New classical modalities of atomic force microscopy continue to emerge to achieve higher spatial, spectral, and temporal resolution for nanometrology of materials. Here, we introduce the concept of a quantum-mechanical modality that capitalizes on squeezed states of probe displacement. We show that such squeezing is enabled nanomechanically when the probe enters the van der Waals regime of interaction with a sample. The effect is studied in the noncontact mode, where we consider the parameter domains characterizing the attractive regime of the probe-sample interaction force.

The original Heisenberg error-disturbance relation was recently shown to be not universally valid and two different approaches to reformulate it were proposed. The first one focuses on how the error and disturbance of two observables $A$ and $B$ depend on a particular quantum state. The second one asks how a joint measurement of $A$ and $B$ affects their eigenstates. Previous experiments focused on the first approach. Here we focus on the second one. First, we propose and implement an extendible method of quantum-walk-based joint measurements of noisy Pauli operators to test the error-disturbance relation for qubits introduced in the work of Busch et al. [Phys. Rev. A 89, 012129 (2014)], where the polarization of the single photon, corresponding to a walker's auxiliary degree of freedom that is commonly known as a coin, undergoes a position- and time-dependent evolution. Then we formulate and experimentally test a universally valid state-dependent relation for three mutually unbiased observables. We therefore establish a method of testing error-disturbance relations.

We study the effective Bloch-wave scattering of a spinless Fermi gas in one-dimensional (1D) optical lattices. By tuning the odd-wave scattering length, we find multiple resonances of Bloch waves scattering at the bottom (and the top) of the lowest band, beyond which an attractive (and a repulsive) two-body bound state starts to emerge. These resonances exhibit comparable widths in the deep lattice limit, and the finite interaction range plays an essential role in determining their locations. Based on exact two-body solutions, we construct an effective microscopic model for the low-energy scattering of fermions. The model can reproduce not only the scattering amplitudes of Bloch waves at the lowest-band bottom or top, but also the attractive or repulsive bound states within a reasonably large energy range below or above the band. These results lay the foundation for quantum simulating topological states in cold Fermi gases confined in 1D optical lattices.

In a recent work, we have derived simple Lindblad-based equations for the thermalization of systems in contact with a thermal reservoir. Here, we apply these equations to the Lipkin-Meshkov-Glick model in contact with blackbody radiation and analyze the dipole matrix elements involved in the thermalization process. We find that the thermalization can be complete only if the density is sufficiently high, while, in the limit of low density, the system thermalizes partially, namely, within the Hilbert subspaces where the total spin has a fixed value. In this regime, and in the isotropic case, we evaluate the characteristic thermalization time analytically, and show that it diverges with the system size in correspondence with the critical points and inside the ferromagnetic region. Quite interestingly, at zero temperature the thermalization time diverges only quadratically with the system size, whereas quantum adiabatic algorithms, aimed at finding the ground state of the same system, imply a cubic divergence of the required adiabatic time.

We develop a theory of infrared (IR)-pump–x-ray-probe spectroscopy for molecular studies. We illustrate advantages of the proposed scheme by means of numerical simulations employing a vibrational wave packet technique applied to x-ray absorption and resonant inelastic x-ray scattering (RIXS) spectra of the water molecule vibrationally excited by a preceding IR field. The promotion of the vibrationally excited molecule to the dissociative $1a_1^{-1}4a_1$ and bound $1a_1^{-1}2b_2$ core-excited states with qualitatively different shapes of the potential energy surfaces creates nuclear wave packets localized along and between the OH bonds, respectively. The projection of these wave packets on the final vibrational states, governed by selection and propensity rules, results in spatial selectivity of RIXS sensitive to the initial vibrationally excited state, which makes it possible to probe selectively the ground state properties along different modes. In addition, we propose to use RIXS as a tool to study x-ray absorption from a selected vibrational level of the ground state when the spectral resolution is sufficiently high to resolve vibrational overtones. The proposed technique has potential applications for advanced mapping of multidimensional potential energy surfaces of ground and core-excited molecular states, for symmetry-resolved spectroscopy, and for steering chemical reactions.

Nonresonant electron-positron pair photoproduction on a nucleus in the field of two pulsed light waves is studied theoretically. The process is considered in detail within the interference kinematic region, when stimulated absorption and emission of photons of external pulsed waves by an electron and a positron occurs in a correlated manner. Within this region, a correspondence between the emission angle and energy of the produced particles appears. The distribution of the obtained differential cross section over the pair kinetic energy is characterized by presence of oscillations, within the interference region. Each of the maxima corresponds to the definite partial process with emission and absorption of an equal number of photons of both waves. It was shown that the differential cross section within the interference region for certain values of the pair energy may exceed the cross section in other scattering kinematics in two orders of the magnitude. Obtained results may be experimentally verified, for example, by scientific facilities at sources of pulsed laser radiation (SLAC, FAIR, ELI, XCELS).

We derive exact monochromatic solutions of both Maxwell's and Poynting's equations in vacuum, finding the six electric and magnetic field components of a beam of light at angular frequency ω directed along an arbitrary axis $z$, having its focal plane at $z=0$. The beam power $P$ (i.e., the integral over the $x-y$ plane of the $z$ component of the Poynting vector $I_z$) does not vary with $z$. Our formulas for the electric and magnetic fields, as well as for $I_z$, are simple enough to allow their numerical evaluation with a pocket scientific calculator. They contain only one (real and positive) adjustable parameter $Q$ which determines the degree of focusing of the beam. In the case of weak focusing ($Q\gg 1$) our solutions merge with the commonly used $\mathrm{TE}{\mathrm{M}}_{0,0}$ Gaussian beam fields.

Using different configurations of applied strong driving and weak probe fields, we find that only a single three-level superconducting quantum circuit (SQC) is enough to realize amplification, attenuation, and frequency conversion of microwave fields. Such a three-level SQC has to possess $\mathrm{\Delta }$-type cyclic transitions. Different from the parametric amplification (attenuation) and frequency conversion in nonlinear optical media, the real energy levels of the three-level SQC are involved in the energy exchange when these processes are completed. We quantitatively discuss the effects of amplification (attenuation) and the frequency conversion for different types of driving fields. The values and conditions are obtained for the optimal gains for amplification (attenuation) and the optimal conversion efficiencies. Our study provides a method to amplify (attenuate) microwave, realize frequency conversion, and also lay a foundation for generating single or entangled microwave photon states using a single three-level SQC.

We study the relationship between the collective phenomena of super- and subradiance and spontaneous synchronization of quantum systems. To this aim we revisit the case of two detuned qubits interacting through a pure dissipative bosonic environment, which contains the minimal ingredients for our analysis. By using the Liouville formalism, we are able to find analytically the ultimate connection between these phenomena. We find that dynamical synchronization is due to the presence of longstanding coherence between the ground state of the system and the subradiant state. We finally show that, under pure dissipation, the emergence of spontaneous synchronization and of subradiant emission occur on the same time scale. This reciprocity is broken in the presence of dephasing noise.

The transmission of polarized light through a two-dimensional randomly rough interface between two dielectric media has been much less studied, by any approach, than the reflection of light from such an interface. We have derived a reduced Rayleigh equation for the transmission amplitudes when $p$- or $s$-polarized light is incident on this type of interface, and have obtained rigorous, purely numerical, nonperturbative solutions of it. The solutions are used to calculate the transmissivity and transmittance of the interface, the mean differential transmission coefficient, and the full angular distribution of the intensity of the transmitted light. These results are obtained for both the case where the medium of incidence is the optically less dense medium and in the case where it is the optically more dense medium. Optical analogs of Yoneda peaks observed in the scattering of x rays from metallic and nonmetallic surfaces are present in the results obtained in the former case. For $p$-polarized incident light we observe Brewster scattering angles, angles at which the diffuse transmitted intensity is zero in a single-scattering approximation, which depend on the angle of incidence in contrast to the Brewster angle for flat-surface reflection.

We study the properties of a refined weak-coupling limit that preserves complete positivity in order to describe non-Markovian dynamics in the spin-boson model. With this tool, we show the system presents a rich non-Markovian phenomenology. This implies a dynamical difference between entanglement and coherence: the latter undergoes revivals, whereas the former not, despite the induced dynamics being fully incoherent. In addition, the evolution presents “quasieternal” non-Markovianity, becoming nondivisible at any time period where the system evolves qualitatively. Furthermore, the method allows for an exact derivation of a master equation that accounts for a reversible energy exchange between system and environment. Specifically, this is obtained in the form of a time-dependent Lamb shift term.

We propose a generation of a low-noise state of optomechanical oscillator by a temperature-dependent force. We analyze the situation in which a quantum optomechanical oscillator (denoted as the membrane) is driven by an external force (produced by the piston). Both systems are embedded in a common heat bath at certain temperature $T$. The driving force the piston exerts on the membrane is bath temperature dependent. Initially, for $T=T_0$, the piston is linearly coupled to the membrane. The bath temperature is then reversibly changed to $T\ne T_0$. The change of temperature shifts the membrane, but simultaneously also increases its fluctuations. The resulting equilibrium state of the membrane is analyzed from the point of view of mechanical, as well as of thermodynamic, characteristics. We compare these characteristics of membrane and derive their intimate connection. Next, we cool down the thermal noise of the membrane, bringing it out of equilibrium, still being in the contact with heat bath. This cooling retains the effective canonical Gibbs state with the effective temperature $T^{☆}$. In such case we study the analogs of the equilibrium quantities for low-noise mechanical states of the membrane.

Various models of quantum gravity imply the Planck-scale modifications of Heisenberg's uncertainty principle into a so-called generalized uncertainty principle (GUP). The GUP effects on high-energy physics, cosmology, and astrophysics have been extensively studied. Here, we focus on the weak-equivalence-principle (WEP) violation induced by the GUP. Results from the WEP test with the ${}^{85}\mathrm{Rb}-{}^{87}\mathrm{Rb}$ dual-species atom interferometer are used to set upper bounds on parameters in two GUP proposals. A ${10}^{45}$-level bound on the Kempf-Mangano-Mann proposal and a ${10}^{27}$-level bound on Maggiore's proposal, which are consistent with bounds from other experiments, are obtained. All these bounds have huge room for improvement in the future.

A method to compute the optimal success probability of discrimination of $N$ arbitrary quantum states is presented, based on the decomposition of any $N$-outcome measurement into sequences of nested two-outcome ones. In this way the optimization of the measurement operators can be carried out in successive steps, optimizing first the binary measurements at the deepest nesting level and then moving on to those at higher levels. We obtain an analytical expression for the maximum success probability after the first optimization step and examine its form for the specific case of $N=3,4$ states of a qubit. In this case, at variance with previous proposals, we are able to provide a compact expression for the success probability of any set of states, whose numerical optimization is straightforward; the results thus obtained highlight some lesser-known features of the discrimination problem.

Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. We demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.

We revisit the properties of qubits under Lorentz transformations and, by considering Lorentz-invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic quantum information theory. We then use this formulation to consider the transformation properties of qubits and density matrices under space-time and gauge transformations. Finally, we use our results to understand the behavior of entanglement between different partitions of quantum systems. Our approach not only clarifies the notation but provides a more intuitive and simple way of gaining insight into the behavior of relativistic qubits. In particular, it allows us to greatly generalize the results in the current literature, as well as substantially simplifying the calculations that are needed.

We present additional magic wavelengths (${\lambda }_{\mathrm{magic}}$) for the clock transitions in the alkaline-earth-metal ions, considering circular polarized light, aside from our previously reported values [Kaur et al., Phys. Rev. A 92, 031402(R) (2015)] for linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities $\left[{\alpha }_d\left(\omega \right)\right]$ of the atomic states associated with the clock transitions play major roles in the evaluation of these ${\lambda }_{\mathrm{magic}}$, hence facilitating choosing circular polarization of lasers in the experiments. Moreover, the actual clock transitions in these ions are carried out among the hyperfine levels. The ${\lambda }_{\mathrm{magic}}$ values in these hyperfine transitions are estimated and found to be different from ${\lambda }_{\mathrm{magic}}$ for the atomic transitions due to different contributions coming from the vector and tensor parts of ${\alpha }_d\left(\omega \right)$. Importantly, we also present ${\lambda }_{\mathrm{magic}}$ values that depend only on the scalar component of ${\alpha }_d\left(\omega \right)$ for their uses in a specially designed trap geometry for these ions so that they can be used unambiguously among any hyperfine levels of the atomic states of the clock transitions. We also present ${\alpha }_d\left(\omega \right)$ values explicitly at 1064 nm for the atomic states associated with the clock transitions, which may be useful for creating high-field-seeking traps for the above ions using the Nd:YAG laser. The tune-out wavelengths at which the states would be free from the Stark shifts are also presented. Accurate values of the electric dipole matrix elements required for these studies are given and trends of electron correlation effects in determining them are also highlighted.