The way a principle system and its environment interact characterizes the non-Markovianity of the dynamics. Herein, we investigate the non-Markovian dynamics of photon polarization in a birefringent crystal. We consider the so-called “quantity of quantum-mechanical process” first defined by Hsieh et al. [Sci. Rep. 7, 13588 (2017)]. The non-Markovianity of the photon dynamics is evaluated by examining the quantity of quantum-mechanical process varying with time, and the difference between the quantity of quantum-mechanical process in a complete dynamics and that in a process composed of two subprocesses. We show that all of the processes identified as Markovian in the seminal study of Liu et al. [Nat. Phys. 7, 931 (2011)] can actually be identified as non-Markovian. The presented method enables us to classify non-Markovianity in the dynamical processes that are classified as Markovian by existing verification criteria. Overall, the results confirm the feasibility of performing the experimental characterization of photon dynamics using an all-optical setup and provide a useful insight into enhancing the accuracy and control of quantum system designs for quantum engineering applications.

Filtering of weak pulses through a medium with infinite periodic structure in the absorption and/or transmission spectrum is analyzed. Two types of filters are considered. The first, named harmonic frequency crystal (HFC), is the filter whose periodic structure is harmonic and described by the sine or cosine function of frequency with the fundamental period. The second, named anharmonic frequency crystal (AHFC), also has a periodic structure with one fundamental period but it is described by the function containing many harmonics of the fundamental period. AHFC demonstrates properties quite similar to those of a high-finesse atomic frequency comb (AFC) with a limited number of absorption peaks separated by transparency windows. Filtering of the pulse through AHFC produces a prompt pulse accompanied by a few delayed pulses. Time spacing $T$ of the delayed pulses is inversely proportional to the comb period. On the contrary, HFC transforms the input pulse into a train of many delayed pulses, generated at times $nT$, where $n$ is an integer. Maximum amplitudes of the delayed pulses follow a wide bell-shaped envelope. Both HFC and AHFC are extensions of AFC, which was proposed to implement quantum memory protocols for single photons. In this paper, it is proposed to create time-bin qubits with the help of a short pulse filtering through HFC. HFC is also proposed to implement tomography of these quantum states. Another promising application of HFC is the optical detection of ultrasound in biological tissues for ultrasound-modulated optical tomography. Since HFC allows one to generate pulses with longer delay with respect to the excitation pulse, one could obtain higher discrimination between weak acoustically generated sidebands and the carrier.

We propose a scheme for the quantum simulation of sub-Ohmic spin-boson models by color centers in free-standing hexagonal boron nitride (hBN) membranes. The electronic spin of a color center that couples to the membrane vibrational spectrum constitutes the physical model. The spin-motion coupling is provided by an external magnetic field gradient. In this Rapid Communication, we show that a class of spectral densities can be attained by engineering geometry and boundary conditions of the hBN resonator. We then put our focus on two extreme cases, i.e., $1/f$- and white-noise spectral densities. Spin coherence and polarization dynamics are studied. Our calculations show coherence revivals at periods set by the bath characteristic frequency signaling the non-Markovian nature of the baths. The nonequilibrium dynamics of the spin polarization exhibits a coherent localization, a property peculiar to the quantum phase transition in extremely sub-Ohmic spin-boson models. Our scheme may find application in understanding the sources of decoherence in solid-state quantum bits.

Quantum states are the ultimate criterion to produce sequences of random numbers. Spatially spread entangled states allow the generation of correlated random sequences in remote locations. The impossibility of observing a quantum state, without disturbing it, ensures that the messages encoded using these sequences cannot be eavesdropped upon. This is the basis of quantum key distribution. It is then of crucial importance knowing whether the sequences generated in the practice by spatially spread entangled states are truly random, or not. Yet, that knowledge is not immediate. One of the obstacles is the very definition of randomness. “Statistical” randomness is related with the frequency of occurrence of strings of data. “Algorithmic” randomness is related with compressibility of the sequence, which is given by Kolmogorov complexity. Sequences generated by entangled pairs of photons are analyzed, focusing on estimations of their complexity. Standard tests of statistical randomness are also applied.

Novel perspectives of controlling molecular systems have recently arisen from the possibility of generating attosecond pulses in the ultraviolet regime and tailoring electron dynamics in its natural time scale. The cornerstone mechanism is the so-called charge migration, he production of a coherent charge transfer with subfemtosecond oscillations across a molecule. Typically, charge migration is induced by the ionization of valence molecular orbitals. However, recent technological developments allow the generation of attosecond pulses in the x-ray regime. In this case, the absorption of photons creates core-hole states. In light elements, core-hole states mainly decay by Auger processes that, driven by electron correlations, involve valence orbitals. We theoretically demonstrate in a fluoroacetylene molecule a double-hole charge migration triggered by attosecond core-electron photoionization, followed by Auger electron relaxations. This opens a new route for inducing with x rays charge transfer processes in the subfemtosecond time scale.

An atom interferometer is a ubiquitous tool for measuring fundamental constants and inertial sensing. While it has been extremely useful in measuring inertial rotations, the fine-structure constant, gravity gradients, and local gravity, the measurement process lacks the ability to probe continuously due to its single-shot nature. In this work, we experimentally demonstrate the diffraction of an atom laser in the Raman-Nath regime, a key step towards the development of an atom-laser-based interferometer. The diffraction orders can be precisely controlled, and momenta up to $\pm 18\hslash k$ can be imparted to the atom laser. We form the “atom laser” by outcoupling a quasicontinuous beam of coherent atoms from a reservoir of ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate lasting up to 400 ms. This atom laser then interacts with a grating formed by a standing wave of far-detuned laser light. By controlling the interaction time, the strength of diffraction into various orders can be controlled. Such diffraction would allow for the construction of an atom-interferometer to probe changes in physical environments continuously up to a few hundred milliseconds.

We consider the practical feasibility of using the direct, electric dipole-dipole interaction between cotrapped molecular ions for robust quantum logic without the need for static polarizing fields. The use of oscillating dipole moments, as opposed to static electric dipoles, dynamically decouples the dipoles from laboratory fields, including the electric fields of the trap itself. Further, this implementation does not require the quantum control of motion, potentially removing a major roadblock to ion trap quantum computing scalability. Since the polarizing field is electromagnetic radiation, even pairs of states with splittings in the THz regime can be fully polarized.

We study $\mathrm{SU}\left(N\right)$ fermions in the limit of infinite on-site repulsion between all species. We focus on states in which every pair of consecutive fermions carries a different spin flavor. Since the particle order cannot be changed (because of the infinite on-site repulsion) and contiguous fermions have a different spin flavor, we refer to the corresponding constrained model as the model of distinguishable quantum particles. We introduce an exact numerical method to calculate equilibrium one-body correlations of distinguishable quantum particles based on a mapping onto noninteracting spinless fermions. In contrast to most many-body systems in one dimension, which usually exhibit either power-law or exponential decay of off-diagonal one-body correlations with distance, distinguishable quantum particles exhibit a Gaussian decay of one-body correlations in the ground state, while finite-temperature correlations are well described by stretched exponential decay.

In a no-signaling world, the outputs of a nonlocal box cannot be completely predetermined, a feature that is exploited in many quantum information protocols exploiting nonlocality, such as device-independent randomness generation and quantum key distribution. This relation between nonlocality and randomness can be formally quantified through the min-entropy, a measure of the unpredictability of the outputs that holds conditioned on the knowledge of any adversary that is limited only by the no-signaling principle. This quantity can easily be computed for the noisy Popescu-Rohrlich (PR) box, the paradigmatic example of nonlocality. In this paper, we consider the min-entropy associated to several copies of noisy PR boxes. In the case where $n$ noisy PR boxes are implemented using $n$ noncommunicating pairs of devices, it is known that each PR box behaves as an independent biased coin: the min-entropy per PR box is constant with the number of copies. We show that this does not hold in more general scenarios where several noisy PR boxes are implemented from a single pair of devices, either used sequentially $n$ times or producing $n$ outcome bits in a single run. In this case, the min-entropy per PR box is smaller than the min-entropy of a single PR box, and it decreases as the number of copies increases.

Variations of phase-matching measurement-device-independent quantum key distribution (PM-MDI QKD) protocols have been investigated before, but it was recently discovered that this type of protocol (under the name of twin-field QKD) can beat the linear scaling of the repeaterless bound on secret key capacity. We propose a variation of PM-MDI QKD protocol, which reduces the sifting cost and uses non-phase-randomized coherent states as test states. We provide a security proof in the infinite key limit. Our proof is conceptually simple and gives tight key rates. We obtain an analytical key rate formula for the loss-only scenario, confirming the square root scaling and also showing the loss limit. We simulate the key rate for realistic imperfections and show that PM-MDI QKD can overcome the repeaterless bound with currently available technology.

In this paper, we investigate the indistinguishability of generalized Bell states (GBSs) by one-way local operations and classical communication (LOCC). We first introduce two sets, i.e., the difference set and the testing set, and show that the GBSs cannot always be distinguished by one-way LOCC if the testing set is a subset of the difference set of GBSs. Then we give a unified upper bound about indistinguishable GBSs by one-way LOCC. The newly derived bound is smaller than those presented in Zhang et al. [Phys. Rev. A 91, 012329 (2015)] and Wang et al. [Quantum Inf. Process. 15, 1661 (2016).]. More precisely, the minimum number of one-way locally indistinguishable GBSs is not more than $2\lceil \sqrt{d}\rceil +\lceil \frac{\sqrt{d}}{4}\rceil +1$.

The recent discovery of fully homomorphic classical encryption schemes has had a dramatic effect on the direction of modern cryptography. Such schemes, however, implicitly rely on the assumption that solving certain computation problems is intractable. Here we present a quantum encryption scheme which is homomorphic for arbitrary classical and quantum circuits which have at most some constant number of non-Clifford gates. Unlike classical schemes, the security of the scheme we present is information theoretic and hence independent of the computational power of an adversary.

We study several magneto-optical trapping configurations in ${}^{87}\mathrm{Rb}$. These unconventional MOTs all use type-II transitions, where the angular momentum of the ground state is greater than or equal to that of the excited state. Some use red-detuned light, and others blue-detuned light. The properties of these MOTs are strongly influenced by the balance between opposing Doppler and Sisyphus forces, and vary widely from one configuration to another. In the blue-detuned MOT, Sisyphus cooling dominates over Doppler heating for all relevant speeds and magnetic fields. We measure the capture velocity of this MOT as a function of intensity and detuning, finding a maximum of $3.8\pm 0.1$ m/s. Atomic densities are particularly high in the blue-detuned MOT, and its lifetime is limited by collisions between the trapped atoms. We present measurements of the loss rate due to these ultracold collisions as a function of laser intensity and detuning. In the red-detuned MOTs, Sisyphus heating dominates at low speeds and Doppler cooling at higher speeds. Consequently, temperatures in the red-detuned MOTs are up to a thousand times higher than in the blue-detuned MOTs. One MOT forms large ring structures, with no density at the center, showing how atoms driven towards a non-zero equilibrium speed remain trapped by orbiting around the center. Another MOT demonstrates that magnetic mixing of the excited-state hyperfine levels can be an important mechanism in type-II MOTs.

We present a scheme to improve the memory quality of linear and nonlinear optical pulse pairs via four-wave mixing (FWM) in an atomic gas. We show that in a linear regime the efficiency and fidelity of the memory of the probe and Stokes pulses can be largely improved through an elimination of the fast-light mode (and hence the suppression of the optical gain induced by the FWM process). We also show that in a nonlinear regime the system may support stable optical soliton pairs with ultraslow propagation velocity and ultralow generation power, which can also be stored and retrieved with a better quality. The improved optical pulse pair memory suggested here may have promising applications in optical information processing and transformation.

The advent of complex, structured, and high-dimensional entangled states brings both new possibilities for experimental and theoretical scenarios and new challenges for the generation and characterization of such states. In particular, spatially structured photonic states offer applications in quantum imaging, information processing, and quantum key distribution. Here we experimentally generate a spatially entangled high-dimensional state composed of at least 10 Schmidt modes in a quantum memory setup and perform characterization using the entropic Einstein-Podolsky-Rosen (EPR)-steering inequality, yielding a genuine violation of $1.06\pm 0.15$ bits. The entanglement of formation of at least $0.70\pm 0.15$ ebit for the measured noisy state is certified using the entropic witness method. We point out and solve the difficulties in estimating the entropy, achieving characterization of the high-dimensional entangled state with highly undersampled data. Finally, the practical supremacy of the entropic EPR-steering witness over a variance-based witness is demonstrated for a wide class of states typical in an experimental scenario, giving prospects for EPR-steering demonstrations and applications in noisy systems or with lossy quantum channels.

In a recent work [Phys. Rev. Lett. 116, 240401 (2016)], a framework known by the name of assemblage moment matrices (AMMs) has been introduced for the device-independent quantification of quantum steerability and measurement incompatibility. In other words, even with no assumption made on the preparation device nor the measurement devices, one can make use of this framework to certify, directly from the observed data, the aforementioned quantum features. Here, we further explore the framework of AMM and provide improved device-independent bounds on the generalized robustness of entanglement, the incompatibility robustness, and the incompatibility weight. We compare the tightness of our device-independent bounds against those obtained from other approaches. Along the way, we also provide an analytic form for the generalized robustness of entanglement for an arbitrary two-qudit isotropic state. When considering a Bell-type experiment in a tripartite or more-partite scenario, we further show that the framework of AMM provides a natural way to characterize a superset to the set of quantum correlations, namely, one which also allows post-quantum steering.

The open driven quantum harmonic oscillator is studied for three different possible mechanisms of driving; a generalization of the forced oscillator, driving due to a time-dependent coupling to a two-level system, and driving due to an adiabatic modulation of the frequency. The first case encompasses all possible configurations going from the standard forced harmonic oscillator to the classical pumping type of driving typically used in quantum optics. In the second case, an additional two-level system, coupled to the oscillator at a time-varying rate, is assumed and the reduced dynamics of the oscillator and the qubit is examined. In the driving due to adiabatic modulation, the dynamics of a harmonic oscillator whose frequency slowly varies in time is studied. The study done in this paper is focused on a harmonic type of driving, although the solutions are derived for an arbitrary type of driving. In all the cases, the oscillator is assumed to be in contact with a zero- or finite-temperature environment, which provides dissipation to the system. The treatment done in this paper is fully analytic and the derivation of the solutions is based on the employment of the double Fourier transform of the Wigner function.

We study a generalized coupling system between a superconducting qubit and two nanomechanical resonators. When the eigenfrequency of the superconducting qubit is twice the frequency of the resonators, we show that one qubit is able to excite simultaneously two resonators. Moreover, tripartite and bipartite macroscopic entangled states are generated, respectively. We give conditions under which general tripartite and bipartite entangled nonorthogonal states become maximally entangled states. Under a large detuning condition, the coupling between two resonators is induced by a superconducting qubit. This coupling strength can be enhanced via a squeezing transformation.

We calculate the spectrum and allowed $E1$ transitions of the superheavy element Og ($Z=118$). A combination of configuration interaction and perturbation theory is used [Dzuba et al., Phys. Rev. A 95, 012503 (2017)]. The spectrum of lighter analog Rn i is also calculated and compared to experiment with good agreement.