We address an imbalanced two-component atomic Fermi gas restricted by a one-dimensional (1D) optical lattice and an external harmonic potential, within the mean-field Bogoliubov–de Gennes formalism. We show that characteristic features of the Fulde-Ferrell-Larkin-Ovchinnikov state are visible in the rf spectra and in the momentum-resolved photoemission spectra of the gas. Specially, Andreev states or midgap states can be clearly resolved, which gives a direct experimentally observable signature of the oscillating order parameter.

We introduce the concept of Shannon dimensionality $D$ as a new way to quantify bipartite entanglement as measured in an experiment. This is applied to orbital-angular-momentum entanglement of two photons, using two state analyzers composed of a rotatable angular-sector phase plate that is lens coupled to a single-mode fiber. We can deduce the value of $D$ directly from the observed two-photon coincidence fringe. In our experiment, $D$ varies between 2 and 6, depending on the experimental conditions. We predict how the Shannon dimensionality evolves when the number of angular sectors imprinted in the phase plate is increased and anticipate that $D\simeq 50$ is experimentally within reach.

We report the experimental demonstration of quantum memory for collective atomic states in a far-detuned optical dipole trap. Generation of the collective atomic state is heralded by the detection of a Raman scattered photon and accompanied by storage in the ensemble of atoms. The optical dipole trap provides confinement for the atoms during the quantum storage while retaining the atomic coherence. We probe the quantum storage by cross correlation of the photon pair arising from the Raman scattering and the retrieval of the atomic state stored in the memory. Nonclassical correlations are observed for storage times up to $60\mu \mathrm{s}$.

We prove that the threshold detection efficiency for a loophole-free Bell experiment using an $n$-qubit Greenberger-Horne-Zeilinger state and the correlations appearing in the $n$-partite Mermin inequality is $n/(2n-2)$. If the detection efficiency is equal to or lower than this value, there are local hidden variable models that can simulate all the quantum predictions. If the detection efficiency is above this value, there is no local hidden variable model that can simulate all the quantum predictions.

We extend the common theme of random Apollonian packing of circles to consider orientable grains with a noncircular shape. Systems of up to ${10}^6$ grains are examined for a range of polygonal and elliptical shapes using both the random Apollonian packing model and the new rotational random Apollonian packing model which takes into account the extra rotational degree of freedom of noncircular grains. We identify the constraining length $D_c$ that limits growth of the grain during the packing process and find that a universal relation exists between grain shape and the scaling properties of the system.

We study the statistics of the work done on a quantum critical system by quenching a control parameter in the Hamiltonian. We elucidate the relation between the probability distribution of the work and the Loschmidt echo, a quantity emerging usually in the context of dephasing. Using this connection we characterize the statistics of the work done on a quantum Ising chain by quenching locally or globally the transverse field. We show that for local quenches starting at criticality the probability distribution of the work displays an interesting edge singularity.

We report on the first results of a sensitive search for scalar coupling of photons to a light neutral boson in the mass range of approximately 1.0 meV (milli-electron volts) and coupling strength greater than ${10}^{-6}{\mathrm{GeV}}^{-1}$ using optical photons. This was a photon regeneration experiment using the “light shining through a wall” technique in which laser light was passed through a strong magnetic field upstream of an optical beam dump; regenerated laser light was then searched for downstream of a second magnetic field region optically shielded from the former. Our results show no evidence for scalar coupling in this region of parameter space.

We experimentally demonstrate increased diffuse transmission of light through strongly scattering materials. Wave front shaping is used to selectively couple light to the open transport eigenchannels, specific solutions of Maxwell’s equations which the sample transmits fully, resulting in an increase of up to 44% in the total angle-integrated transmission compared to the case where plane waves are incident. The results for each of several hundreds of experimental runs are in excellent quantitative agreement with random matrix theory. From our measurements we conclude that with perfectly shaped wave fronts the transmission of a disordered sample tends to a universal value of $2/3$, regardless of the thickness.

The number $N(E)$ of complex zeros of the Riemann zeta function with positive imaginary part less than $E$ is the sum of a “smooth” function $\overline{N}(E)$ and a “fluctuation.” Berry and Keating have shown that the asymptotic expansion of $\overline{N}(E)$ counts states of positive energy less than $E$ in a “regularized” semiclassical model with classical Hamiltonian $H=xp$. For a different regularization, Connes has shown that it counts states “missing” from a continuum. Here we show how the “absorption spectrum” model of Connes emerges as the lowest Landau level limit of a specific quantum-mechanical model for a charged particle on a planar surface in an electric potential and uniform magnetic field. We suggest a role for the higher Landau levels in the fluctuation part of $N(E)$.

We introduce the multiscale entanglement renormalization ansatz, a class of quantum many-body states on a $D$-dimensional lattice that can be efficiently simulated with a classical computer, in that the expectation value of local observables can be computed exactly and efficiently. The multiscale entanglement renormalization ansatz is equivalent to a quantum circuit of logarithmic depth that has a very characteristic causal structure. It is also the ansatz underlying entanglement renormalization, a novel coarse-graining scheme for many-body quantum systems on a lattice.

We propose and study methods for detecting Unruh-like acceleration radiation effects in a Bose-Einstein condensate in a ($1+1$)-dimensional setup. The Bogoliubov vacuum of a Bose-Einstein condensate is used to simulate a scalar field theory, and accelerated atom dots or optical lattices serve as detectors of phonon radiation due to acceleration effects. In particular, we study the dispersive effects of the Bogoliubov spectrum on the ideal case of exact thermalization. Our results suggest that acceleration radiation effects can be observed using currently accessible experimental methods.

With the imminent advent of mesoscopic rotating Bose-Einstein condensates in the lowest Landau level regime, we explore lowest Landau level vortex nucleation. An exact many-body analysis is presented in a weakly elliptical trap for up to 400 particles. Striking non-mean-field features are exposed at filling factors $\gg 1$. For example, near the critical rotation frequency pairs of energy levels approach each other with exponential accuracy. A physical interpretation is provided by requantizing a mean-field theory, where $1/N$ plays the role of Planck’s constant, revealing two vortices cooperatively tunneling between classically degenerate energy minima. The tunnel splitting variation is described in terms of frequency, particle number, and ellipticity.

We investigate the thermodynamic properties of quantum electrodynamics in $1+1$ dimensions. We derive the partition function of the canonical ensemble in discrete light cone quantization and calculate the thermodynamical potential. This central quantity is evaluated for different system sizes and coupling strengths. We investigate the continuum limit and the thermodynamical limit and present basic thermodynamical quantities as a function of temperature for the interacting system. The results are compared to the idealized cases.

We study numerically and analytically the dynamics of a sedimenting suspension of active, reproducing particles, such as growing bacteria in a gravitational field. In steady state we find a nonequilibrium phase transition between a “sedimentation” regime, analogous to the sedimentation equilibrium of passive colloids, and a “uniform” regime, in which the particle density is constant in all but the top and bottom of the sample. We discuss the importance of fluctuations in particle density in locating the phase-transition point, and report the kinetics of sedimentation at early times.

We present an efficient method for probing the orbital angular momentum of optical vortices of arbitrary sizes. This method, based on a multipoint interferometer, has its most important application in measuring the orbital angular momentum of light from astronomical sources, opening the way to interesting new astrophysics. We demonstrate its viability by measuring the orbital angular momentum of Laguerre-Gaussian laser beams.

We generalize the experimental success criterion for quantum teleportation (memory) in continuous-variable quantum systems to be suitable for a non-unit-gain condition by considering attenuation (amplification) of the coherent-state amplitude. The new criterion can be used for a nonideal quantum memory and long distance quantum communication as well as quantum devices with amplification process. It is also shown that the framework to measure the average fidelity is capable of detecting all Gaussian channels in the quantum domain.

We have observed $p$-wave Feshbach molecules for all three combinations of the two lowest hyperfine spin states of ${}^6\mathrm{Li}$. By creating a pure molecular sample in an optical trap, we measured the inelastic collision rates of $p$-wave molecules. We have also measured the elastic collision rate from the thermalization rate of a breathing mode which was excited spontaneously upon molecular formation.

Systems described by an $O(n)$ symmetrical ${\varphi }^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film’s boundary planes ${\mathfrak{B}}_j$, $j=1,2$, are investigated as functions of film thickness $L$ for generic symmetry-preserving boundary conditions ${\partial }_n\mathit{\varphi }={\stackrel{\circ }{c}}_j\mathit{\varphi }$. The $L$-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form $f_{\mathrm{res}}\approx D(c_1{L}^{\Phi /\nu },c_2{L}^{\Phi /\nu })/L^{d-1}$ when $d<4$, where $c_i$ are scaling fields associated with the variables ${\stackrel{\circ }{c}}_i$ and $\Phi$ is a surface crossover exponent. Explicit two-loop renormalization group results for the function $D({\mathsf{c}}_1,{\mathsf{c}}_2)$ at $d=4-ϵ$ dimensions are presented. These show that (i) the Casimir force can have either sign, depending on ${\mathsf{c}}_1$ and ${\mathsf{c}}_2$, and (ii) for appropriate choices of the enhancements ${\stackrel{\circ }{c}}_j$, crossovers from attraction to repulsion and vice versa occur as $L$ increases.

We analyze the coherent transport of a single photon, which propagates in a one-dimensional coupled-resonator waveguide and is scattered by a controllable two-level system located inside one of the resonators of this waveguide. Our approach, which uses discrete coordinates, unifies low and high energy effective theories for single-photon scattering. We show that the controllable two-level system can behave as a quantum switch for the coherent transport of a single photon. This study may inspire new electro-optical single-photon quantum devices. We also suggest an experimental setup based on superconducting transmission line resonators and qubits.

We report on the observation of an interaction blockade effect for ultracold atoms in optical lattices, analogous to the Coulomb blockade observed in mesoscopic solid state systems. When the lattice sites are converted into biased double wells, we detect a discrete set of steps in the well population for increasing bias potentials. These correspond to tunneling resonances where the atom number on each side of the barrier changes one by one. This allows us to count and control the number of atoms within a given well. By evaluating the amplitude of the different plateaus, we can fully determine the number distribution of the atoms in the lattice, which we demonstrate for the case of a superfluid and Mott insulating regime of ${}^{87}\mathrm{Rb}$.