In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particlelike excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world lines in three-dimensional space-time, and the corresponding quantum gates depend only on the topology of the braids formed by these world lines. We show how to find braids that yield a universal set of quantum gates for qubits encoded using a specific kind of quasiparticle which is particularly promising for experimental realization.

We show that recent claims for the nonstationary behavior of the logistic map at the Feigenbaum point based on nonextensive thermodynamics are either incorrect or can be easily deduced from well-known properties of the Feigenbaum attractor. In particular, there is no generalized Pesin identity for this system, the existing attempts at proofs being based on misconceptions about basic notions of ergodic theory. In deriving several new scaling laws of the Feigenbaum attractor, thorough use is made of its detailed structure, but there is no obvious connection to nonextensive thermodynamics.

We study a one-dimensional gas of fermionic atoms interacting via an $s$-wave molecular Feshbach resonance. At low energies the system is characterized by two Josephson-coupled Luttinger liquids, corresponding to paired atomic and molecular superfluids. We show that, in contrast to higher dimensions, the system exhibits a quantum phase transition from a phase in which the two superfluids are locked together to one in which, at low energies, quantum fluctuations suppress the Feshbach resonance (Josephson) coupling, effectively decoupling the molecular and atomic superfluids. Experimental signatures of this quantum transition include the appearance of an out-of-phase gapless mode (in addition to the standard gapless in-phase mode) in the spectrum of the decoupled superfluid phase and a discontinuous change in the molecular momentum distribution function.

We study a model of one-dimensional fermionic atoms with a narrow Feshbach resonance that allows them to bind in pairs to form bosonic molecules. We show that at low energy, a coherence develops between the molecule and fermion Luttinger liquids. At the same time, a gap opens in the spin excitation spectrum. The coherence implies that the order parameters for the molecular Bose-Einstein condensation and the atomic BCS pairing become identical. Moreover, both bosonic and fermionic charge density wave correlations decay exponentially, in contrast with a usual Luttinger liquid. We exhibit a Luther-Emery point where the systems can be described in terms of noninteracting pseudofermions. At this point we discuss the threshold behavior of density-density response functions.

We consider the propagation of a dark soliton in a quasi-1D Bose-Einstein condensate in presence of a random potential. This configuration involves nonlinear effects and disorder, and we argue that, contrarily to the study of stationary transmission coefficients through a nonlinear disordered slab, it is a well-defined problem. It is found that a dark soliton decays algebraically, over a characteristic length which is independent of its initial velocity, and much larger than both the healing length and the 1D scattering length of the system. We also determine the characteristic decay time.

We show how to realize, by means of non-Abelian quantum holonomies, a set of universal quantum gates acting on decoherence-free subspaces and subsystems. In this manner we bring together the quantum coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of all-geometric holonomic control. We discuss the implementation of this scheme in the context of quantum information processing using trapped ions and quantum dots.

We perform molecular dynamics simulations to investigate the relationship between structural order and waterlike dynamic and thermodynamic anomalies in spherically symmetric potentials having either one or two characteristic length scales. Structural order is characterized by translational and orientational order parameters. We find that (i) dynamic and thermodynamic anomalies exist for both one-scale and two-scale ramp potentials, and (ii) waterlike structural order anomalies exist only for the two-scale ramp potential. Our findings suggest that the waterlike relationship between structural order and anomalies is related to the presence of two different length scales in the potential.

The noise properties of pump currents through an open double-quantum-dot setup with nonadiabatic ac driving are investigated. Driving frequencies close to the internal resonances of the double-dot system mark the optimal working points at which the pump current assumes a maximum while its noise power possesses a remarkably low minimum. A rotating-wave approximation provides analytical expressions for the current and its noise power and allows to optimize the noise characteristics. The analytical results are compared to numerical results from a Floquet transport theory.

In systems driven away from equilibrium, the velocity correlation function and the linear-response function to a small perturbation force do not satisfy the fluctuation-response relation (FRR) due to the lack of detailed balance in contrast to equilibrium systems. In this Letter, an equality between an extent of the FRR violation and the rate of energy dissipation is proved for Langevin systems under nonequilibrium conditions. This equality enables us to calculate the rate of energy dissipation by quantifying the extent of the FRR violation, which can be measured experimentally.

Using a coarse-grained molecular dynamics (CMD) approach we study the apparent nonlinear dynamics of water molecules filling or emptying carbon nanotubes as a function of system parameters. Different levels of the pore hydrophobicity give rise to tubes that are empty, water-filled, or fluctuate between these two long-lived metastable states. The corresponding coarse-grained free-energy surfaces and their hysteretic parameter dependence are explored by linking MD to continuum fixed point and bifurcation algorithms. The results are validated through equilibrium MD simulations.

The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information—there is no need for an actual physical quantum computer. The method is illustrated in the example of classical Shannon data compression.

An upper bound is derived for $\Delta$ for a cold dilute fluid of equal amounts of two species of fermion in the unitary limit $k_{f}a\to \infty$ (where $k_f$ is the Fermi momentum, $a$ is the scattering length, and $\Delta$ is a pairing energy: the difference in energy per particle between adding to the system a macroscopic number (but infinitesimal fraction) of particles of one species compared to adding equal numbers of both. The bound is $\delta \le \frac{5}{3}[2(2\xi {)}^{2/5}-(2\xi )]$ where $\xi =ϵ/{ϵ}_{\mathrm{FG}}$, $\delta =2\Delta /{ϵ}_{\mathrm{FG}}$; $ϵ$ is the energy per particle and ${ϵ}_{\mathrm{FG}}$ is the energy per particle of a noninteracting Fermi gas. If the bound is saturated, then systems with unequal densities of the two species will separate spatially into a superfluid phase with equal numbers of the two species and a normal phase with the excess. If the bound is not saturated, then $\Delta$ is the usual superfluid gap. If the superfluid gap exceeds the maximum allowed by the inequality, phase separation occurs.

Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in noninertial frames. In the high acceleration limit, our results can be applied to a nonaccelerated observer falling into a black hole while the accelerated one barely escapes. If the observer escapes with infinite acceleration, the state’s distillable entanglement vanishes.

We investigate the nonlocal properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.

We derive spin squeezing inequalities that generalize the concept of the spin squeezing parameter and provide necessary and sufficient conditions for genuine 2-, or 3-qubit entanglement for symmetric states, and sufficient condition for $N$-qubit states. Our inequalities have a clear physical interpretation as entanglement witnesses, can be easily measured, and are given by complex but elementary expressions.

Unitary Fermi gases, where the scattering length is large compared to the interparticle spacing, can have universal properties, which are independent of the details of the interparticle interactions when the range of the scattering potential is negligible. We prepare an optically trapped, unitary Fermi gas of ${}^6\mathrm{Li}$, tuned just above the center of a broad Feshbach resonance. In agreement with the universal hypothesis, we observe that this strongly interacting many-body system obeys the virial theorem for an ideal gas over a wide range of temperatures. Based on this result, we suggest a simple volume thermometry method for unitary gases. We also show that the observed breathing mode frequency, which is close to the unitary hydrodynamic value over a wide range of temperature, is consistent with a universal hydrodynamic gas with nearly isentropic dynamics.

We propose an effective method to optimize the working parameters (WPs) of microwave-driven quantum gates implemented with multilevel qubits. We show that by treating transitions between each pair of levels independently, intrinsic gate errors due primarily to population leakage to undesired states can be determined by spectroscopic properties of the qubits and minimized by choosing proper WPs. The validity and efficiency of the approach are demonstrated by applying it to optimize the WPs of two coupled rf SQUID flux qubits for controlled-not operation. The result of this independent transition approximation (ITA) is in good agreement with that of dynamic method (DM). The ratio of the speed of ITA to that of DM scales exponentially as $2^n$ when the number of qubits $n$ increases.

We study theoretically the ultracold two-component fermionic gases when a gradient magnetic field is used to tune the scattering length between atoms. For ${}^6\mathrm{Li}$ at the narrow resonance $B_0=543.25\mathrm{G}$, it is shown that the gases would be in a coexistence of the regimes of BCS, Bose-Einstein condensation (BEC), and unitarity limit with the present experimental technique. In the case of thermal and chemical equilibrium, we investigate the density distribution of the gases and show that a double peak of the density distribution can give us a clear evidence for the coexistence of BCS, BEC, and unitarity limit.

The nonequilibrium fluctuations of power flux in a fluidized granular media have been recently measured in an experiment [Phys. Rev. Lett. 92, 164301 (2004)], which was announced to be a verification of the fluctuation relation (FR) by Gallavotti and Cohen. An effective temperature was also identified and proposed to be a useful probe for such nonequilibrium systems. We explain these results in terms of a two-temperature Poisson process. Within this model, supported by independent molecular dynamics simulations, power flux fluctuations do not satisfy the FR and the nature of the effective temperature is clarified. In the pursuit of a hypothetical global quantity fulfilling the FR, this points to the need of considering candidates other than the power flux.

Motivated by the physics of mobile triplets in frustrated quantum magnets, the properties of a two-dimensional model of bosons with correlated hopping are investigated. A mean-field analysis reveals the presence of a pairing phase without single-particle Bose-Einstein condensation (BEC) at low densities for sufficiently strong correlated hopping, and of an Ising quantum phase transition towards a BEC phase at larger density. The physical arguments supporting the mean-field results and their implications for bosonic and quantum spin systems are discussed.