We investigate the fundamental breathing mode of a small-sized elongated Bose-Einstein condensate coupled to a large Fermi sea, which consists of fully spin-polarized atoms in the collisionless regime. Our observations show a dramatic shift of the breathing frequency when the mixture undergoes phase separation at strong interspecies repulsion. We find that the maximum frequency shift in the full phase-separation limit depends essentially on the atom number ratio of the components. We interpret the experimental observations by modeling the complex dynamics of the collisionless fermions within two complementary approaches. One model assumes an adiabatic response of the Fermi sea, while the other one considers single fermion trajectories for a fully phase-separated mixture. Our models capture the observed features over the full range of interest.

We examine the emergence of objectivity via quantum Darwinism through the use of a collision model, i.e., where the dynamics is modeled through sequences of unitary interactions between the system and the individual constituents of the environment, termed “ancillas.” By exploiting versatility of this framework, we show that one can transition from a “Darwinistic” to an “encoding” environment by simply tuning their interaction. Furthermore, we establish that in order for a setting to exhibit quantum Darwinism we require a mutual decoherence to occur between the system and environmental ancillas, thus showing that system decoherence alone is not sufficient. Finally, we demonstrate that the observation of quantum Darwinism is sensitive to a nonuniform system-environment interaction.

Quantum coherence has received significant attention in recent years, but the structure of multipartite coherent states is unclear. In this paper, we generalize important results in multipartite entanglement theory to their counterparts in quantum coherence theory. First, we give a necessary and sufficient condition for when two pure multipartite states are equivalent under local incoherent operations assisted by classical communications (LICC), i.e., two states can be deterministically transformed to each other under LICC operations. Next, we investigate and give the conditions in which such a transformation succeeds only stochastically. Different from the entanglement case for two-qubit states, we find that the stochastic LICC (sLICC) equivalence classes are infinite. Moreover, it is possible that there are some classes of states in multipartite entanglement that can convert into each other, whereas they cannot convert into each other in multipartite coherence. In order to show the difference among sLICC classes, we introduce two coherence monotones: accessible coherence and source coherence, following the logistics given in [Phys. Rev. Lett. 115, 150502 (2015)]. These coherence monotones have a straightforward operational interpretation, namely, the accessible coherence characterizes the proficiency of a state to generate other states via quantum incoherent operations, whereas the source coherence characterizes the set of states that can be reached via quantum incoherent operations acting on the given state of interest.

The quantum Boltzmann machine extends the classical Boltzmann machine learning to the quantum regime, which makes its power to simulate the quantum states beyond the classical probability distributions. We apply the Broyden-Fletcher-Goldfarb-Shanno algorithm to study the corresponding optimization problem in quantum Boltzmann machine especially focus on the target states being a family of states with parameters. As a typical example, we study the target states being the real symmetric two-qubit pure states, and we find two obvious features shown in the numerical results on the minimal quantum relative entropy: First, the minimal quantum relative entropy in the first and the third quadrants is zero; Second, the minimal quantum relative entropy is symmetric with the axes $y=x$ and $y=-x$ even with one qubit hidden layer. Then, we theoretically prove these two features from the geometric viewpoint and the symmetry analysis. Our studies show that the traditional physical tools can be used to help us to understand some interesting results from quantum Boltzmann machine learning.

The core concept of quantum simulation is the mapping of an inaccessible quantum system onto a controllable one by identifying analogous dynamics. We map the Dirac equation of relativistic quantum mechanics in $3+1$ dimensions onto a multilevel superconducting Josephson circuit. Resonant drives determine the particle mass and momentum, and the quantum state represents the internal spinor dynamics which are cast in the language of multilevel quantum optics. Zitterbewegung and wave-packet dynamics are reproduced. The degeneracy of the Dirac spectrum corresponds to a degeneracy of bright and dark states within the system, and particle spin and helicity are employed to interpret the multilevel dynamics. We also simulate the Schwinger mechanism of electron-positron pair production by introducing an analogous electric field as a doubly degenerate Landau-Zener problem. All proposed measurements can be performed well within typical decoherence times. This work opens an avenue for experimental study of the Dirac equation and provides a tool for control of complex dynamics in multilevel systems.

The measurement-device-independent quantum key distribution (MDI-QKD) protocol is immune to imperfect measurement devices. However, its practicality and performance when implemented in continuous-variable (CV) mode are still not satisfactory. We propose a CV-MDI-QKD protocol based on modulated squeezed states, and analyze its security against two-mode Gaussian attack. The results show that the protocol can achieve a higher secret key rate and transmission distance than previous coherent-state and squeezed-state protocols. A method to compensate the imperfection of a practical homodyne detector using phase-sensitive optical amplifiers is also presented. By setting an appropriate optical amplification gain, realistic detectors with ordinary quantum efficiency can be employed. In addition, we discuss the impact of finite-size effects on the secret key rate of the protocol. The methods presented may aid in the practical application of the CV-MDI-QKD protocol.

We investigate the particle-number dependence of some features of the out-of-equilibrium dynamics of $d$-dimensional Fermi gases in the dilute regime. We consider protocols entailing the variation of the external potential which confines the particles within a limited spatial region, in particular, sudden changes of the trap size. To characterize the dynamic behavior of the Fermi gas, we consider various global quantities such as the ground-state fidelity for different trap sizes, the quantum work statistics associated with the protocol considered, and the Loschmidt echo measuring the overlap of the out-of-equilibrium quantum states with the initial ground state. Their asymptotic particle-number dependencies show power laws for noninteracting Fermi gases. We also discuss the effects of short-ranged interactions to the power laws of the average work and its square fluctuations, within the $d$-dimensional Hubbard model and its continuum limit, arguing that they do not generally change the particle-number power laws of the free Fermi gases.

Motivated by a recent experiment [L. Chomaz et al., Nat. Phys. 14, 442 (2018)], we perform numerical simulations of a dipolar Bose-Einstein condensate (BEC) in a tubular, periodic confinement at $T=0$ within density functional theory, where the beyond-mean-field correction to the ground-state energy is included in the local density approximation. We study the excitation spectrum of the system by solving the corresponding Bogoliubov–de Gennes equations. The calculated spectrum shows a roton minimum, and the roton gap decreases by reducing the effective scattering length. As the roton gap disappears, the system spontaneously develops a periodic linear structure formed by denser clusters of atomic dipoles immersed in a dilute superfluid background. This structure shows the hallmarks of a supersolid system, i.e., (i) a finite nonclassical translational inertia along the tube axis and (ii) the appearance of two gapless modes, i.e., a phonon mode associated with density fluctuations and resulting from the translational discrete symmetry of the system, and a Nambu-Goldstone gapless mode corresponding to phase fluctuations, resulting from the spontaneous breaking of the gauge symmetry. A further decrease in the scattering length eventually leads to the formation of a periodic linear array of self-bound droplets.

The question of whether two indistinguishable particles are bosons or fermions can be answered by observing the Hong-Ou-Mandel effect on a beam splitter. However, already for three particles one can consider symmetries that are neither bosonic nor fermionic. In this work, we propose a notion of a genuine multipartite indistinguishability and describe a simple method of quantifying it experimentally.

The stopping cross section for protons passing through hydrogen is calculated for the energy range between 10 keV and 3 MeV. Both the positive and neutral charge states of the projectile are accounted for. The two-center convergent close-coupling method is used to model proton collisions with hydrogen. In this approach, electron-capture channels are explicitly included by expanding the scattering wave function in a basis of both target and projectile pseudostates. Hydrogen collisions with hydrogen are modeled using two methods: the single-center convergent close-coupling approach is used for the calculation of one-electron processes, while two-electron processes are calculated using the Born approximation. The aforementioned approaches are also applied to the calculation of the charge-state fractions. These are then used to combine the proton-hydrogen and hydrogen-hydrogen stopping cross sections to yield the total stopping cross section for protons passing through hydrogen.

The coupling between microwave fields and atoms (or atomlike systems) is inherently weaker than for optical fields, making microwave signal manipulation for applications like quantum information processing technically challenging. In order to better understand this coupling and to develop tools for measuring it, we explore the microwave coupling to atoms using the “atomic candle” technique, and push it beyond the bounds of the small-signal regime in order to deliver a larger signal. In familiar two-level systems, responses beyond the usual Rabi oscillations can arise when a single-tone drive is phase modulated, causing the steady-state populations to oscillate at integer harmonics of the modulation frequency. Resonant behavior of the first two harmonics for frequencies near the Rabi frequency, known as $\alpha$ and $\beta$ Rabi resonances, is widely used for microwave-field magnetometry and as a power standard known as the atomic candle. Here, we explore Rabi resonances beyond the small-signal approximation and report upon experimental observations of higher-order-harmonic population response for microwave hyperfine transitions in cold ${}^{87}\mathrm{Rb}$ atoms, which we compare to numerical simulations.

Crystal-symmetry-protected photonic topological edge states (PTESs) based on air rods in conventional dielectric materials are designed as photonic topological waveguides (PTWs) coupled with side optical cavities. We demonstrate that the cavity coupled with the PTW can change the reflection-free transport of the PTESs, where the cavities with single modes and twofold degenerate modes are taken as examples. The single-mode cavities are able to perfectly reflect the PTESs at their resonant frequencies, forming a dip in the transmission spectra. The dip full width at half depth depends on the coupling strength between the cavity and PTW and thus on the cavity geometry and distance relative to the PTW. The cavities with twofold degenerate modes lead to a more complex PTES transport whose transmission spectra can be in the Fano form. These effects well agree with the one-dimensional PTW-cavity transport theory we build, in which the coupling of the PTW with a cavity is taken as $\delta$ or non-$\delta$ type. Such PTWs coupled with side cavities, combining topological properties and convenient tunability, provide wide diversities for topological photonic devices.

In this work, we demonstrate theoretically via Kraus maps that the fractional topological phase in qudits is robust to phase noise. In our proposal, dephasing noise is inserted in an optical setup designed for measuring the fractional topological phase on photonic qudits encoded in path variables after local unitary operations are applied. Qudit states can be prepared with photon pairs generated by spontaneous parametric down-conversion crossing a multiple-slit array. Polarization as an additional degree of freedom and a two-photon longitudinal interferometer are the basic ingredients of the proposed setup. Although the visibility of the interference pattern decreases when noise is added, our calculation shows that the topological phase is preserved. This result stimulates further studies for the use of fractional topological phase in quantum gates due to its robustness in environments where phase noise is present.

Formulating a lattice gauge theory using only physical degrees of freedom generically leads to nonlocal interactions. A local Hamiltonian is desirable for quantum simulation, and this is possible by treating the Hilbert space as a subspace of a much larger Hilbert space in which Gauss's law is not automatic. Digital quantum simulations of this local formulation will wander into unphysical sectors due to errors from Trotterization or from quantum noise. In this work, oracles are constructed that use local Gauss law constraints to projectively distinguish physical and unphysical wave functions in Abelian lattice gauge theories. Such oracles can be used to detect errors that break Gauss's law.

Monogamy of quantum correlations provides a way to study restrictions on their sharability in multiparty systems. We find the critical exponent of these measures, above which randomly generated multiparty pure states satisfy the usual monogamy relation, and show that the critical power decreases with the increase in the number of parties. For three-qubit pure states, we detect that W-class states are more prone to being nonmonogamous as compared to the GHZ-class states. We also observe a different criticality in monogamy power up to which random pure states remain nonmonogamous. We prove that the “average monogamy” score asymptotically approaches its maximal value on increasing the number of parties. Analyzing the monogamy scores of random three-, four-, five-, and six-qubit pure states, we also report that almost all random pure six-qubit states possess maximal monogamy score, which we confirm by evaluating statistical quantities like mean, variance, and skewness of the distributions. In particular, with the variation of number of qubits, means of the distributions of monogamy scores for random pure states approach to unity—which is the algebraic maximum—thereby conforming to the known results of random states having maximal multipartite entanglement in terms of geometric measures.

Among many quantum key distribution protocols, the round-robin differential-phase-shift (RRDPS) protocol is unique in that it can upper-bound the amount of information leakage without monitoring signal disturbance. To expedite implementation of the protocol, however, the number of pulses forming a single block should be kept small, which significantly decreases the key rates in the original security proof. In the present paper, we refine the security proof of the RRDPS protocol in the finite-sized regime and achieve a tighter estimation for the information leakage with neither monitoring signal disturbance nor changing the original experimental setups. As a consequence, we obtain better key rates in both asymptotic and finite-sized cases while keeping the preferable features of the protocol, such as omission of phase randomization.

Measures of entanglement can be employed for the analysis of numerous quantum information protocols. Due to computational convenience, logarithmic negativity is often the choice in the case of continuous-variable systems. In this work, we analyze a continuous-variable measurement-based entanglement distillation experiment using a collection of entanglement measures. This includes logarithmic negativity, entanglement of formation, distillable entanglement, relative entropy of entanglement, and squashed entanglement. By considering the distilled entanglement as a function of the success probability of the distillation protocol, we show that the logarithmic negativity surpasses the bound on deterministic entanglement distribution at a relatively large probability of success. This is in contrast to the other measures which would only be able to do so at much lower probabilities, hence demonstrating that logarithmic negativity alone is inadequate for assessing the performance of the distillation protocol. In addition to this result, we also observed an increase in the distillable entanglement by making use of upper and lower bounds to estimate this quantity. We thus demonstrate the utility of these theoretical tools in an experimental setting.

We show that any measure of entanglement that on pure bipartite states is given by a strictly concave function of the reduced density matrix is monogamous on pure tripartite states. This includes the important class of bipartite measures of entanglement that reduce to the (von Neumann) entropy of entanglement. Moreover, we show that the convex roof extension of such measures (e.g., entanglement of formation) is monogamous also on mixed tripartite states. To prove our results, we use the definition of monogamy without inequalities recently put forward [Gour and Guo, Quantum 2, 81 (2018)]. Our results promote the concept that monogamy of entanglement is a property of quantum entanglement and not an attribute of some particular measures of entanglement.