Many-body quantum systems present a rich phenomenology which can be significantly altered when they are in contact with an environment. In order to study such setups, a number of approximations are usually performed, either concerning the system, the environment, or both. A typical approach for large quantum interacting systems is to use master equations which are local, Markovian, and in Lindblad form. Here, we present an implementation of the Redfield master equation using matrix product states and operators. We show that this allows us to explore parameter regimes of the many-body quantum system and the environment which could not be probed with previous approaches based on local Lindblad master equations. We also show the validity of our results by comparing with the numerical exact thermofield-based chain-mapping approach.

The dynamics of a periodically driven system whose time evolution is governed by the Schrödinger equation with non-Hermitian Hamiltonians can be perfectly stable. This finding was only obtained very recently and will be enhanced by many exact solutions discovered in this work. The main concern of this study is to investigate the adiabatic following dynamics in such non-Hermitian systems stabilized by periodic driving. We focus on the peculiar behavior of stable cyclic (Floquet) states in the slow-driving limit. It is found that the stable cyclic states can either behave as intuitively expected by following instantaneous eigenstates, or exhibit piecewise adiabatic following by sudden switching between instantaneous eigenstates. We aim to cover broad categories of non-Hermitian systems under a variety of different driving scenarios. We systematically analyze the sudden-switch behavior by a universal route. That is, the sign change of the critical exponent in our asymptotic analysis of the solutions is always found to be the underlying mechanism to determine if the adiabatic following dynamics is trivial or piecewise. This work thus considerably extends our early study on the same topic [Gong and Wang, Phys. Rev. A 97, 052126 (2018)] and shall motivate more interest in non-Hermitian systems.

Time averaging of weak values using the quantum transition path time probability distribution enables us to establish a general uncertainty relation for the weak values of two not necessarily Hermitian operators. This new relation is a weak value analog of the Schrödinger strong value uncertainty relation. It leads to the conclusion that it is possible to determine with high accuracy the simultaneous mean weak values of noncommuting operators by judicious choice of the pre- and postselected states even when the postselected state is not an eigenfunction of one of the respective operators. When the time fluctuations of the two weak values are proportional to each other there is no uncertainty limitation on their variances and, in principle, their means can be determined with arbitrary precision even though their corresponding operators do not commute. To exemplify these properties we consider specific weak value uncertainty relations for the time-energy, coordinate-momentum, and coordinate–kinetic-energy pairs. In addition we analyze spin operators and the Stern-Gerlach experiment in weak and strong inhomogeneous magnetic fields. This classic case leads to anomalous spin values when the field is weak. The weak value uncertainty relation implies that anomalous spin values are associated with large variances so that their measurement demands increased signal averaging. These examples establish the importance of considering the time dependence of weak values in scattering experiments.

Realization of robust coherent quantum phase slips represents a significant experimental challenge. Here we propose a design consisting of multiple nanowire junctions to realize a phase-slip flux qubit. It admits good tunability provided by gate voltages applied on superconducting islands separating nanowire junctions. In addition, the gates and junctions can be identical to or distinct from each other, leading to symmetric and asymmetric setups. We find that the asymmetry can improve the performance of the proposed device compared with the symmetric case. In particular, it can enhance the effective rate of collective quantum phase slips. Furthermore, we demonstrate how to couple two such devices via a mutual inductance. This is potentially useful for quantum gate operations. Our investigation on how symmetry in multiple nanowire junctions affects the device performance should be useful for the application of phase-slip flux qubits in quantum information processing and quantum metrology.

An algorithm for optimizing the nonlinear parameters of all-electron explicitly correlated Gaussian functions is presented. The approach uses the time-dependent variational principle in combination with the imaginary-time propagation of the wave function to determine the optimal linear and nonlinear variational parameters. The approach is tested on the calculation of the ground-state energy of the ${\mathrm{HD}}^{+}$ molecule using complex-valued explicitly correlated Gaussians. The presented results show the efficiency and accuracy of the method.

The theory of the $g$ factor of an electron bound to a deformed nucleus is considered nonperturbatively and results are presented for a wide range of nuclei with charge numbers from $Z=16$ up to $Z=98$. We calculate the nuclear deformation correction to the bound electron $g$ factor within a numerical approach and reveal a sizable difference compared to previous state-of-the-art analytical calculations. We also note particularly low values in the region of filled proton or neutron shells, and thus a reflection of the nuclear shell structure both in the charge and neutron number.

We extend classical coarse-grained entropy, commonly used in many branches of physics, to the quantum realm. We find two coarse grainings, one using measurements of local particle numbers and then total energy, and the second using local energy measurements, which lead to an entropy that is defined outside of equilibrium, is in accord with the thermodynamic entropy for equilibrium systems, and reaches the thermodynamic entropy in the long-time limit, even in genuinely isolated quantum systems. This answers the long-standing conceptual problem, as to which entropy is relevant for the formulation of the second thermodynamic law in closed quantum systems. This entropy could be in principle measured, especially now that experiments on such systems are becoming feasible.

We propose a revised observable for the current in an open tight-binding system. Assuming a conserved number of electrons and within Markovian dynamics, we first derive the general formula using local charge conservation, then a simple expression of the open system current operator is recovered under translation invariance and single-particle approximation. Compared with the established result for a closed system, this expression contains an extra term for each Lindblad operator. In the demonstration with a two-dimensional two-band topological insulator at zero temperature, we show that such an extra term is nontrivial in maintaining the robustness of quantized Hall conductivity against pure dephasing and cooling in an energy basis. Moreover, we show that site-local noise described in two different ways is trivial to the formalism of the current operator, which nevertheless by no means prevents it from affecting conductivity.

We investigate the detailed properties of observational entropy, introduced by Šafránek et al. [Phys. Rev. A 99, 010101 (2019)] as a generalization of Boltzmann entropy to quantum mechanics. This quantity can involve multiple coarse grainings, even those that do not commute with each other, without losing any of its properties. It is well-defined out of equilibrium, and for some coarse grainings it generically rises to the correct thermodynamic value even in a genuinely isolated quantum system. The quantity contains several other entropy definitions as special cases, it has interesting information-theoretic interpretations, and mathematical properties—such as extensivity and upper and lower bounds—suitable for an entropy. Here we describe and provide proofs for many of its properties, discuss its interpretation and connection to other quantities, and provide numerous simulations and analytic arguments supporting the claims of its relationship to thermodynamic entropy. This quantity may thus provide a clear and well-defined foundation on which to build a satisfactory understanding of the second thermodynamical law in quantum mechanics.

In this paper, by minimizing the coherence quantifiers over all states in an $\epsilon$ ball around a given state, we define a generalized smooth quantifier, called the $\epsilon$-smooth measure of coherence. We use it to estimate the difference between the expected state and the actually prepared state and quantify quantum coherence contained in an actually prepared state, and it can been interpreted as the minimal coherence guaranteed to present in an $\epsilon$ ball around given quantum state. We find that the $\epsilon$-smooth measure of any coherence monotone is still a coherence monotone, but it does not satisfy monotonicity on average under incoherent operations. We show the $\epsilon$-smooth measure of coherence is continuous even if the original coherence quantifier is not. We also study the $\epsilon$-smooth measure of distance-based coherence quantifiers, and some interesting properties are given. Moreover, we discuss the dual form of the $\epsilon$-smooth measure of coherence by maximizing over all states in an $\epsilon$ ball around the given state and show that the dual $\epsilon$-smooth measure of coherence provides an upper bound of one-shot coherence distillation.

The fast electrical explosion of fine metal wires in a vacuum will produce calibrated gas cylinders of metal atoms surrounded by a low-density corona. For fully vaporized wires, the integrated-phase technique, based on laser interferometry, provides the dynamic dipole polarizability of metal atoms. A fast-rising current of $\sim 1\mathrm{kA}/\mathrm{ns}$ will vaporize thin 12.7-µm-diameter Au and Cu wires in a vacuum and generate a radial-expanding gas cylinder surrounded by low-density plasma corona. Employing the integrated-phase technique on fast-exploding Au and Cu wires, we find that the dynamic dipole polarizability of Au atoms is $8.3\pm 0.8{\AA }^3$ for 532 nm and $7.0\pm 0.7{\AA }^3$ for 1064 nm. Measurements collected from exploding Cu wire provide dynamic dipole polarizability of $10.2\pm 1{\AA }^3$ for 532 nm and $6.5\pm 0.7{\AA }^3$ for 1064 nm. All experimental values correspond to theoretical predictions based on quantum-mechanical calculations.

We study Efimov physics for three identical bosons interacting via a pairwise square-well potential, analyze the validity of the separable approximation as a function of the interaction strength, and investigate what is needed to improve this approximation. We find separable approximations to be accurate for potentials with just one (nearly) bound dimer state. For potentials with more bound or almost bound dimer states, these states need to be included for an accurate determination of the Efimov spectrum and the corresponding three-body observables. We also show that a separable approximation is insufficient to accurately compute the trimer states for energies larger than the finite-range energy even when the two-body $T$ matrix is highly separable in this energy regime. Additionally, we have analyzed three distinct expansion methods for the full potential that give exact results and thus improve on the separable approximation. With these methods, we demonstrate the necessity to include higher partial-wave components of the off-shell two-body $T$ matrix in the three-body calculations. Moreover, we analyze the behavior of the Efimov states near the atom-dimer threshold and observe the formation of non-Efimovian trimer states as the potential depth is increased. Our results can help to elaborate simpler theoretical models that are capable of reproducing the correct three-body physics in atomic systems.

Understanding fundamentals of few-body physics provides an interesting bottom-up approach for the clarification of many-body properties. The remarkable experimental progress in realizing spin-orbit coupling (SOC) in optical Raman lattices offers a renewed thrust towards discovering novel few-body features induced by the interplay between SOC and optical lattices. Using the Wilson renormalization method to account for high-band effects, we study the low-energy two-body scattering processes of spin-$1/2$ fermions in spin-orbit-coupled optical lattices. We demonstrate that, under weak SOC, adding a small lattice potential would destabilize shallow two-body bound states, contrary to conventional wisdom. On the other hand, when the lattice is sufficiently deep, two-body bound states are always stabilized by increasing the lattice depth. This intriguing nonmonotonic behavior of the bound-state stability derives from the competition between SOC and optical lattices and can be explained by analyzing the low-energy density of states. We also discuss the impact of high-band effects on such a behavior, as well as potential experimental detection.

By decomposing the initial-state wave function into its unique natural orbital expansion, as defined in the 1950s by Löwdin and used in modern studies of entanglement, we analyze the role of electron correlation in the initial state of an atom or molecule in determining the angular distribution of one-photon double ionization. Final-state correlation of the two ejected electrons is treated completely in numerically accurate calculations as the initial states of He, ${\mathrm{H}}^{-}$, and ${\mathrm{H}}_2$ are built up from correlating configurations in strict order of decreasing natural orbital occupations. In the two-electron atoms it is found that the initial-state correlation plays a sometimes modest but generally measurable role. In striking contrast, for ${\mathrm{H}}_2$ a large number of correlating configurations in the ground state is often necessary to produce angular distributions even approximately resembling the correct ones. One-photon double photoionization of oriented ${\mathrm{H}}_2$ is found to be particularly sensitive to left-right correlation along the bond.

We apply the extended multiconfiguration time-dependent Hartree-Fock method to the simulation of a hydrogen molecular ion exposed to an intense laser pulse. By comparing the results obtained by this method with the results obtained by a method in which the time-dependent Schrödinger equation is solved directly on a three-dimensional grid, we find that the results obtained by these two methods are in good agreement with each other when the number of time-dependent expansion terms exceeds 8. We further compare the results with those obtained by the conventional two-state Born-Oppenheimer approximation. In order to interpret the resultant time-dependent wave functions, we decompose the total wave function into the natural electronic and protonic orbitals that diagonalize the single-particle density matrices and find that the pair of electronic and protonic natural orbitals carrying the largest population describes the vibrational excitation, while the pair carrying the second largest population describes the dissociation into $\text{H}+{\mathrm{H}}^{+}$. We also examine the time-dependent motion of the protons in ${\mathrm{H}}_2^{+}$ in terms of the time-dependent adiabatic potential-energy curves, which are defined as the instantaneous eigenvalues of the Hamiltonian matrix governing the time-dependent motion of the protonic orbitals. We show that two potential minima are formed on the lowest-energy adiabatic potential-energy curve and that the nuclear wave packet localized in the inner minimum corresponds to the bound vibrational motion, while the nuclear wave packet localized in the outer minimum corresponds to the dissociation.

Trapped ions are ideally suited for precision spectroscopy, as is evident from the remarkably low systematic uncertainties of single-ion clocks. The major weakness of these clocks is the long averaging time, necessitated by the low signal of a single atom. An increased number of ions can overcome this limitation and allow for the implementation of novel clock schemes. However, this presents the challenge to maintain the excellent control over systematic shifts of a single particle in spatially extended and strongly coupled many-body systems. We measure and deduce systematic frequency uncertainties related to spectroscopy with ion chains in an rf trap array designed for precision spectroscopy on simultaneously trapped ion ensembles. For the example of an ${\mathrm{In}}^{+}$ clock, sympathetically cooled with ${\mathrm{Yb}}^{+}$ ions, we show in our system that the expected systematic frequency uncertainties related to multi-ion operation can be below $1\times {10}^{-19}$. Our results pave the way to advanced spectroscopy schemes such as entangled clock spectroscopy and cascaded clock operation.

We combine a bichromatic white light polarization pulse shaping scheme with angle- and energy-resolved photoelectron spectroscopy to image the dynamics of atomic Rydberg wave packets. Background-free detection of the Rydberg dynamics is performed using shaper-generated bichromatic linearly and circularly polarized femtosecond pump-probe pulse sequences. Photoelectron momentum distributions from linearly polarized bichromatic fields feature pronounced time-, energy-, and angle-dependent dynamics, which result from the interference of $s$-, $d$-, and $g$-type photoelectron wave packets from the ionization of the Rydberg $np$ and $nf$ series. Detailed analysis of the highly differential data allows us to extract the dynamics of both Rydberg wave packets separately. The results are experimentally verified by additional pump-probe studies with bichromatic circularly polarized pulse sequences, which exclusively map the dynamics of the Rydberg $nf$ series via $g$-type photoelectron wave packets.

We present an alternative way of computing nonrelativistic single-particle spectra from holography. To this end, we introduce a mass gap in a holographic Dirac semimetal and subsequently study the nonrelativistic limit of the resulting spectral functions. We use this method to compute the momentum distributions and the equation of state of our nonrelativistic fermions, of which the latter can be used to extract all thermodynamic properties of the system. We find that our results are universal and reproduce many experimentally and theoretically known features of an ultracold Fermi gas at unitarity.

We present an experimental study of the effects of temporal modulation of the pump intensity on a random laser. The nanosecond pump pulses exhibit rapid intensity fluctuations which differ from pulse to pulse. Specific temporal profiles of the pump pulses produce extraordinarily strong emission from the random laser. This process is deterministic and insensitive to the spatial configuration of the scatterers and spontaneous emission noise.

Amplification of an entangled state is a matter of great significance in quantum communication. However, any parametric amplifier (PA) will introduce added noise into the system which unavoidably degrades the entanglement or even makes it disappear. Recently, it has been experimentally demonstrated that amplification of one half of a two-mode squeezed state is possible while preserving entanglement [Phys. Rev. Lett. 103, 010501 (2009)]. However, such entanglement cannot be maintained when the strength of the amplification is large. To solve this problem, we propose a correlation modulation scheme (CMS), which fully exploits the quantum correlation between the two output states from the PA process, to suppress the added noise from the parametric amplifications. For amplifying an entangled state using a PA, we demonstrate that the CMS not only better maintains but also always preserves the entanglement whatever the strength of the PA. Such a CMS may pave the way to low-noise amplification of an entangled state.