We measure the Gouy phase anomaly for matter waves using in-line holography to retrieve the full complex field of an astigmatic electron wave function. Sequential phase shifts of π/2 rad are observed for electron trajectories along the optic axis that pass through each line-focus caustic of subnanometer transverse width. Our observations demonstrate that anomalous phase shifts of matter waves in the vicinity of caustics can be robustly measured using phase retrieval, extending the current scope of singular electron optics.

We have performed ab initio QED calculations of the ${\left(1s\right)}^2{\left(2s\right)}^{2}2p_{3/2}-{\left(1s\right)}^2{\left(2s\right)}^{2}2p_{1/2}$ fine-structure splitting along the boron isoelectronic sequence for all ions with $17\le Z\le 100$. This level splitting was evaluated within the extended Furry picture and by making use of four different screening potentials in order to estimate the effects of interelectronic correlations. The accuracy of the predicted transition energies has been improved significantly when compared with previous computations.

An ideal phase-preserving linear amplifier is a deterministic device that adds to an input signal the minimal amount of noise consistent with the constraints imposed by quantum mechanics. A noiseless linear amplifier takes an input coherent state to an amplified coherent state, but only works part of the time. Such a device is actually better than noiseless, since the output has less noise than the amplified noise of the input coherent state; for this reason we refer to such devices as immaculate. Here we bound the working probabilities of probabilistic and approximate immaculate amplifiers and construct theoretical models that achieve some of these bounds. Our chief conclusions are the following: (i) The working probability of any phase-insensitive immaculate amplifier is very small in the phase-plane region where the device works with high fidelity; (ii) phase-sensitive immaculate amplifiers that work only on coherent states sparsely distributed on a phase-plane circle centered at the origin can have a reasonably high working probability.

It is well known that any given density $\rho \left(\mathbf{x}\right)$ can be realized by a determinantal wave function for $N$ particles. The question addressed here is whether any given density $\rho \left(\mathbf{x}\right)$ and current density $\mathbf{j}\left(\mathbf{x}\right)$ can be simultaneously realized by a (finite kinetic energy) determinantal wave function. In case the velocity field $\mathbf{v}\left(\mathbf{x}\right)=\mathbf{j}\left(\mathbf{x}\right)/\rho \left(\mathbf{x}\right)$ is curlfree, we provide a solution for all $N$, and we provide an explicit upper bound for the energy. If the velocity field is not curl-free, there is a finite energy solution for all $N\ge 4$, but we do not provide an explicit energy bound in this case. For $N=2$ we provide an example of a non-curl-free velocity field for which there is a solution and an example for which there is no solution. The case $N=3$ with a non-curl-free velocity field is left open.

We present a scheme of a compact atomic gravimeter based on atom interferometry. Atoms are maintained against gravity using a sequence of coherent accelerations performed by the Bloch oscillations technique. We demonstrate a sensitivity of $4.8\times {10}^{-8}$ with an integration time of 4 min. Combining this method with an atomic elevator allows us to measure the local gravity at different positions in the vacuum chamber. This method can be of relevance to improve the measurement of the Newtonian gravitational constant $G$.

We analyze the ac Stark shift of a cesium atom interacting with far-off-resonance guided light fields in the nanofiber-based two-color optical dipole trap realized by Vetsch et al. [Phys. Rev. Lett. 104, 203603 (2010)]. Particular emphasis is given to the fictitious magnetic field produced by the vector polarizability of the atom in conjunction with the ellipticity of the polarization of the trapping fields. Taking into account the ac Stark shift, the atomic hyperfine interaction, and a magnetic interaction, we solve the stationary Schrödinger equation at a fixed point in space and find Zeeman-state-dependent trapping potentials. In analogy to the dynamics in magnetic traps, a local degeneracy of these state-dependent trapping potentials can cause spin flips and should thus be avoided. We show that this is possible using an external magnetic field. Depending on the direction of this external magnetic field, the resulting trapping configuration can still exhibit state-dependent displacement of the potential minima. In this case, we find nonzero Franck-Condon factors between motional states of the potentials for different hyperfine-structure levels and propose the possibility of microwave cooling in a nanofiber-based two-color trap.

Simulating exotic phases of matter that are not amenable to classical techniques is one of the most important potential applications of quantum information processing. We present an efficient algorithm for preparing a large class of topological quantum states, the $G$-injective projected entangled pair states (PEPS), on a quantum computer. Important examples include the resonant valence bond states, conjectured to be topological spin liquids. The runtime of the algorithm scales polynomially with the condition number of the PEPS projectors and inverse polynomially in the spectral gap of the PEPS parent Hamiltonian.

Formalizing an old desire of Einstein, “$\psi$-epistemic theories” try to reproduce the predictions of quantum mechanics, while viewing quantum states as ordinary probability distributions over underlying objects called “ontic states.” Regardless of one's philosophical views about such theories, the question arises of whether one can cleanly rule them out by proving no-go theorems analogous to the Bell inequality. In the 1960s, Kochen and Specker (who first studied these theories) constructed an elegant $\psi$-epistemic theory for Hilbert space dimension $d=2$, but also showed that any deterministic $\psi$-epistemic theory must be “measurement contextual” in dimensions 3 and higher. Last year, the topic attracted renewed attention, when Pusey, Barrett, and Rudolph (PBR) showed that any $\psi$-epistemic theory must “behave badly under tensor product.” In this paper, we prove that even without the Kochen-Specker or PBR assumptions, there are no $\psi$-epistemic theories in dimensions $d\ge 3$ that satisfy two reasonable conditions: (1) symmetry under unitary transformations and (2) “maximum nontriviality” (meaning that the probability distributions corresponding to any two nonorthogonal states overlap). This no-go theorem holds if the ontic space is either the set of quantum states or the set of unitaries. The proof of this result, in the general case, uses some measure theory and differential geometry. On the other hand, we also show the surprising result that without the symmetry restriction, one can construct maximally nontrivial $\psi$-epistemic theories in every finite dimension $d$.

We provide a theoretical study of frequency-shifted feedback (FSF) lasers, i.e., lasers with an internal frequency shifter, seeded with a monochromatic wave. The resulting spectrum consists in a set of equidistant modes, labeled by $n$, whose phases vary quadratically with $n$. We prove the emergence of a temporal fractional Talbot effect, leading to generation of Fourier-transform-limited pulses at a repetition rate tunable by the parameters of the FSF cavity (cavity length and frequency shift per round trip), and limited by the spectral bandwidth of the laser. We characterize in detail the output field of this so-called “Talbot laser” and emphasize its specific intensity fluctuations. We evidence connections with some aspects of number theory by the appearance of Gauss sums and theta series in the expression of the laser field. Our predictions are in full agreement with the experimental results published in Guillet de Chatellus et al. [Opt. Express 21, 15065 (2013)]. Practical applications and limitations are discussed.

Cold circular Rydberg atoms are produced and magnetically trapped. The trap is characterized by direct spatial imaging of ion distributions, ion counting, and state-selective field ionization. At room temperature, we observe about 70% of the trapped atoms remaining after 6 ms. We measure a trap oscillation frequency increase of the circular Rydberg atom trap relative to the ground-state atom trap due to the larger magnetic moment of the circular Rydberg atoms. Simulations of the center-of-mass and internal-state evolution of circular states in our magnetic trap are performed and results are in good agreement with experimental observations.

The violation of a Bell inequality certifies the presence of entanglement even if neither party trusts their measurement devices. Recently Moroder et al. [T. Moroder, J.-D. Bancal, Y.-C. Liang, M. Hofmann, and O. Gühne, Phys. Rev. Lett. 111, 030501 (2013)] showed how to make this statement quantitative, using semidefinite programming to calculate how much entanglement is certified by a given violation. Here I adapt their techniques to the case in which Bob's measurement devices are in fact trusted, the setting for Einstein-Podolsky-Rosen steering inequalities. Interestingly, all of the steering inequalities studied turn out to require negativity for their violations. This supports a significant strengthening of Peres's conjecture that negativity is required to violate a bipartite Bell inequality.

We develop a general theoretical framework for the analytical description of the interaction of a model diatomic molecular system with an intense, arbitrarily polarized monochromatic laser field. The model molecule comprises an electron in the field of two zero-range potentials separated by the internuclear distance. This model has an exact analytical solution within the theoretical framework of the quasistationary quasienergy (Floquet) approach. In addition to the development of this general framework, we also present a detailed analysis of the weak-field limit, within which we obtain both the frequency-dependent polarizability and the angle-resolved photodetachment cross section for the model system. These fundamental properties are analyzed for both homonuclear and heteronuclear molecular systems in a linearly polarized laser field, for both ground and excited electronic states, and for arbitrary orientation of the molecular axis relative to the polarization vector of the laser field. The analytical expressions for the polarizability and angle-resolved photoelectron spectra exhibit characteristic double-slit interference patterns, allowing one to study their dependence on the parameters of the problem beyond the level of the Born approximation.

We present a theoretical and experimental study aimed at characterizing statistical regimes in a random laser. Both the theoretical simulations and the experimental results show the possibility of three regions of fluctuations increasing the pumping energy. An initial Gaussian regime is followed by Lévy statistics, and Gaussian statistics is recovered again for high pump pulse energy. These different statistical regimes are possible in a weakly diffusive active medium, while the region of Lévy statistics disappears when the medium is strongly diffusive presenting always a Gaussian regime with smooth emission spectrum. Experiments and theory agree in identification of the key parameters determining the statistical regimes of the random laser.

We construct optimal time-local control pulses based on a multipartite entanglement measure as target functional. The underlying control Hamiltonians are derived in a purely algebraic fashion, and the resulting pulses drive a composite quantum system rapidly into that highly entangled state which can be created most efficiently for a given interaction mechanism, and which bears entanglement that is robust against decoherence. Moreover, it is shown that the control scheme is insensitive to experimental imperfections in first order.

We report a detailed investigation on the properties of intensity correlation spectra for laser beams interacting with cold atoms under the condition of electromagnetically induced transparency (EIT). We describe the transition of their intensity fluctuations from correlation to anticorrelation as the mean intensity of the fields increases. Such a transition occurs for laser frequencies around the EIT resonance, which is characterized by a correlation peak. The transition point between correlation and anticorrelation is independent of power broadening and provides directly the ground-state coherence time. We introduce a method to extract in real time the correlation spectra of the system. The experiments were done in two distinct magneto-optical traps, one for cesium and the other for rubidium atoms, employing different detection schemes. A simplified theory is introduced assuming three-level atoms in $\Lambda$ configuration interacting with a laser with stochastic phase fluctuations, providing a good agreement with the experimental observations.

The calculation of the fundamental limits of nonlinear susceptibilities posits that when a quantum system has a nonlinear response at the fundamental limit, only three energy eigenstates contribute to the first and second hyperpolarizability. This is called the three-level ansatz and is the only unproven assumption in the theory of fundamental limits. In light of the observation that the measured nonlinear response of a majority of molecules falls far short of these limits, the three-level ansatz warrants closer scrutiny. All calculations that are based on direct solution of the Schrödinger equation, including systems of arbitrarily placed electrons and nuclei in external electromagnetic fields and interacting electrons in an arbitrary potential, whose configuration space is sampled using numerical optimization techniques, yield intrinsic hyperpolarizabilities less than 0.709 and intrinsic second hyperpolarizabilities less than 0.6. In this work, we show that relaxing the three-level ansatz and allowing an arbitrary number of states to contribute leads to divergence of the optimized intrinsic hyperpolarizability in the limit of an infinite number of states, what we call the many-state catastrophe. This is not surprising given that the divergent systems are most likely not derivable from the Schrödinger equation, yet obey the sum rules. The sums rules are the second ingredient in limit theory and apply also to systems with more general Hamiltonians. These “exotic Hamiltonians” may not model any real systems found in nature. Indeed, a class of transition moments and energies that come form the sum rules do not have a corresponding Hamiltonian that is expressible in differential form. In this work, we show that the three-level ansatz acts as a constraint that excludes many of the nonphysical Hamiltonians and prevents the intrinsic hyperpolarizability from diverging. We argue that this implies that the true fundamental limit is smaller than previously calculated. Since the three-level ansatz does not lead to the largest possible nonlinear response, contrary to its assertion, we propose the intriguing possibility that the three-level ansatz is true for any system that obeys the Schrödinger equation, yet this assertion may be unprovable.

We construct a theory for long-distance quantum communication based on sharing entanglement through a linear chain of $N$ elementary swapping segments of length $L=Nl$ where $l$ is the length of each elementary swap setup. Entanglement swapping is achieved by linear optics, photon counting, and postselection, and we include effects due to multiphoton sources, transmission loss, and detector inefficiencies and dark counts. Specifically we calculate the resultant four-mode state shared by the two parties at the two ends of the chain, and we derive the two-photon coincidence rate expected for this state and thereby the visibility of this long-range-entangled state. The expression is a nested sum with each sum extending from zero to infinite photons, and we solve the case $N=2$ exactly for the ideal case (zero dark counts, unit-efficiency detectors, and no transmission loss) and numerically for $N=2$ in the nonideal case with truncation at $n_{\max }=3$ photons in each mode. For the general case, we show that the computational complexity for the numerical solution is $n_{\max }^{12N}$.

We have investigated magnetically tunable Feshbach resonances arising from the interaction of Li(${}^{2}S$) with metastable Yb(${}^3{P}_2$) and (${}^3{P}_0$). For Yb(${}^3{P}_2$), all the resonance features are strongly suppressed by inelastic collisions that produce Yb in its lower-lying ${}^3{P}_1$ and ${}^3{P}_0$ states. For Yb(${}^3{P}_0$), sharp resonances exist but they are extremely narrow (widths less than 1 mG).

Boson-fermion pair correlations in a mixture are considered at zero temperature in the $T$-matrix approximation. Special attention is paid to the Luttinger theorem. In a strict random-phase approximation variant of the Nozières-Schmitt-Rink approach, it is shown that this theorem is respected also in the homogeneous infinite matter case. We calculate the corresponding occupation numbers of fermions and bosons and the condensate depletion. We also show that in the limit of very small boson density, our results are in good agreement with the results found in the literature for the Fermi polaron in strongly imbalanced Fermi-Fermi mixtures.

By Bernoulli's law, an increase in the relative speed of a fluid around a body is accompanied by a decrease in the pressure. Therefore, a rotating body in a fluid stream experiences a force perpendicular to the motion of the fluid because of the unequal relative speed of the fluid across its surface. It is well known that light has a constant speed irrespective of the relative motion. Does a rotating body immersed in a stream of photons experience a Bernoulli-like force? We show that, indeed, a rotating dielectric cylinder experiences such a lateral force from an electromagnetic wave. In fact, the sign of the lateral force is the same as that of the fluid-mechanical analog as long as the electric susceptibility is positive ($\epsilon >{\epsilon }_0$), but for negative-susceptibility materials (e.g., metals) we show that the lateral force is in the opposite direction. Because these results are derived from a classical electromagnetic scattering problem, Mie-resonance enhancements that occur in other scattering phenomena also enhance the lateral force.