Schemes for topological quantum computation are usually based on the assumption that the system is initially prepared in a specific state. In practice, this state preparation is expected to be challenging as it involves nontopological operations which heavily depend on the experimental realization and are not naturally robust against noise. Here we show that this assumption can be relaxed by using composite anyons: starting from an unknown state with reasonable physical properties, it is possible to efficiently distill suitable initial states for computation purely by braiding, i.e., reversible gates. This is achieved by encoding logical information in a subsystem code with gauge system corresponding to the internal degrees of freedom of composite objects.

We consider the problem of deciding if some multiparty entangled pure state can be converted, with a nonzero success probability, into a given bipartite pure state shared between two specified parties through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to our question. As a result, a given transformation is possible if and only if it is generically attainable by a simple randomized protocol.

Atomic states are perturbed by externally applied magnetic fields (Zeeman effect). As well as the usual Zeeman splittings, the magnetic field leads to mixing of states with different values of the $J$ quantum number. We report on the direct experimental measurement of this effect using the electron shelving technique (employed to great effect in single-ion spectroscopy and quantum-information processing). Specifically we observe shelving to the metastable ($3p^{6}3d$) ${}^2{D}_{5/2}$ state in a single ${}^{40}\mathrm{Ca}$${}^{+}$ ion, via spontaneous decay on the strongly forbidden $4p\hspace{0.5em}{}^2{P}_{1/2}\leftrightarrow 3d\hspace{0.5em}{}^2{D}_{5/2}$ transition. The rate of this transition is shown to scale as the square of the magnetic-field strength. The scaling and magnitude of the effect is compared to the result derived from first-order perturbation theory. For applications in quantum-information processing the $J$-mixing effect causes a degradation of readout fidelity. We show that this degradation is at a tolerable level for Ca${}^{+}$ and is much less problematic for other trapped ionic species.

We analyze collisional decoherence of atoms or molecules prepared in a coherent superposition of nondegenerate internal states at ultralow temperatures and placed in an ultracold buffer gas. Our analysis is applicable for an arbitrary bath-particle to tracer-particle mass ratio. Both elastic and inelastic collisions contribute to decoherence. We obtain an expression relating the observable decoherence rate to pairwise scattering properties, specifically the scattering lengths and low-temperature scattering amplitudes. We consider the dependence on the bath-particle to tracer-particle mass ratio for the case of light bath and heavy tracer particles. The expressions obtained may be useful in low-temperature applications where accurate estimates of decoherence rates are needed. The results suggest a method for determining the scattering lengths of atoms and molecules in different internal states by measuring decoherence-induced damping of coherent oscillations.

Inner-shell photodetachment from Fe${}^{-}$ was studied in the 48- to 72-eV photon energy range using a merged ion-photon-beam technique. The absolute photodetachment cross sections of Fe${}^{-}$, leading to Fe${}^{+}$ and Fe${}^{2+}$ ion production, were measured. The $3p\to (3d+\varepsilon d)$ photoexcitation in Fe${}^{-}$ negative ions gives rise to shape resonances. In the near-threshold region, shape-resonance profiles with $l=2$ accurately fit the single-photodetachment cross section. Simultaneous double photodetachment was also observed, resulting in an increased Fe${}^{2+}$ production which obeys a Wannier law. Despite the large number of possible terms resulting from the Fe${}^{-}\hspace{0.5em}3d$ open shell, a rough calculation using the $R$-matrix method qualitatively agrees well with the experimental data.

We investigate finite-size effects in quantum quenches on the basis of simple energetic arguments. Distinguishing between the low-energy part of the excitation spectrum, below a microscopic energy scale, and the high-energy regime enables one to define a crossover number of particles that is shown to diverge in the small quench limit. Another crossover number is proposed based on the fidelity between the initial and final ground states. Both criteria can be computed using ground-state techniques that work for systems larger than full-spectrum diagonalization. As examples, two models are studied: one with free bosons in an harmonic trap whose frequency is quenched and the one-dimensional Bose-Hubbard model that is known to be nonintegrable and for which recent studies have uncovered remarkable nonequilibrium behaviors. The diagonal weights of the time-averaged density matrix are computed, and observables obtained from this diagonal ensemble are compared with the ones from statistical ensembles. It is argued that the “thermalized” regime of the Bose-Hubbard model, previously observed in the small quench regime, experiences strong finite-size effects that make a thorough comparison with statistical ensembles difficult. In addition, we show that the nonthermalized regime, emerging on finite-size systems and for large interaction quenches, is not related to the existence of an equilibrium quantum critical point but to the high-energy structure of the energy spectrum in the atomic limit. Its features are reminiscent of the quench from the noninteracting limit to the atomic limit.

Multiply quantized vortices in the BCS-to-BEC (Bose-Einstein condensation) evolution of $p$-wave resonant Fermi gases are investigated theoretically. The vortex structure and the low-energy quasiparticle states are discussed, based on the self-consistent calculations of the Bogoliubov-de Gennes and gap equations. We reveal the direct relation between the macroscopic structure of vortices, such as particle densities, and the low-lying quasiparticle state. In addition, the net angular momentum for multiply quantized vortices with a vorticity $\kappa$ is found to be expressed by a simple equation, which reflects the chirality of the Cooper pairing. Hence, the observation of the particle density depletion and the measurement of the angular momentum will provide the information on the core-bound state and $p$-wave superfluidity. Moreover, the details on the zero energy Majorana state are discussed in the vicinity of the BCS-to-BEC evolution. It is demonstrated numerically that the zero energy Majorana state appears in the weak coupling BCS limit only when the vortex winding number is odd. The $\kappa$ branches of the core-bound states for a vortex state with vorticity $\kappa$ exist; however, only one of them can be the zero energy. This zero energy state vanishes at the BCS-BEC topological phase transition because of interference between the core-bound and edge-bound states.

We study two-component (or pseudo-spin-$\frac{1}{2}$) Bose or Fermi gases in one dimension, in which particles are convertible between the components. Through bosonization and numerical analyses of a simple lattice model, we demonstrate that, in such gases, a strong intercomponent repulsion induces spontaneous population imbalance between the components, namely, the ferromagnetism of the pseudo spins. The imbalanced phase contains gapless charge excitations characterized as a Tomonaga-Luttinger liquid and gapped spin excitations. We uncover a crucial effect of the intercomponent particle hopping on the transition to the imbalanced phase. In the absence of this hopping, the transition is of first order. At the transition point, the energy spectrum reveals certain degeneracy indicative of an emergent $\text{SU}(2)$ symmetry. With an infinitesimal intercomponent hopping, the transition becomes of Ising type. We determine the phase diagram of the model accurately and test the reliability of the weak-coupling bosonization formalism.

We measured the ground-state electric-dipole polarizability of sodium, potassium, and rubidium using a Mach-Zehnder atom interferometer with an electric-field gradient. We find ${\alpha }_{\mathrm{Na}}=24.11(2){}_{\mathrm{stat}}(18){}_{\mathrm{sys}}\times {10}^{-24}{\mathrm{cm}}^3$, ${\alpha }_{\mathrm{K}}=43.06(14)(33)$, and ${\alpha }_{\mathrm{Rb}}=47.24(12)(42)$. Since these measurements were all performed in the same apparatus and subject to the same systematic errors, we can present polarizability ratios with $0.3\%$ uncertainty. We find ${\alpha }_{\mathrm{Rb}}/{\alpha }_{\mathrm{Na}}=1.959(5)$, ${\alpha }_{\mathrm{K}}/{\alpha }_{\mathrm{Na}}=1.786(6)$, and ${\alpha }_{\mathrm{Rb}}/{\alpha }_{\mathrm{K}}=1.097(5)$. We combine our ratio measurements with the higher-precision measurement of sodium polarizability by Ekstrom et al. [Phys. Rev. A 51, 3883 (1995)] to find ${\alpha }_{\mathrm{K}}=43.06(21)$ and ${\alpha }_{\mathrm{Rb}}=47.24(21)$.

We theoretically study the effect of pulse trapping inside one-dimensional photonic crystal with relaxing cubic nonlinearity. We analyze dependence of light localization on pulse intensity and explain its physical mechanism as connected with the formation of a dynamical nonlinear cavity inside the structure. We search for the range of optimal values of parameters (relaxation time and pulse duration) and show that pulse trapping can be observed only for positive nonlinearity coefficients. We suppose that this effect can be useful for realization of optical memory and limiting.

We study transport properties of alkaline-earth-metal atoms governed by the Kondo lattice Hamiltonian plus a harmonic confining potential, and suggest simple dynamical probes of several different regimes of the phase diagram that can be implemented with current experimental techniques. In particular, we show how Kondo physics at strong coupling, at low density, and in the heavy fermion phase is manifest in the dipole oscillations of the conduction band upon displacement of the trap center.

Using numerical solutions to quantum field theory, the creation of boson-antiboson pairs from the vacuum under a very strong localized external electric field is explored. The simulations reveal that the initial linear increase of the number of particles turns into an exponential growth. This self-amplification can be understood as the result of the interaction of the previously generated particles with the creation process. While the number of particles keeps increasing, the spatial shape of the (normalized) charge density of the created particles reaches a universal form that can be related to the bound states of the supercritical potential well. We accompany the space-time resolved quantum field theoretical simulations with a model calculation that allows us to interpret the numerical simulations in terms of simple classical mechanical concepts.

The preprocessing stage of Shor’s algorithm generates a class of quantum states referred to as periodic states, on which the quantum Fourier transform is applied. Such states also play an important role in other quantum algorithms that rely on the quantum Fourier transform. Since entanglement is believed to be a necessary resource for quantum computational speedup, we analyze the entanglement of periodic states and the way it is affected by the quantum Fourier transform. To this end, we derive a formula that evaluates the Groverian entanglement measure for periodic states. Using this formula, we explain the surprising result that the Groverian entanglement of the periodic states built up during the preprocessing stage is only slightly affected by the quantum Fourier transform.

Quantum entanglement has been actively sought in optomechanical and electromechanical systems. The simplest system is a mechanical oscillator interacting with a coherent optical field, while the oscillator also suffers from thermal decoherence. With a rigorous functional analysis, we develop a mathematical framework for treating quantum entanglement that involves infinite degrees of freedom. We show that the quantum entanglement is always present between the oscillator and continuous optical field—even when the environmental temperature is high and the oscillator is highly classical. Such a universal entanglement is also shown to be able to survive more than one mechanical oscillation period if the characteristic frequency of the optomechanical interaction is larger than that of the thermal noise. In addition, we introduce effective optical modes that are ordered by the entanglement strength to better understand the entanglement structure, analogously to the energy spectrum of an atomic system. In particular, we derive the optical mode that is maximally entangled with the mechanical oscillator, which will be useful for future quantum computing and encoding information into mechanical degrees of freedom.

We show that each entanglement witness detecting a given bipartite entangled state provides an estimation of its concurrence. We illustrate our result with several well-known examples of entanglement witnesses and compare the corresponding estimation of concurrence with other estimations provided by the trace norm of partial transposition and realignment.

We present a theoretical study on the orientation-dependent retarding force experienced by slow homonuclear dimers moving at arbitrary alignment with the direction of their flight in a three-dimensional degenerate electron gas of metallic densities. The analytical results are derived within the approximate framework of Brueckner for elastic scattering of an electron by a system of two auxiliary potentials of short range. The influence of the screened field of a single constituent of the slowly moving composite projectile on the scattering electron is modeled by an effective phase shift parameter $\eta$ in the short-range potential in order to characterize the real-constituent system coupling due to displacement. The orientation-dependent closed expressions reveal the dependence of observables on the classical geometry and quantum dynamics. The interplay of wave-interference and multiple scattering in the orientation-dependent friction is analyzed for realistic sets of the input parameters. Comparison with experimental data is made and good agreement is found.

We investigate a four-level superradiant laser whose intensity is proportional to $N^2$ and whose linewidth scales as $1/N^2$. In the absence of spontaneous emissions, we derive the stationary solutions of the atomic full cooperativity, analyze their stabilities, and find the corresponding irreducible representation based on group $U(4)$. We also investigate the spectra of the phase and amplitude fluctuations of the fields inside and outside the cavity and find that the amplitude fluctuations of the output fields cannot be squeezed in the low-frequency limit, which is completely different from the three-level superradiant laser system. Finally, we consider the stationary solutions corresponding to the partial cooperativity due to the symmetry breaking of $U(4)$ induced by the atomic spontaneous emissions.

We study the optomechanical design introduced by M. Li et al. [Phys. Rev. Lett. 103, 223901 (2009)], which is very effective for investigation of the effects of reactive coupling. We show the normal mode splitting that is due solely to reactive coupling rather than due to dispersive coupling. We suggest feeding the waveguide with a pump field along with a probe field and scanning the output probe for evidence of reactive-coupling-induced normal mode splitting.

I investigate the dynamics and power spectrum of two coupled qubits (two-level systems) under incoherent continuous pump and dissipation. New regimes of strong coupling are identified, which are due to additional paths of coherence flow in the system. Dressed states are reconstructed even in the regime of strong decoherence. The results are analytical and offer an exact description of strong coupling in the presence of pumping and decay in a nontrivial (nonlinear) system.

It is shown that the pair plasmas with small temperature asymmetry can support existence of localized as well as delocalized optical vortex solitons. Coexistence of such solitons is possible due to peculiar form of saturating nonlinearity which has a focusing-defocusing nature—for weak amplitudes being focusing becoming defocusing for higher amplitudes. It is shown that delocalized vortex soliton is stable in entire region of its existence while single- and multicharged localized vortex solitons are unstable for low amplitudes and become stable for relativistic amplitudes.