We investigate and employ optical Rydberg resonances in an atomic vapor cell for measurements of high-intensity VHF-band radio frequency (rf) electric fields. An atomic vapor cell with integrated electrodes is used to generate high-intensity 50–500 MHz rf electric fields reaching $\sim 5$ kV/m in a submillimeter gap. The fields are measured using Rydberg electromagnetically induced transparency as an optical readout of field-sensitive $30D_J$ and $35D_J$ Rydberg states of atoms within the gap. The rf electric field is determined by matching observed spectroscopic markers, including ac level shifts, even-harmonic rf sidebands, and rf-induced avoided crossings in the Rydberg manifold to calculated spectra derived from a nonperturbative Floquet theory. In our measurements, rf field frequencies and electric-field amplitudes are determined to an accuracy of $1.0\%$ and $1.5\%$, respectively. In the atom-field interaction, we observe a transition from a quantum regime, characterized by discrete even-harmonic Floquet states separated by an even multiple of the rf field frequency, into a semiclassical regime at very strong fields, in which the spectrum exhibits unresolved resonances whose strengths are smoothly modulated at a frequency of approximately five times the rf frequency. The underlying physics is explored.

We make a theoretical investigation of photoionization of an ${\mathrm{H}}_2$ molecule, induced by the irradiation of an ultrashort extreme ultraviolet (XUV) laser pulse. We consider a system composed of a photoelectron ejected from ${\mathrm{H}}_2$ and the resultant ${{\mathrm{H}}_2}^{+}$ as a bipartite system. In order to clarify how the interparticle correlations among two electrons and two protons in ${\mathrm{H}}_2$ are reflected to the bipartite system, we examine the entanglement between the photoelectron and the vibrational states of ${{\mathrm{H}}_2}^{+}$ as well as the coherence in the vibrational states of ${{\mathrm{H}}_2}^{+}$ by simulating the photoionization process of one-dimensional ${\mathrm{H}}_2$. In the simulation, we solve a time-dependent Schrödinger equation using a symmetry-adapted grid method. On the basis of the simulations with ten different sets of three parameters characterizing an ultrashort XUV laser pulse, i.e., the pulse duration, the wavelength, and the peak intensity, we show that the extent of the entanglement depends sensitively on the coherence in the vibrational states of ${{\mathrm{H}}_2}^{+}$.

We present a theoretical study of the nonlinear dynamics and stationary states of an inhomogeneously broadened spin ensemble coupled to a single-mode cavity driven by an external drive with constant amplitude. Assuming a sizable number of constituents within the ensemble allows us to use a semiclassical approach and to formally reduce the theoretical description to the Maxwell-Bloch equations for the cavity and spin amplitudes. We explore the critical slowing-down effect, quench dynamics, and asymptotic behavior of the system near a steady-state dissipative phase transition accompanied by a bistability effect. Some of our theoretical findings have recently been successfully verified in a specific experimental realization based on a spin ensemble of negatively charged nitrogen-vacancy centers in diamond strongly coupled to a single-mode microwave cavity [see A. Angerer et al., Sci. Adv. 3, e1701626 (2017)].

We numerically study the dynamics and stationary states of a spin ensemble strongly coupled to a single-mode resonator subjected to loss and external driving. Employing a generalized cumulant expansion approach we analyze finite-size corrections to a semiclassical description of amplitude bistability, which is a paradigm example of a driven-dissipative phase transition. Our theoretical model allows us to include inhomogeneous broadening of the spin ensemble and to capture in which way the quantum corrections approach the semiclassical limit for increasing ensemble size $N$. We set up a criterion for the validity of the Maxwell-Bloch equations and show that close to the critical point of amplitude bistability even very large spin ensembles consisting of up to ${10}^4$ spins feature significant deviations from the semiclassical theory.

We propose a trade-off between the Lipschitz constants of the position and momentum probability distributions for arbitrary quantum states. We refer to the trade-off as a quantum reciprocity relation. The Lipschitz constant of a function may be considered to quantify the extent of fluctuations of that function and is, in general, independent of its spread. The spreads of the position and momentum distributions are used to obtain the celebrated Heisenberg quantum uncertainty relations. We find that the product of the Lipschitz constants of position and momentum probability distributions is bounded below by a number that is of the order of the inverse square of the Planck's constant.

In this paper we develop an analog of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also provides a unified framework and starting point for many well-known approximations to the time-evolution operator. In the important special case of periodically driven systems at stroboscopic times, we find relatively simple equations for the coupling constants of the Floquet Hamiltonian, where a straightforward truncation of the couplings leads to a powerful class of approximations. Using our theory, we construct a flow chart that illustrates the connection between various common approximations, which also highlights some missing connections and associated approximation schemes. These missing connections turn out to imply an analytically accessible approximation that is the “inverse” of a rotating frame approximation and thus has a range of validity complementary to it. We numerically test the various methods on the one-dimensional Ising model to confirm the ranges of validity that one would expect from the approximations used. The theory provides a map of the relations between the growing number of approximations for the time-evolution operator. We describe these relations in a table showing the limitations and advantages of many common approximations, as well as the approximations introduced in this paper.

The Einstein-Podolsky-Rosen (EPR) entanglement is of special importance not only for fundamental research in quantum mechanics, but also for quantum information processing. Establishing EPR entanglement between two memory systems, such as atomic ensembles, nitrogen-vacancy centers, and rare-earth-ion-doped solids, is promising for realizing spatial-multimode based quantum communication, quantum computation, and quantum imaging. To date, there have been few reports on realizing EPR entanglement between physical systems in true position and momentum. Here we describe successfully establishing such entanglement between two separated atomic ensembles by using quantum storage. We clearly prove the existence of EPR entanglement in position and momentum between two memories by demonstrating the satisfying of the inseparability criterion with the aid of quantum ghost-imaging and ghost-interference experiments.

In this paper, we study nonbinary toric codes and color codes. While the relationships between the qubit color codes and toric codes have been studied extensively from various perspectives, similar studies for qudit toric codes and color codes are missing. We show that just as in the binary case, qudit color codes can be mapped to qudit toric codes. Qudit color codes are known to have the capability for implementing the generalized Clifford group transversally. The proposed mapping of qudit color codes to toric codes would allow us to port the computational capabilities of the qudit color codes to qudit toric codes. Another application would be to decode qudit color codes via qudit toric codes. Along the way, we show an important structural result for higher-dimensional qudit toric codes. Specifically, we show that the toric codes over prime power dimension can be viewed as a direct sum of copies of codes over the prime dimension. This result simplifies the study of codes over prime power dimension by reducing them to the study of codes over the prime dimension. Furthermore, we provide explicit circuits for the transformation between qudit color codes and toric codes.

We examine the steady-state electron-positron pair-creation rate for supercritical electric potentials with arbitrary spatial dependence. The numerical optimization algorithms predict that the set of external fields that can maximize the production rate for positrons with a given energy take nontrivial spatial shapes. We explain the underlying physical mechanisms based on a simple analytical model that exploits resonances among the negative energy eigenstates of the Dirac Hamiltonian. The results are rather encouraging from an experimental perspective as they suggest that one does not require unachievable infinitely large fields to maximize the possible pair-creation yield. In fact, in many cases smaller electric fields lead surprisingly to larger yields for given energy ranges.

Low-energy elastic and inelastic scattering in the Ps($1s$)-Ps($2s$) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum $L=0$ and parity equal to $+1$. The $s$-wave scattering lengths for the asymptotic Ps($1s$)-Ps($2s$) channel are calculated for each spin configuration. Results obtained for the $s$-wave scattering lengths are $a_{\mathrm{TT}}=7.3\left(2\right)a_0-i0.02\left(1\right)a_0, a_{\mathrm{SS}}=13.2\left(2\right)a_0-i0.9\left(2\right)a_0$, and $a_{\mathrm{ST}}=9.7\left(2\right)a_0$ for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross sections are carried out for Ps atoms initially prepared in different uncoupled spin states.

We present a numerical implementation of the time-dependent surface flux (tSURFF) method [L. Tao and A. Scrinzi, New J. Phys. 14, 013021 (2012).], an efficient computational scheme to extract photoelectron energy spectra, to the time-dependent multiconfiguration self-consistent-field (TD-MCSCF) method. Extending the original tSURFF method developed for single-particle systems, we formulate the equations of motion for the spectral amplitude of orbital functions constituting the TD-MCSCF wave function, from which the angle-resolved photoelectron energy spectrum, and more generally, photoelectron reduced density matrices (RDMs) are readily obtained. The tSURFF method applied to the TD-MCSCF wave function, in combination with an efficient absorbing boundary offered by the infinite-range exterior complex scaling, enables accurate ab initio computations of photoelectron energy spectra from multielectron systems subject to an intense and ultrashort laser pulse with a computational cost significantly reduced compared to that required in projecting the total wave function onto scattering states. We apply the present implementation to the photoionization of Ne exposed to an attosecond extreme-ultraviolet (XUV) pulse and above-threshold ionization of Ar irradiated by an intense mid-infrared laser field, demonstrating both accuracy and efficiency of the present method.

Optical interferometers with suspended mirrors are the archetype of all current audio-frequency gravitational-wave detectors. The radiation pressure interaction between the motion of the mirrors and the circulating optical field in such interferometers represents a pristine form of light-matter coupling, largely due to 30 years of effort in developing high-quality optical materials with low mechanical dissipation. However, in all current suspended interferometers, the radiation pressure interaction is too weak to be useful as a resource, and too strong to be neglected. Here, we demonstrate a meter-long interferometer with suspended mirrors, of effective mass $125\mathrm{g}$, where the radiation pressure interaction is enhanced by strong optical pumping to realize a cooperativity of 50. In conjunction with modest resolved-sideband operation, this regime is efficiently probed via optomechanically induced transparency of a weak on-resonant probe. The low resonant frequency and high-Q of the mechanical oscillator allows us to demonstrate transparency windows barely 100 mHz wide at room temperature. Together with a near-unity ($\approx 99.9\%$) out-coupling efficiency, our system saturates the theoretical delay-bandwidth product, rendering it an optical buffer capable of seconds-long storage times.

We use the maximum entropy principle to circumvent the many-particle hierarchy problem that arises in conventional equation of motion techniques. Our efficient approach enables us to numerically determine the full density matrix of driven-dissipative quantum many-particle systems and gain access to all relevant expectation values and the full statistics and not only moments and correlation functions. We compare the maximum entropy method results with the numerically exact solution of the von Neumann-Lindblad equation for a four-level system resonantly coupled to one cavity mode and demonstrate excellent agreement in terms of entropy, mean photon number, autocorrelation function, and photon statistics. Moreover, we show that our approach can be used as a tool for learning about the relevant processes of quantum systems.

We find a different effect for the behavior of von Neumann entropy. For this we derive the framework for describing von Neumann entropy in non-Hermitian quantum systems and then apply it to a simple interacting $PT$-symmetric bosonic system. We show that our model is well defined even in the $PT$-broken regime with the introduction of a time-dependent metric and that it displays three distinct behaviors relating to the $PT$ symmetry of the original time-independent Hamiltonian. When the symmetry is unbroken, the entropy undergoes rapid decay to zero (so-called “sudden death”) with a subsequent revival. At the exceptional point it decays asymptotically to zero and when the symmetry is spontaneously broken it decays asymptotically to a finite constant value (“eternal life”).

We tackle the dynamical description of the quantum measurement process by explicitly addressing the interaction between the system under investigation and the measurement apparatus, the latter ultimately considered as a macroscopic quantum object. We consider arbitrary positive-operator-valued measures (POVMs) such that the orthogonality constraint on the measurement operators is relaxed. We show that, as with the well-known von Neumann scheme for projective measurements, it is possible to build up a dynamical model holding a unitary propagator characterized by a single time-independent Hamiltonian. This is achieved by modifying the standard model so as to compensate for the possible lack of orthogonality among the measurement operators of arbitrary POVMs.

Standard Bayesian credible-region theory for constructing an error region on the unique estimator of an unknown state in general quantum-state tomography to calculate its size and credibility relies on heavy Monte Carlo sampling of the state space followed by filtering to obtain the correct region sample. This conventional methodology typically gives negligible yield for very small error regions originating from large data sets. In this article, we discuss at length the in-region sampling theory for computing both size and credibility from region-average quantities that avoids this general problem altogether. Among the many possible numerical choices, we study the performance and properties of accelerated hit-and-run Monte Carlo algorithm for in-region sampling and provide its complexity estimates for quantum states. Finally with our in-region concept, by alternatively quantifying the region capacity with the region-average distance between two states in the region (measured for instance with either the Hilbert-Schmidt, trace-class, or Bures distance), we derive approximation formulas to analytically estimate both region capacity and credibility without Monte Carlo computation.

We perform several numerical studies for our recently published adaptive compressive tomography scheme [D. Ahn et al., Phys. Rev. Lett. 122, 100404 (2019)], which significantly reduces the number of measurement settings to unambiguously reconstruct any rank-deficient state without any a priori knowledge besides its dimension. We show that both entangled and product bases chosen by our adaptive scheme perform comparably well with recently known compressed-sensing element-probing measurements, and also beat random measurement bases for low-rank quantum states. We also numerically conjecture asymptotic scaling behaviors for this number as a function of the state rank for our adaptive schemes. These scaling formulas appear to be independent of the Hilbert-space dimension. As a natural development, we establish a faster hybrid compressive scheme that first chooses random bases, and later adaptive bases as the scheme progresses. As an epilogue, we reiterate important elements of informational completeness for our adaptive scheme.

The Bethe logarithm for a large set of states of the helium atom is calculated with a precision of 12–14 significant digits. The numerical data are obtained for the case of infinite mass of a nucleus. Then we study the mass dependence and provide coefficients of the $m_e/M$ expansion, which allows us to calculate accurate values for the Bethe logarithm for any finite mass. An asymptotic expansion for the Rydberg states is analyzed, and a high-quality numerical approximation is found, which ensures 7–8-digit accuracy for the $S$, $P$, and $D$ states of the helium atom.

Near-threshold photodetachment microscopy of mononegative ions is theoretically studied when a homogeneous transverse magnetic field $\mathrm{B}$ is superimposed to the static electric field $\mathrm{E}$. The electron flux distribution is obtained using two different approaches: the quantum source theory with the energy-Green function evaluated by means of the stationary phase approximation and the closed-orbit theory. Here we describe the physical ideas while developing the theory in detail. Both theoretical methods yield consistent descriptions for all field intensities and angular momentum of the detached electrons we have investigated and also reproduce reported experimental results. From our calculations, we have found that the presence of the transverse magnetic field leads to a global displacement of the recorded electron flux distribution along the $\mathrm{E}\times \mathrm{B}$ direction. Furthermore, we found that the shape of the recorded interference pattern changes from circular to elliptical as the magnetic field increases. We have theoretically characterized and quantified those effects on the interference pattern due to the presence of the transverse magnetic field.

In the previous works, we proposed atomic quantum simulations of the U(1) gauge-Higgs model by ultracold Bose gases. By studying extended Bose-Hubbard models (EBHMs) including long-range repulsions, we clarified the locations of the confinement, Coulomb, and Higgs phases. In this paper, we study the EBHM with nearest-neighbor repulsions in one and two dimensions at large fillings by the Gutzwiller variational method. We obtain phase diagrams and investigate dynamical behavior of electric flux from the gauge-theoretical point of view. We also study if the system exhibits glassy quantum dynamics in the absence and presence of quenched disorder. We explain that the obtained results have a natural interpretation in the gauge theory framework. Our results suggest important perspective on many-body localization in strongly correlated systems. They are also closely related to anomalously slow dynamics observed by recent experiments performed on the Rydberg atom chain, and our study indicates existence of similar phenomenon in two-dimensional space.