We develop a diagrammatic scattering theory for interacting bosons in a three-dimensional, weakly disordered potential. We show how collisional energy transfer between the bosons induces the thermalization of the inelastic single-particle current which, after only a few collision events, dominates over the elastic contribution described by the Gross-Pitaevskii ansatz.

We excite spin waves with spatially inhomogeneous Ramsey pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped ${}^{87}\mathrm{Rb}$. The density-dependent frequency shifts of the hyperfine transition simulate the $s$-wave collisional frequency shifts of fermions, including those of optical lattice clocks. As the spin polarizations oscillate in the trap, the frequency shift reverses and it depends on the area of the second Ramsey pulse, exhibiting a predicted beyond mean-field frequency shift. Numerical and analytic models illustrate these observed behaviors.

A statistical analysis of optimal universal cloning shows that it is possible to identify an ideal (but nonpositive) copying process that faithfully maps all properties of the original Hilbert space onto two separate quantum systems, resulting in perfect correlations for all observables. The joint probabilities for noncommuting measurements on separate clones then correspond to the real parts of the complex joint probabilities observed in weak measurements on a single system, where the measurements on the two clones replace the corresponding sequence of weak measurement and postselection. The imaginary parts of weak measurement statics can be obtained by replacing the cloning process with a partial swap operation. A controlled-swap operation combines both processes, making the complete weak measurement statistics accessible as a well-defined contribution to the joint probabilities of fully resolved projective measurements on the two output systems.

We explicitly exhibit a set of four ququad-ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication. Before our work, it was unknown whether there is a set of $d$ locally indistinguishable $d\otimes d$ orthogonal maximally entangled states for some positive integer $d$. We further show that a $2\otimes 2$ maximally entangled state can be used to locally distinguish this set of states without being consumed, thus demonstrate a novel phenomenon of entanglement discrimination catalysis. Based on this set of states, we construct a new set $K$ consisting of four locally indistinguishable states such that $K^{\otimes m}$ (with $4^m$ members) is locally distinguishable for some $m$ greater than one. As an immediate application, we construct a noisy quantum channel with one sender and two receivers whose local zero-error classical capacity can achieve the full dimension of the input space but only with a multi-shot protocol.

The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local optimization employed by DMRG to optimize the wave function is ineffective in updating large-scale features. Here we present a multigrid algorithm that solves these convergence problems by optimizing the wave function at different spatial resolutions. We demonstrate its effectiveness by simulating bosons in continuous space and study nonadiabaticity when ramping up the amplitude of an optical lattice. The algorithm can be generalized to tensor network methods and combined with the contractor renormalization group method to study dilute and weakly doped lattice models.

We present an ab initio determination of the shear viscosity $\eta$ of the unitary Fermi gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity-to-entropy density ratio $\eta /s$. The minimum of $\eta /s$ appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being $(\eta /s{)}_{\min }\approx 0.2\hslash /k_B$, which is close the Kovtun-Son-Starinets universal value $\hslash /(4\pi k_B)$.

Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we propose a general method to measure the entanglement entropy. The method is based on a quantum switch (a two-level system) coupled to a composite system consisting of several copies of the original many-body system. The state of the switch controls how different parts of the composite system connect to each other. We show that, by studying the dynamics of the quantum switch only, the Rényi entanglement entropy of the many-body system can be extracted. We propose a possible design of the quantum switch, which can be realized in cold atomic systems. Our work provides a route towards testing the scaling of entanglement in critical systems as well as a method for a direct experimental detection of topological order.

We discuss a scheme to measure the many-body entanglement growth during quench dynamics with bosonic atoms in optical lattices. By making use of a 1D or 2D setup in which two copies of the same state are prepared, we show how arbitrary order Rényi entropies can be extracted by using tunnel coupling between the copies and measurement of the parity of on-site occupation numbers, as has been performed in recent experiments. We illustrate these ideas for a superfluid-Mott insulator quench in the Bose-Hubbard model, and also for hard-core bosons, and show that the scheme is robust against imperfections in the measurements.

We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an entropic contextual inequality is formulated, analogous to the entropic Bell inequalities derived by Braunstein and Caves [Phys. Rev. Lett. 61, 662 (1988)], that must be satisfied by all noncontextual theories. We find optimal measurements for violation of this inequality. The approach is easily extendable to higher dimensional quantum systems and more measurements. Our theoretical findings can be verified in the laboratory with current technology.

We theoretically demonstrate the possibility of observing the macroscopic Zeno effect for nonlinear waveguides with localized dissipation. We show the existence of stable stationary flows, which are balanced by losses in the dissipative domain. The macroscopic Zeno effect manifests itself in the nonmonotonic dependence of the stationary flow on the strength of the dissipation. In particular, we highlight the importance of the dissipation parameters in observing the phenomenon. Our results are applicable to a large variety of systems, including the condensates of atoms or quasiparticles and optical waveguides.

We demonstrate a simple pulse shaping technique designed to improve the fidelity of spin-dependent force operations commonly used to implement entangling gates in trapped ion systems. This extension of the Mølmer-Sørensen gate can theoretically suppress the effects of certain frequency and timing errors to any desired order and is demonstrated through Walsh modulation of a two qubit entangling gate on trapped atomic ions. The technique is applicable to any system of qubits coupled through collective harmonic oscillator modes.

The asymmetric inclusion process is a lattice-gas model which replaces the “fermionic” exclusion interactions of the asymmetric exclusion process by “bosonic” inclusion interactions. Combining together probabilistic and Monte Carlo analyses, we showcase the model’s rich statistical complexity—which ranges from “mild” to “wild” displays of randomness: Gaussian load and draining, Rayleigh outflow with linear aging, inverse-Gaussian coalescence, intrinsic power-law scalings and power-law fluctuations and condensation.

We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behavior. These models are the quantum analogs of the classical facilitated spin models. Just like their classical counterparts, quantum facilitated models display complex glassy dynamics despite the fact that their stationary state is essentially trivial. In these systems, dynamical arrest is a consequence of kinetic constraints and not of static ordering. These models display a quantum version of dynamic heterogeneity: the dynamics toward relaxation is spatially correlated despite the absence of static correlations. Associated dynamical fluctuation phenomena such as decoupling of time scales is also observed. Moreover, we find that close to the classical limit, quantum fluctuations can enhance glassiness, as recently reported for quantum liquids.

We experimentally demonstrate the entanglement of spatial modes between two photons propagating through separate few-mode optical fibers. Quantum states over the two lowest-order spatial modes are measured with highly efficient spatial-mode analyzers based on acousto-optics. Quantum state tomography verifies the entanglement of the spatial-domain Bell state.

Using computer simulations, we study a membrane of parallel narrow pores filled with one-dimensional wires of hydrogen-bonded water molecules. We show that such a membrane is equivalent to a system of effective charges located at opposite sides of the membrane offering a computationally efficient way to model correlation effects in water-filled nanopore membranes. Based on our simulations we predict that membranes with square pore lattices undergo a continuous order-disorder transition to an antiferroelectric low-temperature phase in which water wires in adjacent pores are oriented in opposite directions. Strong antiferroelectric correlations exist also in the disordered phase far above the critical temperature or in membranes with geometric frustration, leading to a dielectric constant that is reduced considerably with respect to the case of uncoupled water wires. These correlations are also expected to hinder proton translocation through the membrane.

Some novel two-body effects analogous to the well-known three-body Efimov effect are predicted. In the systems considered, particle A is constrained on a truncated or bent one-dimensional line or two-dimensional plane, or on one side of a flat mirror in three dimensions (3D). The constraining potential is fine-tuned such that particle $A$’s ground state wave function is a constant in the region in which it is constrained. Particle $B$ moves in 3D and interacts with particle $A$, resonantly. An infinite sequence of giant two-body bound states are found in each case.

The question of whether the probabilistic nature of quantum mechanical predictions can be alleviated by supplementing the wave function with additional information has received a lot of attention during the past century. A few specific models have been suggested and subsequently falsified. Here we give a more general answer to this question: We provide experimental data that, as well as falsifying these models, cannot be explained within any alternative theory that could predict the outcomes of measurements on maximally entangled particles with significantly higher probability than quantum theory. Our conclusion is based on the assumptions that all measurement settings have been chosen freely (within a causal structure compatible with relativity theory), and that the presence of the detection loophole did not affect the measurement outcomes.

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.

We present a method for determining the average transition path and the free energy along this path in the space of selected collective variables. The formalism is based upon a history-dependent bias along a flexible path variable within the metadynamics framework but with a trivial scaling of the cost with the number of collective variables. Controlling the sampling of the orthogonal modes recovers the average path and the minimum free energy path as the limiting cases. The method is applied to resolve the path and the free energy of a conformational transition in alanine dipeptide.

We present solid evidence for the existence of a well-defined Higgs amplitude mode in two-dimensional relativistic field theories based on analytically continued results from quantum Monte Carlo simulations of the Bose-Hubbard model in the vicinity of the superfluid–Mott insulator quantum critical point, featuring emergent particle-hole symmetry and Lorentz invariance. The Higgs boson, seen as a well-defined low-frequency resonance in the spectral density, is quickly pushed to high energies in the superfluid phase and disappears by merging with the broad secondary peak at the characteristic interaction scale. Simulations of a trapped system of ultracold ${}^{87}\mathrm{Rb}$ atoms demonstrate that the low-frequency resonance is lost for typical experimental parameters, while the characteristic frequency for the onset of a strong response is preserved.