Single-shot images are the standard readout of experiments with ultracold atoms, the imperfect reflection of their many-body physics. The efficient extraction of observables from single-shot images is thus crucial. Here we demonstrate how artificial neural networks can optimize this extraction. In contrast to standard averaging approaches, machine learning allows both one- and two-particle densities to be accurately obtained from a drastically reduced number of single-shot images. Quantum fluctuations and correlations are directly harnessed to obtain physical observables for bosons in a tilted double-well potential at an extreme accuracy. Strikingly, machine learning also enables a reliable extraction of momentum-space observables from real-space single-shot images and vice versa. With this technique, the reconfiguration of the experimental setup between in situ and time-of-flight imaging is required only once to obtain training data, thus potentially granting an outstanding reduction in resources.

We present a general master equation, correct to second order in the system-environment coupling strength, that takes into account the initial system-environment correlations. We assume that the system and its environment are in a joint thermal equilibrium state, and thereafter, a unitary operation is performed to prepare the desired initial system state, with the system Hamiltonian possibly changing thereafter as well. We show that the effect of the initial correlations shows up in the second-order master equation as an additional term, similar in form to the usual second-order term describing relaxation and decoherence in quantum systems. We apply this master equation to a generalization of the paradigmatic spin-boson model, namely, a collection of two-level systems interacting with a common environment of harmonic oscillators, as well as a collection of two-level systems interacting with a common spin environment. We demonstrate that, in general, the initial system-environment correlations need to be accounted for in order to accurately obtain the system dynamics.

It is shown that the photon position operator $\widehat{\vec{X}}$ with commuting components can be written in the momentum representation as $\widehat{\vec{X}}=i\widehat{\vec{D}}$, where $\widehat{\vec{D}}$ is a flat connection in the tangent bundle $T({\mathbb{R}}^3\setminus \{(0,0,k_3)\in {\mathbb{R}}^3:k_3\ge 0\})$ over ${\mathbb{R}}^3\setminus \{(0,0,k_3)\in {\mathbb{R}}^3:k_3\ge 0\}$ equipped with the Cartesian structure. Moreover, $\widehat{\vec{D}}$ is such that the tangent 2-planes orthogonal to the momentum are propagated parallel with respect to $\widehat{\vec{D}}$ and also $\widehat{\vec{D}}$ is an anti-Hermitian (i.e., $\widehat{\vec{X}}$ is Hermitian) operator with respect to the scalar product $\langle \mathrm{\Psi }\left|{\widehat{H}}^{-2s}\right|\mathrm{\Phi }\rangle$. The eigenfunctions ${\mathrm{\Psi }}_{\vec{X}}\left(\vec{x}\right)$ of the position operator $\widehat{\vec{X}}$ are found.

We describe a quantum-assisted machine learning method in which multivariate data are encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space occurs through applying a low-depth quantum circuit with a tree-tensor-network (TTN) topology acting as an unsupervised feature extractor to identify the most relevant quantum states in a data-driven fashion and then applying a supervised linear classifier encoding the class decision in a small-dimensional quantum register. We present tools for making TTN classifiers amenable to implementation on gate-based quantum computing devices, including an embedding map with accuracy similar to the recently defined exponential machines (A. Novikov et al., arXiv:1605.03795) but which produces valid quantum state embeddings of classical data vectors, and the use of manifold-based gradient optimization schemes to produce isometric operations mapping quantum states to a register of qubits defining a class decision. We detail methods for efficiently obtaining one-point and two-point correlation functions of the vectors defining the decision boundary of the quantum model, which can be used for model interpretability, as well as methods for obtaining classification decisions from partial data vectors. Further, we show that the use of isometric tensors can significantly aid in the human interpretability of the correlation functions extracted from the decision weights and may produce models that are less susceptible to adversarial perturbations. Finally, we discuss in detail the problem of compiling classically optimized isometric TTN models into unitary operations to be run on quantum computers and how isometric models requiring postselection on quantum hardware can be used to precondition variational Ansätze for models without postselection. We demonstrate our methodologies in applications utilizing the MNIST database of handwritten digits and a multivariate time-series data set of human activity recognition.

We investigate the delocalization of quantum information in the nonequilibrium dynamics of the $XY$ spin chain with asymptotically decaying interactions $\sim 1/r^{\alpha }$. As a figure of merit, we employ the tripartite mutual information (TMI), the sign of which indicates if quantum information is predominantly shared globally. Interestingly, the sign of the TMI distinguishes regimes of the exponent $\alpha$ that are known for different behaviors of information propagation. While an effective causal region bounds the propagation of information, if interactions decay sufficiently fast, this information is mainly delocalized, which leads to the necessity of global measurements. Furthermore, the results indicate that mutual information is monogamous for all possible partitionings in this case, implying that quantum entanglement is the dominant correlation. If interactions decay sufficiently slow, though information can propagate (quasi-)instantaneously, it is mainly accessible by local measurements at early times. Furthermore, it takes some finite time until correlations start to become monogamous, which suggests that entanglement is not the dominant correlation at early times. Our findings give new insights into the dynamics and structure of quantum information in many-body systems with long-range interactions, and might get verified on state-of-the-art experimental platforms.

Starting from a recently developed model based on the generalized Lorenz-Mie theory, we simulate and experimentally investigate the resonance spectrum and the scattered light field of whispering-gallery modes (WGMs) in a liquid droplet excited with a free-space visible laser beam. Depending on the illumination configuration and the spectral region, we observe WGMs with diverse quality factors and coupling efficiencies. Through imaging of scattering patterns, we show a robust agreement between theory and experiment. Our study provides an insight of the free-space optical coupling phenomenon, opening pathways for a controlled excitation of ultrahigh-quality WGMs in a plethora of liquid and solid optical microresonators for sensing and imaging applications.

Numerical modeling of scattering of a plane elliptically polarized monochromatic wave on a silicon spherical nanoparticle is carried out. In the resulting light field near the particle, the topology of strips, formed by the axes of the polarization ellipses and the normal vectors to their planes, is studied. The strips may have one half-twist only if they enclose a circular polarization singularity line, while almost all other strips, even enclosing the linear polarization singularity lines, are trivial. The correlation between the twisting indices of different strips is found, and their relation to the topological features of points of the singular lines is analyzed.

We analyze the requirements for fault-tolerant quantum computation with atom-atom gates based on cavity quantum electrodynamics (cQED) mediated by a photon with a finite pulse length. For short photon pulses, the distorted shape of the reflected pulses from the cQED system is a serious error source. In the previous study by Goto and Ichimura [Phys. Rev. A 82, 032311 (2010)], only the photon loss is minimized without considering the shape distortion to optimize the system parameters. Here we show an improved optimization method to minimize the infidelity due to the shape distortion and the photon losses in a well-balanced manner for the fault-tolerant scheme using probabilistic gates [Phys. Rev. A 80, 040303(R) (2009)]. Under this optimization, we discuss the fault-tolerant quantum computing requirement for short pulses. Finally, we show that reducing the cavity length is an effective way to reduce the errors of this type of gate in the case of short photon pulses.

We study the geometric Uhlmann phase of entangled mixed states in a composite system made of two coupled spin-$\frac{1}{2}$ particles with a magnetic field acting on one of them. Within a uniform noisy quantum channel setup, an exact analytical expression for this geometric phase in each subsystem is derived. We find an explicit connection to the concurrence of the density matrix of such a channel, which allows us to characterize the features of the Uhlmann phase in terms of the degree of entanglement in the system. In the space of field direction and coupling parameter, it exhibits a phase singularity revealing a topological transition between orders characterized by different winding numbers. The transition occurs for fields lying in the equator of the sphere of directions and at critical values of the coupling which can be controlled by tuning the depolarization strength. Notably, under these conditions the concurrence of the composite system is bounded to the range $[0,1/2]$. We also compare the calculated Uhlmann phase to an interferometric phase, which has been formulated as an alternative for density matrices. The latter does not present a phase vortex, although they coincide in the weak entanglement regime for vanishing depolarization (pure states). Otherwise, they behave clearly different in the strong-entanglement regime.

Recently, it was shown that quantum steerability is stronger than the bound set by the instrumental causal network. This implies that quantum instrumentality cannot simulate Einstein-Podolsky-Rosen (EPR) -nonlocal correlations completely. Here we show that quantum instrumentality uniquely and completely singles out the nonlocal advantage of quantum coherence, unlike EPR correlation.

Charge transfer processes between weakly bound entities play an important role in various chemical and biological environments. In this combined experimental and theoretical work, we investigate the nature of charge-transfer processes in homogeneous atomic and heterogeneous atomic-molecular clusters. Our results reveal fundamentally different processes to be at play in pure argon clusters compared to mixed argon-nitrogen systems: We demonstrate that the former species decay via photon-mediated charge transfer while a nonradiative direct process is found dominant in the atomic-molecular cases. Our results are of general interest for studies on charge redistribution in more complex and biologically relevant samples where molecules are involved.

Shell-confined atoms can serve as a generalized model to explain both the free and confined conditions. In this scenario, an atom is trapped inside two concentric spheres of inner $\left(R_a\right)$ and outer $\left(R_b\right)$ radii. The choice of $R_a$ and $R_b$ renders four different quantum-mechanical systems. In hydrogenic atoms, they are termed (i) the free hydrogen atom (FHA), (ii) the confined hydrogen atom, (iii) the shell-confined hydrogen atom (SCHA), and (iv) the left-confined hydrogen atom (LCHA). By placing $R_a$ and $R_b$ at the location of radial nodes of respective free $n$ and $\ell$ states, a new kind of degeneracy may arise. At a given $n$ of the FHA, $\frac{n(n+1)(n+2)}{6}$ isoenergic states with energy $-\frac{Z^2}{2n^2}$ exist. Furthermore, within a given $n$, the individual contribution of each of these four potentials has also been enumerated. This incidental degeneracy concept is further explored and analyzed in certain well-known plasma (Debye and exponential-cosine-screened) systems. Multipole oscillator strength $f^{\left(k\right)}$ and polarizability ${\alpha }^{\left(k\right)}$ are evaluated for systems (i)–(iv) in some low-lying states $(k=1-4)$. In excited states, negative polarizability is also observed. In this context, the metallic behavior of H-like systems in the SCHA is discussed and demonstrated. Additionally, analytical closed-form expression of $f^{\left(k\right)}$ and ${\alpha }^{\left(k\right)}$ are reported for $1s,2s,2p,3d,4f,5g$ states of the FHA. Finally, Shannon entropy and Onicescu information energies are investigated in ground states in the SCHA and LCHA in both position and momentum spaces.

The length scale separation in dilute quantum gases in quasi-one-dimensional or quasi-two-dimensional traps has spatially divided the system into two distinct regimes. Whereas universal relations defined in strict one or two dimensions apply in a scale that is much larger than the characteristic length of the transverse confinements, physical observables in the short distances are inevitably governed by three-dimensional contacts. Here, we show that $p$-wave contacts defined in different length scales are intrinsically connected by a universal relation, which depends on a simple geometric factor of the transverse confinements. While this universal relation is derived for one of the $p$-wave contacts, it establishes a concrete example of how dimensional crossover interplays with contacts and universal relations for arbitrary partial wave scatterings.

A simple phenomenological model, justified by rigorous electromagnetic analysis, is used to examine far-field polarization modulation introduced by a metallic screen with two subwavelength slits in uniform, partially polarized illumination. The accuracy of this intuitive model is assessed numerically, by employing the Fourier modal method, as regards the wavelength, the screen metal, and the slit depth, width, and separation. The Stokes parameters and the degree of polarization are evaluated paraxially in the far zone of the slits. We demonstrate that a uniform, partially linearly polarized incident beam can be rendered unpolarized by the nanoslits. Our work provides insight into the pivotal role that surface plasmons have in polarization modulation in photonics.

The Hong-Ou-Mandel effect lies at the heart of quantum interferometry, having multiple applications in the field of quantum information processing and no classical counterpart. Despite its popularity, only a few works have considered polarization-frequency interaction within the interferometer. In this paper, we fill this gap. Our system of interest is a general biphoton polarization state that experiences effective dephasing noise by becoming entangled with the same photons' frequency state, as the photons propagate through birefringent media. The photons then meet at a beam splitter, where either coincidence or bunching occurs, after which the polarization-frequency interaction continues on the output paths. Along with performing extensive theoretical analysis on the coincidence probability and different polarization states, we outline multiple interesting applications that range from constructing Bell states to an alternative delayed choice quantum eraser.

The quantum speed limit for open quantum systems in the non-Markovian regime is analyzed. We provide a lower bound for the time required to transform an initial state to a final state in terms of thermodynamic quantities such as the energy fluctuation, entropy production rate, and dynamical activity. Such bound was already analyzed for Markovian evolution satisfying detailed balance condition. Here we generalize this approach to deal with arbitrary evolution governed by a time-local generator. Our analysis is illustrated by three paradigmatic examples of qubit evolution: amplitude damping, pure dephasing, and the eternally non-Markovian evolution.

We present a detailed thermodynamic analysis of a three-level quantum heat engine coupled continuously to hot and cold reservoirs. The system is driven by an oscillating external field and is described by the Markovian quantum master equation. We use the general form of the dissipator which is consistent with thermodynamics. We calculate the heat, power, and efficiency of the system for the heat-engine operating regime and also examine the thermodynamic uncertainty relation. The efficiency of the system is strongly dependent on the structure of the dissipator, and the correlations between different levels can be an obstacle for ideal operation. In quantum systems, the heat flux is decomposed into the population and coherent parts. The coherent part is specific to quantum systems, and in contrast to the population part, it cannot be expressed by a simple series expansion in the linear-response regime. We discuss how the interplay between the population and coherent parts affects the performance of the heat engine.

The process of entanglement swapping showed that suitable measurements can generate nonlocal correlations even from particles that never interacted directly. This fact was generalized to the concept of bilocality for a quantum network, where there are three observers sharing two independent sources. Since then, the nonlocality nature was explored in various quantum networks. In this work, we consider the nonlocality of $(2^n-1)$-partite tree-tensor networks, which are widely used in quantum communications. We derive the Bell-type inequalities which are respectively satisfied by all $(2^n-2)$-local correlations and all local correlations, and demonstrate the maximal quantum violations of these inequalities and the robustness to noise in these tree networks.