We investigate the decay properties of the quantum coherence and nonclassical correlations of two photonic qubits, which are partially entangled in their orbital angular momenta, through Kolmogorov turbulent atmosphere. It is found that the decay of quantum coherence and quantum discord may be qualitatively different from that of entanglement when the initial state of two photons is not maximally entangled. We derive two universal decay laws for quantum coherence and quantum discord, respectively, and show that the decay of quantum coherence is more robust than nonclassical correlations.

We develop a variational method to obtain many-body ground states of the Bose-Hubbard model using feedforward artificial neural networks. A fully-connected network with a single hidden layer works better than a fully-connected network with multiple hidden layers, and a multi-layer convolutional network is more efficient than a fully-connected network. AdaGrad and Adam are optimization methods that work well. Moreover, we show that many-body ground states with different numbers of atoms can be generated by a single network.

In this study, we examine the dynamics of a macroscopic quantum system in interaction with a non-equilibrium environment. The system is conveniently described as a particle confined in a double-well potential. The environment is composed of two independent equilibrium environments at different temperatures. We use the time-dependent perturbation theory to describe the dynamics without any explicit Born and Markov assumptions. We demonstrate that in two environments at same temperatures the short-time dynamics is affected by the interference between two environments through the system. In the non-equilibrium environment, the quantum coherence of the system essentially has an oscillatory dependence on the temperature difference between two environments. Nonetheless, for a wide range of temperature differences, the non-equilibrium environment enhances the quantum coherence. This effect is weakened by the force the macroscopic system exerts on environmental particles.

We argue that in the case of identical particles the most natural identification of separability, that is of absence of non-classical correlations, is via the factorization of mean values of commuting observables. It thus follows that separability and entanglement depend both on the state and on the choice of observables and are not absolute notions. We compare this point of view with a recent novel approach to the entanglement of identical particles, which allows for the definition of an entanglement entropy from a suitably defined reduced particle density matrix, without the need of labeling the system constituents. We contrast this figure of merit with the aforementioned lack of an absolute notion of entanglement by considering few paradigmatic examples.

I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum coherence and quantum correlations. Once confined to thought experiments, they are nowadays created and manipulated by exerting an exquisite experimental control of atoms, molecules and photons. It is important to identify and quantify such quantum features, as they are deemed to be key resources to achieve supraclassical performances in computation and communication protocols. The information geometry viewpoint elucidates the advantage provided by quantum superpositions in phase estimation. Also, it enables to link measures of coherence and entanglement to observables, which can be evaluated in a laboratory by a limited number of measurements.

We demonstrate a generalized notion of eigenstate thermalization for translation-invariant quasifree fermionic models: the vast majority of eigenstates satisfying a finite number of suitable constraints (e.g. fixed energy and particle number) have the property that their reduced density matrix on small subsystems approximates the corresponding generalized Gibbs ensemble. To this end, we generalize analytic results by Lai and Yang (Phys. Rev. B 91, 081110 (2015)) and illustrate the claim numerically by example of the Jordan-Wigner transform of the XX spin chain.

We analyze the multipole excitation of atoms with twisted light, i.e., by a vortex light field that carries orbital angular momentum. A single trapped $^{40}$Ca$^+$ ion serves as a localized and positioned probe of the exciting field. We drive the $S_{1/2} \to D_{5/2}$ transition and observe the relative strengths of different transitions, depending on the ion's transversal position with respect to the center of the vortex light field. On the other hand, transition amplitudes are calculated for a twisted light field in form of a Bessel beam, a Bessel-Gauss and a Gauss-Laguerre mode. Analyzing experimental obtained transition amplitudes we find agreement with the theoretical predictions at a level of better than 3\%. Finally, we propose measurement schemes with two-ion crystals to enhance the sensing accuracy of vortex modes in future experiments.

We consider a model of an electron in a crystal moving under the influence of an external electric field: Schroedinger's equation in one spatial dimension with a potential which is the sum of a periodic function $V$ and a smooth function $W$. We assume that the period of $V$ is much shorter than the scale of variation of $W$ and denote the ratio of these scales by $\epsilon$. We consider the dynamics of $\textit{semiclassical wavepacket}$ asymptotic (in the limit $\epsilon \downarrow 0$) solutions which are spectrally localized near to a $\textit{crossing}$ of two Bloch band dispersion functions of the periodic operator $- \frac{1}{2} \partial_z^2 + V(z)$. We show that the dynamics is qualitatively different from the case where bands are well-separated: at the time the wavepacket is incident on the band crossing, a second wavepacket is `excited' which has $\textit{opposite}$ group velocity to the incident wavepacket. We then show that our result is consistent with the solution of a `Landau-Zener'-type model.

We study the effect of many-body quantum interference on the dynamics of coupled periodically kicked systems whose classical dynamics is chaotic and shows an unbounded energy increase. We specifically focus on a $N$ coupled kicked rotors model: we find that the interplay of quantumness and interactions dramatically modifies the system dynamics inducing a transition between energy saturation and unbounded energy increase. We discuss this phenomenon both numerically and analytically, through a mapping onto a $N$-dimensional Anderson model. The thermodynamic limit $N\to\infty$, in particular, always shows unbounded energy growth. This dynamical delocalization is genuinely quantum and very different from the classical one: using a mean field approximation we see that the system self-organizes so that the energy per site increases in time as a power law with exponent smaller than one. This wealth of phenomena is a genuine effect of quantum interference: the classical system for $N\geq 2$ always behaves ergodically with an energy per site linearly increasing in time. Our results show that quantum mechanics can deeply alter the regularity/ergodicity properties of a many body driven system.

Local implementation of non-local quantum gates is necessary in a distributed quantum computer. Here, we demonstrate the non-local implementation of controlled-unitary quantum gates proposed by Eisert \emph{et al.} [Phys. Rev. A 62, 052317 (2000)] using the five-qubit IBM quantum computer. Further, we analyze the same quantum task in the presence of a controller using a GHZ-like state as the quantum channel. Finally, we verify the fidelity and accuracy of the implementation through the techniques of quantum state and process tomographies.

The Minkowski vacuum state is expressed as an entangled state between the left and right Rindler wedges when it is constructed on the Rindler vacuum. In this paper, we further examine the entanglement structure and extend the expression to the future (expanding) and past (shrinking) Kasner spacetimes. This clarifies the origin of the quantum radiation produced by an Unruh--DeWitt detector in uniformly accelerated motion in the four-dimensional Minkowski spacetime. We also investigate the two-dimensional massless case where the quantum radiation vanishes but the same entanglement structure exists.

We study the entropy dynamics of a dephasing model, where a two-level system (TLS) is coupled with a squeezed thermal bath via non-demolition interaction. This model is exactly solvable, and the time dependent states of both the TLS and its bath can be obtained exactly. Based on these states, we calculate the entropy dynamics of both the TLS and the bath, and find that the dephasing rate of the system relies on the squeezing phase of the bath. In zero temperature and high temperature limits, we prove that both the system and bath entropy increases monotonically. Moreover, we find that the dephasing rate of the system relies on the squeezing phase of the bath, and this phase dependence cannot be precisely derived from the Born-Markovian approximation which is widely adopted in open quantum systems.

We experimentally explore the topological Maxwell metal bands by mapping the momentum space of condensed-matter models to the tunable parameter space of superconducting quantum circuits. An exotic band structure that is effectively described by the spin-1 Maxwell equations is imaged. Three-fold degenerate points dubbed Maxwell points are observed in the Maxwell metal bands. Moreover, we engineer and observe the topological phase transition from the topological Maxwell metal to a trivial insulator, and report the first experiment to measure the Chern numbers that are higher than one.

We propose a method for finding an initial state vector which by ordinary Hamiltonian time evolution follows a single branch of many-worlds quantum mechanics. The resulting deterministic system appears to exhibit random behavior as a result of the successive emergence over time of information present in the initial state but not previously observed.

We study the degree of second-order coherence of the emission of a high-power multi-quantum well superluminescent diode with a lateral tapered amplifier section with and without feedback. When operated in an external cavity, the degree of second-order coherence changed from the almost thermal case of g$^{(2)}$(0)$\approx$1.9 towards the mostly coherent case of g$^{(2)}$(0)$\approx$1.2 when the injection current at the tapered section was increased. We found good agreement with semi-classical laser theory near and below threshold while above laser threshold a slightly higher g$^{(2)}$(0) was observed. As a free running device, the superluminescent diode yielded more than 400 mW of optical output power with good spatial beam quality of $M^2_{slow} < 1.6$. In this case, the DSOC dropped only slightly from 1.9 at low powers to 1.6 at the maximum output power. To our knowledge, this is the first investigation of a high-power tapered superluminescent diode concerning the degree of second-order coherence. Such a device might be useful for real-world applications probing the second order coherence function, such as ghost imaging.

We consider many-body quantum systems dissipatively coupled by a cascade network, i.e. a setup in which interactions are mediated by unidirectional environmental modes propagating through a linear optical interferometer. In particular we are interested in the possibility of inducing different effective Hamiltonian interactions by properly engineering an external dissipative network of beam- splitters and phase-shifters. In this work we first derive the general structure of the master equation for a symmetric class of translation-invariant cascade networks. Then we show how, by tuning the parameters of the interferometer, one can exploit interference effects to tailor a large variety of many-body interactions.

The electro-mechanical control of an on-chip GaAs optical router operating at the single-photon level is demonstrated. The routing of single photons is achieved by electro-mechanical tuning of the splitting ratio of an optical beam splitter in the form of a nanobeam waveguide directional coupler (DC). One of the two waveguides forming the DC is located at the free end of a cantilever, which can be displaced vertically downwards by applying an actuation voltage, $V_{act}$, between the cantilever and the substrate. The resulting out-of-plane separation between the waveguides is used to control the splitting ratio of the DC. In the absence of $V_{act}$, photons emitted by an InGaAs self-assembled quantum dot embedded within the fixed arm of the device are split $83$:$17$ between the co-planar through and drop ports of the DC respectively. As $V_{act}$ is applied the drop port displaces downwards by over $400$ nm causing the splitting ratio to approach $100$:$0$. The single-photon nature of the collected emission is verified with autocorrelation measurements. The proposed system is compact, easy to fabricate and scalable with applications in on-chip photon routing as well as in-situ fine tuning of photonic elements.

We consider a pair of dipoles for which direct electrostatic dipole-dipole interactions may be significantly larger than the coupling to transverse radiation. We derive a master equation using the Coulomb gauge, which naturally enables us to include the inter-dipole Coulomb energy within the system Hamiltonian rather than the interaction. In contrast, the standard master equation for a two- dipole system, which depends entirely on well-known gauge-invariant S-matrix elements, is usually derived using the multipolar gauge, wherein there is no explicit inter-dipole Coulomb interaction. We show using a generalised arbitrary-gauge light-matter Hamiltonian that this master equation is obtained in other gauges only if the inter-dipole Coulomb interaction is kept within the interaction Hamiltonian rather than the unperturbed part as in our derivation. Thus, our master equation, while still gauge-invariant, depends on different S-matrix elements, which give separation-dependent corrections to the standard matrix elements describing resonant energy transfer and collective decay. The two master equations coincide in the large separation limit where static couplings are negligible. We provide an application of our master equation by finding separation-dependent corrections to the natural emission spectrum of the two-dipole system.

A quantum money scheme enables a trusted bank to provide untrusted users with verifiable quantum banknotes that cannot be forged. In this work, we report an experimental demonstration of the preparation and verification of unforgeable quantum banknotes. We employ a security analysis that takes experimental imperfections fully into account. We measure a total of $3.6\times 10^6$ states in one verification round, limiting the forging probability to $10^{-7}$ based on the security analysis. Our results demonstrate the feasibility of preparing and verifying quantum banknotes using currently available experimental techniques.

We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.