In two recent papers [Blum and Lohmann, Phys. Rev. Lett. 116, 033201 (2016); Lohmann et al., Phys. Rev. A 94, 032331 (2016)], the possibility of continuously varying the degree of entanglement between an elastically scattered electron and the valence electron of an alkali-metal target was discussed. To estimate how well such a scheme may work in practice, we present results for elastic electron scattering from lithium in the energy regime of $1–5\mathrm{eV}$ and the full range of scattering angles $0^{\circ }–{180}^{\circ }$. The most promising regime for Bell correlations in this particular collision system are energies between about 1.5 and 3.0 eV, in an angular range around ${110}^{\circ }\pm {10}^{\circ }$. In addition to the relative exchange asymmetry parameter, we present the differential cross section that is important when estimating the count rate and hence the feasibility of experiments using this system.

We present a concept for a multistage Zeeman decelerator that is optimized particularly for applications in molecular beam scattering experiments. The decelerator consists of a series of alternating hexapoles and solenoids, that effectively decouple the transverse focusing and longitudinal deceleration properties of the decelerator. It can be operated in a deceleration and acceleration mode, as well as in a hybrid mode that makes it possible to guide a particle beam through the decelerator at constant speed. The deceleration features phase stability, with a relatively large six-dimensional phase-space acceptance. The separated focusing and deceleration elements result in an unequal partitioning of this acceptance between the longitudinal and transverse directions. This is ideal in scattering experiments, which typically benefit from a large longitudinal acceptance combined with narrow transverse distributions. We demonstrate the successful experimental implementation of this concept using a Zeeman decelerator consisting of an array of 25 hexapoles and 24 solenoids. The performance of the decelerator in acceleration, deceleration, and guiding modes is characterized using beams of metastable helium (${}^{3}S$) atoms. Up to 60% of the kinetic energy was removed for He atoms that have an initial velocity of 520 m/s. The hexapoles consist of permanent magnets, whereas the solenoids are produced from a single hollow copper capillary through which cooling liquid is passed. The solenoid design allows for excellent thermal properties and enables the use of readily available and cheap electronics components to pulse high currents through the solenoids. The Zeeman decelerator demonstrated here is mechanically easy to build, can be operated with cost-effective electronics, and can run at repetition rates up to 10 Hz.

We theoretically study high-order-harmonic generation (HHG) from solids driven by intense laser pulses using a one-dimensional model periodic crystal. By numerically solving the time-dependent Schrödinger equation directly on a real-space grid, we successfully reproduce experimentally observed unique features of solid-state HHG such as the linear cutoff-energy scaling and the sudden transition from a single- to multiple-plateau structure. Based on the simulation results, we propose a simple model that incorporates vector-potential-induced intraband displacement, interband tunneling, and recombination with the valence-band hole. One key parameter is the peak-to-valley amplitude of the pulse vector potential, which determines the crystal momentum displacement during the half cycle. When the maximum peak-to-valley amplitude $A_{\mathrm{peak}}$ reaches the half width $\frac{\pi }{a}$ of the Brillouin zone with $a$ being the lattice constant, the HHG spectrum exhibits a transition from a single- to multiple-plateau structure, and even further plateaus appear at $A_{\mathrm{peak}}=\frac{2\pi }{a},\frac{3\pi }{a},\cdots$. The multiple cutoff positions are given as functions of $A_{\mathrm{peak}}$ and the second maximum $A_{\mathrm{peak}}^{\prime }$, in terms of the energy difference between different bands. Using our recipe, one can draw electron trajectories in the momentum space, from which one can deduce, for example, the time-frequency structure of HHG without elaborate quantum-mechanical calculations. Finally, we reveal that the cutoff positions depend on not only the intensity and wavelength of the pulse, but also its duration, in marked contrast to the gas-phase case. Our model can be viewed as a solid-state and momentum-space counterpart of the familiar three-step model, highly successful for gas-phase HHG, and provide a unified basis to understand HHG from solid-state materials and gaseous media.

We study the single-particle dispersion of a spin-orbit-coupled (SOC) Bose-Einstein condensate (BEC) under the periodical modulation of the Raman coupling. This modulation introduces a further coupling of the SOC dressed eigenlevels, thus creating a second generation of modulation-dressed eigenlevels. Theoretical calculations show that these modulation-dressed eigenlevels feature a pair of avoided crossings and a richer spin-momentum locking, which we observe using BEC transport measurements. Furthermore, we use the pair of avoided crossings to engineer a tunable Stueckelberg interferometer that gives interference fringes in the spin polarization of BECs.

We introduce shaken lattice interferometry with atoms trapped in a one-dimensional optical lattice. By phase modulating (shaking) the lattice, we control the momentum state of the atoms. Through a sequence of shaking functions, the atoms undergo an interferometer sequence of splitting, propagation, reflection, reverse propagation, and recombination. Each shaking function in the sequence is optimized with a genetic algorithm to achieve the desired momentum state transitions. As with conventional atom interferometers, the sensitivity of the shaken lattice interferometer increases with interrogation time. The shaken lattice interferometer may also be optimized to sense signals of interest while rejecting others, such as the measurement of an ac inertial signal in the presence of an unwanted dc signal.

We theoretically present an economical and convenient way to study ground-state properties of a strongly interacting superfluid Fermi gas. Our strategy is that complicated strong-coupling calculations are used only to evaluate quantum fluctuation corrections to the chemical potential $\mu$. Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated $\mu$ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of $\mu$ in a superfluid ${}^6\mathrm{Li}$ Fermi gas, we show that an extended $T$-matrix approximation (ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where our results indicate that many-body corrections are dominated by superfluid fluctuations. Since precise determinations of physical quantities are not always easy in cold Fermi gas physics, our approach would greatly reduce experimental and theoretical efforts toward the understanding of ground-state properties of this strongly interacting Fermi system.

We propose and analyze an experimental scheme using the quantum kicked rotor to observe the newly predicted coherent forward-scattering peak together with its long-known twin brother, the coherent backscattering peak. Contrary to coherent backscattering, which arises already under weak-localization conditions, coherent forward scattering is only triggered by Anderson or strong localization. So far, coherent forward scattering has not been observed in conservative systems with elastic scattering by spatial disorder. We propose to turn to the quantum kicked rotor, which has a long and successful history as an accurate experimental platform to observe dynamical localization, i.e., Anderson localization in momentum space. We analyze the coherent forward-scattering effect for the quantum kicked rotor by extensive numerical simulations, both in the orthogonal and unitary class of disordered quantum systems, and show that an experimental realization involving phase-space rotation techniques is within reach of state-of-the-art cold-atom experiments.

A rigorous description of volume and surface spontaneous parametric down-conversion in one-dimensional nonlinear layered structures is developed considering exact continuity relations for the fields' amplitudes at the boundaries. The nonlinear process is described by the quantum momentum operator that provides the Heisenberg equations whose solution is continuous at the boundaries. The transfer-matrix formalism is applied. The volume and surface contributions are clearly identified. Numerical analysis of a structure composed of 20 alternating GaN/AlN layers is given as an example.

A century after its conception, quantum mechanics still hold surprises that contradict many “common sense” notions. The contradiction is especially sharp in case one consider trajectories of truly quantum objects such as single photons. From a classical point of view, trajectories are well defined for particles, but not for waves. The wave-particle duality forces a breakdown of this dichotomy and quantum mechanics resolves this in a remarkable way: Trajectories can be well defined, but they are utterly different from classical trajectories. Here, we give an operational definition to the trajectory of a single photon by introducing a technique to mark its path using its spectral composition. The method demonstrates that the frequency degree of freedom can be used as a bona fide quantum measurement device (meter). The analysis of a number of setups, using our operational definition, leads to anomalous trajectories which are noncontinuous and in some cases do not even connect the source of the photon to where it is detected. We carried out an experimental demonstration of these anomalous trajectories using a nested interferometer. We show that the two-state vector formalism provides a simple explanation for the results.

During recent developments in quantum theory it has been clarified that observable quantities (such as energy and position) may be represented by operators $\mathrm{\Lambda }$ (with real spectra) that are manifestly non-Hermitian in a preselected friendly Hilbert space ${\mathcal{H}}^{\left(F\right)}$. The consistency of these models is known to require an upgrade of the inner product, i.e., mathematically speaking, a transition ${\mathcal{H}}^{\left(F\right)}\to {\mathcal{H}}^{\left(S\right)}$ to another, standard, Hilbert space. We prove that whenever we are given more than one candidate for an observable (i.e., say, two operators ${\mathrm{\Lambda }}_0$ and ${\mathrm{\Lambda }}_1$) in advance, such an upgrade need not exist in general.

The existence of Greenberger-Horne-Zeilinger (GHZ) contradictions in many-qutrit systems was a long-standing theoretical question until its (affirmative) resolution in 2013. To enable experimental tests, we derive Mermin inequalities from concurrent observable sets identified in those proofs. These employ a weighted sum of observables, called $\mathcal{M}$, in which every term has the chosen GHZ state as an eigenstate with eigenvalue unity. The quantum prediction for $\mathcal{M}$ is then just the number of concurrent observables, and this grows asymptotically as $2^N/3$ as the number of qutrits $N\to \infty$. The maximum classical value falls short for every $N\ge 3$, so that the quantum to classical ratio (starting at 1.5 when $N=3$) diverges exponentially ($\sim 1.{064}^N$) as $N\to \infty$, where the system is in a Schrödinger-cat-like superposition of three macroscopically distinct states.

We study local-realistic inequalities, Bell-type inequalities, for bipartite pure states of finite dimensional quantum systems—qudits. There are a number of proposed Bell-type inequalities for such systems. Our interest is in relating the value of the Bell-type inequality function with a measure of entanglement. Interestingly, we find that one of these inequalities, the Son-Lee-Kim inequality, can be used to measure entanglement of a pure bipartite qudit state and a class of mixed two-qudit states. Unlike the majority of earlier schemes in this direction, where the number of observables needed to characterize the entanglement increases with the dimension of the subsystems, this method needs only four observables. We also discuss the experimental feasibility of this scheme. It turns out that current experimental setups can be used to measure the entanglement using our scheme.

Oblivious transfer (OT) is an important tool in cryptography. It serves as a subroutine to other complex procedures of both theoretical and practical significance. A common attribute of OT protocols is that one party (Alice) has to send a message to another party (Bob) and has to stay oblivious to whether Bob did receive the message. Specific (OT) protocols vary by exact definition of the task—in the all-or-nothing protocol, Alice sends a single bit-string message, which Bob is able to read with only $50\%$ probability, whereas in a 1-out-of-2 OT protocol Bob reads one out of two messages sent by Alice. These two flavors of protocol are known to be equivalent. Recently, a computationally secure all-or-nothing OT protocol based on quantum states was developed by A. Souto et al. [Phys. Rev. A 91, 042306 (2015)], which, however, cannot be reduced to a 1-out-of-2 OT protocol by standard means. Here we present an elaborate reduction of this protocol that retains the security of the original.

Optimization of the fidelity of control operations is of critical importance in the pursuit of fault-tolerant quantum computation. We apply optimal control techniques to demonstrate that a single drive via the cavity in circuit quantum electrodynamics can implement a high-fidelity two-qubit all-microwave gate that directly entangles the qubits via the mutual qubit-cavity couplings. This is performed by driving at one of the qubits' frequencies which generates a conditional two-qubit gate, but will also generate other spurious interactions. These optimal control techniques are used to find pulse shapes that can perform this two-qubit gate with high fidelity, robust against errors in the system parameters. The simulations were all performed using experimentally relevant parameters and constraints.

We propose several concatenated quantum relay continuous-variable quantum key distribution schemes based on the parametric amplifier (PA) and the beam splitter (BS). Instead of using only one BS in the traditional relay scheme, the proposed schemes provide two operations that involve both PA and BS, activating the beam splitting and recombining operations in turn. These schemes would benefit the system performance improvement by providing signal amplification and establishing quantum correlations. We show that the different effects of the relay schemes will cause different system performances because of the varied signal-to-noise ratio (SNR) of output fields. The system's secret key rate will be increased when equipping with the PA-BS relay scheme, because the output fields of the PA are entangled with the correlated quantum noises while input fields of the BS are superimposed, subsequently leading to the quantum noise reduction of the total output fields of relay station, while the reversed BS-PA relay scheme has little advantage over the traditional counterpart that contains only one BS in relay data postprocessing because it will not cause any SNR improvement. Moreover, the reinforced PA-PA relay scheme results in a slight improvement due to the increased SNR. These quantum relay schemes can be performed through the beam splitting, the recombining operations, and the relay data postprocessing, such that it would be suitable for secret information exchange in complex networks with intermediate stations.

Atomic properties of Cd-like ${\mathrm{W}}^{26+}$, In-like ${\mathrm{W}}^{25+}$, and Sn-like ${\mathrm{W}}^{24+}$ ions are evaluated by using a relativistic $\text{CI}+\text{all}$-order approach that combines configuration-interaction and the coupled-cluster methods. The energies, transition rates, and lifetimes of low-lying levels are calculated and compared with available theoretical and experimental values. The magnetic-dipole transition rates are calculated to determine the branching ratios and lifetimes for the $4f^3$ states in ${\mathrm{W}}^{25+}$ and for the $4f^4$ states in ${\mathrm{W}}^{24+}$ ions. Excellent agreement of the $\text{CI}+\text{all}$-order values provided a benchmark test of this method for the $4f^n$ configurations validating the recommended values of tungsten ion properties calculated in this work.

In this paper, a quantum Stern-Gerlach thought experiment is introduced where, in addition to the intrinsic angular momentum of an atom, the magnetic field is considered to be a quantum mechanical field. A free falling spin polarized Bose-Einstein condensate passes close to a flux qubit and interacts with the quantum superimposed magnetic field of the flux qubit. Such an interaction results a macroscopic quantum entanglement of the path of a Bose-Einstein condensate with the magnetic flux quantum state of the flux qubit. In this paper, three regimes of coupling between the flux qubit and a free falling Bose-Einstein condensate are discussed. This paper also explains how to produce a path entangled Bose-Einstein condensate where the condensate can be located at physically distinct locations simultaneously. This paper highlights new insights about the foundations of the quantum Stern-Gerlach experiment.

We discuss the effect of dissipation on heating which occurs in periodically driven quantum many-body systems. We especially focus on a periodically driven Bose-Hubbard model coupled to an energy and particle reservoir. Without dissipation, this model is known to undergo parametric instabilities which can be considered as an initial stage of heating. By taking the weak on-site interaction limit as well as the weak system-reservoir coupling limit, we find that parametric instabilities are suppressed if the dissipation is stronger than the on-site interaction strength and stable steady states appear. Our results demonstrate that periodically driven systems can emit energy, which is absorbed from external drivings, to the reservoir so that they can avoid heating.

Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly interacting bosons in one dimension in the Tonks-Girardeau regime of infinitely strong repulsive interactions. Using the Fredholm determinant approach and the Bose-Fermi mapping, we show how the problem can be reduced to a single-particle basis, wherein the finite-temperature effects enter the solution via an effective “dressing” of the single-particle wave functions by the Fermi-Dirac occupation factors. We demonstrate the utility of our approach and its computational efficiency in two nontrivial out-of-equilibrium scenarios: collective breathing-mode oscillations in a harmonic trap and collisional dynamics in the Newton's cradle setting involving real-time evolution in a periodic Bragg potential.

We present the design of a tunable two-dimensional photonic crystal that exhibits multiple topological phases, including a conventional insulator phase, a quantum spin Hall phase, and a quantum anomalous Hall phase under different combinations of geometric parameters and external magnetic fields. Our photonic crystal enables a platform to study the topology evolution attributed to the interplay between crystalline symmetry and time-reversal symmetry. A four-band tight-binding model unambiguously reveals that the topological property is associated with the pseudospin orientations and that it is characterized by the spin Chern number. The emerging quantum anomalous Hall phase features a single helical edge state that is locked by a specific pseudospin. Simulation results demonstrate that the propagation of such a single helical edge state is robust against magnetic impurities. Potential applications, such as spin splitters, are described.