We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum nonlocality. The resulting monogamy relations are stronger than those obtained from the no-signaling principle alone. In many cases, they yield tight quantum bounds on the amount of violation of single and multiple qubit correlation Bell inequalities. In contrast with the two-qubit case, a rich structure of possible violation patterns is shown to exist in the multipartite scenario.

We discuss the entanglement properties of symmetric states of $n$ qubits. The Majorana representation maps a generic such state into a system of $n$ points on a sphere. Entanglement invariants, either under local unitaries (LU) or stochastic local operations and classical communication (SLOCC), can then be addressed in terms of the relative positions of the Majorana points. In the LU case, an overcomplete set of invariants can be built from the inner product of the radial vectors pointing to these points; this is detailed for the well-documented three-qubits case. In the SLOCC case, a cross ratio of related Möbius transformations are shown to play a central role, exemplified here for four qubits. Finally, as a side result, we also analyze the manifold of maximally entangled 3 qubit state, both in the symmetric and generic case.

The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk where a single particle is traveling through an active, fluctuating medium. Employing two archetype ergodic many-particle systems, namely, (i) a hard-point gas composed of two unequal masses and (ii) a Fermi-Pasta-Ulam chain, we demonstrate that the corresponding perturbation profiles coincide with the diffusion profiles of the single-particle Lévy walk approach. The parameters of the random walk can be related through elementary algebraic expressions to the physical parameters of the corresponding test many-body systems.

An efficient algorithm is developed to construct disconnectivity graphs by a random walk over basins of attraction. This algorithm can detect a large number of local minima, find energy barriers between them, and estimate local thermal averages over each basin of attraction. It is applied to the Sherrington-Kirkpatrick (SK) spin glass Hamiltonian where existing methods have difficulties even for a moderate number of spins. Finite-size results are used to make predictions in the thermodynamic limit that match theoretical approximations and recent findings on the free energy landscapes of SK spin glasses.

We propose and analyze a method to detect and characterize the drift of a nonstationary quantum source. It generalizes a standard measurement for detecting phase diffusion of laser fields to quantum systems of arbitrary Hilbert space dimension, qubits in particular. We distinguish diffusive and systematic drifts, and examine how quickly one can determine that a source is drifting. We show that for single-photon wave packets our measurement is implemented by the Hong-Ou-Mandel effect.

We study a single species of fermionic atoms in an “effective” magnetic field at total filling factor ${\nu }_f=1$, interacting through a $p$-wave Feshbach resonance, and show that the system undergoes a quantum phase transition from a ${\nu }_f=1$ fermionic integer quantum Hall state to ${\nu }_b=1/4$ bosonic fractional quantum Hall state as a function of detuning. The transition is in the ($2+1$)D Ising universality class. We formulate a dual theory in terms of quasiparticles interacting with a ${\mathbb{Z}}_2$ gauge field and show that charge fractionalization follows from this topological quantum phase transition. Experimental consequences and possible tests of our theoretical predictions are discussed.

The boundary between the classical and quantum worlds has been intensely studied. It remains fascinating to explore how far the quantum concept can reach with use of specially fabricated elements. Here we employ a tunable flux qubit with basis states having persistent currents of $1\mu \mathrm{A}$ carried by a million pairs of electrons. By tuning the tunnel barrier between these states we see a crossover from quantum to classical. Released from nonequilibrium, the system exhibits spontaneous coherent oscillations. For high barriers the lifetime of the states increases dramatically while the tunneling period approaches the phase coherence time and the oscillations fade away.

Probing the real time dynamics of a reacting molecule remains one of the central challenges in chemistry. Here we show how the time-dependent wave function of an excited-state reacting molecule can be completely reconstructed from resonant coherent anti-Stokes Raman spectroscopy. The method assumes knowledge of the ground potential but not of any excited potential. The excited-state potential can in turn be constructed from the wave function. The formulation is general for polyatomics and applies to bound as well as dissociative excited potentials. We demonstrate the method on the ${\mathrm{Li}}_2$ molecule.

We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in Hilbert space. This implies that the overwhelming majority of states in Hilbert space are not physical as they can only be produced after an exponentially long time. We establish this fact by making use of a time-dependent generalization of the Suzuki-Trotter expansion, followed by a well-known counting argument. This also demonstrates that a computational model based on arbitrarily rapidly changing Hamiltonians is no more powerful than the standard quantum circuit model.

We propose a scheme for the creation of stable three-dimensional bright solitons in Bose-Einstein condensates, i.e., the matter-wave analog of so-called spatiotemporal “light bullets.” Off-resonant dressing to Rydberg $nD$ states is shown to provide nonlocal attractive interactions, leading to self-trapping of mesoscopic atomic clouds by a collective excitation of a Rydberg atom pair. We present detailed potential calculations and demonstrate the existence of stable solitons under realistic experimental conditions by means of numerical simulations.

The contact $\mathcal{I}$, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter $1/(k_{F}a)$, where $k_F$ is the Fermi wave vector and $a$ is the $s$-wave scattering length, and the temperature $T/T_F$, where $T_F$ is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.

We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum discord. The minimal distillable entanglement is equal to the one-way information deficit. The quantum discord is shown to be equal to the minimal partial distillable entanglement that is the part of entanglement which is lost, when we ignore the subsystem which is not measured. We then show that any entanglement measure corresponds to some measure of quantum correlations. This powerful correspondence also yields necessary properties for quantum correlations. We generalize the results to multipartite measurements on a part of the system and on the total system.

We report the implementation of projective measurement on a single $1/2$ nuclear spin of the ${}^{171}\mathrm{Yb}$ atom by measuring the polarization of cavity-enhanced fluorescence. To obtain cavity-enhanced fluorescence having a nuclear-spin-dependent polarization, we construct a two-mode cavity QED system, in which two cyclic transitions are independently coupled to each of the orthogonally polarized cavity modes, by manipulating the energy level of ${}^{171}\mathrm{Yb}$. This system can associate the nuclear spin degrees of freedom with the polarization of photons, which will facilitate the development of hybrid quantum systems.

In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a “measure” problem that results from improper weighting of phase space. This issue is addressed considering a generic collision process whereby a large number of particles or agents randomly and repeatedly interact in pairs, with prescribed conservation law(s). We find a sufficient condition under which the stationary single-particle distribution function maximizes an entropylike functional, that is free of the measure problem. This condition amounts to a factorization property of the Jacobian associated with the binary collision law, from which the proper weighting of phase space directly follows.

We address the coherence of the dynamics of spin-currents with components transverse to an external magnetic field for the spin-$1/2$ Heisenberg chain. We study current autocorrelations at finite temperatures and the real-time dynamics of currents at zero temperature. Besides a coherent Larmor oscillation, we find an additional collective oscillation at higher frequencies, emerging as a coherent many-magnon effect at low temperatures. Using numerical and analytical methods, we analyze the oscillation frequency and decay time of this coherent current-mode versus temperature and magnetic field.

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate $r$. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate $r^{*}$. Resetting also alters fundamentally the late time decay of the survival probability of a stationary target when there are multiple searchers: while the typical survival probability decays exponentially with time, the average decays as a power law with an exponent depending continuously on the density of searchers.

We place two atoms in quantum superposition states and observe coherent phase evolution for $3.4\times {10}^{15}$ cycles. Correlation signals from the two atoms yield information about their relative phase even after the probe radiation has decohered. This technique allowed a frequency comparison of two ${}^{27}\mathrm{Al}^{+}$ ions with fractional uncertainty ${3.7}_{-0.8}^{+1.0}\times {10}^{-16}/\sqrt{\tau /\mathrm{s}}$. Two measures of the $Q$ factor are reported: The $Q$ factor derived from quantum coherence is ${3.4}_{-1.1}^{+2.4}\times {10}^{16}$, and the spectroscopic $Q$ factor for a Ramsey time of 3 s is $6.7\times {10}^{15}$. We demonstrate a method to detect the individual quantum states of two ${\mathrm{Al}}^{+}$ ions in a ${\mathrm{Mg}}^{+}\mathrm{\text{−}}{\mathrm{Al}}^{+}\mathrm{\text{−}}{\mathrm{Al}}^{+}$ linear ion chain without spatially resolving the ions.

It has recently become possible to focus a beam of high-energy electrons to a spot smaller than an atom, with vast potential for the study of condensed matter. We devise an experiment that can image, with subangstrom resolution, the distribution of such an electron beam as it scatters within an atomic lattice. Our experiments reveal the acute sensitivity of the scattered electron distribution to 0.1 Å shifts of the impact point. Scattering due to plasmon excitations is also examined. Implications for the study of the atomic and electronic structure of condensed matter are discussed.

We report on the experimental study of an exceptional point (EP) in a dissipative microwave billiard with induced time-reversal invariance ($\mathcal{T}$) violation. The associated two-state Hamiltonian is non-Hermitian and nonsymmetric. It is determined experimentally on a narrow grid in a parameter plane around the EP. At the EP the size of $\mathcal{T}$ violation is given by the relative phase of the eigenvector components. The eigenvectors are adiabatically transported around the EP, whereupon they gather geometric phases and in addition geometric amplitudes different from unity.

We show that block entanglement entropies in one-dimensional systems close to a quantum critical point can, in principle, be measured in terms of the population of low-lying energy levels following a certain type of local quantum quench.