High-precision surface-roughness estimation plays an important role in many applications. However, the classical estimating methods are limited by shot noise and can only achieve a precision of 0.1 nm with a white-light interferometer. Here, we propose two weak-measurement schemes to estimate surface roughness through a spectrum analysis and intensity analysis. The estimating precision with the spectrum analysis is about ${10}^{-5}$ nm by using a currently available spectrometer with a resolution of $\mathrm{\Delta }\lambda =0.04$ pm and the corresponding sensitivity is better than 0.1 THz/nm. The precision and sensitivity of the light intensity analysis scheme achieved is as high as 0.07 nm and 1/nm, respectively. By introducing a modulated phase, we show that the sensitivity and precision achieved in our schemes can be effectively retained in a wider dynamic range. We further provide the experimental design of a surface profiler based on our schemes. It simultaneously meets the requirements of high precision, high sensitivity, and a wide measurement range, making it a promising practical tool.

Entanglement and polarization are mutually constrained by the relationship $C^2+P^2=1$, which engages the concurrence $C$ of a pure, two-qubit state and the degree of polarization $P$ of either of its two subsystems. How the above constraint generalizes for mixed states is an open question. We address mixed, two-qubit states of the $X$ type, i.e., those whose density matrix has nonzero elements only in the two main diagonals. We focus on mixed states that arise out of a pure, two-qubit state that is subjected to either the amplitude damping channel or the depolarizing channel. We derive alternative constraints for concurrence and polarization and test them experimentally with polarization-entangled photons. We argue that our theoretical results hold also for classical light, whenever two binary degrees of freedom can be entangled.

We study Krylov complexity $C_K$ and operator entropy $S_K$ in operator growth. We find that for a variety of systems, including chaotic ones and integrable theories, the two quantities always enjoy a logarithmic relation $S_K\sim \text{ln}{C}_K$ at long times, where dissipative behavior emerges in unitary evolution. Otherwise, the relation does not hold any longer. Universality of the relation is deeply connected to irreversibility of operator growth.

The optimal quantum measurements for estimating individual parameters might be incompatible with each other, so they cannot be jointly performed. The tradeoff between the estimation precisions for different parameters can be characterized by information regret: the difference between the Fisher information and its quantum limit. We show that the information-regret-tradeoff relation can give us not only an intuitive picture of the potential for improving the joint scheme for estimating the centroid and the separation but also some clues to the optimal measurements for the sequential scheme. In particular, we show that, for two incoherent point sources with a very small separation, the optimal measurement for the separation must extract little information about the centroid and vice versa.

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

The two-photon annihilation of a positron with an electron bound in the $1s$ state of a H-like ion is calculated within the fully relativistic QED framework. The interaction with the nucleus is treated nonperturbatively, thus allowing the calculations to be carried out for the annihilation with strongly bound inner shells of heavy ions. Infrared divergences, appearing when one of the emitted photons approaches the low-frequency limit, are accurately eliminated from final expressions. The total cross section of the two-photon and one-photon annihilation processes are compared for a wide range of collision energies and nuclear charge numbers. It is demonstrated that the two-photon annihilation channel dominates over the one-photon channel for the low- and medium-$Z$ ions, whereas for the high-$Z$ ions the situation reverses.

We study theoretically the fragmentation of the helium dimer, ${}^4\mathrm{He}_2$, into singly charged ions in collisions with relativistic highly charged projectiles. We discuss the main mechanisms driving this process with the focus on the fragmentation caused by direct ionization of both atomic sites of the dimer in a single collision with the projectile. This direct mechanism dominates the ${\mathrm{He}}_2\to {\mathrm{He}}^{+}+{\mathrm{He}}^{+}$ breakup events with the kinetic energies of the emerging ionic fragments below 4–5 eV. We explore the energy and angular distributions of the ${\mathrm{He}}^{+}$ ions produced in collisions with 1 and 7 GeV/u ${\mathrm{U}}^{92+}$ projectiles and show that their shape is significantly affected by relativistic and higher-order effects in the interaction between the projectile and the dimer. We also show that the shape of the energy spectrum is quite sensitive to the binding energy of the ${\mathrm{He}}_2$ dimer, which can be exploited for its precise determination. The contribution of the direct mechanism to the total cross section for the ${\mathrm{He}}_2$ fragmentation by 1 and 7 GeV/u ${\mathrm{U}}^{92+}$ was calculated to be 3.65 Mb and $2.4\mathrm{Mb}$, respectively, representing roughly half of this cross section.

Spin-orbit coupling plays an important role in understanding exotic quantum phases. In this work, we present a scheme to combine spin-orbital-angular-momentum (SOAM) coupling and strong correlations in ultracold atomic gases. Essential ingredients of this setting is the interplay of SOAM coupling and Raman-induced spin-flip hopping, engineered by lasers that couples different hyperfine spin states. In the presence of SOAM coupling only, we find rich quantum phases in the Mott-insulating regime, which support different types of spin defects such as spin vortex and composite vortex with antiferromagnetic core surrounded by the outer spin vortex. Based on an effective exchange model, we find that these competing spin textures are a result of the interplay of Dzyaloshinskii-Moriya and Heisenberg exchange interactions. In the presence of both SOAM coupling and Raman-induced spin-flip hopping, more many-body phases appear, including canted-antiferromagnetic and stripe phases. Our prediction suggests that SOAM coupling could induce rich exotic many-body phases in the strongly interacting regime.

After release from the trap the momentum distribution of an impenetrable gas asymptotically approaches that of a spinless noninteracting Fermi gas in the initial trap. This phenomenon is called dynamical fermionization and, very recently, has been experimentally confirmed in the case of the Lieb-Liniger model in the Tonks-Girardeau regime. We prove analytically and confirm numerically that following the removal of axial confinement the strongly interacting Bose-Fermi mixture exhibits dynamical fermionization and the asymptotical momentum distribution of each component has the same shape as its density profile at $t=0$. Under a sudden change of the trap frequency to a new nonzero value the dynamics of both fermionic and bosonic momentum distributions presents characteristics which are similar to the case of single component bosons experiencing a similar quench. Our results are derived using a product representation for the correlation functions which, in addition to analytical considerations, can be implemented numerically very easily with complexity which scales polynomially in the number of particles.

We reflect on the prospect of exploiting the recoil associated with absorption and emission of photons to perform spectroscopy of a single molecular ion. For this recoil to be detectable, the molecular ion is sympathetically cooled by a laser-cooled atomic ion to near their common quantum-mechanical ground state within a trapping potential. More specifically, we present a general framework for simulating the expected photon recoil spectra in regimes where either the natural transition linewidth ${\mathrm{\Gamma }}_t$ of the molecular ion or the spectral width ${\mathrm{\Gamma }}_L$ of the exciting light source exceeds the motional frequencies of the two-ion system. To exemplify the framework, we present two complementary cases: spectroscopy of the broad $3\mathrm{s} {}^2\mathrm{S}_{1/2}-3\mathrm{p} {}^2\mathrm{P}_{3/2}$ electronic transition (${\mathrm{\Gamma }}_t/2\pi =41.8\mathrm{M}\mathrm{Hz}$) of a single ${}^{24}\mathrm{Mg}^{+}$ ion at $\lambda =279.6$ nm by a narrow laser source $({\mathrm{\Gamma }}_L/2\pi \lesssim 1\mathrm{MHz})$ and mid-infrared vibrational spectroscopy of the very narrow $|v=0,J=1\rangle -|v^{\prime }=1,J^{\prime }=0\rangle$ transition $({\mathrm{\Gamma }}_t/2\pi =2.50\mathrm{Hz})$ at $\lambda =6.17\mu \mathrm{m}$ in the ${}^1\mathrm{\Sigma }^{+}$ electronic ground state of ${}^{24}\mathrm{MgH}^{+}$ by a broadband laser source $({\mathrm{\Gamma }}_L/2\pi \gtrsim 50\mathrm{MHz})$. The atomic ion ${}^{24}\mathrm{Mg}^{+}$ has been picked to introduce a simple system to make comparisons with experimental results while still capturing most of the physics involved in electronic excitations of molecular ions.

The emerging quantum technologies rely on our ability to establish and control quantum systems in nonclassical states, exhibiting entanglement and quantum coherence. It is thus crucial to understand how entanglement and coherence can be created in the most efficient way. In this Letter we study optimal ways to create a large amount of quantum coherence via quantum channels. For this, we compare different scenarios, where the channel is acting on an incoherent state, on states which have coherence, and also on subsystems of multipartite quantum states. We show that correlations in multipartite systems do not enhance the ability of a quantum channel to create coherence. We also study the ability of quantum channels to destroy coherence, proving that a channel can destroy more coherence when acting on a subsystem of a bipartite state. Crucially, we also show that the destroyed coherence on a multipartite system can exceed the upper bound of those on the single system when the total state is entangled. Our results significantly simplify the evaluation of the coherence generating capacity of quantum channels, which we also discuss.

A relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles was constructed by Razavi [Il Nuovo Cimento B 63, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the time-of-arrival problem that goes beyond Razavi's original results. This allows us to use time-of-arrival eigenfunctions that exhibit unitary arrival to construct time-of-arrival distributions. The expectation value is also calculated and shown that particles can arrive earlier or later than expected classically. Last, the constructed time-of-arrival distribution and expectation value are shown to be consistent with special relativity.

We propose delayed-choice experiments carried out with macroscopic qubits, realized as macroscopically distinct coherent states $|\alpha \rangle$ and $|-\alpha \rangle$. Quantum superpositions of $|\alpha \rangle$ and $|-\alpha \rangle$ are created via a unitary interaction $U\left(\theta \right)$ based on a nonlinear Hamiltonian, in analogy with polarizing beam splitters used in photonic experiments. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality: This would otherwise suggest changes to the macroscopic qubit value based on a future measurement setting $\varphi$. We therefore consider weak macroscopic realism (wMR), which for the system at time $t$ specifies a hidden variable ${\lambda }_{\theta }$ to determine the macroscopic qubit value, independently of $\varphi$. Using entangled cat states, we demonstrate a quantum eraser where the choice to measure a which-way or wave-type property is delayed. Consistency with wMR is possible, if we interpret the macroscopic qubit value to be determined by ${\lambda }_{\theta }$ without specification of the state at the level of $\hslash$. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the Wheeler-Chaves-Lemos-Pienaar dimension witness inequality, for the macroscopic qubits. This negates all two-dimensional nonretrocausal wMR models. However, one can interpret consistently with wMR, thus avoiding conclusions of macroscopic retrocausality, by noting extra dimensions, and that violations require further unitary dynamics $U$ after $t$. The violations are then explained as failure of deterministic macroscopic realism, which specifies the validity of ${\lambda }_{\theta }$ prior to the dynamics $U\left(\theta \right)$ determining the measurement setting $\theta$. Finally, although there is consistency with wMR for macroscopic observations, Einstein-Podolsky-Rosen–type paradoxes pointing to the incompleteness of quantum mechanics exist at a microscopic level, based on fringe distributions.

Variational algorithms are promising candidates to be implemented on near-term quantum computers. In our work, we investigate the variational Hamiltonian ansatz (VHA), where a parametrized trial state of the quantum mechanical wave function is optimized to obtain the ground-state energy. In the VHA, the trial state is given by a noninteracting reference state modified by unitary rotations using generators that are part of the Hamiltonian describing the system. The lowest energy is obtained by optimizing the angles of those unitary rotations. A standard procedure to optimize the variational parameters is to use gradient-based algorithms. However, shot noise and the intrinsic noise of the quantum device affect the evaluation of the required gradients. We study how different methods for obtaining the gradient, specifically the finite-difference and the parameter-shift rule, are affected by shot noise and the noise of the quantum computer. To this end, we simulate a simple quantum circuit, as well as the two-site and six-site Hubbard models.

The successive ionization potentials (IPs) and electron affinities (EAs) for superheavy elements with $111\le Z\le 114$, namely, Rg, Cn, Nh, and Fl, are reexamined using the relativistic Fock-space coupled-cluster method with nonperturbative single (S), double (D), and triple (T) cluster amplitudes (FS-CCSDT). For most of the considered quantities, the triple-amplitude contributions turn out to be important. The Breit and frequency-dependent Breit corrections are evaluated by means of the configuration-interaction method. The quantum-electrodynamics corrections to the IPs and EAs are taken into account within the model-QED-operator approach. The obtained results are within 0.10 eV uncertainty.

We theoretically studied the tunneling ionization time of atomic $p_{\pm }$ orbitals by introducing a weak linearly polarized second-harmonic field to the attoclock frame. In our scheme, the ionization time is retrieved by analyzing the relative phase dependence of ionization yield, where one can be free from handling the Coulomb interaction on the emitted electron. By solving the time-dependent Schrödinger equation, we verified that at low laser intensity the ionization time delays are both close to zero for the $2p_{\pm }$ orbitals, though their offset angles in the photoelectron angular distributions are different. As the laser intensity increases, the atomic orbitals are deformed significantly, which affects the tunneling-ionization-time distribution. With our scheme, the orbital deformation-induced ionization time delay is unambiguously determined. Furthermore, the depletion of the ground state at the high laser intensity enhances the relative contribution of early ionization events and thus the ionization peak shifts to the earlier time. This effect is also directly revealed by our scheme.

In this paper, we show that an effective spin Hamiltonian with various types of couplings can be engineered using quantum simulators in atomic-molecular-optical laboratories, dubbed the $XY$-Gamma model. We analytically solve the one-dimensional short-range interacting case with the Jordan-Wigner transformation and establish the phase diagram. In the gapless phase, an incommensurate spiral order is manifested by the vector-chiral correlations. Between distinct gapped phases, a logarithmic scaling behavior of local measures, including spin correlations and the steered quantum coherence, is identified for the quantum critical points, yielding a compelling value of the correlation-length critical exponent. We derive explicit scaling forms of the excitation gap near the quantum critical points. The extracted critical exponents reveal the quantum phase transition on the boundary of Tomonaga-Luttinger liquid belongs to Lifshitz universality class. Our results may provide useful insights into the underlying mechanism in quantum criticality for state-of-the-art experiments of quantum simulation.

An accurate knowledge of the scattering length is fundamental in ultracold quantum gas experiments and essential for the characterization of the system as well as for a meaningful comparison to theoretical models. Here, we perform a careful characterization of the $s$-wave scattering length $a_{\mathrm{s}}$ for the four highest-abundance isotopes of erbium, in the magnetic field range from 0 to 5 G. We report on cross-dimensional thermalization measurements and apply the Enskog equations of change to numerically simulate the thermalization process and to analytically extract an expression for the so-called number of collisions per rethermalization (NCPR) to obtain $a_{\mathrm{s}}$ from our experimental data. We benchmark the applied cross-dimensional thermalization technique with the experimentally more demanding lattice modulation spectroscopy and find good agreement for our parameter regime. Our experiments are compatible with a dependence of the NCPR with $a_{\mathrm{s}}$, as theoretically expected in the case of strongly dipolar gases. Surprisingly, we experimentally observe a dependency of the NCPR on the density, which might arise due to deviations from an ideal harmonic trapping configuration. Finally, we apply a model for the dependency of the background scattering length with the isotope mass, allowing us to estimate the number of bound states of erbium.

Self-organized phases in cold atoms as a result of light-mediated interactions can be induced by coupling to internal or external degrees of the atoms. There has been growing interest in the interaction of internal spin degrees of freedom with the optomechanical dynamics of the external center-of-mass motion. We present a model for the coupling between magnetic and optomechanical structuring in a $J=1/2\to J^{\prime }=3/2$ system in a single-mirror feedback scheme, which is representative of a larger class of diffractively coupled systems such as longitudinally pumped cavities and counterpropagating-beam schemes. For negative detunings, a linear stability analysis demonstrates that optical pumping and optomechanical driving cooperate to create magnetic ordering. However, for long-period transmission gratings the magnetic driving will strongly dominate the optomechanical driving, unless one operates very close to the existence range of the magnetic instability. At small lattice periods, in particular at wavelength-scale periods, the optomechanical driving will dominate.

The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\mathcal{PT}$-symmetric, quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet nontrivial exactly solvable dilation problem for two-dimensional time-dependent $\mathcal{PT}$-symmetric Hamiltonians. Our system is initially set in the unbroken $\mathcal{PT}$-symmetric phase, then goes across the so-called exceptional point, and ends in the broken $\mathcal{PT}$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\mathcal{PT}$-symmetric system are analytically worked out. By investigating the large-time behaviors, we give an effective method to choose and adjust the dilation parameters. Our result also shows that the exceptional points do not have much physical relevance in a time-dependent system.