In a topological quantum computer, braids of non-Abelian anyons in a $\left(2+1\right)$-dimensional space time form quantum gates, whose fault tolerance relies on the topological, rather than geometric, properties of the braids. Here we propose to create and exploit redundant geometric degrees of freedom to improve the theoretical accuracy of topological single- and two-qubit quantum gates. We demonstrate the power of the idea using explicit constructions in the Fibonacci model. We compare its efficiency with that of the Solovay-Kitaev algorithm and explain its connection to the leakage errors reduction in an earlier construction [H. Xu and X. Wan, Phys. Rev. A 78, 042325 (2008)].

In the absence of a reference frame for transformations associated with group $G$, any quantum state that is noninvariant under the action of $G$ may serve as a token of the missing reference frame. We here present a measure of the quality of such a token: the relative entropy of frameness. This is defined as the relative entropy distance between the state of interest and the nearest $G$-invariant state. Unlike the relative entropy of entanglement, this quantity is straightforward to calculate, and we find it to be precisely equal to the $G$-asymmetry, a measure of frameness introduced by Vaccaro et al. It is shown to provide an upper bound on the mutual information between the group element encoded into the token and the group element that may be extracted from it by measurement. In this sense, it quantifies the extent to which the token successfully simulates a full reference frame. We also show that despite a suggestive analogy from entanglement theory, the regularized relative entropy of frameness is zero and therefore does not quantify the rate of interconversion between the token and some standard form of quantum reference frame. Finally, we show how these investigations yield an approach to bounding the relative entropy of entanglement.

It is revealed that quantum repeating devices and quantum seals have a very close relationship, thus the theory in one field can be applied to the other. Consequently, it is shown that the fidelity bounds and optimality of quantum repeating devices for decoding quantum information can be violated when they are used for decoding classical information from quantum states and the security bounds for protocols sealing quantum data exist.

The effect of pump-wave misalignment on the oscillation spectra of a semilinear photorefractive oscillator is studied numerically and compared with the results of experiments performed with ${\text{BaTiO}}_3:\text{Co}$ and ${\text{KNbO}}_3:\text{Ag},\text{Fe}$ crystals.

Various types of unravelings of Lindblad master equation have been used to define the geometric phase for an open quantum system. Approaches of this type were criticized for lacking in unitary symmetry of the Lindblad equation [A. Bassi and E. Ippoliti, Phys. Rev. A 73, 062104 (2006)]. We utilize quantum state diffusion (QSD) approach to demonstrate that a geometric phase invariant on the symmetries of the Lindblad equation can be defined. It is then shown that such a definition of the geometric phase could be either invariant on the decomposition of the initial mixed state or gauge invariant, but not both. This alternative is inherent to the definitions based on quantum trajectories. The QSD geometric phase is computed for a qubit in different types of environments.

We investigate the non-Markovian dynamics of two-state systems in structured reservoirs. We establish a connection between two theoretical quantum approaches, the pseudomodes [B. M. Garraway, Phys. Rev. A 55, 2290 (1997)] and the recently developed non-Markovian quantum jump method [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. This connection provides a clear physical picture of how the structured reservoir affects the system dynamics, suggesting the role of the pseudomodes as effective description of environmental memory.

We propose a scheme for realizing quantum phase gates for two atoms trapped in separate cavities connected by an optical fiber. In the scheme, the atoms, cavities, and fiber mode are in resonance. In contrast to the original scheme [A. Serafini, S. Mancini, and S. Bose, Phys. Rev. Lett. 96, 010503 (2006)], the gates are performed within the null- and single-excitation subspaces in virtue of the asymmetric encoding for two atomic qubits and can function beyond the limit that the atom-cavity coupling is much smaller than the cavity-fiber coupling. We study the stability of the gates and the influences of dissipation and show that such gates are robust.

Realistic simulations of current ultracold atom experiments in optical lattices show that the ramping up of the optical lattice is significantly nonadiabatic, implying that experimentally prepared Mott insulators are not really in the ground state of the atomic system. The nonadiabaticity is even larger in the presence of a secondary quasiperiodic lattice simulating “disorder.” Alternative ramping schemes are suggested that improve the adiabaticity when the disorder is not too large.

We study the evolution of density in an expanding Bose-Einstein condensate that initially has a spatially varying phase, concentrating on behavior when these phase variations are large. In this regime large density fluctuations develop during expansion. Maxima have a characteristic density that diverges with the amplitude of phase variations and their formation is analogous to that of caustics in geometrical optics. We analyze in detail caustic formation in a quasi-one-dimensional condensate, which before expansion is subject to a periodic or random optical potential, and we discuss the equivalent problem for a quasi-two-dimensional system. We also examine the influence of many-body correlations in the initial state on caustic formation for a Bose gas expanding from a strictly one-dimensional trap. In addition, we study a similar arrangement for noninteracting fermions, showing that Fermi surface discontinuities in the momentum distribution give rise in that case to sharp peaks in the spatial derivative of the density. We discuss recent experiments and argue that fringes reported in time of flight images [Chen et al., Phys. Rev. A 77, 033632 (2008)] are an example of caustic formation.

Cavity-enhanced light scattering from an ultracold gas in an optical lattice constitutes a quantum measurement with a controllable form of the measurement backaction. Time-resolved counting of scattered photons alters the state of the atoms without particle loss implementing a quantum nondemolition measurement. The conditional dynamics is given by the interplay between photodetection events (quantum jumps) and no-count processes. The class of emerging atomic many-body states can be chosen via the optical geometry and light frequencies. Light detection along the angle of a diffraction maximum (Bragg angle) creates an atom-number-squeezed state, while light detection at diffraction minima leads to the macroscopic superposition states (Schrödinger cat states) of different atom numbers in the cavity mode. A measurement of the cavity transmission intensity can lead to atom-number-squeezed or macroscopic superposition states depending on its outcome. We analyze the robustness of the superposition with respect to missed counts and find that a transmission measurement yields more robust and controllable superposition states than the ones obtained by scattering at a diffraction minimum.

We propose and study an approach to realize quantum switch for single-photon transport in a coupled superconducting transmission-line-resonator (TLR) array with one controllable hopping interaction. We find that the single photon with arbitrary wave vector can transport in a controllable way in this system. We also study how to realize controllable hopping interaction between two TLRs via a Cooper-pair box (CPB). When the frequency of the CPB is largely detuned from those of the two TLRs, the variables of the CPB can be adiabatically eliminated and thus a controllable interaction between two TLRs can be obtained.

We develop the concept of a unitary $t$-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group $U\left(2^n\right)$ on $n$ qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an $O\left(n\right)$-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on $n$ qubits with quantum circuits of size $O\left(n\right)$ without requiring any ancilla qubits, thereby improving upon previous approaches.

The cross section for dissociative recombination of ${\text{BeH}}^{+}$ is calculated by the solution of the time-dependent Schrödinger equation in the local complex potential approximation. The effects of couplings between resonant states and the Rydberg states converging to the ground state of the ion are studied. The relevant potentials, couplings, and autoionization widths are extracted using ab initio electron scattering and structure calculations, followed by a diabatization procedure. The calculated cross sections show a sizable magnitude at low energy, followed by a high-energy peak centered around 1 eV. The electronic couplings between the neutral states induce oscillations in the cross section. Analytical forms for the cross sections at low collision energies are given.

The time-dependent Schrödinger equation for $\mathrm{H}_2{}^{+}$ in a time-varying electromagnetic field is solved in the fixed-nuclei approximation using a previously developed finite-element discrete-variable representation in prolate spheroidal coordinates. Amplitudes for single- and two-photon ionization are obtained using the method of exterior complex scaling to effectively propagate the field-free solutions from the end of the radiation pulse to infinite times. Cross sections are presented for one- and two-photon ionization for both parallel and perpendicular polarizations of the photon field, as well as photoelectron angular distributions for two-photon ionization.

A theoretical approach was developed for an exact numerical description of a pair of ultracold atoms interacting via a central potential, which is trapped in a three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates is explicitly considered using a configuration-interaction (exact-diagonalization) technique. Deviations from the harmonic approximation are discussed for several heteronuclear alkali-metal atom pairs trapped in a single site of an optical lattice. The consequences are discussed for the analysis of a recent experiment [C. Ospelkaus et al., Phys. Rev. Lett. 97, 120402 (2006)] in which radio-frequency association was used to create diatomic molecules from a fermionic and a bosonic atom and to measure their binding energies close to a magnetic Feshbach resonance.

We calculate numerically the energy spectrum of the six dimensional problem of two interacting Bosons in a three-well optical lattice. The particles interact via a full Born-Oppenheimer potential, which can be adapted to model the behavior of the $s$-wave scattering length at Feshbach resonances. By adjusting the parameters of the corresponding Bose-Hubbard (BH) Hamiltonian the deviation between the numerical energy spectrum and the BH spectrum is minimized. This defines the optimal BH parameter set, which we compare to the standard parameters of the BH model. The range of validity of the BH model with these parameter sets is examined, and an analytical prediction of the interaction parameter is introduced. Furthermore, an extended BH model and implications due to the energy dependence of the scattering length and couplings to higher Bloch bands at a Feshbach resonance are discussed.

We study the many-body state of ultracold bosons in a bistable optical lattice potential in an optomechanical resonator in the weak-coupling limit. Interesting physics arises as a result of bistability and discontinuous jumps in the cavity field. Of particular interest is the situation where the optical cavity is engineered so that a single input beam can result in two radically different stable ground states for the intracavity gas: superfluid and Mott insulator. Furthermore, the system we describe can be used as an adjustable template for investigating the coupling between cavity fields, nanomechanical systems operating in the quantum regime, and ultracold atomic gases.

We experimentally studied the evolution of quasieigenmodes as classical dynamics undergoing a transition from being regular to chaotic in open quantum billiards. In a deformation-variable microcavity, we traced all high-$Q$ cavity modes in a wide range of frequency as the cavity deformation increased. By employing an internal parameter, we were able to obtain a mode-dynamics diagram at a given deformation, showing avoided crossings between different mode groups, and could directly observe the coupling strengths induced by ray chaos among encountering modes. We also show that the observed mode-dynamics diagrams reflect the underlying classical ray dynamics in the phase space.

The ground-state fidelity has been introduced recently as a tool to investigate quantum phase transitions. Here, we apply this concept in the context of a crossover problem. Specifically, we calculate the fidelity susceptibility for the BCS ground-state wave function, when the intensity of the fermionic attraction is varied from weak to strong in an interacting Fermi system, through the BCS-Bose-Einstein Condensation crossover. Results are presented for contact and finite-range attractive potentials and for both continuum and lattice models. We conclude that the fidelity susceptibility can be useful also in the context of crossover problems.