We calculate the effect of order parameter fluctuations on the fermionic single-particle excitations in the superfluid state of neutral fermions interacting with short-range attractive forces. We show that in dimensions $D\le 3$ the singular effective interaction between the fermions mediated by the gapless Bogoliubov-Anderson mode prohibits the existence of well-defined quasiparticles. We explicitly calculate the single-particle spectral function in the BEC regime in $D=3$ and show that in this case the quasiparticle residue and the density of states are logarithmically suppressed.

We study the realization of lattice models, where cold atoms and molecules move as extra particles in a dipolar crystal of trapped polar molecules. The crystal is a self-assembled floating mesoscopic lattice structure with quantum dynamics given by phonons. We show that within an experimentally accessible parameter regime extended Hubbard models with tunable long-range phonon-mediated interactions describe the effective dynamics of dressed particles.

We use quantum discord to characterize the correlations present in the model called deterministic quantum computation with one quantum bit (DQC1), introduced by Knill and Laflamme [Phys. Rev. Lett. 81, 5672 (1998)]. The model involves a collection of qubits in the completely mixed state coupled to a single control qubit that has nonzero purity. The initial state, operations, and measurements in the model all point to a natural bipartite split between the control qubit and the mixed ones. Although there is no entanglement between these two parts, we show that the quantum discord across this split is nonzero for typical instances of the DQC1 ciruit. Nonzero values of discord indicate the presence of nonclassical correlations. We propose quantum discord as figure of merit for characterizing the resources present in this computational model.

We study the low temperature physics of an ultracold atomic gas in the potential formed inside a pumped optical resonator. Here, the height of the cavity potential, and hence the quantum state of the gas, depends not only on the pump parameters, but also on the atomic density through a dynamical ac-Stark shift of the cavity resonance. We derive the Bose-Hubbard model in one dimension and use the strong coupling expansion to determine the parameter regime in which the system is in the Mott-insulator state. We predict the existence of overlapping, competing Mott-insulator states, and bistable behavior in the vicinity of the shifted cavity resonance, controlled by the pump parameters. Outside these parameter regions, the state of the system is in most cases superfluid.

The generalized $n$-qubit Greenberger-Horne-Zeilinger (GHZ) states and their local unitary equivalents are the only states of $n$ qubits that are not uniquely determined among pure states by their reduced density matrices of $n-1$ qubits. Thus, among pure states, the generalized GHZ states are the only ones containing information at the $n$-party level. We point out a connection between local unitary stabilizer subgroups and the property of being determined by reduced density matrices.

We consider two configurations of a random directed polymer of length $L$ confined to a plane and ending in two points separated by $2u$. Defining the mean free-energy $\overline{F}$ and the free-energy difference $F^{\prime }$ of the two configurations, we determine the joint distribution function ${\mathcal{P}}_{L,u}(\overline{F},F^{\prime })$ using the replica approach. We find that for large $L$ and large negative free energies $\overline{F}$, the joint distribution function factorizes into longitudinal [$P_{L,u}(\overline{F})$] and transverse [$P_u(F^{\prime })$] components, which furthermore coincide with results obtained previously via different independent routes.

We have observed tunneling suppression and photon-assisted tunneling of Bose-Einstein condensates in an optical lattice subjected to a constant force plus a sinusoidal shaking. For a sufficiently large constant force, the ground energy levels of the lattice are shifted out of resonance and tunneling is suppressed; when the shaking is switched on, the levels are coupled by low-frequency photons and tunneling resumes. Our results agree well with theoretical predictions and demonstrate the usefulness of optical lattices for studying solid-state phenomena.

The lateral Casimir-Polder force between an atom and a corrugated surface should allow one to study experimentally nontrivial geometrical effects in the electromagnetic quantum vacuum. Here, we derive the theoretical expression of this force in the scattering approach. We show that large corrections to the “proximity force approximation” could be measured using present-day technology with a Bose-Einstein condensate used as a vacuum field sensor.

We present an optical cavity QED configuration that is described by a dissipative version of the Lipkin-Meshkov-Glick model of an infinitely coordinated spin system. This open quantum system exhibits both first- and second-order nonequilibrium quantum phase transitions as a single, effective field parameter is varied. Light emitted from the cavity offers measurable signatures of the critical behavior, including that of the spin-spin entanglement.

We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in quantum information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body systems.

We demonstrate experimentally a gating ratchet with cold rubidium atoms in a driven near-resonant optical lattice. A single-harmonic periodic modulation of the optical potential depth is applied, together with a single-harmonic rocking force. Directed motion is observed as a result of the breaking of the symmetries of the system.

A theoretical framework is presented which allows us to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study relaxation of charged-particle beams. It is shown that a fully matched beam relaxes to the Lynden-Bell distribution. However, when a mismatch is present and the beam oscillates, parametric resonances lead to a core-halo phase separation. The approach developed accounts for both the density and the velocity distributions in the final stationary state.

We investigate few-boson tunneling in a one-dimensional double well, covering the full crossover from weak interactions to the fermionization limit of strong correlations. Based on exact quantum-dynamical calculations, it is found that the tunneling dynamics of two atoms evolves from Rabi oscillations to correlated pair tunneling as we increase the interaction strength. Near the fermionization limit, fragmented-pair tunneling is observed and analyzed in terms of the population imbalance and two-body correlations. For more atoms, the tunneling dynamics near fermionization is shown to be sensitive to both atom number and initial configuration.

It is well known that attractive condensates do not posses a stable ground state in three dimensions. The widely used Gross-Pitaevskii theory predicts the existence of metastable states up to some critical number $N_{\mathrm{cr}}^{\mathrm{GP}}$ of atoms. It is demonstrated here that fragmented metastable states exist for atom numbers well above $N_{\mathrm{cr}}^{\mathrm{GP}}$. The fragments are strongly overlapping in space. The results are obtained and analyzed analytically as well as numerically. The implications are discussed.

For molecular substances exhibiting harmonic and nonharmonic vibrations, we present a first-principles approach to predict enthalpy differences between phases at finite temperatures, including solid-solid and melting. We apply it to the complex hydride ${\mathrm{LiBH}}_4$. Using ab initio molecular dynamics, we predict a structure for the high-$T$ solid phase of lithium borohydride, and we propose an approximation to account for nonharmonic vibrations. We then predict the enthalpy changes for solid-solid transition, melting, and an H-storage reaction, all in agreement with experiment.

We study motion of small particles in turbulence when the particle relaxation time falls in the range of inertial time scales of the flow. Because of inertia, particles drift relative to the fluid. We demonstrate that the collective drift of two close particles makes them see local velocity increments fluctuate fast. This allows us to introduce Langevin description for separation dynamics. We describe the behavior of the Lyapunov exponent and give the analogue of Richardson’s law for separation above viscous scale.

Quantum computing using two coherent states as a qubit basis is a proposed alternative architecture with lower overheads but has been questioned as a practical way of performing quantum computing due to the fragility of diagonal states with large coherent amplitudes. We show that using error correction only small amplitudes ($\alpha >1.2$) are required for fault-tolerant quantum computing. We study fault tolerance under the effects of small amplitudes and loss using a Monte Carlo simulation. The first encoding level resources are orders of magnitude lower than the best single photon scheme.

We investigate the relation between the scaling of block entropies and the efficient simulability by matrix product states (MPSs) and clarify the connection both for von Neumann and Rényi entropies. Most notably, even states obeying a strict area law for the von Neumann entropy are not necessarily approximable by MPSs. We apply these results to illustrate that quantum computers might outperform classical computers in simulating the time evolution of quantum systems, even for completely translational invariant systems subject to a time-independent Hamiltonian.

We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number $N=263193$.

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.