We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.

In contrast with charge vortices, spin vortices in a two-dimensional ferromagnetic condensate move inertially (if the condensate has zero magnetization along an axis). The Magnus force, which prevents the inertial motion of the charge vortices, cancels for spin vortices, because they are composed of two oppositely rotating vortices. The inertial mass of spin vortices varies inversely with the strength of spin-dependent interactions and directly with the width of the condensate layer, and can be measured as a part of experiments on how spin vortices orbit one another. For ${\mathrm{Rb}}^{87}$ in a $1\mu \mathrm{m}$ thick trap, $m_v\sim {10}^{-21}\mathrm{kg}$.

We present a microscopic theory of the Andreev gap, i.e., the phenomenon that the density of states (DOS) of normal chaotic cavities attached to superconductors displays a hard gap centered around the Fermi energy. Our approach is based on a solution of the quantum Eilenberger equation in the regime $t_D\ll t_E$, where $t_D$ and $t_E$ are the classical dwell time and Ehrenfest time, respectively. We show how quantum fluctuations eradicate the DOS at low energies and compute the profile of the gap to leading order in the parameter $t_D/t_E$.

We investigate the possibilities and limitations of passive Hamiltonian protection of a quantum memory against depolarizing noise. Without protection, the lifetime of a single qubit is independent of $N$, the number of qubits composing the memory. In the presence of a protecting Hamiltonian, the lifetime increases at most logarithmically with $N$. We construct an explicit time-independent Hamiltonian which saturates this bound, exploiting the noise itself to achieve the protection.

We investigate the conditions which determine the shape of a particle condensate in situations when it emerges as a result of spontaneous breaking of translational symmetry. We consider a model with particles hopping between sites of a one-dimensional grid and interacting if they are at the same site or at neighboring sites. We predict the envelope of the condensate and the scaling of its width with the system size for various interaction potentials and show how to tune the shape from a delta peak to a rectangular or paraboliclike form.

Minicharged particles arise in many extensions of the standard model. Their contribution to the vacuum polarization modifies Coulomb’s law via the Uehling potential. In this Letter, we argue that tests for electromagnetic fifth forces can therefore be a sensitive probe of minicharged particles. In the low mass range $\lesssim \mu \mathrm{eV}$ existing constraints from Cavendish type experiments provide the best model-independent bounds on minicharged particles.

The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

We present numerical calculations, simulation results, and analytical considerations for the frequency-dependent dielectric constant of single-file water in narrow nanopores, described by a recently developed dipole lattice model. We find Debye relaxation over all length scales with relaxation times that strongly depend on pore length. This behavior is analyzed in terms of the dynamics of orientational defects leading to simple quantitative expressions for the static dielectric susceptibility and the relaxation time in the limits of short and long pores. Based on these formulas, we suggest how the predicted macroscopic order of nanopore water can be probed via dielectric spectroscopy and explain how the excitation energy, diffusion constant, and effective interaction of the defects that destroy the order can be extracted from such measurements.

It is hard to stabilize the $p$-wave superfluid state of cold atomic gas in free space due to inelastic collisional losses. We consider the $p$-wave Feshbach resonance in an optical lattice, and show that it is possible to have a stable $p$-wave superfluid state where the multiatom collisional loss is suppressed through the quantum Zeno effect. We derive the effective Hamiltonian for this system, and calculate its phase diagram in a one-dimensional optical lattice. The results show rich phase transitions between the $p$-wave superfluid state and different types of insulator states induced either by interaction or by dissipation.

A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of channel uses, even when we allow code states which are entangled across several uses of the channel. Such a statement was previously only known for classical channels and the quantum identity channel. By relating the problem to the additivity of minimum output entropies, we show that a strong converse holds for a large class of channels, including all unital qubit channels, the $d$-dimensional depolarizing channel and the Werner-Holevo channel. This further justifies the interpretation of the classical capacity as a sharp threshold for information transmission.

We study the emergence of macrorealism in a harmonic oscillator subject to consecutive measurements of a squeezed action. We demonstrate a breakdown of dynamical realism in a wide parameter range that is maximized in a scaling limit of extreme squeezing, where it is based on measurements of smooth observables, implying that macroscopic realism is not valid in the harmonic oscillator. We propose an indirect experimental test of these predictions with entangled photons by demonstrating that local realism in a composite system implies dynamical realism in a subsystem.

We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for all multipartite symmetric states in the general $N$-qubit case. For this purpose, we introduce 2 parameters playing a crucial role, namely, the diversity degree and the degeneracy configuration of a symmetric state. Those parameters give rise to a simple method of identifying operational families of SLOCC entanglement classes of all symmetric $N$-qubit states, where the number of families grows as the partition function of the number of qubits.

We demonstrate an atom interferometer in which atoms are laser cooled into a 1D optical lattice, suddenly released, and later subjected to a pulsed optical lattice. For short pulses, a simple analytical theory predicts the signal. We investigate both short and longer pulses where the analytical theory fails. Longer pulses yield higher precision and larger signals, and we observe a coherent signal at times that can differ significantly from the expected echo time. The interferometer has potential for precision measurements of $\hslash /m_A$, and can probe the dynamics of atoms in an optical lattice.

We demonstrate the capability of continuous variable Gaussian states to communicate multipartite quantum information. A quantum teamwork protocol is presented according to which an arbitrary possibly entangled multimode state can be faithfully teleported between two teams each comprising many cooperative users. We prove that $N$-mode Gaussian weighted graph states exist for arbitrary $N$ that enable unconditional quantum teamwork implementations for any arrangement of the teams. These perfect continuous variable maximally multipartite entangled resources are typical among pure Gaussian states and are unaffected by the entanglement frustration occurring in multiqubit states.

We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper pair box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.

Quantum mechanical systems, whose degrees of freedom are so-called $\mathrm{su}(2{)}_k$ anyons, form a bridge between ordinary SU(2) quantum magnets (of arbitrary spin-$S$) and systems of interacting non-Abelian anyons. Anyonic spin-$1/2$ chains exhibit a topological protection mechanism that stabilizes their gapless ground states and which vanishes only in the limit ($k\to \infty$) of the ordinary spin-$1/2$ Heisenberg chain. For anyonic spin-1 chains the phase diagram closely mirrors the one of the biquadratic SU(2) spin-1 chain. Our results describe, at the same time, nucleation of different 2D topological quantum fluids within a “parent” non-Abelian quantum Hall state, arising from a macroscopic occupation with localized, interacting anyons. The edge states between the “nucleated” and the parent liquids are neutral, and correspond precisely to the gapless modes of the anyonic chains.

We investigate whether the many-body ground states of bosons in a generalized two-mode model with localized inhomogeneous single-particle orbitals and anisotropic long-range interactions (e.g., dipole-dipole interactions) are coherent or fragmented. It is demonstrated that fragmentation can take place in a single trap for positive values of the interaction couplings, implying that the system is potentially stable. Furthermore, the degree of fragmentation is shown to be insensitive to small perturbations on the single-particle level.

We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a ${}^6\mathrm{Li}\mathrm{\text{−}}{}^{40}\mathrm{K}$ mixture using quantum Monte Carlo methods. The ground-state energy and the average light- and heavy-particle excitation spectrum for the unpolarized superfluid state are nearly independent of the mass ratio. In the majority light system, the polarized superfluid is close to the energy of a phase separated mixture of nearly fully polarized normal and unpolarized superfluid. For a majority of heavy particles, we find an energy minimum for a normal state with a ratio of $\sim 3:1$ heavy to light particles. A slight increase in attraction to $k_{F}a\approx 2.5$ yields a ground state energy of nearly zero for this ratio. A cold unpolarized system in a harmonic trap at unitarity should phase separate into three regions, with a shell of unpolarized superfluid in the middle.

We have measured the short-range attractive force between crystalline Ge plates, and found contributions from both the Casimir force and an electrical force possibly generated by surface patch potentials. Using a model of surface patch effects that generates an additional force due to a distance dependence of the apparent contact potential, the electrical force was parametrized using data at distances where the Casimir force is relatively small. Extrapolating this model, to provide a correction to the measured force at distances less than $5\mu \mathrm{m}$, shows a residual force that is in agreement, within experimental uncertainty, with five models that have been used to calculate the Casimir force.

We study the trajectories of a single colloidal particle as it hops between two energy wells which are sculpted using optical traps. Whereas the dynamical behaviors of such systems are often treated by master-equation methods that focus on particles as actors, we analyze them instead using a trajectory-based variational method called maximum caliber (MaxCal). We show that the MaxCal strategy accurately predicts the full dynamics that we observe in the experiments: From the observed averages, it predicts second and third moments and covariances, with no free parameters. The covariances are the dynamical equivalents of Maxwell-like equilibrium reciprocal relations and Onsager-like dynamical relations.