We present a scheme to improve the noise threshold for fault-tolerant topological one-way computation with constant overhead. Certain cluster states of finite size, say star clusters, are constructed with logical qubits through an efficient verification process to achieve high fidelity. Then, the star clusters are connected near-deterministically with verification to form a three-dimensional cluster state to implement topological one-way computation. The necessary postselection for verification is localized within the star clusters, ensuring the scalability of computation. By using the Steane seven-qubit code for the logical qubits, this scheme works with a high error rate of $2\%$ and reasonable resources comparable to or less than those for the other fault-tolerant schemes. A higher noise threshold would be achieved by adopting a larger code.

A simple derivation of the optimal state estimation of a quantum bit was obtained by using the no-signaling principle. In particular, the no-signaling principle determines a unique form of the guessing probability independent of figures of merit, such as the fidelity or information gain. This proves that the optimal estimation for a quantum bit can be achieved by the same measurement for almost all figures of merit.

We investigate how multiphoton quantum states obtained through optical parametric amplification can be manipulated by performing a measurement on a small portion of the output light field. We study in detail how the macroqubit features are modified by varying the amount of extracted information and the strategy adopted at the final measurement stage. At last the obtained results are employed to investigate the possibility of performing a microscopic-macroscopic nonlocality test free from auxiliary assumptions.

We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowledge of this transition polarizability is required in a number of high-precision experiments, such as microwave atomic clocks and searches for $\mathit{CP}$-violating permanent electric dipole moments. While the traditional polarizability arises in the second order of interaction with the externally applied electric field, the differential polarizability involves an additional contribution from the hyperfine interaction of atomic electrons with nuclear moments. We derive formulas for the scalar and tensor polarizabilities including contributions from magnetic dipole and electric quadrupole hyperfine interactions. Numerical results are presented for Al, Rb, Cs, ${\mathrm{Yb}}^{+}$, ${\mathrm{Hg}}^{+}$, and Fr.

We study the superfluid pairing in a two-species gas of heteronuclear fermionic molecules with equal density. The interplay of the isotropic $s$-wave interaction and anisotropic long-range dipolar interaction reveals rich physics. We find that the single-particle momentum distribution has a characteristic ellipsoidal shape that can be reasonably represented by a deformation parameter $\alpha$ defined similarly to the normal phase. Interesting momentum-dependent features of the order parameter are identified. We calculate the critical temperatures of both the singlet and triplet superfluids, suggesting a possible pairing symmetry transition by tuning the $s$-wave or dipolar interaction strength.

We study theoretically the ground states of two-dimensional Bose-Hubbard models which are frustrated by gauge fields. Motivated by recent proposals for the implementation of optically induced gauge potentials, we focus on the situation in which the imposed gauge fields give rise to a pattern of staggered fluxes of magnitude $\alpha$ and alternating in sign along one of the principal axes. For $\alpha =1/2$ this model is equivalent to the case of uniform flux per plaquette $n_{\varphi }=1/2$, which, in the hard-core limit, realizes the “fully frustrated” spin-1/2 $\mathit{XY}$ model. We show that the mean-field ground states of this frustrated Bose-Hubbard model typically break translational symmetry. Given the presence of both a non-zero superfluid fraction and translational symmetry breaking, these phases are supersolid. We introduce a general numerical technique to detect broken symmetry condensates in exact diagonalization studies. Using this technique we show that, for all cases studied, the ground state of the Bose-Hubbard model with staggered flux $\alpha$ is condensed, and we obtain quantitative determinations of the condensate fraction. We discuss the experimental consequences of our results. In particular, we explain the meaning of gauge invariance in ultracold-atom systems subject to optically induced gauge potentials and show how the ability to imprint phase patterns prior to expansion can allow very useful additional information to be extracted from expansion images.

We demonstrate an experiment which utilizes a Sagnac interferometer to measure a change in optical frequency of 129 $\pm$ 7 $\text{kHz}/\sqrt{\text{Hz}}$ with only 2 mW of continuous-wave, single-mode input power. We describe the measurement of a weak value and show how even higher-frequency sensitivities may be obtained over a bandwidth of several nanometers. This technique has many possible applications, such as precision relative frequency measurements and laser locking without the use of atomic lines.

We investigate a nonlinear localization microscopy method based on Rabi oscillations of single emitters. We demonstrate the fundamental working principle of this technique using a cryogenic far-field experiment in which subwavelength features smaller than $\lambda /10$ are obtained. Using Monte Carlo simulations, we show the superior localization accuracy of this method under realistic conditions and a potential for higher acquisition speed or a lower number of required photons as compared to conventional linear schemes. The method can be adapted to other emitters than molecules and allows for the localization of several emitters at different distances to a single measurement pixel.

Resonant features in low-energy photoionization cross sections are reported in coupled-channel calculations for O ii including relativistic fine structure. The calculations reveal extensive near-threshold resonant structures in the small energy region between the fine structure levels of the ground state $2p^2({}^3{P}_{0,1,2})$ of the residual ion O iii. Although the resonances have not yet been observed, they are similar to other experimentally observed features. They are expected to significantly enhance the very-low-temperature dielectronic recombination rates, potentially leading to the resolution of an outstanding nebular abundances anomaly. Higher energy partial and total photoionization cross sections of the ground configuration levels $2p^3({}^4{S}_{3/2}^o,{}^2{D}_{3/2,5/2}^o,{}^2{P}_{1/2,3/2}^o)$ are found to be in agreement with experimental measurements on synchrotron-based photon sources [1–3], thereby identifying the excited O iii levels present in the ion beams. These are also the first results from a recently developed version of Breit-Pauli $R$-matrix (BPRM) codes, with inclusion of two-body magnetic interaction terms. The improved relativistic treatment could be important for other astrophysical applications and for more precise benchmarking of experimental measurements.

We theoretically study strong-field ionization of a heteronuclear diatomic molecule, CO, by calculating the photoelectron angular distributions (PADs) and the total ionization rates using linearly and circularly polarized laser fields. We find that, although the PADs of CO generally do not have inversion symmetry, they become more inversion symmetric as the photoelectron energy increases. Heteronuclear features of CO upon ionization are better understood by comparing the results with those of a representative of homonuclear molecules, ${\mathrm{N}}_2$, in that, although there are some similarities between CO and ${\mathrm{N}}_2$ due to the same orbital symmetry, ${\sigma }_g$, there are some differences between them in terms of the ionization suppression and orientation dependence of the total ionization yield. Namely, CO behaves more like an atom in the low-intensity range in a sense that ionization takes place mainly from the neighborhood of the C core, while it behaves more like a double-core molecule in the high-intensity range since ionization takes place from the neighborhood of both C and O cores. This explains why ionization suppression of CO is not seen at the low intensity but it becomes more visible at the high intensity range.

As an “input” state of a linear (Mach-Zehnder or Ramsey) interferometer, the phase-squeezed state proposed by Berry and Wiseman exhibits the best sensitivity approaching to the Heisenberg limit [Phys. Rev. Lett. 85, 5098 (2000)]. Similar with the Berry and Wiseman’s state, we find that two kinds of phase-squeezed states can be generated dynamically with atomic Bose-Einstein condensates confined in a symmetric double-well potential, which shows squeezing along spin operator ${\mathrm{Ŝ}}_y$ and antisqueezing along ${\mathrm{Ŝ}}_z$, leading to subshot-noise phase estimation.

We propose a scheme to create coherent superpositions of annular flow of strongly interacting bosonic atoms in a one-dimensional ring trap. The nonrotating ground state is coupled to a vortex state with mesoscopic angular momentum by means of a narrow potential barrier and an applied phase that originates from either rotation or a synthetic magnetic field. We show that superposition states in the Tonks-Girardeau regime are robust against single-particle loss due to the effects of strong correlations. The coupling between the mesoscopically distinct states scales much more favorably with particle number than in schemes relying on weak interactions, thus making particle numbers of hundreds or thousands feasible. Coherent oscillations induced by time variation of parameters may serve as a “smoking gun” signature for detecting superposition states.

We extend the input-output formalism of quantum optics to analyze few-photon transport in waveguides with an embedded qubit. We provide explicit analytical derivations for one- and two-photon scattering matrix elements based on operator equations in the Heisenberg picture.

Zitterbewegung (ZB), the trembling of free relativistic electrons in a vacuum, could be simulated by a single trapped ion. We focus on the variations of ZB under different parity conditions and find no ZB in the case of odd or even parity. ZB occurs only for the admixture of the odd- and even-parity states. We also show that a similar role is played by the parity operator for the trapped ion in Fock-state representation and the space-inversion operator for a realistic relativistic electron. Although the ZB effect is invisible in a relativistic electron, preparation of the trapped ion in different parity states is a sophisticated job, which makes it possible to observe the parity-relevant ZB effects with currently available techniques.

Using an exactly soluble one-dimensional atomic model, we explore the idea that the recently observed high-order nonlinearity in optical filaments is due to virtual transitions involving the continuum states. We show that the model’s behavior is qualitatively comparable with the experimentally observed crossover from self-focusing to defocusing at high intensities, and only occurs at intensities which result in significant ionization. Based on these observations, we conjecture that this continuum electron nonlinear refraction exhibits strong memory effects and, most importantly, the change of its sign is effectively masked by the defocusing due to free electrons.

We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

We demonstrate improved detection of small trapped atomic ensembles through advanced postprocessing and optimal analysis of absorption images. A fringe-removal algorithm reduces imaging noise to the fundamental photon-shot-noise level and proves beneficial even in the absence of fringes. A maximum-likelihood estimator is then derived for optimal atom-number estimation in well-localized ensembles and is applied to real experimental data to measure the population differences and intrinsic atom shot noise between spatially separated ensembles each comprising between $10$ and $2000$ atoms. The combined techniques improve our signal-to-noise ratio by a factor of $3$, to a minimum resolvable population difference of $17$ atoms, close to our ultimate detection limit.

We study the state decay of two qubits interacting with a common harmonic oscillator reservoir. We find both a decoherence error and the error caused by the amplitude change of the superradiant state. We show that frequent $\pi$-phase pulses can eliminate both types of errors and therefore protect a two-qubit odd-parity state more effectively than the frequent measurement method. This shows that the methods using dynamical decoupling and the quantum Zeno effects actually can give rather different results when the operation frequency is finite.

The absolute cross sections for the competing decay-channel fluorescence, dissociation, and ionization of photoexcited long-lived superexcited ${\mathrm{H}}_2$ molecular levels have been measured from the ionization threshold of ${\mathrm{H}}_2$ up to the H($1s$) $+$ H($n=3$) dissociation limit. The total and partial natural widths of these levels have been determined. Good agreement is found with first principles calculations carried out with the multichannel quantum defect theory for excited levels of ${}^1{\Pi }_u^{-}$ symmetry, which represent $70\%$ of the levels studied experimentally. The calculations reproduce the balance between the competing decay processes as well as its substantial evolution from level to level.

This work is an extended version of a paper published previously [S. de Man et al., Phys. Rev. Lett. 103, 040402 (2009)], where we presented measurements of the Casimir force between a gold-coated sphere and a plate coated with either gold or an indium tin oxide (I TO) layer. The experiment, which was performed in air, showed that I TO conducts sufficiently to prevent charge accumulation but is still transparent enough to halve the Casimir attraction when compared to gold. Here we report all the experimental details that, owing to the limited space available, were omitted in the previous article. We discuss the performance of our setup in terms of stability of the calibration procedure and reproducibility of the Casimir force measurement. We also introduce and demonstrate a technique to obtain the spring constant of our force sensor. Furthermore, we present a thorough description of the experimental method, a comprehensive explanation of data elaboration and error analysis, and a complete characterization of the dielectric function and of the surface roughness of the samples used in the actual experiment.