Quantum Fisher information (QFI) is a key concept in quantum state estimation, and Berry curvature (BC) is another basic concept to describe geometric properties of quantum states. In this paper, we consider pure states undergoing unitary parametrization processes and show that the BC serves as a lower bound for the product of QFIs corresponding to two different parameters through the Heisenberg uncertainty relation. This relation between QFI and BC implies that the estimation precisions of two different parameters are mutually restrictive due to finite BC, and the notion of QFI squeezing is introduced. A scenario of general su(2) parametrization is considered in detail to verify the relation between the QFI and BC.

We use the Koashi-Imoto decomposition of the degrees of freedom of joint system-environment initial states to investigate the reduced dynamics. We show that a subset of joint system-environment initial states guarantees completely positive reduced dynamics if and only if the system privately owns all quantum degrees of freedom and can locally access the classical degrees of freedom, without disturbing all joint initial states in the given subset. Furthermore, we show that the quantum mutual information for such kinds of states must be independent of the quantum degrees of freedom.

We model repetitive quantum error correction (QEC) with the single-error-correcting five-qubit code on a network of individually controlled qubits with always-on Ising couplings. We use our previously designed universal set of quantum gates based on sequences of shaped decoupling pulses. In addition to being accurate quantum gates, the sequences also provide dynamical decoupling (DD) of low-frequency phase noise. The simulation involves integrating the unitary dynamics of six qubits over the duration of tens of thousands of control pulses, using classical stochastic phase noise as a source of decoherence. The combined DD and QEC protocol dramatically improves the coherence, with the QEC alone being responsible for more than an order of magnitude infidelity reduction.

We investigate the nonsequential double ionization (NSDI) process of an atom in IR+XUV two-color intense laser fields, where the photon energy of the XUV laser is higher than the atomic ionization threshold. By using the frequency-domain theory, we consider the NSDI as a process caused by the collision-ionization mechanism and obtain the NSDI spectrum that presents a multiplateau structure. With the help of channel analysis, we find that the height of a plateau in the NSDI spectrum is determined by the number of XUV photons absorbed by the electrons. Furthermore, to explain the interference structure in the NSDI spectrum, we also compare the contributions of forward and backward collisions to the NSDI probability. We find that the forward collision dominates the contributions to the NSDI when two electrons are ejected along the same direction and both forward and backward collisions make a comparable contribution to NSDI when the two electrons are ejected along opposite directions. By applying the saddle-point approximation, we obtain an energy-circle formula, which may illustrate the formation of the NSDI spectrum structure.

We propose a simple scheme for the realization of a topological quasienergy band structure with ultracold atoms in a periodically driven optical square lattice. It is based on a circular lattice shaking in the presence of a superlattice that lowers the energy on every other site. The topological band gap, which separates the two bands with Chern numbers $\pm 1$, is opened in a way characteristic of Floquet topological insulators, namely, by terms of the effective Hamiltonian that appear in subleading order of a high-frequency expansion. These terms correspond to processes where a particle tunnels several times during one driving period. The interplay of such processes with particle interactions also gives rise to new interaction terms of several distinct types. For bosonic atoms with on-site interactions, they include nearest-neighbor density-density interactions introduced at the cost of weakened on-site repulsion as well as density-assisted tunneling. Using exact diagonalization, we investigate the impact of the individual induced interaction terms on the stability of a bosonic fractional Chern insulator state at half filling of the lowest band.

This work contains a detailed analysis of the properties of the ground state of a two-component two-site Bose-Hubbard model, which captures the physics of a binary mixture of Bose-Einstein condensates trapped in a double-well potential. The atom-atom interactions within each species and among the two species are taken as variable parameters, while the hopping terms are kept fixed. To characterize the ground state, we use observables such as the imbalance of population and its quantum uncertainty. The quantum many-body correlations present in the system are further quantified by studying the degree of condensation of each species, the entanglement between the two sites, and the entanglement between the two species. The latter is measured by means of the Schmidt gap, the von Neumann entropy, or the purity obtained after tracing out a part of the system. A number of relevant states are identified, e.g., Schrödinger catlike many-body states, in which the outcome of the population imbalance of both components is completely correlated, and other states with even larger von Neumann entropy which have a large spread in Fock space.

We have experimentally determined the terahertz- (THz-) wave parametric gain of stimulated Raman scattering (SRS) by phonon-polaritons in $\mathrm{LiNb}{\mathrm{O}}_3$. Our approach is based on ultrabright THz-wave generation from SRS under stimulated Brillouin scattering suppression with subnanosecond pump pulses. To obtain the frequency dependence of the parametric gain, we measured the crystal-length dependence of the THz-wave output directly using a surface-coupling configuration. We found that the product of the parametric gain and the threshold crystal length is constant throughout the tuning range. Our result provides a physical basis for the design and performance enhancement of SRS-based ultrabright tabletop THz-wave sources for various applications.

We investigate spontaneous four-wave mixing (SFWM) in a single-channel side-coupled integrated spaced sequence of resonators (SCISSOR). Analytic expressions for the number of photon pairs generated, as well as the biphoton wave function (joint spectral amplitude) describing the pairs, are derived and numerically computed for different pump pulse durations and numbers of ring resonators. In the limit of a long input pump pulse, we show a strong analogy between super-linear scaling of generation efficiency with respect to the number of rings in the structure and Dicke superradiance. More generally, we discuss in detail the factors that influence the shape of the biphoton wave function, as well as the conditions for observing super-SFWM.

We present a model of quantum metrology inspired by the computational model known as deterministic quantum computation with one quantum bit (DQC1). Using only one pure qubit together with $l$ fully mixed qubits we obtain measurement precision (defined as root-mean-square error for the parameter being estimated) at the standard quantum limit, which is typically obtained using the same number of uncorrelated qubits in fully pure states. In principle, the standard quantum limit can be exceeded using an additional qubit which adds only a small amount of purity. We show that the discord in the final state vanishes only in the limit of attaining infinite precision for the parameter being estimated.

It has been argued that it is incompatible to maintain unitary time evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time dependent. We demonstrate here that the time-dependent Dyson equation and the time-dependent quasi-Hermiticity relation can be solved consistently in such a scenario for a time-dependent Dyson map and time-dependent metric operator, respectively. These solutions are obtained at the cost of rendering the non-Hermitian Hamiltonian to be a nonobservable operator as it ceases to be quasi-Hermitian when the metric becomes time dependent.

The Casimir free energy and pressure of thin metal films deposited on metallic plates are considered using the Lifshitz theory and the Drude and plasma model approaches to the role of conduction electrons. The bound electrons are taken into account by using the complete optical data of film and plate metals. It is shown that for films of several tens of nanometers thickness the Casimir free energy and pressure calculated using these approaches differ by hundreds and thousands percent and can be easily discriminated experimentally. According to our results, the free energy of a metal film does not vanish in the limiting case of ideal metal if the Drude model approach is used in contradiction with the fact that the fluctuating field cannot penetrate in its interior. Numerical computations of the Casimir free energy and pressure of Ag and Au films deposited on Cu and Al plates have been performed using both theoretical approaches. It is shown that the free energy of a film can be both negative and positive depending on the metals used. For a Au film on a Ag plate and vice versa the Casimir energy of a film changes its sign with increasing film thickness. Applications of the obtained results for resolving the Casimir puzzle and the problem of stability of thin films are discussed.

We identify a systematic present in two-photon direct frequency comb spectroscopy (DFCS) which is a result of chirped laser pulses and is a manifestation of the first-order Doppler effect. We carefully analyze this systematic and propose methods for its mitigation within the context of our measurement of the hydrogen $1S-3S$ transition. We also report on our determination of the absolute frequency of this transition, which is comparable to a previous measurement using continuous-wave spectroscopy [O. Arnoult et al., Eur. Phys. J. D 60, 243 (2010)], but was obtained with a different experimental method.

A theoretical method is presented for the estimation of cross sections and rates for excitation and charge-transfer processes in low-energy hydrogen-atom collisions with neutral atoms, based on an asymptotic two-electron model of ionic-covalent interactions in the neutral atom-hydrogen-atom system. The calculation of potentials and nonadiabatic radial couplings using the method is demonstrated. The potentials are used together with the multichannel Landau–Zener model to calculate cross sections and rate coefficients. The main feature of the method is that it employs asymptotically exact atomic wave functions, which can be determined from known atomic parameters. The method is applied to $\text{Li}+\text{H}, \text{Na}+\text{H}$, and $\text{Mg}+\text{H}$ collisions, and the results compare well with existing detailed full-quantum calculations. The method is applied to the astrophysically important problem of $\text{Ca}+\text{H}$ collisions, and rate coefficients are calculated for temperatures in the range 1000–20 000 K.

This paper generalizes the Siegert pseudostate (SPS) formulation of scattering theory to arbitrary finite-range potentials without any symmetry in the three-dimensional (3D) case. The orthogonality and completeness properties of 3D SPSs are established. The SPS expansions for scattering states, outgoing-wave Green's function, scattering matrix, and scattering amplitude, that is, all major objects of scattering theory, are derived. The theory is illustrated by calculations for several model potentials. The results enable one to apply 3D SPSs as a purely discrete basis capable of representing both discrete and continuous spectra in solving various stationary and time-dependent quantum-mechanical problems.

Electric noise from metallic surfaces is a major obstacle towards quantum applications with trapped ions due to motional heating of the ions. Here, we discuss how the same noise source can also lead to pure dephasing of motional quantum states. The mechanism is particularly relevant at small ion-surface distances, thus imposing a constraint on trap miniaturization. By means of a free induction decay experiment, we measure the dephasing time of the motion of a single ion trapped 50 $\mu \mathrm{m}$ above a Cu-Al surface. From the dephasing times we extract the integrated noise below the secular frequency of the ion. We find that none of the most commonly discussed surface noise models for ion traps describes both the observed heating as well as the measured dephasing satisfactorily. Thus, our measurements provide a benchmark for future models for the electric noise emitted by metallic surfaces.

The cutoff regime of high-order harmonic generation (HHG) by atoms in an intense laser field is studied numerically and analytically. We find that the cutoff regime is characterized by equal dephasing between the successive harmonics. The change of the harmonic phase locking when HHG evolves from the cutoff to the plateau regime determines the optimal bandwidth of the spectral region which should be used for attosecond pulse generation via the amplitude gating technique. The minimal pulse duration which can be obtained with this technique in argon without using dispersion elements is approximately 0.08–0.1 of the laser cycle for different intensities and frequencies of the fundamental. The cutoff regime is also characterized by a linear dependence of the harmonic phase on the fundamental intensity. The proportionality coefficient grows as the cube of the fundamental wavelength, thus this dependence becomes very important for the HHG by midinfrared fields. Moreover, for every high harmonic there is a range of laser intensities providing the generation in the cutoff regime and the atomic response magnitude in this regime can be greater than that in the plateau regime. Thus, the cutoff regime substantially contributes to the harmonic energy emitted under typical experimental conditions where the laser intensity varies in time and space.

Since the well-known $\mathcal{PT}$ symmetry has its fundamental significance and implication in physics, where $\mathcal{PT}$ denotes a joint operation of space inversion $\mathcal{P}$ and time reversal $\mathcal{T}$, it is important and intriguing to explore exotic $\mathcal{PT}$-invariant topological metals and to physically realize them. Here we develop a theory for a different type of topological metals that are described by a two-band model of $\mathcal{PT}$-invariant topological nodal loop states in a three-dimensional Brillouin zone, with the topological stability being revealed through the $\mathcal{PT}$-symmetry-protected nontrivial ${\mathbb{Z}}_2$ topological charge even in the absence of both $\mathcal{P}$ and $\mathcal{T}$ symmetries. Moreover, the gapless boundary modes are demonstrated to originate from the nontrivial topological charge of the bulk nodal loop. Based on these exact results, we propose an experimental scheme to realize and to detect tunable $\mathcal{PT}$-invariant topological nodal loop states with ultracold atoms in an optical lattice, in which atoms with two hyperfine spin states are loaded in a spin-dependent three-dimensional optical lattice and two pairs of Raman lasers are used to create out-of-plane spin-flip hopping with site-dependent phase. It is shown that such a realistic cold-atom setup can yield topological nodal loop states, having a tunable band-touching ring with the twofold degeneracy in the bulk spectrum and nontrivial surface states. The nodal loop states are actually protected by the combined $\mathcal{PT}$ symmetry and are characterized by a ${\mathbb{Z}}_2$-type invariant (or topological charge), i.e., a quantized Berry phase. Remarkably, we demonstrate with numerical simulations that (i) the characteristic nodal ring can be detected by measuring the atomic transfer fractions in a Bloch-Zener oscillation; (ii) the topological invariant may be measured based on the time-of-flight imaging; and (iii) the surface states may be probed through Bragg spectroscopy. The present proposal for realizing topological nodal loop states in cold-atom systems may provide a unique experimental platform for exploring exotic $\mathcal{PT}$-invariant topological physics.

We investigate an optomechanical system which realizes the Jaynes-Cummings (JC) model known in cavity QED. Such a system consists of a single photon and an optomechanical cavity with two optical cavity modes and one mechanical mode. Under the resonance condition when the mechanical frequency is close to the frequency difference between the optical modes, the photon and phonons can be strongly coupled. We present an analytic solution of single-photon scattering and show that the spectrum of the scattered photon exhibits excitation-number-dependent Rabi splitting of the JC model. In addition, we examine the response of the mechanical mode to a sequence of single photons, with one photon in the cavity at a time. We show that sequential photon scattering can efficiently excite the mechanical mode and generate sub-Poisson phonon statistics.

We analyze the impact of delayed optical feedback (OF) on the spatiotemporal dynamics of the Lugiato-Lefever model. First, we carry out linear stability analysis and reveal the role of the OF strength and phase on the shape of the bistable curve as well as on Turing, Andronov-Hopf, and traveling-wave instability regions. Further, we demonstrate how the OF impacts the spatial dynamics by shifting the regions with different spatial eigenvalue spectra. In addition, we reveal a clustering behavior of cavity solitons as a function of the OF strength at fixed OF phase. Depending on the feedback parameters, OF can also induce a drift bifurcation of a stationary cavity soliton, as well as an Andronov-Hopf bifurcation of a drifting soliton. We present an analytical expression for the threshold of the drift bifurcation and show that above a certain value of the OF strength the system enters a region of spatiotemporal chaos.

It is known that any bipartite unitary operator of Schmidt rank 3 is equivalent to a controlled unitary under local unitaries. We propose a standard form of such operators. Using the form we improve the upper bound for the entanglement cost to implement such operators under local operations and classical communications (LOCC), and provide a corresponding protocol. A part of our protocol is based on a recursive-control protocol which is helpful for implementing other unitary operators. We show that any bipartite permutation unitary of Schmidt rank 3 can be implemented using LOCC and two ebits. We give two protocols for implementing bipartite permutation unitaries of any Schmidt rank $r$ and showed that one of the protocol uses $O\left(r\right)$ ebits of entanglement and $O\left(r\right)$ bits of classical communication, while these two types of costs for the other protocol scale as $O(rlogr)$ but the actual values are smaller for all $r<1100$. Based on this we obtain upper bounds of the number of nonlocal controlled-not gates needed to implement bipartite classical reversible maps using classical circuits under two different conditions. We also quantify the entangling power of bipartite permutation unitaries of Schmidt ranks 2 and 3. We show that they are respectively 1 ebit and some value between ${log}_{2}9–16/9$ and ${log}_{2}3$ ebits.