Finite clusters of fast-rotating spinless bosons in a harmonic trap

Rapidly rotating two-dimensional ultracold Bose–Einstein condensates of spinless bosons in a harmonic trap have attracted considerable interest during the recent years. It is expected that, in the fast-rotation limit, the system of bosons will exhibit collective behavior similar to that of two-dimensional electrons in the fractional quantum Hall effect regime. It is predicted that the most robust correlated bosonic state in this regime will be the Bose Laughlin state at a half filling factor. An exact treatment of such a state is generally a formidable task due to the inherent many-particle nature of the wave function. We report in this work that a transformation to Jacobi coordinates allows one to obtain much desirable exact analytic closed-form expressions for various quantities of interest corresponding to a Bose Laughlin wave function for various finite systems of particles.     

Self-assembly of rod-coil block copolymers from weakly to moderately segregated regimes

We report on the self-assembly behaviour of two homologue series of rod-coil block copolymers in which, the rod, a π -conjugated polymer, is maintained fixed in size and chemical structure, while the coil is allowed to vary both in molecular weight and chemical nature. This allows maintaining constant the liquid crystalline interactions, expressed by Maier-Saupe interactions, ω , while varying the tendency towards microphase separation, expressed by the product between the Flory-Huggins parameter and the total polymerization degree, χN . Therefore, the systems presented here allow testing directly some of the theoretical predictions for the self-assembly of rod-coil block copolymers in a weakly segregated regime. The two rod-coil block copolymer systems investigated were poly(DEH-p-phenylenevinylene-b-styrene), whose self-assembly takes place in the very weakly segregated regime, and poly(DEH-p-phenylenevinylene-b-4vinylpyridine), for which the self-assembly behaviour occurs under increased tendency towards microphase separation, hereby referred to as moderately segregated regime. Experimental results for both systems are compared with predictions based on Landau expansion theories.     

Coherent population transfer in a chain of tunnel coupled quantum dots

We consider the dynamics of a single electron in a chain of tunnel coupled quantum dots, exploring the formal analogies of this system with some of the laser-driven multilevel atomic or molecular systems studied by Bruce W. Shore and collaborators over the last 30 years. In particular, we describe two regimes for achieving complete coherent transfer of population in such a multistate system. In the first regime, by carefully arranging the coupling strengths, the flow of population between the states of the system can be made periodic in time. In the second regime, by employing a “counterintuitive” sequence of couplings, the coherent population trapping eigenstate of the system can be rotated from the initial to the final desired state, which is an equivalent of the STIRAP technique for atoms or molecules. Our results may be useful in future quantum computation schemes.     

General Considerations on the Finite-Size Corrections for Coulomb Systems in the Debye--Hückel Regime

We study the statistical mechanics of classical Coulomb systems in a low coupling regime (Debye--Hückel regime) in a confined geometry with Dirichlet boundary conditions for the electric potential. We use a method recently developed by the authors which relates the grand partition function of a Coulomb system in a confined geometry with a certain regularization of the determinant of the Laplacian on that geometry with Dirichlet boundary conditions. We study several examples of fully confining geometry in two and three dimensions and semi-confined geometries where the system is confined only in one or two directions of the space. We also generalize the method to study systems confined in arbitrary geometries with smooth boundary. We find a relation between the expansion for small argument of the heat kernel of the Laplacian and the large-size expansion of the grand potential of the Coulomb system. This allow us to find the finite-size expansion of the grand potential of the system in general. We recover known results for the bulk grand potential (in two and three dimensions) and the surface tension (for two-dimensional systems). We find the surface tension for three-dimensional systems. For two-dimensional systems our general calculation of the finite-size expansion gives a proof of the existence a universal logarithmic finite-size correction predicted some time ago, at least in the low coupling regime. For three-dimensional systems we obtain a prediction for the curvature correction to the grand potential of a confined system.     

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.     

Pairing in spin polarized two-species fermionic mixtures with mass asymmetry

We discuss on the pairing mechanism of fermions with mismatch in their Fermi momenta due to a mass asymmetry. Using a variational ansatz for the ground state we also discuss the BCS-BEC crossover of this system. It is shown that the breached pairing solution with a single Fermi surface is stable in the BEC regime. We also include the temperatures effect on the fermion pairing within an approximation that is valid for temperatures much below the critical temperature.     

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state S, coupled to all other intra-molecular vibrational states R of the same molecule, and also to its environment Q. Molecular states forming the first reservoir R are characterized by a discrete dense spectrum, whereas the environment reservoir Q states form a continuous spectrum. Assuming the equidistant reservoir R states we find the exact analytical solution of the quantum dynamic equations. S-Q and R-Q couplings yield to spontaneous decay of the S and R states, whereas S-R exchange leads to recurrence cycles and Loschmidt echo at frequencies of S-R transitions and double resonances at the interlevel reservoir R transitions. Due to these couplings the system S time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system S dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are possible four dynamic regimes of the evolution: (i) independent of the environment Q exponential decay suppressing backward R - S transitions, (ii) Loschmidt echo regime, (iii) incoherent dynamics with multicomponent Loschmidt echo, when the system state is exchanged its energy with many states of the reservoir, (iv) cycle mixing regime, when long time system dynamics looks as a random-like. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.     

Modeling of a two-regime crystallization in a multicomponent lipid system under shear flow

The kinetics of phase transitions of milk fat triacylglycerols, as model multicomponent lipid systems, were studied under shear in a Couette cell at 17 °C, 17.5 °C and 20 °C under shear rates ranging from 0 to 2880s^-1 using synchrotron X-ray diffraction. Two-dimensional diffraction patterns were captured during the crystallization process. No effect of shear on onset time for phase α from the liquid was observed. Afterwards a two-regime crystallization process was observed. During the first regime, as observed in other systems, shear reduced the onset time of the phase transition from phase α to 2880s⁻. The model previously developed for palm oil (ODE model) worked well to describe this regime, confirming the general value of the proposed ODE model. However, the ODE model did not satisfactorily describe the second regime. We found that, as the system gets closer to equilibrium, the growth regime becomes controlled by diffusion, manifested by the kinetics following a dependence. This regime was found to be consistent with a mechanism combining step growth at a kink with progressive selection of the crystallizing moieties. This mechanism is in agreement with the displacement of the diffraction peak positions, which revealed how increased shear rate promotes the crystallization of the higher melting fraction affecting the composition of the crystallites.     

Global firing induced by network disorder in ensembles of active rotators

We study the influence of repulsive interactions on an ensemble of coupled excitable rotators. We find that a moderate fraction of repulsive interactions can trigger global firing of the ensemble. The regime of global firing, however, is suppressed in sufficiently large systems if the network of repulsive interactions is fully random, due to self-averaging in its degree distribution. We thus introduce a model of partially random networks with a broad degree distribution, where self-averaging due to size growth is absent. In this case, the regime of global firing persists for large sizes. Our results extend previous work on the constructive effects of diversity in the collective dynamics of complex systems.     

LOFF and breached pairing with cold atoms

We investigate here the Cooper pairing of fermionic atoms with mismatched Fermi surfaces using a variational construct for the ground state. We determine the state for different values of the mismatch of chemical potential for weak as well as strong coupling regimes including the BCS BEC cross over region. We consider Cooper pairing with both zero and finite net momentum. Within the variational approximation for the ground state and comparing the thermodynamic potentials, we show that (i) the LOFF phase is stable in the weak coupling regime; (ii) the LOFF window is maximum on the BEC side near the Feshbach resonance; and (iii) the existence of stable gapless states with a single Fermi surface for negative average chemical potential on the BEC side of the Feshbach resonance.     

An analytical estimate of the period for the delayed logistic application and the Lotka-Volterra system

We first introduce a simple and new method for the quantitative analysis of some nonlinear oscillating systems. It is shown that if the dynamics of the system reduces to piecewise exponential growth and exponential damping phases, then the amplitude and period of the motion can be computed with accuracy in the nonlinear regime without invoking linear stability arguments or perturbative expansions. This method is then successfully applied to the delayed logistic application and to the Lotka-Volterra prey-predator model. For both of these systems, we provide an accurate analytical expression for the period of the oscillations in the nonlinear regime. Received: 27 April 1998 / Received in final form: 25 June 1998 / Accepted: 29 June 1998     

Quantum State Transfer in Trapped-Ion-Cavity Systems

We study the information transfer and entanglement transfer in a system consisting of single trapped ions in cavities by the three-mode cross-Kerr-like interaction among the cavity field （photons）, the centre-of-mass motion （phonons） and the internal state of the trapped ion in the Lamb-Dicke and large detuning regime.     

Modification of instability processes by multiplicative noises

We study two dynamical systems submitted to white and Gaussian random noise acting multiplicatively. The first system is an imperfect pitchfork bifurcation with a noisy departure from onset. The second system is a pitchfork bifurcation in which the noise acts multiplicatively on the non-linear term of lowest order. In both cases noise suppresses some solutions that exist in the deterministic regime. Besides, for the first system, the imperfectness of the bifurcation reduces the regime of on-off intermittency. For the second system, the unstable mode can achieve a jump of finite amplitude at instability but without hysteresis. We finally identify a generic property that is verified by the stationary probability density function of the dynamical variable when a control parameter is varied.     

Stochastic resonance phenomena in spin chains

We discuss stochastic resonance-like effects in the context of coupled quantum spin systems. We focus here on an information-theoretic approach and analyze the steady state quantum correlations (entanglement) as well as the global correlations in the system when subject to different forms of local decoherence. In the presence of decay, it has been shown that the system displays quantum correlations only when the noise strength is above a certain threshold. We extend this result to the case of a Heisenberg XYZ exchange interaction and revise and clarify the mechanisms underlying this behaviour. In the presence of pure dephasing, we show that the system always remains separable in the steady state. When both types of noise are present, we show that the system can still exhibit entanglement for long times, provided that the pure dephasing rate is not too large.     

Q parameter estimation using numerical simulations for linear and nonlinear transmission systems

We compare the Q parameter obtained from scalar, semi-analytical and full vector models for realistic transmission systems. One set of systems is operated in the linear regime, while another is using solitons at high peak power. We report in detail on the different results obtained for the same system using different models. Polarisation mode dispersion is also taken into account and a novel method to average Q parameters over several independent simulation runs is described.     

Laser ablation of energetic polymer solutions: effect of viscosity and fluence on the splashing behavior

Laser plasma thrusters are a new kind of propulsion system for small satellites, and work with the thrust created by the laser ablation of a target. Liquid polymer solutions are very promising fuels for such systems, provided that no splashing of the target occurs, because ejection of droplets strongly decreases the performances of the system. We have investigated the nanosecond infrared laser ablation of glycidyl azide polymer solutions containing carbon nanoparticles as absorber. Shadowgraphy imaging revealed two cases, namely splashing regime and solid-like behavior. The transition between both regimes depends on the viscosity of the solution and on the laser fluence, and is explained by the recoil force acting on the target. Appropriate conditions to avoid splashing were identified, showing that this liquid polymer solution is a suitable fuel for laser plasma thrusters.     

Fractional quantum Hall regime of a gas of ultracold atoms

We study the physics of a rapidly rotating gas of ultracold bosonic atoms. In the limit of very rapid rotation of the trap the system exhibits a fractional quantum Hall regime analogous to that of electrons in the fractional quantum Hall effect. We show that the ground state of the system is a 1/2-Laughlin liquid, a highly correlated atomic liquid. Exotic excitations consisting of localized quasiholes of 1/2 of an atom can be created by focusing lasers at the desired positions. We show how to manipulate these quasiholes in order to probe directly their 1/2-statistics.     

Simultaneous implementation of n SWAP gates using superconducting charge qubits coupled to a cavity

Based on superconducting quantum interference devices (SQUIDs) coupled to a cavity, we propose a scheme for implementing n SWAP gates simultaneously. In our scheme, the SQUID works in the charge regime, the quantum logic gate operations are performed in the subspace spanned by two charge states |0〉 and |1〉. The interaction between the qubits and the cavity field can be achieved by turning the gate voltage and the external flux. Especially, the gate operation time is independent of the number of the qubits, and the gate operation is insensitive to the initial state of the cavity mode. We also analyze the experimental feasibility that the conditions of the large detuning can be achieved by adjusting the frequency of the cavity mode, and the operation time satisfies the requirement for the designed experiment by choosing suitable detuning and the quality factor of the cavity. Based on the simple operation, our scheme may be realized in this solid-state system, and our idea may be realized in other systems.     

Exact relaxation in a class of nonequilibrium quantum lattice systems

A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we introduce an experimentally accessible setting where relaxation to a steady state is exact, namely, for the Bose-Hubbard model quenched from a Mott quantum phase to the free strong superfluid regime. We rigorously prove that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments--thus maximizing the entanglement. Remarkably, for this to be true, no time average is necessary. Our argument includes a central limit theorem and exploits the finite speed of information transfer. We also show that for all periodic initial configurations (charge density waves) the system relaxes locally, and identify experimentally accessible signatures in optical lattices as well as implications for the foundations of statistical mechanics.