We report the statistical analysis of the movement of a submicron particle confined in a harmonic potential in the presence of a torque. The absolute value of the torque can be found from the auto- and cross-correlation functions of the particle’s coordinates. We experimentally prove this analysis by detecting the torque produced onto an optically trapped particle by an optical beam with orbital angular momentum.

The ground and excited states of a one-dimensional (1D) spin-$\frac{1}{2}$ Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I and II phonons and spin waves, the latter behaving quadratically for small wave numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.

We study, within the spin-boson dynamics, the synchronization of a quantum tunneling system with an external, time-periodic driving signal. As a main result, we find that at a sufficiently large system-bath coupling strength (i.e., for a friction strength $\alpha >1$) the thermal noise plays a constructive role in yielding forced synchronization. This noise-induced synchronization can occur when the driving frequency is larger than the zero-temperature tunneling rate. As an application evidencing the effect, we consider the charge transfer dynamics in molecular complexes.

The principal signatures of a deterministic dynamics in the statistical properties of extreme events are identified. Explicit expressions are derived for generic classes of dynamical systems giving rise to quasiperiodic, strongly chaotic, and intermittent chaotic behaviors.

We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.

We have trapped rubidium atoms in the magnetic field produced by a superconducting atom chip operated at liquid helium temperatures. Up to $8.2\times {10}^5$ atoms are held in a Ioffe-Pritchard trap at a distance of $440\mu \mathrm{m}$ from the chip surface, with a temperature of $40\mu \mathrm{K}$. The trap lifetime reaches 115 s at low atomic densities. These results open the way to the exploration of atom-surface interactions and coherent atomic transport in a superconducting environment, whose properties are radically different from normal metals at room temperature.

We study the sweep through the quantum phase transition from the superfluid to the Mott state for the Bose-Hubbard model with a time-dependent tunneling rate $J(t)$. In the experimentally relevant case of exponential decay $J(t)\propto e^{-\gamma t}$, an adapted mean-field expansion for large fillings $n$ yields a scaling solution for the fluctuations. This enables us to analytically calculate the evolution of the number and phase variations (on-site) and correlations (off-site) for slow ($\gamma \ll \mu$), intermediate, and fast (nonadiabatic $\gamma \gg \mu$) sweeps, where $\mu$ is the chemical potential. Finally, we derive the dynamical decay of the off-diagonal long-range order as well as the temporal shrinkage of the superfluid fraction in a persistent ring-current setup.

We suggest a general spectral method for calculating the statistics of multistep birth-death processes and chemical reactions of the type $mA\to nA$ ($m$ and $n$ are positive integers) which possess an absorbing state. The method employs the generating function formalism in conjunction with the Sturm-Liouville theory of linear differential operators. It yields accurate results for the extinction statistics and for the quasistationary probability distribution, including large deviations, of the metastable state. The power of the method is demonstrated on the example of binary annihilation and triple branching $2A\to \varnothing$, $A\to 3A$, representative of the rather general class of dissociation-recombination reactions.

We establish the theoretical feasibility of direct analog simulation of the compact $U(1)$ lattice gauge theories in optical lattices with dipolar bosons. We discuss the realizability of the topological Coulomb phase in extended Bose-Hubbard models in several optical lattice geometries. We predict the testable signatures of this emergent phase in noise correlation measurements, thus suggesting the possible emergence of artificial light in optical lattices.

We report the first realization of a guided quasicontinuous atom laser by rf outcoupling a Bose-Einstein condensate from a hybrid optomagnetic trap into a horizontal atomic waveguide. This configuration allows us to cancel the acceleration due to gravity and keep the de Broglie wavelength constant at $0.5\mu \mathrm{m}$ during 0.1 s of propagation. We also show that our configuration, equivalent to pigtailing an optical fiber to a (photon) semiconductor laser, ensures an intrinsically good transverse mode matching.

We study the Fermi gas at unitarity and at $T=0$ by assuming that, at high polarizations, it is a normal Fermi liquid composed of weakly interacting quasiparticles associated with the minority spin atoms. With a quantum Monte Carlo approach we calculate their effective mass and binding energy, as well as the full equation of state of the normal phase as a function of the concentration $x=n_{\downarrow }/n_{\uparrow }$ of minority atoms. We predict a first order phase transition from normal to superfluid at $x_c=0.44$ corresponding, in the presence of harmonic trapping, to a critical polarization $P_c=(N_{\uparrow }-N_{\downarrow })/(N_{\uparrow }+N_{\downarrow })=77\%$. We calculate the radii and the density profiles in the trap and predict that the frequency of the spin dipole mode will be increased by a factor of 1.23 due to interactions.

We present quantum feedback control for deterministic entanglement generation at the single-photon level. The protocol of controlling both total photon number and phase difference is based on the cascade structure of cavities placed in an optical closed loop, quantum nondemolition measurement with cross-Kerr interactions, and Lyapunov stability for feedback design.

We study the Loschmidt echo for a system of electrons interacting through mean-field Coulomb forces. The electron gas is modeled by a self-consistent set of hydrodynamic equations. It is observed that the quantum fidelity drops abruptly after a time that is proportional to the logarithm of the perturbation amplitude. The fidelity drop is related to the breakdown of the symmetry properties of the wave function.

Based on doubly detuned Raman transitions between (meta)stable atomic or molecular states and recently developed atom counting techniques, a detection scheme for sound waves in dilute Bose-Einstein condensates is proposed whose accuracy might reach down to the level of a few or even single phonons. This scheme could open up a new range of applications including the experimental observation of quantum radiation phenomena such as the Hawking effect in sonic black-hole analogues or the acoustic analogue of cosmological particle creation.

We predict the robust existence of a novel quantum orbital stripe order in the $p$-band Bose-Hubbard model of two-dimensional triangular optical lattices with cold bosonic atoms. An orbital angular momentum moment is formed on each site exhibiting a stripe order both in the superfluid and Mott-insulating phases. The stripe order spontaneously breaks time-reversal, lattice translation, and rotation symmetries. In addition, it induces staggered plaquette bond currents in the superfluid phase. Possible signatures of this stripe order in the time of flight experiment are discussed.

The real-space densities of a polarized strongly interacting two-component Fermi gas of ${}^6\mathrm{Li}$ atoms reveal two low-temperature regimes, both with a fully paired core. At the lowest temperatures, the unpolarized core deforms with increasing polarization. Sharp boundaries between the core and the excess unpaired atoms are consistent with a phase separation driven by a first-order phase transition. In contrast, at higher temperatures the core does not deform but remains unpolarized up to a critical polarization. The boundaries are not sharp in this case, indicating a partially polarized shell between the core and the unpaired atoms. The temperature dependence is consistent with a tricritical point in the phase diagram.

We use Bogoliubov theory to calculate the beyond mean field correction to the equation of state of a weakly interacting Bose gas in the presence of a tight 2D optical lattice. We show that the lattice induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations. Using the hydrodynamic theory of superfluids, we calculate the corresponding shift of the collective frequencies of a harmonically trapped gas. We find that this correction can be of the order of a few percent and hence easily measurable in current experiments. The behavior of the quantum depletion of the condensate is also discussed.

We analyze the asymptotic security of the family of Gaussian modulated quantum key distribution protocols for continuous-variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.

A fully general approach to the security analysis of continuous-variable quantum key distribution (CV-QKD) is presented. Provided that the quantum channel is estimated via the covariance matrix of the quadratures, Gaussian attacks are shown to be optimal against all collective eavesdropping strategies. The proof is made strikingly simple by combining a physical model of measurement, an entanglement-based description of CV-QKD, and a recent powerful result on the extremality of Gaussian states [M. M. Wolf et al., Phys. Rev. Lett. 96, 080502 (2006)].

A theory of lattice Boltzmann (LB) models for hydrodynamic simulation is developed upon a novel relation between entropy construction and roots of Hermite polynomials. A systematic procedure is described for constructing numerically stable and complete Galilean invariant LB models. The stability of the new LB models is illustrated with a shock tube simulation.