We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner function gradually deviates from the corresponding classical phase-space probability density. These clear differences that develop due to nonlinearity can serve as experimental signatures, in the near future, that NEMS resonators are entering the quantum domain.

Systems with long-range interactions display a short-time relaxation towards quasistationary states whose lifetime increases with system size. With reference to the Hamiltonian mean field model, we here show that a maximum entropy principle, based on Lynden-Bell’s pioneering idea of “violent relaxation,” predicts the presence of out-of-equilibrium phase transitions separating the relaxation towards homogeneous (zero magnetization) or inhomogeneous (nonzero magnetization) quasistationary states. When varying the initial condition within a family of “water bags” with different initial magnetization and energy, first- and second-order phase transition lines are found that merge at an out-of-equilibrium tricritical point. Metastability is theoretically predicted and numerically checked around the first-order phase transition line.

We study the stationary Josephson effect for neutral fermions across the BCS-BEC (Bose-Einstein condensate) crossover, by solving numerically the Bogoliubov–de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.

We have measured the critical atom number in an array of harmonically trapped two-dimensional (2D) Bose gases of rubidium atoms at different temperatures. We found this number to be about 5 times higher than predicted by the semiclassical theory of Bose-Einstein condensation (BEC) in the ideal gas. This demonstrates that the conventional BEC picture is inapplicable in an interacting 2D atomic gas, in sharp contrast to the three-dimensional case. A simple heuristic model based on the Berezinskii-Kosterlitz-Thouless theory of 2D superfluidity and the local density approximation accounts well for our experimental results.

We study the nonlocal properties of states resulting from the mixture of an arbitrary entangled state $\rho$ of two $d$-dimensional systems and completely depolarized noise, with respective weights $p$ and $1-p$. We first construct a local model for the case in which $\rho$ is maximally entangled and $p$ at or below a certain bound. We then extend the model to arbitrary $\rho$. Our results provide bounds on the resistance to noise of the nonlocal correlations of entangled states. For projective measurements, the critical value of the noise parameter $p$ for which the state becomes local is at least asymptotically $\log (d)$ larger than the critical value for separability.

We describe a fast quantum computer based on optically controlled electron spins in charged quantum dots that are coupled to microcavities. This scheme uses broadband optical pulses to rotate electron spins and provide the clock signal to the system. Nonlocal two-qubit gates are performed by phase shifts induced by electron spins on laser pulses propagating along a shared waveguide. Numerical simulations of this scheme demonstrate high-fidelity single-qubit and two-qubit gates with operation times comparable to the inverse Zeeman frequency.

An essentially exact approach to compute the wave function in the time-dependent many-boson Schrödinger equation is derived and employed to study accurately the process of splitting a trapped condensate. As the trap transforms from a single to double well the ground state changes from a coherent to a fragmented state. We follow the role played by many-body excited states during the splitting process. Among others, a “counterintuitive” regime is found in which the evolution of the condensate when the splitting is sufficiently slow is not to the fragmented ground state, but to a low-lying excited state which is a coherent state. Experimental implications are discussed.

An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The overlap is simply related to the area under the $E(\tau )$ curve, i.e., the energy as a function of imaginary time. This has important applications to, for example, quantum Monte Carlo simulations where the overlap becomes as a simple by-product of routine simulations. As a result, we find that the practical definition of a good variational wave function for quantum Monte Carlo simulations, i.e., fast convergence to the ground state, is equivalent to a good overlap with the actual ground state of the system.

We present a new approach to study the thermodynamic properties of $d$-dimensional classical systems by reducing the problem to the computation of ground state properties of a $d$-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of $T(t)\approx (pN)/(k_B\log t)$ and $\gamma (t)\approx (Nt{)}^{-\overline{c}/N}$, for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.

We consider a model for periodic patterns of charges constrained over a cylindrical surface. In particular we focus on patterns of chiral helices, achiral rings, or vertical lamellae, with the constraint of global electroneutrality. We study the dependence of the patterns’ size and pitch angle on the radius of the cylinder and salt concentration. We obtain a phase diagram by using numerical and analytic techniques. For pure Coulomb interactions, we find a ring phase for small radii and a chiral helical phase for large radii. At a critical salt concentration, the characteristic domain size diverges, resulting in an achiral macroscopic phase-segregated structure. We discuss possible consequences and generalizations of our model.

Conventional quantum computing schemes are incompatible with nanometer-scale “hardware,” where the closely packed spins cannot be individually controlled. We report the first experimental demonstration of a global control paradigm: logical qubits delocalize along a spin chain and are addressed via the two terminal spins. Using NMR studies on a three-spin molecule, we implement a globally clocked quantum mirror that outperforms the equivalent swap network. We then extend the protocol to support dense qubit storage and demonstrate this experimentally via Deutsch and Deutsch-Jozsa algorithms.

We observe the proliferation of vortices in the Berezinskii-Kosterlitz-Thouless regime on a two-dimensional array of Josephson-coupled Bose-Einstein condensates. As long as the Josephson (tunneling) energy $J$ exceeds the thermal energy $T$, the array is vortex free. With decreasing $J/T$, vortices appear in the system in ever greater numbers. We confirm thermal activation as the vortex-formation mechanism and obtain information on the size of bound vortex pairs as $J/T$ is varied.

We study a mechanical model known as a Galton board—a particle rolling on a tilted plane under gravitation and bouncing off a periodic array of rigid pegs. Incidentally, this model is identical to a periodic Lorentz gas where an electron is driven by a uniform electric field. Previous heuristic and experimental studies have suggested that the particle’s speed $v(t)$ should grow as $t^{1/3}$ and its coordinate $x(t)$ as $t^{2/3}$. We find exact limit distributions for the rescaled velocity $t^{-1/3}v(t)$ and position $t^{-2/3}x(t)$. In addition, we determine that the particle’s motion is recurrent; i.e., the particle comes back to the top of the board with a probability of one.

We study the spin dynamics of quasi-one-dimensional $F=1$ condensates both at zero and finite temperatures for arbitrary initial spin configurations. The rich dynamical evolution exhibited by these nonlinear systems is explained by surprisingly simple principles: minimization of energy at zero temperature and maximization of entropy at high temperature. Our analytical results for the homogeneous case are corroborated by numerical simulations for confined condensates in a wide variety of initial conditions. These predictions compare qualitatively well with recent experimental observations and can, therefore, serve as a guidance for ongoing experiments.

It is shown that fermionic polar molecules or atoms in a bilayer optical lattice can undergo the transition to a state with circulating currents, which spontaneously breaks the time reversal symmetry. Estimates of relevant temperature scales are given, and experimental signatures of the circulating current phase are identified. Related phenomena in bosonic and spin systems with ring exchange are discussed.

A scheme for addressing individual atoms in one- or two-dimensional optical lattices loaded with one atom per site is proposed. The scheme is based on position-dependent atomic population transfer induced by several standing-wave driving fields. This allows various operations important in quantum-information processing, such as manipulation and measurement of any single-atom, two-qubit operations between any pair of adjacent atoms, and patterned loading of the lattice with one atom per every $n$th site for arbitrary $n$. The proposed scheme is robust against considerable imperfections and actually within reach of current technology.

We show that trapped ions can be used to simulate a highly symmetrical Hamiltonian with eigenstates naturally protected against local sources of decoherence. This Hamiltonian involves long-range coupling between particles and provides a more efficient protection than nearest neighbor models discussed in previous works. Our results open the perspective of experimentally realizing, in controlled atomic systems, complex entangled states with decoherence times up to 9 orders of magnitude longer than isolated quantum systems.

We predict a nonequilibrium critical phenomenon in the space-time density evolution of a fermionic gas above the temperature of transition into the superfluid phase. On the BCS side of the Bose-Einstein condensation-BCS crossover, the evolution of a localized density disturbance exhibits a negative echo at the point of the initial inhomogeneity. Approaching the Bose-Einstein condensation side, this effect competes with the slow spreading of the density of bosonic molecules. However, even here the echo dominates for large enough times. This effect may be used as an experimental tool to locate the position of the transition.

We load atoms into every site of an optical lattice and selectively spin flip atoms in a sublattice consisting of every other site. These selected atoms are separated from their unselected neighbors by less than an optical wavelength. We also show spin-dependent transport, where atomic wave packets are coherently separated into adjacent sites according to their internal state. These tools should be useful for quantum information processing and quantum simulation of lattice models with neutral atoms.

We analyze the Bogoliubov spectrum of the three-site Bose-Hubbard model with a finite number of Bose particles by using a semiclassical approach. The Bogoliubov spectrum is shown to be associated with the low-energy regular component of the classical Hubbard model. We identify the full set of the integrals of motion of this regular component and, quantizing them, obtain the energy levels of the quantum system. The critical values of the energy, above which the regular Bogoliubov spectrum evolves into a chaotic spectrum, is indicated as well.