Laser spectroscopy has been performed on a beam of neutral ${}^4\mathrm{He}$ atoms. By using transverse laser cooling and focusing, we are able to prepare a bright beam of atoms in the metastable state $2{}^3{S}_1$ deflected from the original effusive atomic beam. The initial state preparation is completed with optical pumping on the $2{}^3{P}_1\leftarrow 2{}^3{S}_1$ transition at the wavelength of 1083 nm, followed by laser spectroscopy on the $2{}^3{P}_{1,2}\leftarrow 2{}^3{S}_1$ transitions. The $2{}^3{P}_1-2{}^3{P}_2$ fine-structure splitting is determined to be $2291177.69\pm 0.36\mathrm{kHz}$. The quantum interference effect is included in data extraction. This is the most precise laser spectroscopy measurement of the interval. Our result is in agreement with both the latest QED-based calculation and the most precise measurement conducted with microwave spectroscopy.

We study the effect of decoherence on a quantum von Neumann measurement process. We discuss the effect of phonon noise on the direct measurement of two-electron spin states in a double quantum dot achieved by monitoring the noise of the current flowing through a quantum point contact coupled to one of the dots. We show that although the decoherence is damaging to the procedure at the extremely low temperatures characteristic of spin-in-quantum-dots experiments, and may even be fatal, increasing the temperature leads to a revival of the usefulness of the protocol: At higher temperatures, when the reservoir becomes an effective source of energy, it can enhance system fluctuations, and under such conditions the decoherence becomes advantageous to the measurement scheme and leads to the enhancement of the distinguishability between the measured states. Hence, the uncontrollable interaction of the measured system with the environment can be either an advantage or a disadvantage for a quantum measurement, depending on the characteristics of the decoherence process.

We demonstrate that amplification of arbitrarily weak randomness is possible using quantum resources. We present a randomness amplification protocol that involves Bell experiments. We find a Bell inequality that can amplify arbitrarily weak randomness and give a detailed analysis of the protocol involving it. Our analysis includes finding a sufficient violation of the Bell inequality as a function of the initial quality of randomness. It has a very important property that for any quality the required violation is strictly lower than possible to obtain using quantum resources. Among other things, this means that the protocol takes a finite amount of time to amplify arbitrarily weak randomness.

We present an improved statistical fluctuation analysis for measurement-device-independent quantum key distribution with a three-intensity decoy-state method. Taking the statistical fluctuations for different sources jointly, we present more tightened formulas for some key quantities used in calculating the secure final key. Numerical simulation shows that, given the total number of pulses ${10}^{12}$, our method improves the key rate by about 97% for a distance of 50 km compared with the result given by Xu et al. [F. Xu et al., Phys. Rev. A 89, 052333 (2014)], and improves the key rate by $145\%$ for a distance of 100 km compared with the result from full optimization of all parameters but treating the statistical fluctuations traditionally, i.e., treating the fluctuations for different sources separately.

For a many-electron system, whether the particle density $\rho \left(\mathbf{r}\right)$ and the total current density $\mathbf{j}\left(\mathbf{r}\right)$ are sufficent to determine the one-body potential $V\left(\mathbf{r}\right)$ and vector potential $A\left(\mathbf{r}\right)$ is still an open question. For the one-electron case, a Hohenberg-Kohn theorem exists formulated with the total current density. Here we show that the generalized Hohenberg-Kohn energy functional ${\mathcal{E}}_{V_0,{\mathbf{A}}_0}(\rho ,\mathbf{j})=\langle \psi (\rho ,\mathbf{j}),H(V_0,{\mathbf{A}}_0)\psi (\rho ,\mathbf{j})\rangle$ can be minimal for densities that are not the ground-state densities of the fixed potentials $V_0$ and ${\mathbf{A}}_0$. Furthermore, for an arbitrary number of electrons and under the assumption that a Hohenberg-Kohn theorem exists formulated with $\rho$ and $\mathbf{j}$, we discuss the possibility of a variational principle in total current-density-functional theory such as that of Hohenberg-Kohn.

We report on a significant discrepancy between recently published, highly accurate variational calculations and precise measurements of the spectrum of Rydberg states in ${}^{87}\mathrm{Rb}$ on the energy scale of fine splitting. Introducing a modified effective single-electron potential, we determine the spectrum of the outermost bound electron from a standard WKB approach. Overall very good agreement with precise spectroscopic data is obtained.

Neutral muonic helium is an exotic atomic system consisting of an electron, a muon, and a nucleus. Being a three-body system, it possesses a clear hierarchy. This allows us to consider it as a hydrogenlike atom with a compound nucleus, which is, in turn, another hydrogenlike system. There are a number of corrections to the Bohr energy levels, all of which can be treated as contributions of generic hydrogenlike theory. While the form of those contributions is the same for all hydrogenlike atoms, their relative numerical importance differs from atom to atom. Here, the leading contribution to the (electronic) Lamb shift in neutral muonic helium is found in a closed analytic form together with the most important corrections. We believe that the Lamb shift in neutral muonic hydrogen is measurable, at least through a measurement of the (electronic) $1s\text{−}2s$ transition. We present a theoretical prediction for the $1s\text{−}2s$ transitions with an uncertainty of 3 ppm ($9\mathrm{GHz}$), as well as for the $2s\text{−}2p$ Lamb shift with an uncertainty of $1.3\mathrm{GHz}$.

The present work deals with a set of problems in isotope shifts of neutral barium spectral lines. Some well-known transitions $(6s^{21}{S}_0-6s6p{}^{1,3}{P}_1^o$ and $6s^{21}{S}_0-6p^{23}{P}_0)$ are investigated. Values of the changes in the nuclear mean-square charge radius are deduced from the available experimental isotope shifts using our ab initio electronic factors. The three sets $\left\{\delta {\langle r^2\rangle }^{A,A^{\prime }}\right\}$ obtained from these lines are consistent with each other. The combination of the available nuclear mean-square radii with our electronic factors for the $6s5d{}^3{D}_{1,2}-6s6p{}^1{P}_1^o$ transitions produces isotope shift values in conflict with the laser spectroscopy measurements of U. Dammalapati et al. [Eur. Phys. J. D 53, 1 (2009)].

We provide spectroscopic data for the $a{}^3{\Sigma }^{+}$ state of the ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ molecule. The experiment is done in an ultrasonic beam apparatus, starting from the ground state $X{}^1{\Sigma }^{+}$ and driving the population to the $a{}^3{\Sigma }^{+}$ state, using a $\Lambda$ scheme with fixed pump and scanning dump laser. The signals are observed as dips of the total fluorescence. The intermediate level is chosen to be strongly perturbed by the $B{}^1\Pi /c{}^3{\Sigma }^{+}$ states mixing to overcome the singlet-triplet transfer prohibition. We observed highly resolved hyperfine spectra of various rovibrational levels of the $a{}^3{\Sigma }^{+}$ state from $v_a=2$ up to the highest vibrational levels for rotational quantum numbers $N_a=4,6,8$. By the typical experimental linewidth of 17 MHz, the vibrational dependence of the hyperfine splitting is clearly revealed for NaK. The absolute frequency measurements of the vibrational levels are used for improvement of the $a{}^3{\Sigma }^{+}$ potential curve and of the derived scattering length of all natural isotope combinations. Applying the $\Lambda$ scheme in the reverse direction can provide a pathway for efficient transfer of ultracold ${}^{23}\mathrm{Na}{}^{39}\mathrm{K}$ molecules from the $\text{Na}\left(3s\right)+\text{K}\left(4s\right)$ asymptote to the lowest levels of the ground state. We show spectra that couple the absolute ground state $v_X=0,J=0$ with an appropriate intermediate state for direct realization of the reverse path. The refined theoretical model of the coupled excited states of the $\text{Na}\left(3s\right)+\text{K}\left(4p\right)$ asymptote allows predictions of efficient paths for ${}^{23}\mathrm{Na}{}^{40}\mathrm{K}$; one example is calculated.

A scheme for efficient correction of driving-field frequency drifts in Ramsey interferometry is proposed. The two off-resonant $\pi /2$ pulses of duration $T$ used in the traditional Ramsey setup are supplemented with an additional pulse of duration $2T$ (approximate $\pi$ pulse), which is applied midway between the Ramsey pulses and has a detuning of opposite sign to theirs. This scheme, which resembles a Hahn's spin-echo pulse embedded into the Ramsey setup, corrects small-to-moderate random errors in the detuning of the driving field. This allows the observation of Ramsey fringes of high contrast even with a noisy driving field or in inhomogeneously broadened atomic ensembles. The contrast is further improved by replacing the refocusing $2T$ pulse by a composite $\pi$ pulse. We demonstrate the validity of the concept by comparing experimental results from usual Ramsey measurements with Hahn-Ramsey measurements. These experimental results are obtained from microwave-optical double-resonance spectroscopy on ${}^{171}\mathrm{Yb}{}^{+}$ ions in a segmented linear Paul trap. In the same way, we verify qualitatively the predicted advantage from using a composite $\pi$ pulse for refocusing.

In the quest to reach lower temperatures of ultracold gases in optical-lattice experiments, nonadiabaticities during lattice loading represent one of the limiting factors that prevent the same low temperatures being reached as in experiments without lattices. Simulating the loading of a bosonic quantum gas into a one-dimensional optical lattice with and without a trap, we find that the redistribution of atomic density inside a global confining potential is by far the dominant source of heating. Based on these results we propose adjusting the trapping potential during loading to minimize changes to the density distribution. Our simulations confirm that a very simple linear interpolation of the trapping potential during loading already significantly decreases the heating of a quantum gas, and we discuss how loading protocols minimizing density redistributions can be designed.

A single-particle Green's function (propagator) is introduced to study the deflection of laser-cooled cesium atoms in an atomic fountain due to microwave magnetic field gradients in the Ramsey ${\mathrm{TE}}_{011}$ cavity. The deflection results in a state-dependent loss of atoms at apertures in the physics package, resulting in a frequency bias. A model accounting only for motion in one dimension transverse to the symmetry axis of the fountain is discussed in detail and then generalized to two transverse dimensions. Results for fractional frequency shifts due to transverse field gradients are computed for NIST-F1 and NIST-F2 cesium fountains. The shifts are found to be negligible except in cases of higher rf power applied to the cavities.

The unconditional squeezing of the collective spins of an atomic ensemble in a laser driven optical cavity [I. D. Leroux, M. H. Schleier-Smith, and V. Vuletić, Phys. Rev. Lett 104, 073602 (2010)] is studied and analyzed theoretically. Surprisingly, we find that the largely detuned driving laser can improve the scaling of cavity squeezing from $S^{-2/5}$ to $S^{-2/3}$, where $S$ is the total atomic spin. Moreover, we also demonstrate that the experimental imperfection of photon scattering into free space can be efficiently suppressed by detuning.

We study macroscopic superpositions in the orbital rather than the spatial degrees of freedom, in a three-dimensional, double-well system. We show that the ensuing dynamics of $N$ interacting excited ultracold bosons, which, in general, requires at least eight single-particle modes and $\left(\genfrac{}{}{0pt}{}{N+7}{N}\right)$ Fock vectors, is described by a surprisingly small set of many-body states. An initial state with half the atoms in each well, and purposely excited in one of them, gives rise to the tunneling of axisymmetric and transverse vortex structures. We show that transverse vortices tunnel orders of magnitude faster than axisymmetric ones and are therefore more experimentally accessible. The tunneling process generates macroscopic superpositions only distinguishable by their orbital properties and within experimentally realistic times.

We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for the Brownian particle in the Born-Markov approximation and we discuss the appearance of additional terms, for various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed (superlocalized) with respect to the position of the Brownian particle. We analyze various restrictions to the validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the dynamical stability of the system, by applying a Gaussian approximation to the time-dependent Wigner function, and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose a possible experimental realization of the physics discussed here, by considering an impurity particle embedded in a degenerate quantum gas.

We study the dynamic response of an $s$-wave BCS-BEC (atomic-molecular) condensate to detuning quenches within the two-channel model beyond the weak-coupling BCS limit. At long times after the quench, the condensate ends up in one of three main asymptotic states (nonequilibrium phases), which are qualitatively similar to those in other fermionic condensates defined by a global complex order parameter. In phase I the amplitude of the order parameter vanishes as a power law, in phase II it goes to a nonzero constant, and in phase III it oscillates persistently. We construct exact quench phase diagrams that predict the asymptotic state (including the many-body wave function) depending on the initial and final detunings and on the Feshbach resonance width. Outside of the weak-coupling regime, both the mechanism and the time dependence of the relaxation of the amplitude of the order parameter in phases I and II are modified. Also, quenches from arbitrarily weak initial to sufficiently strong final coupling do not produce persistent oscillations in contrast to the behavior in the BCS regime. The most remarkable feature of coherent condensate dynamics in various fermion superfluids is an effective reduction in the number of dynamic degrees of freedom as the evolution time goes to infinity. As a result, the long-time dynamics can be fully described in terms of just a few new collective dynamical variables governed by the same Hamiltonian only with “renormalized” parameters. Combining this feature with the integrability of the underlying (e.g., the two-channel) model, we develop and consistently present a general method that explicitly obtains the exact asymptotic state of the system.

We find a flat band and a self-trapping band through the coupling of two unidirectional edge modes, which was originally achieved by Wang et al. [Phys. Rev. Lett. 100, 013905 (2008); Nature 461, 772 (2009)] in two-dimensional magneto-optical photonic crystals. We break up a square-lattice yttrium-iron-garnet photonic crystal forming a waveguide and two edges. Given a proper interval of the two edges, two unidirectional edge modes with opposite group velocity directions can be coupled. The coupling leads to a wide flat band in which the group velocity is near zero, and a self-trapping band in which light is totally localized around the source. The position of the flat band and the group velocity can be adjusted by the external magnetic field. Numerical simulations and theoretical analysis both demonstrate the two interesting band structures.

Optomechanical and electromechanical cavities have been widely used in quantum memories and quantum transducers. We theoretically investigate the robustness of optomechanical and electromechanical quantum memories against the noise of the control laser. By solving the Langevin equations and using the covariance matrix formalism in the presence of laser noise, the storing fidelity of Gaussian states is obtained. It is shown that the destructive effect of phase noise is more significant in higher values of coupling laser amplitude and optomechanical coupling strength $G$. However, by further increasing the coupling coefficient, the interaction time between photons and phonons decreases below the coherence time of laser frequency noise and the destructive effect of laser phase noise on the storing fidelity drops as well.

Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal witness, which is a necessary and sufficient test of two-photon polarization entanglement. It allows us to detect entanglement for any two-qubit mixed state and to establish tight upper and lower bounds on its amount. A different element of this method is the sequential character of its main components, which allows us to obtain relatively complicated information about quantum correlations with the help of simple linear-optical elements. As such, this proposal realizes a universal two-qubit entanglement test within the present state of the art of quantum optics. We show the optimality of our setup with respect to the minimal number of measured quantities.

We study teleportation with identical massive particles. Indistinguishability imposes that the relevant degrees of freedom to be teleported are not particles, but rather addressable orthogonal modes. We discuss the performances of teleportation under the constraint of conservation of the total number of particles. The latter inevitably decreases the teleportation fidelity. Moreover, even though a phase reference, given by the coupling to a reservoir, circumvents the constraint, it does not restore perfect deterministic teleportation. The latter is only achievable with some special resource entangled states and when the number of particles tends to infinity. Interestingly, some of such states are the many-particle atomic coherent states and the ground state of cold atoms loaded into a double well potential, which are routinely prepared in experiments.