Atomic autoionization following O $1s$ resonant excitation in ${\mathrm{O}}_2$ is studied using high-resolution electron spectroscopy. The resonant Auger spectrum showing evidence of ultrafast dissociation as well as the autoionization of oxygen atoms is measured and discussed. Evidence of the electronic Doppler effect is observed in both electronic decay mechanisms.

Universal quantum computation (UQC) using Majorana fermions on a two-dimensional topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions does not include any two-qubit gate and also no single-qubit $\pi /8$ phase gate. In principle, it is possible to create these crucial extra gates using quantum interference of Majorana fermion currents. However, it is not clear if the motion of the various order parameter defects (vortices, domain walls, etc.), to which the Majorana fermions are bound in a TS medium, can be quantum coherent. We show that these obstacles can be overcome using a semiconductor quantum wire network in the vicinity of an $s$-wave superconductor, by constructing topologically protected two-qubit gates and any arbitrary single-qubit phase gate in a topologically unprotected manner, which can be error corrected using magic-state distillation. Thus our strategy, using a judicious combination of topologically protected and unprotected gate operations, realizes UQC on a quantum wire network with a remarkably high error threshold of $0.14$ as compared to ${10}^{-3}$ to ${10}^{-4}$ in ordinary unprotected quantum computation.

Entanglement of a system changes due to interactions with the environment. A typical type of interaction is amplitude damping. If we add a detector to monitor the environment and only select the no-damping outcome, this amplitude damping is modified into a weak measurement. Here we show that the entanglement change of a two-qubit state due to amplitude damping or weak measurement can be probabilistically reversed. For the amplitude-damping case, the entanglement partially recovers under most conditions. For the weak-measurement case, the recovery of the initial entangled state is exact. The reversal procedure involves another weak measurement, preceded and followed by bit flips applied to both qubits. We propose a linear optics scheme for the experimental demonstration of these procedures.

We have performed high-resolution two-photon dark-state spectroscopy of an ultracold gas of ${}^{87}\mathrm{Rb}$${}_2$ molecules in the $a^3{\Sigma }_u^{+}$ state at a magnetic field of about 1000 G. The vibrational ladder as well as the hyperfine and low-lying rotational structure are mapped out. Energy shifts in the spectrum are observed due to singlet-triplet mixing at binding energies as deep as a few hundred $\text{GHz}\times h$. This information, together with data from other sources, is used to optimize the potentials of the $a^3{\Sigma }_u^{+}$ and $X^1{\Sigma }_g^{+}$ states in a coupled-channel model. We find that the hyperfine structure depends weakly on the vibrational level. This provides a possible explanation for inaccuracies in recent Feshbach resonance calculations.

We investigate the possibility of measuring the thermal Casimir force and its gradient in the configuration of a plate and a microfabricated cylinder attached to a micromachined oscillator. The Lifshitz-type formulas in this configuration are derived using the proximity force approximation. The accuracy of the obtained expressions is determined from a comparison with exact results available in ideal metal case. Computations of the thermal correction to both the Casimir force and its gradient are performed in the framework of different theoretical approaches proposed in the literature. The correction to the Casimir force and its gradient due to lack of parallelism of the plate and cylinder is determined using the nonmultiplicative approach. The error introduced in the theory due to the finite length of the cylinder is estimated. We propose that both static and dynamic experiments measuring the thermal Casimir interaction between a cylinder and a plate using a micromachined oscillator can shed additional light on the thermal Casimir force problem. Specifically, it is shown that the static experiment is better adapted for the measurement of thermal effects.

In this article we present a Monte Carlo calculation of the critical temperature and other thermodynamic quantities for the unitary Fermi gas with a population imbalance (unequal number of fermions in the two spin components). We describe an improved worm-type algorithm that is less prone to autocorrelations than the previously available methods and show how this algorithm can be applied to simulate the unitary Fermi gas in presence of a small imbalance. Our data indicate that the critical temperature remains almost constant for small imbalances $h=\Delta \mu /{\varepsilon }_F\lesssim 0.2$. We obtain the continuum result $T_c=0.171(5){\varepsilon }_F$ in units of Fermi energy and derive a lower bound on the deviation of the critical temperature from the balanced limit, $T_c(h)-T_c(0)>-0.5{\varepsilon }_F{h}^2$. Using an additional assumption a tighter lower bound can be obtained. We also calculate the energy per particle and the chemical potential in the balanced and imbalanced cases.

We show that the visibility in interference experiments with Bose-Einstein condensates is directly related to the condensate fraction. The probability distribution of the contrast over many runs of an interference experiment thus gives the full counting statistics of the condensed atom number. For two-dimensional Bose gases, we discuss the universal behavior of the probability distribution in the superfluid regime and provide analytical expressions for the distributions for both homogeneous and harmonically trapped samples. They are non-Gaussian and unimodal with a variance that is directly related to the superfluid density. In general, the visibility is a self-averaging observable only in the presence of long-range phase coherence. Close to the transition temperature, the visibility distribution reflects the universal order-parameter distribution in the vicinity of the critical point.

Vortex streets are formed from sheared initial conditions in classical fluids even without viscosity, which is called the Kelvin-Helmholtz instability. We demonstrate that similar vortex streets are generated from sheared initial conditions by the direct numerical simulation of the Gross-Pitaevskii (GP) equation which describes the dynamics of the Bose-Einstein condensates. Furthermore, we show the vortex-lattice formation from sheared initial conditions analogous to the rigid-body rotation in the GP equation under a rotating harmonic potential. The vortex-lattice formation by the dynamical instability in the system without energy dissipation differs from the vortex-lattice formation process by the imaginary time evolution of the GP equation where the lowest energy state is obtained.

Interesting spin Hamiltonians can be realized with ultracold atoms in a two-component Mott insulator (2CMI) [Adv. Phys. 56, 243 (2007); Rev. Mod. Phys. 80, 885 (2008)]. It was recently demonstrated that the application of a magnetic field gradient to the 2CMI enables new techniques of thermometry [Phys. Rev. Lett. 103, 245301 (2009)] and adiabatic cooling [e-print arXiv:1006.4674]. Here we present a theoretical description which provides quantitative analysis of these two techniques. We show that adiabatic reduction of the field gradient is capable of cooling below the Curie or Néel temperature of certain spin-ordered phases.

Motivated by atomic optics experiments, we investigate a class of fidelity functions describing the reconstruction of quantum states by time-reversal operations as $M_{\mathrm{Da}}(t)=|\langle \psi |e^{i{H}_{2}t/2}{e}^{i{H}_{1}t/2}{e}^{-i{H}_{2}t/2}{e}^{-i{H}_{1}t/2}|\psi \rangle |{}^2$. We show that the decay of $M_{\mathrm{Da}}$ is quartic in time at short times and that it freezes well above the ergodic value at long times, when $H_2-H_1$ is not too large. The long-time saturation value of $M_{\mathrm{Da}}$ contains easily extractable information on the strength of decoherence in these systems.

We discuss a clusterlike one-dimensional system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system and is well protected against external local perturbations. All these facts show that the system is topologically ordered. We also find a string order parameter to characterize the quantum phase transition. Besides, we investigate two-site correlations including entanglement, quantum discord, and mutual information. We study the different divergence behaviors of the correlations. The quantum correlation decays exponentially in both topological and magnetic phases, and diverges in reversed power law at the critical point. And we find that in topological order systems, the global difference of topology induced by dimension can be reflected in local quantum correlations.

The capability of faithfully transmit quantum states and entanglement through quantum channels is one of the key requirements for the development of quantum devices. Different solutions have been proposed to accomplish such a challenging task, which, however, require either an ad hoc engineering of the internal interactions of the physical system acting as the channel or specific initialization procedures. Here we show that optimal dynamics for efficient quantum-state and entanglement transfer can be attained in generic quantum systems with homogeneous interactions by tuning the coupling between the system and the two attached qubits. We devise a general procedure to determine the optimal coupling, and we explicitly implement it in the case of a channel consisting of a spin-$\frac{1}{2}$$\mathit{XY}$ chain. The quality of quantum-state and entanglement transfer is found to be very good and, remarkably, almost independent of the channel length.

In this article, we investigate the structure and dynamics of miscellaneous mixtures of Bose-Einstein condensates confined within a time-independent anisotropic parabolic trap potential. In the zero-temperature mean-field approximation leading to coupled Gross-Pitaevskii equations for the macroscopic wave functions of the condensates, we show that these equations can be mapped onto the higher-dimensional time-gated Manakov system up to a first-order of accuracy. Paying particular attention to two-species mixtures and looking forward deriving a panel of miscellaneous excitations to the above equations, we analyze the singularity structure of the system by means of Weiss et al.’s [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 24, 522 (1983); 25, 13 (1984).] methodology and provide its general Lax representation. As a result, we unearth a typical spectrum of localized and periodic coherent patterns while depicting elastic and nonelastic interactions among such structures alongside the splitting and resonance phenomena occurring during their motion.

We report results for the Thomas-Fermi ground state of a spin-polarized dipolar interacting Bose-Einstein condensate for the case when the external magnetic field $\mathbf{B}$ is not orientated parallel to a principal axis but is aligned parallel to a symmetry plane of a harmonic anisotropic trap. For a dipole interaction strength parameter ${\varepsilon }_D\ne 0$ the release energy of the condensate depends on the trap orientation angle ${\vartheta }_T$ between the principal axis ${\mathbf{e}}_{z,T}$ of the trap and the field $\mathbf{B}$. From the quasiclassical Josephson equation of macroscopic quantum physics we determine the low-lying eigenfrequencies of small-amplitude collective modes of the condensate density for various trap frequencies ${\omega }_a$ and trap orientation angles ${\vartheta }_T$. For the special case of a spherical harmonic trap with trap frequency $\omega$ it is rigorously shown for $-\frac{1}{2}<{\varepsilon }_D<1$ that a pure $s$-wave symmetry breather excitation of the condensate density exists, that oscillates at a constant frequency ${\Omega }_s=\sqrt{5}\omega$ around the ground-state cloud, despite the well-known fact that the shape of the ground-state cloud of a spin-polarized dipolar condensate is for ${\varepsilon }_D\ne 0$ not isotropic. For ${\vartheta }_T\ne 0$ the small-amplitude modes of the particle density with isotropic and quadrupolar symmetry consist of two groups. There exist four modes that are combinations of basis functions, with $s$-wave, $d_{x^2-y^2}$- and $d_{z^2}$-wave, and $d_{\mathit{xz}}$-wave symmetry, and two modes that are combinations of basis functions with $d_{\mathit{yz}}$- and $d_{\mathit{xy}}$-wave symmetry. A characteristic difference in the dependence of the frequencies of these six collective modes on the dipole interaction strength parameter ${\varepsilon }_D$ for prolate and oblate harmonic triaxial traps, respectively, is suggested to be used as an experimental method to measure the $s$-wave scattering length $a_s$ of the atoms.

We develop the ideas of the quantum renormalization group and quantum information by exploring the low-energy-state dynamics of entanglement resources of a system close to its quantum critical point. We demonstrate that low-energy-state dynamical quantities of one-dimensional magnetic systems can show a quantum phase transition point and show scaling behavior in the vicinity of the transition point. To present our idea, we study the evolution of two spin entanglements in the one-dimensional Ising model in the transverse field. The system is initialized as the so-called thermal ground state of the pure Ising model. We investigate the evolution of the generation of entanglement with increasing magnetic field. We obtain that the derivative of the time at which the entanglement reaches its maximum with respect to the transverse field diverges at the critical point and its scaling behaviors versus the size of the system are the same as the static ground-state entanglement of the system.

In a counterfactual quantum key distribution scheme, a secret key can be generated merely by transmitting the split vacuum pulses of single particles. We improve the efficiency of the first quantum key distribution scheme based on the counterfactual phenomenon. This scheme not only achieves the same security level as the original one but also has higher efficiency. We also analyze how to achieve the optimal efficiency under various conditions.

A promising technique for measuring single electron spins is magnetic resonance force microscopy (MRFM), in which a microcantilever with a permanent magnetic tip is resonantly driven by a single oscillating spin. The most effective experimental technique is the oscillating cantilever-driven adiabatic reversals (OSCAR) protocol, in which the signal takes the form of a frequency shift. If the quality factor of the cantilever is high enough, this signal will be amplified over time to the point where it can be detected by optical or other techniques. An important requirement, however, is that this measurement process occurs on a time scale that is short compared to any noise which disturbs the orientation of the measured spin. We describe a model of spin noise for the MRFM system and show how this noise is transformed to become time dependent in going to the usual rotating frame. We simplify the description of the cantilever-spin system by approximating the cantilever wave function as a Gaussian wave packet and show that the resulting approximation closely matches the full quantum behavior. We then examine the problem of detecting the signal for a cantilever with thermal noise and spin with spin noise, deriving a condition for this to be a useful measurement.

We numerically study elongated helical spin textures in ferromagnetic spin-1 Bose-Einstein condensates subject to dipolar interparticle forces. Stationary states of the Gross-Pitaevskii equation are solved and analyzed for various values of the helical wave vector and dipolar coupling strength. We find two helical spin textures which differ by the nature of their topological defects. The spin structure hosting a pair of Mermin-Ho vortices with opposite mass flows and aligned spin currents is stabilized for a nonzero value of the helical wave vector.

We employ a semiclassical picture to study dynamics in a bosonic Josephson junction with various initial conditions. Phase diffusion of coherent preparations in the Josephson regime is shown to depend on the initial relative phase between the two condensates. For initially incoherent condensates, we find a universal value for the buildup of coherence in the Josephson regime. In addition, we contrast two seemingly similar on-separatrix coherent preparations, finding striking differences in their convergence to classicality as the number of particles increases.

We propose a scheme to realize the itinerant ferromagnetism of two-component cold fermionic atoms in the $p$-orbital bands in optical lattices. The band flatness in the two-dimensional honeycomb lattice dramatically amplifies the interaction effect, driving the ferromagnetic transition even with a relatively weak repulsive interaction. This scheme has the advantage that the stability of the system can be maintained without causing decay to the molecular state as one approaches the Feshbach resonance from the side with the positive scattering length. Experimental signatures and detections are also discussed.