We theoretically demonstrate nontrivial topological effects for a probe field in a Raman medium undergoing molecular modulation processes. The medium is driven by two noncollinear pump beams. We show that the angle between the pumps is related to an effective gauge potential and an effective magnetic field for the probe field in the synthetic space consisting of a synthetic frequency dimension and a spatial dimension. As a result of such an effective magnetic field, the probe field can exhibit a topologically protected one-way edge state in the synthetic space, as well as Landau levels which manifest as suppression of both diffraction and sideband generation. Our work identifies a previously unexplored route towards creating topological photonics effects and highlights an important connection between topological photonics and nonlinear optics.

Many methods now exist to prepare free electrons into orbital-angular-momentum states, and the predicted applications of these electron states as probes of materials and scattering processes are numerous. The development of electron orbital-angular-momentum measurement techniques has lagged behind. We show that coupling between electron orbital angular momentum and a spatially varying magnetic field produces an angular-momentum-dependent focusing effect. We propose a design for an orbital-angular-momentum measurement device built on this principle. As the method of measurement is noninterferometric, the device works equally well for mixed, superposed, and pure final orbital-angular-momentum states. The energy and orbital-angular-momentum distributions of inelastically scattered electrons may be simultaneously measurable with this technique.

‘‘Condensation” in Fermi-Dirac statistics [D. S. Kothari and B. Nath, Nature 151, 420 (1943)], which appears as a natural consequence of Born's reciprocity principle [M. Born, Proc. R. Soc. London A 165, 291 (1938); M. Born, Nature 141, 328 (1938)], is examined from a theoretical perspective. Since fermions obey the Pauli exclusion principle, it is conceptually different from Bose-Einstein condensation, which permits macroscopic occupation of bosons at the single-particle level below a critical temperature. Yet, in accordance with the Cahill and Glauber [Phys. Rev. A 59, 1538 (1999)] formulation for fermionic fields, and in close kinship to bosonic fields, we have shown that in analogy to Bose-Einstein condensation, it is possible to associate an intrinsic notion of symmetry breaking and the thermodynamic “order parameter” to characterize the foregoing hitherto unexplored phenomenon in an ideal Fermi-Dirac gas as condensation-like coherence within fermions.

We present the theory of time-dependent point transformations to find independent dynamical normal modes for two-dimensional systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent modes can indeed be defined is identified, and a geometrical analogy is put forward. The results explain and unify recent work to design fast operations on trapped ions, needed to implement a scalable quantum-information architecture: Transport, expansions, and the separation of two ions, two-ion phase gates, as well as the rotation of an anisotropic trap for an ion, are treated and shown to be analogous to a mechanical system of two masses connected by springs with time-dependent stiffness.

We develop a systematic coarse-graining procedure for systems of $N$ qubits. We exploit the underlying geometrical structures of the associated discrete phase space to produce a coarse-grained version with reduced effective size. Our coarse-grained spaces inherit key properties of the original ones. In particular, our procedure naturally yields a subset of the original measurement operators, which can be used to construct a coarse discrete Wigner function. These operators also constitute a systematic choice of incomplete measurements for the tomographer wishing to probe an intractably large system.

Einstein-Podolsky-Rosen (EPR) steering describes the ability to steer remotely quantum states of an entangled pair by measuring locally one of its particles. Here we report on an experimental demonstration of single-system steering. The application to quantum communication is also investigated. Single-system steering refers to steering of a single $d$-dimensional quantum system that can be used in a unifying picture to certify the reliability of tasks employed in both quantum communication and quantum computation. In our experiment, high-dimensional quantum states are implemented by encoding polarization and orbital angular momentum of photons with dimensionality of up to 12.

The ${\mathrm{HfF}}^{+}$ cation is a very promising system to use in the search for the electron electric dipole moment (EDM), and a corresponding experiment is carried out by JILA group [H. Loh, K. C. Cossel, M. C. Grau, K.-K. Ni, E. R. Meyer, J. L. Bohn, J. Ye, and E. A. Cornell, Science 342, 1220 (2013); K.-K. Ni, H. Loh, M. Grau, K. C. Cossel, J. Ye, and E. A. Cornell, J. Mol. Spectrosc. 300, 12 (2014). Here we theoretically investigate the cation to search for another effect which violates time-reversal ($T$) and spatial parity ($P$) symmetries—the nuclear magnetic quadrupole moment (MQM) interaction with electrons. We report an accurate ab initio relativistic electronic structure calculations of the molecular parameter $W_M=0.494 \frac{{10}^{33}\mathrm{Hz}}{e{\mathrm{cm}}^2}$ that is required to interpret the experimental data in terms of the MQM of the Hf nucleus. For this we have implemented and applied the combined Dirac-Coulomb(-Gaunt) and relativistic effective core potential approaches to treat electron correlation effects from all of the electrons and to take into account high-order correlation effects using the coupled cluster method with single, double, triple and noniterative quadruple cluster amplitudes. We discuss interpretation of the MQM effect in terms of the strength constants of $T,P$-odd nuclear forces, proton and neutron EDMs, the QCD parameter $\theta$, and quark chromo-EDMs.

We observe interspecies Feshbach resonances due to $s$-wave bound states in ultracold ${}^{39}\mathrm{K}-{}^{133}\mathrm{Cs}$ scattering for three different spin mixtures. The resonances are observed as joint atom loss and heating of the K sample. We perform least-squares fits to obtain improved K-Cs interaction potentials that reproduce the observed resonances, and carry out coupled-channel calculations to characterize the scattering and bound-state properties for ${}^{39}\mathrm{K}$-Cs, ${}^{40}\mathrm{K}$-Cs, and ${}^{41}\mathrm{K}$-Cs. Our results open up the possibilities of tuning interactions in K-Cs atomic mixtures and of producing ultracold KCs molecules.

We show that the Josephson plasma frequency for a condensate in a double-well potential, whose dynamics is described by the Gross-Pitaevskii (GP) equation, can be obtained with great precision by means of the usual Bogoliubov approach, whereas the two-mode model—commonly constructed by means of a linear combination of the low-lying states of the GP equation—generally provides accurate results only for weak interactions. A proper two-mode model in terms of the Bogoliubov functions is also discussed, revealing that in general a two-mode approach is formally justified only for not too large interactions, even in the limit of very small amplitude oscillations. Here we consider specifically the case of a one-dimensional system, but the results are expected to be valid in arbitrary dimensions.

We perform an ab initio study of the ultimate capabilities and limits of applicability of the method for few-cycle pulse formation via the resonant interaction of extreme ultraviolet (XUV) radiation with atoms dressed by a moderately strong infrared (IR) laser field proposed in two earlier works [Y. V. Radeonychev et al., Phys. Rev. Lett. 105, 183902 (2010) and V. A. Polovinkin et al., Opt. Lett. 36, 2296 (2011)]. Taking into account all the multiphoton processes in the systems under consideration on the basis of numerical solution of the three-dimensional time-dependent Schrödinger equation (TDSE) in the single-active-electron approximation, we show the possibilities to produce 1.1-fs pulses from 124.6-nm XUV radiation via the linear Stark effect in atomic hydrogen, as well as 500-as pulses from 58.4-nm XUV radiation via excited-state ionization in helium. We derive a generalized analytical solution, which takes into account the interplay between sub-laser-cycle Stark effect and excited-state ionization and allows us to analyze the results of TDSE calculations. We found that the ultimate intensity of the IR field suitable for few-cycle pulse formation via the linear Stark effect or excited-state ionization is limited by the threshold for atomic ionization from the resonant excited state or the ground state, respectively. We show that the pulses with shorter duration can be produced in the medium of ions with higher values of the ionization potential.

The gravity gradient is one of the most serious systematic effects in atomic tests of the equivalence principle (EP). While differential acceleration measurements performed with different atomic species under free fall test the validity of the EP, minute displacements between the test masses in a gravity gradient produce a false EP-violating signal that limits the precision of the test. We show that gravity inversion and modulation using a gimbal mount can suppress the systematics due to gravity gradients caused by both moving and stationary parts of the instrument as well as the environment, strongly reducing the need to overlap two species.

A linear response theory for open quantum systems is formulated by means of the time-local and time-nonlocal quantum master equations, where a relevant quantum system interacts with a thermal reservoir as well as with an external classical field. A linear response function that characterizes how a relaxation process deviates from its intrinsic process by a weak external field is obtained by extracting the linear terms with respect to the external field from the quantum master equation. It consists of four parts. One represents the linear response of a quantum system when system-reservoir correlation at an initial time and correlation between reservoir states at different times are neglected. The others are correction terms due to these effects. The linear response function is compared with the Kubo formula in the usual linear response theory. To investigate the properties of the linear response of an open quantum system, an exactly solvable model for a stochastic dephasing of a two-level system is examined. Furthermore, the method for deriving the linear response function is applied for calculating two-time correlation functions of open quantum systems. It is shown that the quantum regression theorem is not valid for open quantum systems unless their reduced time evolution is Markovian.

We consider quantum phase-space dynamics using Wigner's representation of quantum mechanics. We stress the usefulness of the integral form for the description of Wigner's phase-space current $\mathit{J}$ as an alternative to the popular Moyal bracket. The integral form brings out the symmetries between momentum and position representations of quantum mechanics, is numerically stable, and allows us to perform some calculations using elementary integrals instead of Groenewold star products. Our central result is an explicit, elementary proof which shows that only systems up to quadratic in their potential fulfill Liouville's theorem of volume preservation in quantum mechanics. Contrary to a recent suggestion, our proof shows that the non-Liouvillian character of quantum phase-space dynamics cannot be transformed away.

By applying a Foldy-Wouthuysen-like transformation and a low-momentum approximation to the usual quantum field theoretical Dirac Hamiltonian in one spatial dimension, we introduce a Hamiltonian for which the kinetic portion and the original potential are diagonal in the corresponding spinor space and a second potential occurs that is off diagonal. This two-potential Hamiltonian is applied to study the electron-positron pair creation process from the vacuum. Here the diagonal potential provides only the energy degeneracy of the lower and upper manifold of continuum states, which is one requirement for the permanent creation of particles. The off-diagonal potential actually triggers the creation process by providing the necessary coupling between the degenerate states. It also provides a concrete example of a model system for pair creation where the creation rate is perturbative in the coupling strength.

Individual addressing of qubits is essential for scalable quantum computation. Spatial addressing allows unlimited numbers of qubits to share the same frequency, while enabling arbitrary parallel operations. We demonstrate addressing of long-lived ${}^{43}\mathrm{Ca}^{+}$ “atomic clock” qubits held in separate zones ($960\mu \text{m}$ apart) of a microfabricated surface trap with integrated microwave electrodes. Such zones could form part of a “quantum charge-coupled device” architecture for a large-scale quantum information processor. By coherently canceling the microwave field in one zone we measure a ratio of Rabi frequencies between addressed and nonaddressed qubits of up to 1400, from which we calculate a spin-flip probability on the qubit transition of the nonaddressed ion of $1.3\times {10}^{-6}$. Off-resonant excitation then becomes the dominant error process, at around $5\times {10}^{-3}$. It can be prevented either by working at higher magnetic field, or by polarization control of the microwave field. We implement polarization control with error $2\times {10}^{-5}$, which would suffice to suppress off-resonant excitation to the $\sim {10}^{-9}$ level if combined with spatial addressing. Such polarization control could also enable fast microwave operations.

Memory-assisted measurement-device-independent quantum key distribution (MA-MDI-QKD) has recently been proposed as a possible intermediate step towards the realization of quantum repeaters. Despite its relaxing some of the requirements on quantum memories, the choice of memory in relation to the layout of the setup and the protocol has a stark effect on our ability to beat existing no-memory systems. Here, we investigate the suitability of nitrogen vacancy (NV) centers, as quantum memories, in MA-MDI-QKD. We particularly show that moderate cavity enhancement is required for NV centers if we want to outperform no-memory QKD systems. Using system parameters mostly achievable by today's state of the art, we then anticipate some total key rate advantage in the distance range between 300 and 500 km for cavity-enhanced NV centers. Our analysis accounts for major sources of error including the dark current, the channel loss, and the decoherence of the quantum memories.

To generate a NOON state with a large photon number $N$, the number of operational steps could be large and the fidelity will decrease rapidly with $N$. Here we propose a method to generate a type of quantum entangled states, $\left(\right|NN00\rangle +|00NN\rangle )/\sqrt{2}$, called “double NOON” states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the “double” NOON state creation needs only $N+2$ operational steps. One application of double NOON states is to get a phase error of $1/\left(2N\right)$ in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $\left(\right|2N,0\rangle +|0,2N\rangle )/\sqrt{2}$ is needed, which requires at least $2N$ operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\le 10$ even for imperfect devices is feasible with the present circuit QED technique.

The degree of thermalization of electronically excited state manifolds of an absorber can be tested via optical spectroscopy. In the thermalized-manifold case, the ratio of absorption and emission is expected to follow a universal Boltzmann-type frequency scaling, known as the Kennard-Stepanov relation. Here, we investigate absorption and emission spectral profiles of rubidium, cesium, and potassium molecular dimers in a high-pressure argon buffer-gas environment and study the effect of collisionally induced redistribution. We find that, despite the use of nonlinear excitation techniques, the ratio of absorption and emission well follows the Kennard-Stepanov scaling for a variety of molecular transitions. We conclude that the upper electronic state rovibrational manifold of the molecular gas is well in thermodynamic equilibrium. Further, we demonstrate an accurate, calibration-free determination of the gas temperature from the measured spectroscopic data.

We have measured the spontaneous neutral particle emission from copper-cluster anions (${\mathrm{Cu}}_n{}^{-}, n=3–6$) stored at cryogenic temperatures in one of the electrostatic ion storage rings of the Double ElectroStatic Ion Ring ExpEriment facility at Stockholm University. The measured rate of emission from the stored ${\mathrm{Cu}}_3{}^{-}$ ions follows a single power-law decay for about 1 ms but then decreases much more rapidly with time. The latter behavior may be due to a decrease in the density of available final states in ${\mathrm{Cu}}_3$ as the excitation energies of the decaying ions approach the electron detachment threshold. The emissions from ${\mathrm{Cu}}_4{}^{-}, {\mathrm{Cu}}_5{}^{-}$, and ${\mathrm{Cu}}_6{}^{-}$ are well described by sums of two power laws that are quenched by radiative cooling of the stored ions with characteristic times between a few and hundreds of milliseconds. We relate these two-component behaviors to populations of stored ions with higher and lower angular momenta. In a separate experiment, we studied the laser-induced decay of ${\mathrm{Cu}}_6{}^{-}$ ions that were excited by 1.13- or 1.45-eV photons after 46 ms of storage.

A method for efficiently trapping nanoparticles using a dielectrophoresis (DEP)-assisted plasmonic trap is presented. The proposed method overcomes the range limitations of a conventional plasmonic trap by employing a long-range DEP force to draw a nanoparticle closer to the plasmonic trap. To create the plasmonic trap, a $\mathsf{C}$-shaped engraving is used as it can trap a nanoparticle in a very small volume near the surface. A nanopillar is selected as the electrode to generated the DEP force as its height allows the force to extend further away from the surface. Extensive numerical simulations are performed to evaluate the performance improvement of the proposed scheme over conventional plasmonic trapping methods. The simulations show that the proposed scheme increases the probability of a successful trapping event by a factor of approximately three.