imaging after their double ionization. This approach yields a favorably detailed insight into the temporal evolution of the alignment succeeding the aligning laser pulse. Particular emphasis is put on analyzing higher order coherences induced in the density matrix as these coherences determine the details of the temporal evolution of the aligned molecular ensemble. The recorded data enable an extraction of polarizability anisotropies for the dimers and of their rotational constants in the vibrational ground state. At the elevated level of rotational excitation obtained, centrifugal distortion starts influencing the temporal evolution of the alignment.

We compare direct state measurement (DSM, or weak state tomography) to conventional state reconstruction (tomography) through accurate Monte Carlo simulations. We find that DSM is much less precise than tomography, but it is surprisingly robust to its inherent bias, which introduces an unavoidable error in the reconstruction. In addition to studying DSM and proposing a method to estimate such bias from the experimental data, we show that the number of DSM measurements can be optimized and that the dimensionality of the DSM pointer is irrelevant: Both finite- and infinite-dimensional pointers provide comparable reconstructions.

I use a time-dependent Lagrangian formalism and a variational trial function to study the dynamics of a two-component vortex in a spin-orbit-coupled Bose-Einstein condensate (BEC). For a single-component BEC, various experiments have validated this theoretical approach, for example a thermal quench that yields a quantized vortex in roughly 25% of trials [Freilich et al., Science 329, 1182 (2010)]. To be definite, I assume the specific spin-orbit form used by Lin and coworkers [Nature (London) 462, 628 (2009); Nature (London) 471, 83 (2011)] in recent NIST experiments, which introduces a spatial asymmetry because of the external Raman laser beams. I here generalize this formalism to include a two-component order parameter that has quantized circulation in each component but not necessarily with the same circulation. For example, a singly quantized vortex in just one component yields a BEC analog of the half-quantized vortex familiar in ${}^3$He-A and in $p$-wave chiral superconductors. This and other unusual two-component vortices have both periodic trajectories and unbounded trajectories that leave the condensate, depending on the initial conditions. The optimized phase of the order parameter induces a term in the particle current that cancels the contribution from the vector potential, leaving pure circulating current around the vortex.