The relation between single particle and ensemble measurements is addressed for semiconductor CdSe nanocrystals. We record their fluorescence at the single molecule level and analyze their emission intermittency, which is governed by unusual random processes known as Lévy statistics. We report the observation of statistical aging and ergodicity breaking, both related to the occurrence of Lévy statistics. Our results show that the behavior of ensemble quantities, such as the total fluorescence of an ensemble of nanocrystals, can differ from the time-averaged individual quantities, and must be interpreted with care.

We introduce lattice models with explicit $\mathcal{N}=2$ supersymmetry. In these interacting models, the supersymmetry generators $Q^{\pm }$ yield the Hamiltonian $H=\{Q^{+},Q^{-}\}$ on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers; the Hamiltonian of our simplest model contains a hopping term and a repulsive potential. We analyze these models using conformal field theory, the Bethe ansatz, and cohomology. The simplest model provides a manifestly supersymmetric lattice regulator for the supersymmetric point of the massless $(1+1)$-dimensional Thirring (Luttinger) model. Generalizations include a quantum monomer-dimer model on a two-leg ladder.

We demonstrate a direct connection between the density profile of a system of ultracold trapped bosonic particles in the rapid-rotation limit and its condensate fraction. This connection can be used to probe the crossover from condensed vortex-lattice states to uncondensed quantum-fluid states that occurs in rapidly rotating boson systems as the particle density decreases or the rotation frequency increases. We illustrate our proposal with a series of examples, including ones based on models of realistic finite trap systems, and comment on its application to freely expanding boson density profile measurements.

We study the dynamics of Bose-Einstein condensates in an optical lattice and harmonic trap. The condensates are set in motion by displacing the trap and initially follow simple semiclassical paths, shaped by the lowest energy band. Above a critical displacement, the condensate undergoes Bragg reflection. For high atom densities, the first Bragg reflection generates a train of solitons and vortices, which destabilize the condensate and trigger explosive expansion. At lower densities, soliton and vortex formation requires multiple Bragg reflections, and damps the center-of-mass motion.

A theory of systems with long-range correlations based on the consideration of binary $N$-step Markov chains is developed. In our model, the conditional probability that the $i$th symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding $N$ symbols. The correlation and distribution functions as well as the variance of number of symbols in the words of arbitrary length $L$ are obtained analytically and numerically. If the persistent correlations are not extremely strong, the variance is shown to be nonlinearly dependent on $L$. A self-similarity of the studied stochastic process is revealed. The applicability of the developed theory to the coarse-grained written and DNA texts is discussed.

We propose to subject two Bose-Einstein condensates to a periodic potential, so that one condensate undergoes the Mott-insulator transition to a state with precisely one atom per lattice site. We show that photoassociation of heteronuclear molecules within each lattice site is described by the quantum optical Jaynes-Cummings Hamiltonian. In analogy with studies of this Hamiltonian with cavity fields and trapped ions, we are thus able to engineer quantum optical states of atomic matter wave fields and we are able to reconstruct these states by quantum state tomography.

We show that, by loading a Bose-Einstein condensate of two different atomic species into an optical lattice, it is possible to achieve a Mott-insulator phase with exactly one atom of each species per lattice site. A subsequent photoassociation leads to the formation of one heteronuclear molecule with a large electric dipole moment, at each lattice site. The melting of such a dipolar Mott insulator creates a dipolar superfluid, and eventually a dipolar molecular condensate.

A gaseous Bose-Einstein condensate irradiated by a far off-resonance laser has long-range interatomic correlations caused by laser-induced dipole-dipole interactions. These correlations, which are tunable via the laser intensity and frequency, can produce a “roton” minimum in the excitation spectrum—behavior reminiscent of the strongly correlated superfluid liquid He II.

The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: $\beta =(3-\sqrt{5})/2$ and ${\nu }_{\perp }=2$. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.

We show that a symmetric threshold crossing detector can be described by a symbolic dynamics of a static three-symbol encoding which is highly efficient to detect subthreshold events in noisy nonstationary data. After computing instantaneous word statistics and running cylinder entropies, we introduce a mean-field transformation of the three-symbol dynamics considered as a Potts-spin lattice onto a distribution of two symbols. This transformed word statistics enables one to derive an estimator of the signal-to-noise ratio (SNR). Subthreshold events are then proven by a prominent peak of the SNR estimator as a function of the noise intensity.

In the Mott-insulator regime, two species of ultracold atoms in an optical lattice can exhibit the low-energy counterflow motion. We construct effective Hamiltonians for the three classes of the two-species (fermion-fermion, boson-boson, and boson-fermion–type) insulators and reveal the conditions when the resulting ground state supports super-counter-fluidity (SCF), with the alternative being phase segregation. We emphasize a crucial role of breaking the isotopic symmetry between the species for realizing the SCF phase.

A new paradigm for distributed quantum systems where information is a valuable resource is developed. After finding a unique measure for information, we construct a scheme for its manipulation in analogy with entanglement theory. In this scheme, instead of maximally entangled states, two parties distill local states. We show that, surprisingly, the main tools of entanglement theory are general enough to work in this opposite scheme. Up to plausible assumptions, we show that the amount of information that must be lost during the protocol of concentration of local information can be expressed as the relative entropy distance from some special set of states.

We study the two transverse quadrupole modes of a cigar-shaped Bose-Einstein condensate with a single centered vortex. We show that the counterrotating mode is more strongly damped than in the absence of a vortex, whereas the corotating mode is not affected appreciably by the vortex. We interpret this result as a decay of the counterrotating quadrupole mode into two excitations of the vortex line, the so-called Kelvin modes. This is supported by direct observation of the vortex line.

Magnetically and optically confined Bose-Einstein condensates were studied near a microfabricated surface. Condensate fragmentation observed in microfabricated magnetic traps was not observed in optical dipole traps at the same location. The measured condensate lifetime was $\ge 20\mathrm{s}$ and independent of the atom-surface separation under both magnetic and optical confinement. Radio-frequency spin-flip transitions driven by technical noise were directly observed for optically confined condensates and could limit the condensate lifetime in microfabricated magnetic traps.

We have investigated the properties of Bose-Einstein condensates of sodium atoms in the upper hyperfine ground state. Condensates in the high-field seeking $|F=2,m_F=-2⟩$ state were created in a large volume optical trap from initially prepared $|F=1,m_F=-1⟩$ condensates using a microwave transition at 1.77 GHz. We found condensates in the stretched state $|F=2,m_F=-2⟩$ to be stable for several seconds at densities in the range of ${10}^{14}\mathrm{\text{atoms}}/{\mathrm{c}\mathrm{m}}^3$. In addition, we studied the clock transition $|F=1,m_F=0⟩\to |F=2,m_F=0⟩$ in a sodium Bose-Einstein condensate and determined a density-dependent frequency shift of $(2.44\pm 0.25\pm 0.5)\times {10}^{-12}\mathrm{H}\mathrm{z}{\mathrm{c}\mathrm{m}}^3$.

Loop models in two dimensions can be related to $\mathrm{O}(N)$ models. The low-temperature dense-loops phase of such a model, or of its reformulation using a supergroup as symmetry, can have a Goldstone broken-symmetry phase for $N<2$. We argue that this phase is generic for $-2<N<2$ when crossings of loops are allowed, and distinct from the model of noncrossing dense loops first studied by Nienhuis [Phys. Rev. Lett. 49, 1062 (1982)]. Our arguments are supported by our numerical results, and by a lattice model solved exactly by Martins et al. [Phys. Rev. Lett. 81, 504 (1998)].

All the states of $N$ qubits can be classified into $N-1$ entanglement classes from 2-entangled to $N$-entangled (fully entangled) states. Each class of entangled states is characterized by an entanglement index that depends on the partition of $N$. The larger the entanglement index of a state, the more entangled or the less separable is the state in the sense that a larger maximal violation of Bell’s inequality is attainable for this class of state.

We discuss a closure of a polymer chain released from a state with given end-to-end distance. Considering the situation as a first passage problem for a non-Markovian process, we express the survival probability through the three-time distribution of the end-to-end distance and evaluate it numerically by solving a Volterra equation. We also show how the Wilemski-Fixmann approximation emerges within this scheme and discuss its geometrical nature.

In quasiclassical spectral theory, “resurgence” means that long periodic orbits can be expressed by short ones in such a way that the spectral determinant is real. The question has thus long been posed whether long scattering orbits can be expressed by short orbits in such a way as to make the quasiclassical scattering matrix unitary. We here find a resurgent and manifestly Hermitean expression for Wigner’s $R$ matrix, implying a unitary scattering matrix. The result is particularly important if the average resonance width is comparable with the average resonance spacing.

We study the average shape of a fluctuation of a time series $x(t)$, which is the average value $⟨x(t)-x(0){⟩}_T$ before $x(t)$ first returns at time $T$ to its initial value $x(0)$. For large classes of stochastic processes, we find that a scaling law of the form $⟨x(t)-x(0){⟩}_T=T^{\alpha }f(t/T)$ is obeyed. The scaling function $f(s)$ is, to a large extent, independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.