We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ a coherent state of light in a linear combination of optical modes, linear-optics transformations, and measurements with single-photon threshold detectors. This provides a general framework for transforming protocols in quantum communication into a form in which they can be implemented with current technology. We explore the similarity between properties of the original qubit protocols and the coherent-state protocols obtained from the mapping and make use of the mapping to construct additional protocols in the context of quantum communication complexity and quantum digital signatures. Our results have the potential of bringing a wide class of quantum communication protocols closer to their experimental demonstration.

We derive the ground-state energy for a small number of ultracold atoms in an isotropic harmonic trap using effective quantum field theory (EFT). Atoms are assumed to interact through pairwise energy-independent and energy-dependent delta-function potentials with strengths proportional to the scattering length $a$ and effective range volume $V$, respectively. The calculations are performed systematically up to the order of $l^{-4}$, where $l$ denotes the harmonic-oscillator length. The effective three-body interaction contains a logarithmic divergence in the cutoff energy, giving rise to a nonuniversal three-body interaction in the EFT. Our EFT results are confirmed by nonperturbative numerical calculations for a Hamiltonian with finite-range two-body Gaussian interactions. For this model Hamiltonian, we explicitly calculate the nonuniversal effective three-body contribution to the energy.

The electron loss to the continuum has been studied for the collision system ${\mathrm{U}}^{88+}+{\mathrm{N}}_2\to {\mathrm{U}}^{89+}+{\left[{\mathrm{N}}_2\right]}^{*}+e^{-}$ at the low-relativistic projectile energy of 90 MeV/u. Using a magnetic electron spectrometer, the energy distribution of cusp electrons emitted at an angle of $0^{\circ }$ with respect to the projectile beam was measured in coincidence with the up-charged projectile. At the experimental collision energy ionization of the berylliumlike ${\mathrm{U}}^{88+}$ projectile proceeds predominantly from the $L$ shell, but a contribution from the $K$ shell could also be identified experimentally. The measurement is shown to be in accordance with fully relativistic Dirac calculations applying first-order perturbation theory. Furthermore, the underlying continuum electron distribution in the projectile frame is illustrated.

Superconducting atom chips and Rydberg atoms are promising tools for quantum information processing operations based on the dipole blockade effect. Nevertheless, one has to face the severe problem of stray electric fields in the vicinity of the chip. We demonstrate a simple method circumventing this problem. Microwave spectroscopy reveals extremely long coherence lifetimes (in the millisecond range) for a qubit stored in a Rydberg level superposition close to the chip surface. This is an essential step for the development of quantum simulations with Rydberg atoms and of a hybrid quantum information architecture based on atomic ensembles and superconducting circuits.

A theoretical model of the influence of detection-bandwidth properties on observed line shapes in laser absorption spectroscopy is described. The model predicts artificial frequency shifts, extra broadenings, and line asymmetries that must be taken into account in order to obtain accurate central frequencies and other spectroscopic parameters. This reveals sources of systematic effects most probably underestimated, so far potentially affecting spectroscopic measurements. This may impact many fields of research, from atmospheric and interstellar physics to precision spectroscopic measurements devoted to metrological applications, tests of quantum electrodynamics, or other fundamental laws of nature. Our theoretical model is validated by linear absorption experiments performed on ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{NH}}_3$ molecular lines recorded by precision laser spectroscopy in two distinct spectral regions, near- and midinfrared. Possible means of recovering original line-shape parameters or experimental conditions under which the detection bandwidth has a negligible impact, given a targeted accuracy, are proposed. Particular emphasis is put on the detection-bandwidth adjustments required to use such high-quality molecular spectra for a spectroscopic determination of the Boltzmann constant at the 1 ppm level of accuracy.

We propose a scheme for the detection of quantum phase transitions in the one-dimensional (1D) Bose-Hubbard (BH) and 1D Extended Bose-Hubbard (EBH) models, using the nondemolition measurement technique of quantum polarization spectroscopy. We use collective measurements of the effective total angular momentum of a particular spatial mode to characterize the Mott insulator to superfluid phase transition in the BH model and the transition to a density wave state in the EBH model. We extend the application of collective measurements to the ground states at various deformations of a superlattice potential.

We present an alternative theoretical model for a recent experiment [A. Fleischer et al., Nature Photon. 8, 543 (2014)] which used bichromatic, counter-rotating high-intensity laser pulses to probe the conservation of spin angular momentum in high-order-harmonic generation. We separate elliptical polarizations into independent circular fields with definite angular momentum, instead of using the expectation value of spin for each photon in the conservation equation, and we find good agreement with the experimental results. In our description the generation of each individual harmonic conserves spin angular momentum, in contrast to the model proposed by Fleischer et al. Our model also correctly describes analogous processes in standard perturbative optics.

We propose a stroboscopic method to dynamically decouple the effects of two-body atom-atom interactions for ultracold bosonic atoms, and realize a system dominated by elastic three-body interactions. Using this method, we show that it is possible to achieve the optimal scaling behavior predicted for interaction-based quantum metrology with three-body interactions. Specifically, we show that for ultracold bosons quenched in an optical lattice, we can measure the three-body interaction strength with a precision proportional to ${\overline{n}}^{-5/2}$ using homodyne quadrature interferometry, and ${\overline{n}}^{-7/4}$ using conventional collapse-and-revival techniques, where $\overline{n}$ is the mean number of atoms per lattice site. Both precision scalings surpass the nonlinear scaling of ${\overline{n}}^{-3/2}$, which was previously proposed and achieved with a physical system. Our method of achieving a decoupled three-body interacting system may also have applications in the creation of exotic three-body states and phases.

Quantum properties of correlations have a key role in disparate fields of physics including quantum information processing, quantum foundations, and strongly correlated systems. We tackle a specific aspect of the fundamental quantum marginal problem: We address the issue of deducing the global properties of correlations of tripartite quantum states based on the knowledge of their bipartite reductions, focusing on relating specific properties of bipartite correlations to global correlation properties. We prove that strictly classical bipartite correlations may still require global entanglement and that unentangled (albeit not strictly classical) reductions may require global genuine multipartite entanglement rather than simple entanglement. On the other hand, for three qubits, the strict classicality of the bipartite reductions rules out the need for genuine multipartite entanglement. Our work sheds light on the relation between local and global properties of quantum states and on the interplay between classical and quantum properties of correlations.

The observation of features, often referred to as “Wigner cusps” in a scattering cross section at the opening of a new scattering channel has been widely reported in electron scattering, and has been attributed to strong coupling between the two scattering channels. Recently a series of cusps were observed in positron scattering from the noble gases [A. C. L. Jones et al., Phys. Rev. Lett. 105, 073201 (2010)]. In this case, the strong opening of the positronium formation cross section resulted in a cusplike feature, or bump, in the total elastic scattering cross section. The positronium formation channel is typically the largest partial scattering cross section in the region of the electronic excitation and ionization thresholds in most atoms and molecules, and it is plausible that similar features may exist in other atomic and molecular species. We have undertaken measurements of the isoelectronic targets of helium—${\mathrm{H}}_2$, and neon—${\mathrm{H}}_2\mathrm{O}$, ${\mathrm{NH}}_3$, and ${\mathrm{CH}}_4$, in an effort to better understand the mechanisms leading to these threshold features.

We analyze some crucial questions regarding the practical feasibility of quantum simulation for lattice gauge models. Our analysis focuses on two models suitable for the quantum simulation of the Schwinger Hamiltonian, or QED in $1+1$ dimensions, which we investigate numerically using tensor networks. In particular, we explore the effect of representing the gauge degrees of freedom with finite-dimensional systems and show that the results converge rapidly; thus even with small dimensions it is possible to obtain a reasonable accuracy. We also discuss the time scales required for the adiabatic preparation of the interacting vacuum state and observe that for a suitable ramping of the interaction the required time is almost insensitive to the system size and the dimension of the physical systems. Finally, we address the possible presence of noninvariant terms in the Hamiltonian that is realized in the experiment and show that for low levels of noise it is still possible to achieve a good precision for some ground-state observables, even if the gauge symmetry is not exact in the implemented model.

Because the state vectors of isolated systems can be changed in entangled states by processes in other isolated systems, keeping only the density matrix fixed, it is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying only on density matrices. The density matrix is defined here by the formula giving the mean values of physical quantities, which implies the same properties as the usual definition in terms of state vectors and their probabilities. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semigroup. Here, new transformation properties are studied for general symmetry transformations forming groups, not just semigroups. Arguments that such symmetries should act on the density matrix as in ordinary quantum mechanics are presented, but all of these arguments are found to be inconclusive.

We present a theory for the emission of fermion pairs from a superfluid Fermi gas induced by photon absorption. In solid-state physics, this type of process is called double photoemission (DPE). The spectrum of the induced two-particle current (or DPE current) provides direct insight into the correlation of condensate fermion pairs. A general formalism for two-particle current induced by DPE is developed by treating the coupling of two Fermi gases with the time-dependent perturbation theory. This formalism is used to calculate the energy distributions of the DPE current from a superfluid Fermi gas in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BCS-BEC) crossover at $T=0$. We show that the DPE current has distinct contributions of the condensed pair components and uncorrelated pair states. The angular dependence of DPE current in the BCS-BEC crossover is also calculated. The DPE current of tightly bound molecules in the BEC region is determined to be quite different from that of the weakly bound Cooper pairs.

Controlled-phase (cphase) gates can be realized with trapped neutral atoms by making use of the Rydberg blockade. Achieving the ultrahigh fidelities required for quantum computation with such Rydberg gates, however, is compromised by experimental inaccuracies in pulse amplitudes and timings, as well as by stray fields that cause fluctuations of the Rydberg levels. We report here a comparative study of analytic and numerical pulse sequences for the Rydberg cphase gate that specifically examines the robustness of the gate fidelity with respect to such experimental perturbations. Analytical pulse sequences of both simultaneous and stimulated Raman adiabatic passage (STIRAP) are found to be at best moderately robust under these perturbations. In contrast, optimal control theory is seen to allow generation of numerical pulses that are inherently robust within a predefined tolerance window. The resulting numerical pulse shapes display simple modulation patterns and can be rationalized in terms of an interference between distinct two-photon Rydberg excitation pathways. Pulses of such low complexity should be experimentally feasible, allowing gate fidelities of order 99.90–99.99% to be achievable under realistic experimental conditions.

We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the two-dimensional surface code with a noiseless syndrome extraction. First, we show how to implement MLD exactly in time $O\left(n^2\right)$, where $n$ is the number of code qubits. Our implementation uses a reduction from MLD to simulation of matchgate quantum circuits. This reduction however requires a special noise model with independent bit-flip and phase-flip errors. Secondly, we show how to implement MLD approximately for more general noise models using matrix product states (MPS). Our implementation has running time $O\left(n{\chi }^3\right)$, where $\chi$ is a parameter that controls the approximation precision. The key step of our algorithm, borrowed from the density matrix renormalization-group method, is a subroutine for contracting a tensor network on the two-dimensional grid. The subroutine uses MPS with a bond dimension $\chi$ to approximate the sequence of tensors arising in the course of contraction. We benchmark the MPS-based decoder against the standard minimum weight matching decoder observing a significant reduction of the logical error probability for $\chi \ge 4$.

We describe a method to observe the dynamics of an excited-state transition in a room-temperature atomic vapor using hyperfine quantum beats. Our experiment using cesium atoms consists of a pulsed excitation of the $D{}_2$ transition and continuous-wave driving of an excited-state transition from the $6P{}_{3/2}$ state to the $7S{}_{1/2}$ state. We observe quantum beats in the fluorescence from the $6P{}_{3/2}$ state which are modified by the driving of the excited-state transition. The Fourier spectrum of the beat signal yields evidence of Autler-Townes splitting of the $6P{}_{3/2}$, $F=5$ hyperfine level and Rabi oscillations on the excited-state transition. A detailed model provides qualitative agreement with the data, giving insight to the physical processes involved.

For the hydrogenlike ${\mathrm{Ar}}^{17+}$ ion, the $1s$ Lamb shift was absolutely determined with a $1.4\%$ accuracy based on Lyman-$\alpha$ wavelength measurements that have negligible uncertainties from nuclear size effects. The result agrees with state-of-the-art quantum electrodynamics (QED) calculations, and demonstrates the suitability of Lyman-$\alpha$ transitions in highly charged ions as x-ray energy standards, accurate at the five parts-per-million level. For the heliumlike ${\mathrm{Ar}}^{16+}$ ion the transition energy for the $1s2p{}^1{P}_1\to 1s^2{}^1{S}_0$ line was also absolutely determined on an even higher level of accuracy. Additionally, we present relative measurements of transitions in ${\mathrm{S}}^{15+},{\mathrm{S}}^{14+}$, and ${\mathrm{Fe}}^{24+}$ ions. The data for the heliumlike ${\mathrm{S}}^{14+},{\mathrm{Ar}}^{16+}$, and ${\mathrm{Fe}}^{24+}$ ions stringently confirm advanced bound-state QED predictions including screened QED terms that had recently been contested.

We propose a method for the emulation of artificial spin-orbit coupling in a system of ultracold, neutral atoms trapped in a tight-binding lattice. This scheme does not involve near-resonant laser fields, avoiding the heating processes connected to the spontaneous emission of photons. In our case, the necessary spin-dependent tunnel matrix elements are generated by a rapid, spin-dependent, periodic force, which can be described in the framework of an effective, time-averaged Hamiltonian. An additional radio-frequency coupling between the spin states leads to a mixing of the spin bands.

In ongoing experiments ultracold molecules are first created in a weakly bound level of their electronic ground-state manifold, requiring further manipulation with optical fields to transfer them in their absolute ground state. We performed a detailed theoretical analysis of the spectroscopic properties of potassium rubidium diatomic to determine efficient routes for this purpose via stimulated Raman adiabatic passage. We used state-of-the-art molecular potentials, spin-orbit coupling and transition dipole moment to perform our calculations. The dependence of spin-orbit couplings with internuclear distance are of crucial importance as the relevant transitions mainly occur in the chemical bond domain. Two main mechanisms involving a different pair of excited electronic states are modeled and compared for the various isotopologues ${}^{39}\mathrm{K}{}^{85}\mathrm{Rb}$, ${}^{39}\mathrm{K}{}^{87}\mathrm{Rb}$, ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$, and ${}^{41}\mathrm{K}{}^{87}\mathrm{Rb}$, starting from the uppermost levels of their lowest triplet state $a^3{\Sigma }^{+}$ towards the lowest vibrational level of their ground state $X^1{\Sigma }^{+}$. The present model confirms the experimental findings. In addition, it predicts a transfer scheme which involves more efficient transitions.

We present quantum observable Markov decision processes (QOMDPs), the quantum analogs of partially observable Markov decision processes (POMDPs). In a QOMDP, an agent is acting in a world where the state is represented as a quantum state and the agent can choose a superoperator to apply. This is similar to the POMDP belief state, which is a probability distribution over world states and evolves via a stochastic matrix. We show that the existence of a policy of at least a certain value has the same complexity for QOMDPs and POMDPs in the polynomial and infinite horizon cases. However, we also prove that the existence of a policy that can reach a goal state is decidable for goal POMDPs and undecidable for goal QOMDPs.