It is proven that periodically varying and sign definite nonlinearity in a general case does not prevent collapse in two-dimensional and three-dimensional nonlinear Schrödinger equations: at any oscillation frequency of the nonlinearity blowing up solutions exist. Contrary to the results known for a sign-alternating nonlinearity, an increase of the frequency of oscillations accelerates collapse. The effect is discussed from the viewpoint of scaling arguments. For the three-dimensional case a sufficient condition for the existence of collapse is rigorously established. The results are discussed in the context of the mean field theory of Bose-Einstein condensates with time-dependent scattering length.

A scheme for optimal Gaussian cloning of optical coherent states is proposed and experimentally demonstrated. Its optical realization is based entirely on simple linear optical elements and homodyne detection. The optimality of the presented scheme is limited only by detection inefficiencies. Experimentally, we achieved a cloning fidelity of about 65%, which almost touches the optimal value of $2/3$.

The continuous-time random walk (CTRW) model exhibits a nonergodic phase when the average waiting time diverges. Using an analytical approach for the nonbiased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the nonergodic properties of the random walk which show strong deviations from Boltzmann-Gibbs theory. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann-Gibbs theory, while in the nonergodic phase yields a generalized nonergodic statistical law.

We show by means of an exact numerical approach that the momentum distribution of a free expanding gas of hard-core bosons on a one-dimensional lattice approaches that of noninteracting fermions, acquiring a Fermi edge. Yet there is a power-law decay of the one-particle density matrix ${\rho }_x\sim 1/\sqrt{x}$, as usual for hard-core bosons in the ground state, which accounts for a large occupation of the lowest natural orbitals for all expansion times. The fermionization of the momentum distribution function, which is not observed in equilibrium, is analyzed in detail.

Using a scaling transformation we exactly determine the dynamics of an harmonically confined Tonks-Girardeau gas under arbitrary time variations of the trap frequency. We show how during a one-dimensional expansion a “dynamical fermionization” occurs as the momentum distribution rapidly approaches an ideal Fermi gas distribution, and that under a sudden change of the trap frequency the gas undergoes undamped breathing oscillations displaying alternating bosonic and fermionic character in momentum space. The absence of damping in the oscillations is a peculiarity of the truly Tonks regime.

Genuine 3-qubit entanglement comes in two different inconvertible types represented by the Greenberger-Horne-Zeilinger (GHZ) state and the $W$ state. We describe a specific method based on local positive operator valued measures and classical communication that can convert the ideal $N$-qubit GHZ state to a state arbitrarily close to the ideal $N$-qubit $W$ state. We then experimentally implement this scheme in the 3-qubit case and characterize the input and the final state using 3-photon quantum state tomography.

We present a new experimental protocol for performing universal gates in a register of superconducting qubits coupled by fixed on-chip linear reactances. The qubits have fixed, detuned Larmor frequencies and can remain, during the entire gate operation, biased at their optimal working point where decoherence due to fluctuations in control parameters is suppressed to first order. Two-qubit gates are performed by simultaneously irradiating two qubits at their respective Larmor frequencies with appropriate amplitude and phase, while one-qubit gates are performed by the usual single-qubit irradiation pulses.

Studies of Feshbach resonance phenomena in fermionic alkali gases have drawn heavily on the intuition afforded by a Fermi-Bose theory which presents the Feshbach molecule as a featureless Bose particle. While this model may provide a suitable platform to explore the ${}^6\mathrm{Li}$ system, we argue that its application to ${}^{40}\mathrm{K}$, where the hyperfine structure is inverted, is inappropriate. Introducing a three-state Fermi model, where a spin state is shared by the open and closed channel states, we show that effects of “Pauli blocking” appear in the internal structure of the condensate wave function.

We report the first isoelectronic differential force measurements between an Au-coated probe and two Au-coated films, made out of Au and Ge. These measurements, performed at submicron separations using soft microelectromechanical torsional oscillators, eliminate the need for a detailed understanding of the probe-film Casimir interaction. The observed differential signal is directly converted into limits on the parameters $\alpha$ and $\lambda$ which characterize Yukawa-like deviations from Newtonian gravity. We find $\alpha \lesssim {10}^{12}$ for $\lambda \sim 200\mathrm{nm}$, an improvement of $\sim 10$ over previous limits.

We study the clustering properties of particles sliding downwards on a fluctuating surface evolving through the Kardar-Parisi-Zhang equation, a problem equivalent to passive scalars driven by a Burgers fluid. Monte Carlo simulations on a discrete version of the problem in one dimension reveal that particles cluster very strongly: the two-point density correlation function scales with the system size with a scaling function which diverges at small argument. Analytic results are obtained for the Sinai problem of random walkers in a quenched random landscape. This equilibrium system too has a singular scaling function which agrees remarkably with that for advected particles.

We study a single-species polarized Fermi gas tuned across a narrow $p$-wave Feshbach resonance. We show that in the course of a Bose-Einstein condensation (BEC)-BCS crossover, the system can undergo a magnetic-field-tuned quantum phase transition from a $p_x$-wave to a $p_x+i{p}_y$-wave superfluid. The latter state, that spontaneously breaks time-reversal symmetry, furthermore undergoes a topological $p_x+i{p}_y$ to $p_x+i{p}_y$ transition at zero chemical potential $\mu$. In two dimensions, for $\mu >0$ it is characterized by a Pfaffian ground state exhibiting topological order and non-Abelian excitations familiar from fractional quantum Hall systems.

We consider a resonantly interacting boson-fermion mixture of ${}^{40}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$ atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for ${}^{40}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$ atoms, and ${}^{40}\mathrm{K}\mathrm{\text{−}}{}^{87}\mathrm{Rb}$ molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.

We study the dynamics of a narrow bright soliton in a one-dimensional lattice of condensed attractive atoms when the soliton width is comparable to the lattice spacing. If a momentum is imprinted to a stationary state, the soliton can have oscillations around a site or it can undergo a random motion along the array. The motion is very sensitive to the atomic background distribution, and a thermal cloud or quantum field fluctuations can induce a random motion of the soliton.

We propose an efficient method to verify the upper bound of the fraction of counts caused by multiphoton pulses in practical quantum key distribution using weak coherent light, given whatever type of Eve’s action. The protocol simply uses two coherent states for the signal pulses and vacuum for the decoy pulse. Our verified upper bound is sufficiently tight for quantum key distribution with a very lossy channel, in both the asymptotic and nonasymptotic case. So far our protocol is the only decoy-state protocol that works efficiently for currently existing setups.

There has been much interest in quantum key distribution. Experimentally, quantum key distribution over 150 km of commercial Telecom fibers has been successfully performed. The crucial issue in quantum key distribution is its security. Unfortunately, all recent experiments are, in principle, insecure due to real-life imperfections. Here, we propose a method that can for the first time make most of those experiments secure by using essentially the same hardware. Our method is to use decoy states to detect eavesdropping attacks. As a consequence, we have the best of both worlds—enjoying unconditional security guaranteed by the fundamental laws of physics and yet dramatically surpassing even some of the best experimental performances reported in the literature.

We compare the frequencies of the $6s{}^{2}S_{1/2}(F=0)\to 5d{}^{2}D_{3/2}(F=2)$ reference transition in ${}^{171}\mathrm{Yb}^{+}$ for two single ions stored in independent traps. The quadrupole moment of the $5d{}^{2}D_{3/2}$ state is measured to be $9.32(48)\times {10}^{-40}{\mathrm{C}\mathrm{m}}^2$ and from the quadratic Stark shift the relevant scalar and tensor polarizabilities are determined to be ${\alpha }_S(S_{1/2})-{\alpha }_S(D_{3/2})=-6.9(1.4)\times {10}^{-40}{\mathrm{J}\mathrm{m}}^2/{\mathrm{V}}^2$ and ${\alpha }_T(D_{3/2})=-13.6(2.2)\times {10}^{-40}{\mathrm{J}\mathrm{m}}^2/{\mathrm{V}}^2$, respectively. In the absence of external perturbations we find a mean frequency difference between the two trapped ions of 0.26(42) Hz, corresponding to a relative difference of $3.8(6.1)\times {10}^{-16}$. This is comparable to the agreement found in the most accurate comparisons between cesium fountain clocks.

Scalability of a quantum computation requires that the information be processed on multiple subsystems. However, it is unclear how the complexity of a quantum algorithm, quantified by the number of entangling gates, depends on the subsystem size. We examine the quantum circuit complexity for exactly universal computation on many -level systems (qudits). Both a lower bound and a constructive upper bound on the number of two-qudit gates result, proving a sharp asymptotic of gates. This closes the complexity question for all -level systems ( finite). The optimal asymptotic applies to systems with locality constraints, e.g., nearest neighbor interactions.

On the basis of general considerations, we propose a Langevin equation accounting for critical phenomena occurring in the presence of two symmetric absorbing states. We study its phase diagram by mean-field arguments and direct numerical integration in physical dimensions. Our findings fully account for and clarify the intricate picture known so far from the aggregation of partial results obtained with microscopic models. We argue that the direct transition from disorder to one of two absorbing states is best described as a (generalized) voter critical point and show that it can be split into an Ising and a directed percolation transition in dimensions larger than one.

We investigate the influence of spontaneous symmetry breaking on the decoherence of a many-particle quantum system. This decoherence process is analyzed in an exactly solvable model system that is known to be representative of symmetry broken macroscopic systems in equilibrium. It is shown that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum coherent. This universal time scale is $t_{\mathrm{spon}}\simeq 2\pi N\hslash /(k_{B}T)$, given in terms of the number of microscopic degrees of freedom $N$, temperature $T$, and the constants of Planck ($\hslash$) and Boltzmann ($k_B$).

Error filtration is a method for encoding the quantum state of a single particle into a higher dimensional Hilbert space in such a way that it becomes less sensitive to noise. We have realized a fiber optics demonstration of this method and illustrated its potentialities by carrying out the optical part of a quantum key distribution scheme over a line whose phase noise is too high for a standard implementation of BB84 to be secure. By filtering out the noise, a bit error rate of $15.3\%\pm 0.1\%$, which is beyond the security limit, can be reduced to $10.6\%\pm 0.1\%$, thereby guaranteeing the cryptographic security.