We propose a scheme for producing directed motion in a lattice system by applying a periodic driving potential. By controlling the dynamics by means of the effect known as coherent destruction of tunneling, we demonstrate a novel ratchetlike effect that enables particles to be coherently manipulated and steered without requiring local control. Entanglement between particles can also be controllably generated, which points to the attractive possibility of using this technique for quantum information processing.

Reversible computing requires preservation of all information throughout the entire computational process; this implies that all errors that appear as a result of the interaction of the information-carrying system with uncontrolled degrees of freedom must be corrected. But this can only be done at the expense of an increase in the entropy of the environment corresponding to the dissipation, in the form of heat, of the “noisy” part of the system’s energy. This Letter gives an expression of that energy in terms of the effective noise temperature, and analyzes the relationship between the energy dissipation rate and the rate of computation. Finally, a generalized Clausius principle based on the concept of effective temperature is presented.

We derive expressions for the effective diffusion coefficient of Richardson’s pairs in plastically strained solids as a function of the pair separation distance $R$. We predict that a crossover from superdiffusive to diffusive mixing takes place when $R$ becomes comparable to the coherence length of the shearing events underlying the plastic deformation. Molecular dynamics simulations on nanocrystalline and amorphous systems support this analysis, which thus provides new insight on deformation mechanisms in these systems. Superdiffusive mixing is experimentally observable by monitoring the rate of dissolution of precipitates as a function of their initial size.

We experimentally demonstrate a cancellation of back-action noise in optical measurements. Back-action cancellation was first proposed within the framework of gravitational-wave detection by dual resonators as a way to drastically improve their sensitivity. We have developed an experiment based on a high-finesse Fabry-Perot cavity to study radiation-pressure effects in ultrasensitive displacement measurements. Using an intensity-modulated intracavity field to mimic the quantum radiation-pressure noise, we report the first observation of back-action cancellation due to a coherent mechanical response of the mirrors in the cavity to the radiation-pressure noise. We have observed a sensitivity improvement by a factor larger than 20 both in displacement and weak-force measurements.

We study the dynamic critical behavior of the worm algorithm for the two- and three-dimensional Ising models, by Monte Carlo simulation. The autocorrelation functions exhibit an unusual three-time-scale behavior. As a practical matter, the worm algorithm is slightly more efficient than the Swendsen-Wang algorithm for simulating the two-point function of the three-dimensional Ising model.

We study a mixture of fermionic and bosonic cold atoms on a two-dimensional optical lattice, where the fermions are prepared in two isospin states and the bosons have Bose-Einstein condensed. Number density fluctuations of the condensate form delocalized bosonic modes which couple to the fermionic atoms similarly to the electron-phonon coupling in crystals. We study the phase diagram for this system at fixed fermion density of one per site. We find that tuning of the lattice parameters and interaction strengths drives the system to undergo antiferromagnetic ordering, $s$-wave and $d$-wave pairing superconductivity, or a charge density-wave phase. We use functional renormalization group analysis where retardation effects are fully taken into account. We calculate response functions and also provide estimates of the energy gap associated with the dominant order, and how it depends on different parameters of the problem.

We study a quantum phase transition between fermion superfluid (SF) and band insulator (BI) of fermions in optical lattices. The destruction of the band insulator is driven by the energy gain in promoting fermions from valance band to various conducting bands to form Cooper pairs. We show that the transition must take place in lattice height $V_o/E_R$ between 2.23 and 4.14. The latter is the prediction of mean-field theory while the former is the value for opening a band gap. As one moves across resonance to the molecule side, the SF-BI transition evolves into the SF–Mott-insulator transition of bosonic molecules. We shall also present the global phase diagram for SF-insulator transition for the BCS-BEC family.

Degeneracies near the real axis in a complex-extended parameter space of a Hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.

Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information, and Rao’s entropy differential metric. Therefore, thermodynamic length is of central interest in understanding matter out of equilibrium. In this Letter, we will consider how to define thermodynamic length for a small system described by equilibrium statistical mechanics and how to measure thermodynamic length within a computer simulation. Surprisingly, Bennett’s classic acceptance ratio method for measuring free energy differences also measures thermodynamic length.

The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with the quantum phase transitions featured by the corresponding system. This approach provides a universal conceptual framework to study quantum critical phenomena which is differential geometric and information theoretic at the same time.

We demonstrate a scheme for controlling a large quantum system by acting on a small subsystem only. The local control is mediated to the larger system by some fixed coupling Hamiltonian. The scheme allows us to transfer arbitrary and unknown quantum states from a memory to the large system (“upload access”) as well as the inverse (“download access”). We study the sufficient conditions of the coupling Hamiltonian and give lower bounds on the fidelities for downloading and uploading.

The spectrum of two spin-up and two spin-down fermions in a trap is calculated using a correlated Gaussian basis throughout the range of the BCS-BEC crossover. These accurate calculations provide a few-body solution to the crossover problem. This solution is used to study the time evolution of the system as the scattering length is changed, mimicking experiments with Fermi gases near Fano-Feshbach resonances. The structure of avoiding crossings in the spectrum allow us to understand the dynamics of the system as a sequence of Landau-Zener transitions. Finally, we propose a ramping scheme to study atom-molecule coherence.

We present spatially resolved radio-frequency spectroscopy of a trapped Fermi gas with resonant interactions and observe a spectral gap at low temperatures. The spatial distribution of the spectral response of the trapped gas is obtained using in situ phase-contrast imaging and 3D image reconstruction. At the lowest temperature, the homogeneous rf spectrum shows an asymmetric excitation line shape with a peak at $0.48(4){\epsilon }_F$ with respect to the free atomic line, where ${\epsilon }_F$ is the local Fermi energy.

We show that, if a given electromagnetic property of a particle is allowed to vary during an evolution where the particle will accrue a topological phase, then it is both the time average and the statistical variance of this property which will affect the observable phenomena. The time average is shown to affect the topological aspect of the phase. This is in addition to a second smaller dynamical phase term, which depends upon only the variance of the changing property. The theory is illustrated in reference to the time dependence of the dipole moment in both the Aharonov-Casher and He-McKellar-Wilkens effects.

In the quest for signatures of coherent transport we consider exciton trapping in the continuous-time quantum walk framework. The survival probability displays different decay domains, related to distinct regions of the spectrum of the Hamiltonian. For linear systems and at intermediate times the decay obeys a power law, in contrast with the corresponding exponential decay found in incoherent continuous-time random walk situations. To differentiate between the coherent and incoherent mechanisms, we present an experimental protocol based on a frozen Rydberg gas structured by optical dipole traps.

Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.

The ground state phase diagram of fermion mixtures in optical lattices is analyzed as a function of interaction strength, fermion filling factor, and tunneling parameters. In addition to standard superfluid, phase-separated or coexisting superfluid–excess-fermion phases found in homogeneous or harmonically trapped systems, fermions in optical lattices have several insulating phases, including a molecular Bose-Mott insulator (BMI), a Fermi-Pauli (band) insulator (FPI), a phase-separated BMI-FPI mixture or a Bose-Fermi checkerboard (BFC). The molecular BMI phase is the fermion mixture counterpart of the atomic BMI found in atomic Bose systems, the BFC or BMI-FPI phases exist in Bose-Fermi mixtures, and lastly the FPI phase is particular to the Fermi nature of the constituent atoms of the mixture.

We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a pistonlike problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate nonadditive and nonmonotonic changes in the force due to these lateral walls.

We investigate the quantum dynamics of number fluctuations inside an atomic condensate during coherent spin mixing among internal states of the ground state hyperfine manifold, by quantizing the semiclassical nonrigid pendulum model in terms of the conjugate variable pair: the relative phase and the atom number. Our result provides a theoretical basis that resolves the resolution limit, or the effective “shot-noise” level, for counting atoms that is needed to clearly detect quantum correlation effects in spin mixing.

We study the ground states of cold atoms in the tight-binding bands built from $p$ orbitals on a two dimensional honeycomb optical lattice. The band structure includes two completely flat bands. Exact many-body ground states with on-site repulsion can be found at low particle densities, for both fermions and bosons. We find crystalline order at $n=\frac{1}{6}$ with a $\sqrt{3}\times \sqrt{3}$ structure breaking a number of discrete lattice symmetries. In fermionic systems, if the repulsion is strong enough, we find the bonding strength becomes dimerized at $n=\frac{1}{2}$. Experimental signatures of crystalline order can be detected through the noise correlations in time of flight experiments.