We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the noninteracting regime. We derive the diffusion constant as a function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.

We present experimental results on the measurement of fidelity decay under contrasting system dynamics using a nuclear magnetic resonance quantum information processor. The measurements were performed by implementing a scalable circuit in the model of deterministic quantum computation with only one quantum bit. The results show measurable differences between regular and complex behavior and for complex dynamics are faithful to the expected theoretical decay rate. Moreover, we illustrate how the experimental method can be seen as an efficient way for either extracting coarse-grained information about the dynamics of a large system or measuring the decoherence rate from engineered environments.

In the presence of a small magnetic field $h$, the elementary excitations in the scaling two-dimensional Ising model are studied perturbatively in $h$ in the ferromagnetic phase. For excitations with large numbers $n$, the mass spectrum is obtained in the first order in $h$. The decay widths of excitations with energies above the stability threshold are calculated in the leading $h^3$ order.

We propose a setup with ultracold atomic gases that can be used to make a nonrelativistic superstring in four spacetime dimensions. In particular, we consider for the creation of the superstring a fermionic atomic gas that is trapped in the core of a vortex in a Bose-Einstein condensate. We explain the required tuning of experimental parameters to achieve supersymmetry between the fermionic atoms and the bosonic modes describing the oscillations in the vortex position. Furthermore, we discuss the experimental consequences of supersymmetry.

A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired perturbations of quantum systems significantly even for long interaction times. As a first application the stabilization of a quantum memory is discussed which is perturbed by one- and two-qubit interactions.

We report the experimental realization and the characterization of polarization and momentum hyperentangled two-photon states, generated by a new parametric source of correlated photon pairs. By adoption of these states an ”all-versus-nothing” test of quantum mechanics was performed. The two-photon hyperentangled states are expected to find at an increasing rate a widespread application in state engineering and quantum information.

We develop and exploit a source of two-photon, four-dimensional entanglement to report the first two-particle all-versus-nothing test of local realism with a linear optics setup, but without resorting to a noncontextuality assumption. Our experimental results are in good agreement with quantum mechanics while in extreme contradiction to local realism. Potential applications of our experiment are briefly discussed.

Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum-information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal and a nonlinear quantity, namely, the Renyi entropy, from local measurements on two pairs of polarization-entangled photons. We also introduce a “phase marking” technique which allows the selection of uncorrupted outcomes even with nondeterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of nonlinear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell–Clauser-Horne-Shimony-Holt inequalities.

The thermodynamic and dynamical properties of an Ising model with both short-range and long-range, mean-field-like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short-range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long-range interactions and are expected to be valid even when the interaction is slowly decaying with distance.

We show that a many-atom Bose system at zero temperature has, in general, a liquid phase in addition to its well-known gaseous phase. A universal phase diagram is presented that is applicable to all Bose systems with a $-C_6/r^6$ type of interaction at large interparticle separations. We show that the predicted phase structure has implications on the stability of a gaseous Bose-Einstein condensate (BEC) even at dilute densities that are routinely achieved under existing experimental conditions. We also predict that ${}^4\mathrm{He}$ should have a gaseous BEC phase below a critical density of $5.58\times {10}^{15}1/{\mathrm{cm}}^3$.

Spinor Bose condensates loaded in optical lattices have a rich phase diagram characterized by different magnetic order. Here we apply the density matrix renormalization group to accurately determine the phase diagram for spin-1 bosons loaded on a one-dimensional lattice. The Mott lobes present an even or odd asymmetry associated to the boson filling. We show that for odd fillings the insulating phase is always in a dimerized state. The results obtained in this work are also relevant for the determination of the ground state phase diagram of the $S=1$ Heisenberg model with biquadratic interaction.

The singular nature of a noninteger spiral phase plate allows easy manipulation of spatial degrees of freedom of photon states. Using two such devices, we have observed very high-dimensional spatial entanglement of twin photons generated by spontaneous parametric down-conversion.

We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the spectral gap, which characterizes the approach to stationarity at large times. We observe boundary induced crossovers in and between massive, diffusive, and Kardar-Parisi-Zhang scaling regimes.

We calculate the Lyapunov exponents for particles suspended in a random three-dimensional flow, concentrating on the limit where the viscous damping rate is small compared to the inverse correlation time. In this limit Lyapunov exponents are obtained as a power series in $ϵ$, a dimensionless measure of the particle inertia. Although the perturbation generates an asymptotic series, we obtain accurate results from a Padé-Borel summation. Our results prove that particles suspended in an incompressible random mixing flow can show pronounced clustering when the Stokes number is large and we characterize two distinct clustering effects which occur in that limit.

Simulations show that a local perturbation (a “hot spot”) at the inlet of a microchannel can be a source of traveling concentration waves in a binary fluid and can be exploited to create periodic, oscillatory patterns within the channel. We isolate two distinctly different types of traveling periodic patterns and estimate the wavelength of the structures. Our findings provide the first example of how a local perturbation can be used to create well-defined periodic patterns in two-phase flow within a confined geometry and can lead to new routes for creating gradient materials.

We report the realization of an entangled quantum superposition of $M\sim 12$ photons by multiple universal cloning of a single-photon qubit via the high gain, quantum-injected optical parametric amplification. The system has been found extremely resilient to decoherence. By quantum tomography, the nonseparability and the quantum superposition are demonstrated for the mesoscopic output state of the dynamic “closed system.”

The physical properties of arbitrary half-integer spins $F=N-1/2$ fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for $F\ge 3/2$ depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular-superfluid instability made of $2N$ fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the ${\mathbb{Z}}_N$ generalized Ising universality class. We discuss the possible Mott phases at $1/2N$ filling.

We propose a new test statistic based on a score process for determining the statistical significance of a putative signal that may be a small perturbation to a noisy experimental background. We derive the reference distribution for this score test statistic; it has an elegant geometrical interpretation as well as broad applicability. We illustrate the technique in the context of a model problem from high-energy particle physics. Monte Carlo experimental results confirm that the score test results in a significantly improved rate of signal detection.

By using the diffusion Monte Carlo method we calculate the one- and two-body density matrix of an interacting Fermi gas at $T=0$ in the BCS to Bose-Einstein condensate (BEC) crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.

An analytic solution of the Gross-Pitaevskii equation for a rotating Bose-Einstein condensate of trapped atoms describes the onset of vorticity when the rotational speed is increased, starting with the entry of the first vortex and followed by the formation of growing symmetric Wigner molecules. It explains the staircase of angular momentum jumps and the behavior of the bosonic occupancies observed in numerical studies. The similarity of this behavior and mesoscopic superconductors is discussed.