Quantum reflection refers to a nonvanishing reflection probability in the absence of a classically turning point. Much attention has been paid to such reflections due to their fundamental, intriguing physics and potential practical applications. Here we propose a scheme to realize a quantum reflection of nonlocal nonlinear optical beams in a cold Rydberg atomic gas via electromagnetically induced transparency working in a dispersion regime. Based on the long-range interaction between Rydberg atoms, we found that the system supports low-power nonlocal optical solitons. Such nonlocal solitons can display a sharp transition between reflection, trapping, and transmission when scattered by a linear attractive potential, created by gate photons stored in another Rydberg state. Different from conventional physical systems explored up to now, the quantum reflection of the nonlocal optical solitons in the Rydberg atomic gas exhibits interesting anomalous behavior, which can be actively manipulated by tuning the incident velocity and intensity of the probe field, as well as the nonlocality of the Kerr nonlinearity inherent in the Rydberg atomic gas. The results reported here are not only useful for developing Rydberg nonlinear optics but also helpful for characterizing the physical property of the Rydberg gas and for designing novel nonlinear optical devices.

Recent experiments have demonstrated the feasibility of exploiting spectral singularities in open quantum and wave systems, so-called exceptional points, for sensors with strongly enhanced response. Here, we study theoretically the influence of classical parametric noise on the performance of such sensors. Within a Lindblad-type formalism for stochastic Hamiltonians we discuss the resolvability of frequency splittings and the dynamical stability of the sensor, and show that these properties are interrelated. Of central importance are the different features of exceptional points in the spectra of the Hamiltonian and the corresponding Liouvillian. Two realistic examples, a parity-time-symmetric dimer and a whispering-gallery microcavity with asymmetric backscattering, illustrate the findings.

This paper points out the importance of the assumption of locality of physical interactions, and the concomitant necessity of propagation of an entity (in this case, off-shell quanta—virtual gravitons) between two nonrelativistic test masses in unveiling the quantum nature of linearized gravity through a laboratory experiment. At the outset, we will argue that observing the quantum nature of a system is not limited to evidencing $O\left(\hslash \right)$ corrections to a classical theory: it instead hinges upon verifying tasks that a classical system cannot accomplish. We explain the background concepts needed from quantum field theory and quantum information theory to fully appreciate the previously proposed table-top experiments, namely forces arising through the exchange of virtual (off-shell) quanta, as well as local operations and classical communication (LOCC) and entanglement witnesses. We clarify the key assumption inherent in our evidencing experiment, namely the locality of physical interactions, which is a generic feature of interacting systems of quantum fields around us, and naturally incorporate microcausality in the description of our experiment. We also present the types of states the matter field must inhabit, putting the experiment on firm relativistic quantum-field-theoretic grounds. At the end, we use a nonlocal theory of gravity to illustrate how our mechanism may still be used to detect the qualitatively quantum nature of a force when the scale of nonlocality is finite. We find that the scale of nonlocality, including the entanglement entropy production in local and nonlocal gravity, may be revealed from the results of our experiment.

We study the role of driving in a two-level system evolving under the presence of a structured environment in different regimes. We find that adding a periodic modulation to the two-level system can greatly enhance the survival of the geometric phase for many time periods in an intermediate coupling to the environment. In this regime, where there are some non-Markovian features characterizing the dynamics, we note that adding driving to the system leads to a suppression of non-Markovianity altogether, allowing for a smooth dynamical evolution and an enhancement of the robustness condition of the geometric phase. As the model studied herein is the one used to model experimental situations such as hybrid quantum classical systems feasible with current technologies, this knowledge can aid the search for physical setups that best retain quantum properties under dissipative dynamics.

Quantum teleportation is considered a basic primitive in many quantum information processing tasks and has been experimentally confirmed in various photonic and matter-based setups. Here, we consider teleportation of quantum information encoded in modes of a fermionic field. In fermionic systems, superselection rules lead to a more differentiated picture of entanglement and teleportation. In particular, one is forced to distinguish between single-mode entanglement swapping and qubit teleportation with or without authentication via Bell inequality violation, as we discuss here in detail. We focus on systems subject to parity superselection where the particle number is not fixed, and contrast them with systems constrained by particle number superselection which are relevant for possible practical implementations. Finally, we analyze the consequences for the operational interpretation of fermionic mode entanglement and examine the usefulness of so-called mixed maximally entangled states for teleportation.

Quantum algorithm design plays a crucial role in exploiting the computational advantage of quantum devices. Here we develop a deep-reinforcement-learning based approach for quantum adiabatic algorithm design. Our approach is generically applicable to a class of problems with solution hard-to-find but easy-to-verify, e.g., searching and NP-complete problems. We benchmark this approach in Grover-search and 3-SAT problems, and find that the adiabatic algorithm obtained by our RL approach leads to significant improvement in the resultant success probability. In application to Grover search, our RL design automatically produces an adiabatic quantum algorithm that has the quadratic speedup. We find for all our studied cases that quantitatively the RL-designed algorithm has a better performance compared to the analytically constructed nonlinear Hamiltonian path when the encoding Hamiltonian is solvable, and that this RL-design approach remains applicable even when the nonlinear Hamiltonian path is not analytically available. In 3-SAT we find RL design has fascinating transferability—the adiabatic algorithm obtained by training on a specific choice of clause number leads to better performance consistently over the linear algorithm on different clause numbers. These findings suggest the applicability of reinforcement learning for automated quantum adiabatic algorithm design. Further considering the established complexity equivalence of circuit and adiabatic quantum algorithms, we expect the RL-designed adiabatic algorithm to inspire novel circuit algorithms as well. Our approach is potentially applicable to different quantum hardware from trapped ions and optical lattices to superconducting-qubit devices.

We present an efficient approach to optimizing pulse sequences for implementing fast entangling two-qubit gates on trapped ion quantum information processors. We employ a two-phase procedure for optimizing gate fidelity, which we demonstrate for multi-ion systems in linear Paul trap and microtrap architectures. The first phase involves a global optimization over a computationally inexpensive cost function constructed under strong approximations of the gate dynamics. The second phase involves local optimizations that utilize a more precise ordinary differential equation description of the gate dynamics, which captures the nonlinearity of the Coulomb interaction and the effects of finite laser repetition rate. We propose two gate schemes that are compatible with this approach, and we demonstrate that they outperform existing schemes in terms of achievable gate speed and fidelity for feasible laser repetition rates. In optimizing sub-microsecond gates in microtrap architectures, the proposed schemes achieve orders-of-magnitude-higher fidelities than previous proposals. Finally, we investigate the impact of pulse imperfections on gate fidelity and evaluate error bounds for a range of gate speeds.

Qubitization is a modern approach to estimate Hamiltonian eigenvalues without simulating its time evolution. While in this way approximation errors are avoided, its resource and gate requirements are more extensive: qubitization requires additional qubits to store information about the Hamiltonian, and Toffoli gates to probe them throughout the routine. Recently, it was shown that storing the Hamiltonian in a unary representation can alleviate the need for such gates in one of the qubitization subroutines. Building on that principle, we develop an alternative decomposition of the entire algorithm: without Toffoli gates, we can encode the Hamiltonian into qubits within logarithmic depth.

A quantum memory for photonic entanglement is the basic component in quantum networks. Photons entangled in multiple degrees of freedom enable the mutual transformation of Hilbert spaces for the same particle and different particles, thereby connecting heterogeneous nodes in the quantum network. So far, the quantum storage for photonic entanglement is limited to two degrees of freedom. Here, we demonstrate the heralded storage of single-photon hybrid entanglement involving three degrees of freedom (polarization, orbital angular momentum, and path) using a solid-state medium. The fidelity of the output state with the ideal maximum entangled state is $94.0\pm 0.8\%$. The quantum property of the retrieved state is verified by testing the hypothesis of noncontextual hidden-variable theories. These results demonstrate the entanglement interface between light and matter involving multiple degrees of freedom, paving the way for the construction of hybrid quantum networks.

We show that the motion of a cold trapped ion can be squeezed by modulating the intensity of a phase-stable optical lattice placed inside the trap. The method we propose is reversible (unitary) and state selective: it effectively implements a controlled-squeeze gate. This resource could be useful for quantum information processing with continuous variables. We show that the controlled-squeeze gate can prepare coherent superpositions of states which are squeezed along complementary quadratures. Furthermore, we show that these states, which we denote “$\mathcal{X}$ states,” exhibit a high sensitivity to small displacements along two complementary quadratures, which makes them useful for quantum metrology.

Radio-frequency-induced micromotion in trapped ion systems is typically minimized or circumvented to avoid off-resonant couplings for adiabatic processes such as multi-ion gate operations. Nonadiabatic entangling gates (so-called “fast gates”) do not require resolution of specific motional sidebands and are, therefore, not limited to time scales longer than the trapping period. We find that fast gates designed for micromotion-free environments have a significantly reduced fidelity in the presence of micromotion. We show that when fast gates are designed to account for the radio-frequency-induced micromotion, they can, in fact, outperform fast gates in the absence of micromotion. The state-dependent force due to the laser induces energy shifts that are amplified by the state-independent forces producing the micromotion. This enhancement is present for all trapping parameters and is robust to realistic sources of experimental error. This result paves the way for fast two-qubit entangling gates on scalable two-dimensional architectures, where micromotion is necessarily present on at least one interion axis.

Preparing the eigenstate, especially the ground state, of a complex Hamiltonian is of great importance in quantum simulations. Many proposals have been introduced and experimentally realized, among which are quantum variational eigensolver and heat-bath algorithmic cooling, with the former hindered by local minima and the latter lacking of complex system Hamiltonians. Here we introduce a dissipative quantum-classical hybrid scheme, the probabilistic eigensolver. The scheme repeatedly uses an ancilla qubit to acquire information on the system, based on which it postselectively lowers the average energy of the system. The optimal reduction is achieved through classical optimization with a single variational parameter. We describe the implementation of the probabilistic eigensolver with trapped-ion systems and demonstrate the performance by numerically simulating the ground-state preparation of several paradigmatic models, including the Rabi and the Hubbard models. We believe the scheme would enrich the functionalities of universal quantum simulators and be useful as a module for various quantum-computation tasks.

The remarkable progress in the field of laser spectroscopy induced by the invention of the frequency-comb laser has enabled many high-precision tests of fundamental theory and searches for new physics. Extending frequency-comb-based spectroscopy techniques to the vacuum and extreme ultraviolet spectral range would enable frequency measurements of transitions in, e.g., heavier hydrogen-like systems and open up new possibilities for tests of quantum electrodynamics and measurements of fundamental constants. The two main approaches, full-repetition rate up-conversion in a resonator and two-pulse amplification and up-conversion for the Ramsey-comb technique, rely on high-order harmonic generation (HHG), which is known to induce spurious phase shifts from plasma formation. After our initial report [Phys. Rev. Lett. 123, 143001 (2019)], in this article we give a detailed account of how the Ramsey-comb spectroscopy technique is used to probe the dynamics of this plasma with high precision and enables accurate spectroscopy in the vacuum ultraviolet. It is based on recording Ramsey fringes that track the phase evolution of a superposition state in xenon atoms excited by two up-converted frequency-comb laser pulses. In this manner, phase shifts up to 1 rad induced by the HHG process could be observed at nanosecond timescales with mrad-level accuracy at 110 nm. We also show that such phase shifts can be reduced to a negligible level of a few mrad. As a result, we were able to measure the $5p^6\to 5p^{5}8s{}^2{[3/2]}_1$ transition in ${}^{132}\mathrm{Xe}$ at 110 nm (the seventh harmonic of 770 nm) with sub-MHz accuracy, leading to a transition frequency of $2726086012471\left(630\right)\mathrm{kHz}$. This value is ${10}^4$ times more precise than the previous determination and the fractional accuracy of $2.3\times {10}^{-10}$ is 3.6 times better than the previous best spectroscopic measurement using high-order harmonic generation. Additionally, the isotope shifts between ${}^{132}\mathrm{Xe}$ and two other isotopes (${}^{134}\mathrm{Xe}$ and ${}^{136}\mathrm{Xe}$) were determined with an accuracy of 420 kHz. The method can be readily extended to achieve kHz-level accuracy by increasing the pulse delay, e.g., to measure the $1S-2S$ transition in ${\mathrm{He}}^{+}$. Therefore, the Ramsey-comb method shows great promise for high-precision spectroscopy of targets requiring vacuum ultraviolet and extreme ultraviolet wavelengths.

We compute the Rydberg spectrum of a single ${\mathrm{Ca}}^{+}$ ion in a Paul trap by incorporating various internal and external coupling terms of the ion to the trap in the Hamiltonian. The coupling terms include spin-orbit coupling in ${\mathrm{Ca}}^{+}$, charge (electron and ionic core) coupling to the radio frequency and static fields, ion-electron coupling in the Paul trap, and ion center-of-mass coupling. The electronic Rydberg states are precisely described by a one-electron model potential for $e^{-}+{\mathrm{Ca}}^{2+}$, and accurate eigenenergies, quantum defect parameters, and static and tensor polarizabilities for a number of excited Rydberg states are obtained. The time-periodic rf Hamiltonian is expanded in the Floquet basis, and the trapping-field-broadened Rydberg lines are compared with recent observations of ${\mathrm{Ca}}^{+}\left(23P\right)$ and ${\mathrm{Ca}}^{+}\left(52F\right)$ Rydberg lines.

We study the dynamics of a Bose-Einstein condensate in the quasiperiodic kicked rotor described by a Gross-Pitaevskii equation confined in a toroidal trap. As the interactions are increased, Bogoliubov excitations appear and deplete the condensate; we characterize this instability by considering the population of the first Bogoliubov mode, and we show that it does not prevent, for small enough interaction strengths, the observation of the quasi–insulator-to-metal transition that replaces the Anderson transition of the noninteracting case. However, the predicted subdiffusion in momentum space is not observed in the stable region within experimentally accessible times. For higher interaction strengths, the condensate may be strongly depleted before this dynamical regimes set in.

Large clouds of cold atoms prepared in a magneto-optical trap can develop spatiotemporal instabilities when the frequency of the trapping lasers is brought close to the atomic resonance. This system bears close similarities with trapped plasmas, whereby effective Coulomb interactions are induced by the exchange of scattered photons and lead to collective nonlinear dynamics of the trapped atoms. We report in this paper a detailed experimental study of the instability threshold, and comparisons with three-dimensional simulations of the interacting, laser-driven cloud.

We study the effect of interactions on the conversion of atomic-to-molecular Bose-Einstein condensates via stimulated Raman adiabatic passage. Both energetic instability during avoided crossings and dynamical instability during chaotic intervals limit adiabaticity and impose low sweep-rate boundaries on the efficiency of the process. For the diabatic traverse of avoided crossings, we find a reciprocal power-law dependence of the final unconverted population on sweep rate. For the traverse of chaos, we find a sharp low-rate boundary determined by the dynamical instability parameters. The interplay of these two mechanisms determines which instability controls the failure of molecular production. A judicious choice of sweep parameters is hence required to restore the process efficiency.

A nonlinear medium with nonreciprocal propagation of electromagnetic field pulses is proposed and studied. The medium consists of a long waveguide surrounded by two-level media implanted in a straight spiral. Respective Maxwell-Bloch system describing evolution of the pulses in the waveguide with nonlinear feedback is derived. The influence of the neighbors' dipole fields taken into account in the tight bounding approximation manifests itself in the appearance of the nonlinear differential terms. Under the condition of unidirectional propagation of field pulses, the Maxwell-Bloch system of equations is reduced to an integrable system. Analysis of obtained exact solutions have shown that these differential terms are responsible for the nonreciprocity of the propagation of field pulses in the waveguide. Using the soliton solution as an example, it is shown that the spiral arrangement of atoms yields critical dependence of the evolution of field pulses on the direction of their propagation or on the chirality of the medium.

We achieve interface states with a high reflectance in photonic heterostructures composed of two kinds of all-dielectric one-dimensional photonic crystals (1DPCs) with symmetric unit cells. The reflectance of interface states can be controlled flexibly by tuning the mismatch degree between the imaginary phases of the two kinds of 1DPCs. Assisted by the interface state with a high reflectance as well as a high-$Q$ factor, the Goos-Hänchen (GH) shift can be greatly enhanced to larger than three orders of wavelengths. Our work provides a route, completely under the current experimental conditions, to design high-performance sensitive sensors, wavelength division demultiplexers, and polarization beam splitters based on this giant GH shift together with a high reflectance.