We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, $V_{ij}\propto {\left|i-j\right|}^{-\alpha }$, where the exponent of the interaction range $\alpha$ can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing $\alpha$, the critical exponent experiences a sharp increase at about ${\alpha }_c\simeq 1.2$ and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For $\alpha <{\alpha }_c$, we find that the system is mostly localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for $\alpha >{\alpha }_c$, the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.

Ultracold gases in the strongly correlated regime have been proven to simulate quantum magnetic models under certain conditions: the mapping of the double-well system onto the Lipkin-Meshkov-Glick spin model is a paradigmatic case. A suitable definition of the length in the Hilbert space of the system leads to the concept of a correlation length, whose divergence is a characteristic property of continuous quantum phase transitions. We calculate the finite-size scaling of some observables like the magnetization or the population imbalance, as well as of the Schmidt gap, obtaining in this way the critical exponents associated with such transitions. The systematic definition of the Schmidt gap in extended Hamiltonians provides a good tool to analyze the set of critical exponents associated with transitions in systems formed by a larger number of traps. This demonstrates, thus, the potential use of mesoscopic Bose-Einstein condensates as quantum simulators of condensed matter systems.

We study optical forces acting on a subwavelength particle with anisotropic polarizability and discover an optomechanical effect that resembles the Hall effect for electrons. While in the classical Hall effect the transverse Lorentz force and the transverse voltage appear due to the static magnetic field which induces the nondiagonal components of the electric conductivity tensor; in our case the imaginary parts of the nondiagonal elements of the polarizability tensor are responsible for the transverse scattering force. We calculate this force for the examples of the ellipsoidal plasmonic nanoparticles and the spherical particle with gyromagnetic properties, and show that the transverse force depends on the physical origin of the anisotropy of the polarizability, and on the electromagnetic wave structure around the particle. Moreover, this force primarily occurs in the inhomogeneous field only.

Even-order harmonics (EOHs) are generated for oriented molecules and for atoms under specific conditions. Here, we focus on the most common situations where EOHs are not observed in far-field measurements. We propose an experiment to show that the EOHs are produced close to the nucleus but are not detected in the far-field measurements due to destructive interferences of the propagated EOHs of the emitted radiation. However, Rydberg gas atoms (e.g., rubidium), which are out of the focus of the laser beam, are expected to be ionized due to their weak interaction with a specific EOH of helium, which is not observed by the far-field detector. The ionization energy of the Rydberg gas atoms should be in resonance with the single-photon energy of a specific EOH.

We analyze the interaction between orthogonally polarized solitons and dispersive waves via four-wave mixing in a birefringent fiber. We calculate analytically the efficiency of the phase-sensitive scattering between orthogonally polarized solitons and dispersive waves. Experiments performed by using a photonic crystal fiber perfectly match the analytical predictions.

We discuss relations between several relativistic spin observables and derive a Lorentz-invariant characteristic of a reduced spin density matrix. A relativistic position operator that satisfies all the properties of its nonrelativistic analog does not exist. Instead we propose two causality-preserving positive operator-valued measures (POVMs) that are based on projections onto one-particle and antiparticle spaces, and on the normalized energy density. They predict identical expectation values for position. The variances differ by less than a quarter of the squared de Broglie wavelength and coincide in the nonrelativistic limit. Since the resulting statistical moment operators are not canonical conjugates of momentum, the Heisenberg uncertainty relations need not hold. Indeed, the energy density POVM leads to a lower uncertainty. We reformulate the standard equations of the spin dynamics by explicitly considering the charge-independent acceleration, allowing a consistent treatment of backreaction and inclusion of a weak gravitational field.

We consider the problem of optimally identifying the state of a probe qudit, prepared with given prior probability in a pure state belonging to a finite set of possible states which together span a $D$-dimensional subspace of the $d$-dimensional Hilbert space the qudit is defined in. It is assumed that we do not know some or all of the states in the set, but for each unknown state we are given a reference qudit into which this state is encoded. We show that from the measurement for optimal state identification with $d=D$ one can readily determine the optimal figure of merit for qudits with $d>D$, without solving a new optimization problem. This result is applied to the minimum-error identification and to the optimal unambiguous identification of two qudit states with $d\ge 2$, where either one or both of the states are unknown, and also to the optimal unambiguous identification of $N$ equiprobable linearly independent unknown pure qudit states with $d\ge N$. In all cases the optimal figure of merit, averaged over the unknown states, increases with growing dimensionality $d$ of the qudits.

We developed a countermeasure against blinding attacks on low-noise detectors with a background-noise-cancellation scheme in quantum key distribution (QKD) systems. Background-noise cancellation includes self-differencing and balanced avalanche photon diode (APD) schemes and is considered a promising solution for low-noise APDs, which are critical components in high-performance QKD systems. However, its vulnerability to blinding attacks has been recently reported. In this work, we propose a countermeasure that prevents this potential security loophole from being used in detector blinding attacks. An experimental QKD setup is implemented and various tests are conducted to verify the feasibility and performance of the proposed method. The obtained measurement results show that the proposed scheme successfully detects occurring blinding-attack-based hacking attempts.

We study the suppression of qubit dephasing through Uhrig dynamical decoupling (UDD) in nontrivial environments modeled within the spin-boson formalism. In particular, we address the case of (i) a qubit coupled to a bosonic bath with power-law spectral density, and (ii) a qubit coupled to a single harmonic oscillator that dissipates energy into a bosonic bath, which embodies an example of a structured bath for the qubit. We then model the influence of random time jitter in the UDD protocol by sorting pulse-application times from Gaussian distributions centered at appropriate values dictated by the optimal protocol. In case (i) we find that, when few pulses are applied and a sharp cutoff is considered, longer coherence times and robust UDD performances (against random timing errors) are achieved for a super-Ohmic bath. On the other hand, when an exponential cutoff is considered, a super-Ohmic bath is undesirable. In case (ii) the best scenario is obtained for an overdamped harmonic motion. Our study provides relevant information for the implementation of optimized schemes for the protection of quantum states from decoherence.

The present work reports results from systematic multiconfiguration Dirac–Hartree–Fock calculations of electronic isotope shift factors for a set of transitions between low-lying levels of neutral aluminium. These electronic quantities together with observed isotope shifts between different pairs of isotopes provide the changes in mean-square charge radii of the atomic nuclei. Two computational approaches are adopted for the estimation of the mass- and field-shift factors. Within these approaches, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy and to estimate theoretical error bars of the isotope shift factors.

For laser-cooling considerations, we have theoretically investigated the electronic, rovibrational, and hyperfine structures of the BaF molecule. The highly diagonal Franck-Condon factors and the branching ratios for all possible transitions within the lowest-lying four electronic states have also been calculated. Meanwhile, the mixing between the metastable $A^{{\prime }^2}\mathrm{\Delta }$ and $A^2\mathrm{\Pi }$ states and, further, the lifetime of the $\mathrm{\Delta }$ state have been estimated since the loss procedure via the $\mathrm{\Delta }$ state might fatally break the main quasicycling $\mathrm{\Sigma }-\mathrm{\Pi }$ transition for cooling and trapping. The resultant hyperfine splittings of each rovibrational state in the $X^2{\mathrm{\Sigma }}^{+}$ state provide benchmarks for sideband modulations of the cooling and repumping lasers and the remixing microwaves to address all necessary levels. The calculated Zeeman shift and $g$ factors for both $X$ and $A$ states serve as benchmarks for selection of the trapping laser polarizations. Our study paves the way for future laser cooling and magneto-optical trapping of the BaF molecule.

Bragg diffraction of an atomic wave packet in a retroreflective geometry with two counterpropagating optical lattices exhibits a light shift induced phase. We show that the temporal shape of the light pulse determines the behavior of this phase shift: In contrast to Raman diffraction, Bragg diffraction with Gaussian pulses leads to a significant suppression of the intrinsic phase shift due to a scaling with the third power of the inverse Doppler frequency. However, for box-shaped laser pulses, the corresponding shift is twice as large as for Raman diffraction. Our results are based on approximate but analytical expressions as well as a numerical integration of the corresponding Schrödinger equation.

We study the out-of-equilibrium dynamics of two interacting atoms in a one-dimensional harmonic trap after a quench by a tightly pinned impurity atom. We make use of an approximate variational calculation called the Lagrange-mesh method to solve the Schrödinger equation as a function of interparticle interaction and impurity quench strength. We investigate the out-of-equilibrium dynamics by calculating the Loschmidt echo which quantifies the irreversibility of the system following the quench, while its probability distribution after long times can be used to identify distinct dynamical regimes. These quantities are related to the spectral function which describes the full dynamical spectrum, and we show through a thorough examination of the parameter space the existence of distinct scattering states and collective oscillations. This work demonstrates how these dynamics are strongly dependent on the interaction strength between the atoms and may be tuned to observe the establishment of the orthogonality catastrophe in few-body systems.

We employ ptychography, a phase-retrieval imaging technique, to show experimentally that a partially coherent high-energy matter (electron) wave emanating from an extended source can be decomposed into a set of mutually independent modes of minimal rank. Partial coherence significantly determines the optical transfer properties of an electron microscope and so there has been much work on this subject. However, previous studies have employed forms of interferometry to determine spatial coherence between discrete points in the wave field. Here we use the density matrix to derive a formal quantum mechanical description of electron ptychography and use it to measure a full description of the spatial coherence of a propagating matter wave field, at least within the fundamental uncertainties of the measurements we can obtain.

We study a system of $N$ noninteracting spinless fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the confining trap breaks the translational invariance and introduces an edge where the average density of fermions vanishes. Far from the edge, near the center of the trap (the so-called “bulk regime”), where the fermions do not feel the curvature of the trap, physical properties of the fermions have traditionally been understood using the local density (or Thomas-Fermi) approximation. However, these approximations drastically fail near the edge where the density vanishes and thermal and quantum fluctuations are thus enhanced. The main goal of this paper is to show that, even near the edge, novel universal properties emerge, independently of the details of the shape of the confining potential. We present a unified framework to investigate both the bulk and the edge properties of the fermions. We show that for large $N$, these fermions in a confining trap, in arbitrary dimensions and at finite temperature, form a determinantal point process. As a result, any $n$-point correlation function, including the average density profile, can be expressed as an $n\times n$ determinant whose entry is called the kernel, a central object for such processes. Near the edge, we derive the large-$N$ scaling form of the kernels, parametrized by $d$ and $T$. In $d=1$ and $T=0$, this reduces to the so-called Airy kernel, that appears in the Gaussian unitary ensemble (GUE) of random matrix theory. In $d=1$ and $T>0$ we show a remarkable connection between our kernel and the one appearing in the ($1+1$)-dimensional Kardar-Parisi-Zhang equation at finite time. Consequently, our result provides a finite-$T$ generalization of the Tracy-Widom distribution, that describes the fluctuations of the position of the rightmost fermion at $T=0$, or those of the largest single-fermion momentum. In $d>1$ and $T\ge 0$, while the connection to GUE no longer holds, the process is still determinantal whose analysis provides a new class of kernels, generalizing the $1d$ Airy kernel at $T=0$ obtained in random matrix theory. Some of our finite-temperature results should be testable in present-day cold-atom experiments, most notably our detailed predictions for the temperature dependence of the fluctuations near the edge.

We demonstrate the existence of stationary states composed of vortex lines attached to planar dark solitons in scalar Bose-Einstein condensates. Dynamically stable states of this type are found at low values of the chemical potential in channeled condensates, where the long-wavelength instability of dark solitons is prevented. In oblate, harmonic traps, U-shaped vortex lines attached by both ends to a single planar soliton are shown to be long-lived states. Our results are reported for parameters typical of current experiments, and open up a way to explore the interplay of different topological structures. These configurations provide Dirichlet boundary conditions for vortex lines and thereby mimic open strings attached to D-branes in string theory. We show that these similarities can be formally established by mapping the Gross-Pitaevskii theory into a dual effective string theory for open strings via a boson-vortex duality in 3+1 dimensions. Combining a one-form gauge field living on the soliton plane which couples to the end points of vortex lines and a two-form gauge field which couples to vortex lines, we obtain a gauge-invariant dual action of open vortex lines with their end points attached to dark solitons.

We present a special-relativistic analysis of deformable interferometers where counterpropagating beams share a common optical path. The optical path is allowed to change rather arbitrarily and need not be stationary. We show that the phase shift has two contributions: One contribution is independent of the refractive index $n$ and has the form of a line integral. This term gives the Wang empirical formula for deformable Sagnac interferometers. The second term is quadratic in $n$ and has the form of a double integral. The analysis provides a unifying framework incorporating the Sagnac, Wang, and Fizeau effects in a single scheme, gives a rigorous proof of Wang empirical formula, and can be used to study various perturbations of Sagnac interferometers.

We derive the relativistically exact eikonal equation for ring interferometers undergoing deformation. For ring interferometers that undergo slow deformation we describe the two leading terms in the adiabatic expansion of the phase shift. The leading term is independent of the refraction index $n$ and is given by a line integral generalizing results going back to Sagnac for nondeforming interferometers to all orders in $\beta =\left|\mathbf{v}\right|/c$. In the nonrelativistic limit this term is $O\left(\beta \right)$. The next term in the adiabaticity has the form of a double integral, it is of order ${\beta }^0$ and depends on the refractive index $n$. It accounts for nonreciprocity due to changing circumstances in the fiber. The adiabatic correction is often comparable to the Sagnac term. In particular, this is the case in Fizeau's interferometer. Besides providing a mathematical framework that puts all ring interferometers under a single umbrella, our results strengthen earlier results and generalize them to fibers with chromatic dispersion.

We theoretically investigate the phase sensitivity with parity detection on an SU(1,1) interferometer with a coherent state combined with a squeezed vacuum state. This interferometer is formed with two parametric amplifiers for beam splitting and recombination instead of beam splitters. We show that the sensitivity of phase estimation approaches the Heisenberg limit and give the corresponding optimal condition. Moreover, we derive the quantum Cramér-Rao bound of the SU(1,1) interferometer.