Off-diagonal long-range order (ODLRO) in the two-electron reduced density matrix (2-RDM) has long been recognized as a mathematical characteristic of conventional superconductors. The large eigenvalue of the 2-RDM has been shown to be a useful measure of this long-range order. The 2-RDM can be represented as the sum of a connected (cumulant) piece and an unconnected piece. In this work, we show that the cumulant 2-RDM also has a large eigenvalue in the limit of ODLRO. The largest eigenvalue of the cumulant 2-RDM, we prove, is bounded from above by $N$. In the limit of extreme pairing, such as Cooper pairing, the largest eigenvalue and the trace of the cumulant 2-RDM approach their extreme values of $N$ and $-N$, respectively. While the trace of the cumulant 2-RDM, which is computable from only a knowledge of the 1-RDM, can reflect ODLRO, it alone does not appear to be a sufficient criterion. The large eigenvalue of the cumulant 2-RDM, we show, implies the large eigenvalue of the 2-RDM and, hence, is a natural measure of ODLRO that vanishes in the mean-field limit.

Absolute photoabsorption cross sections of negatively charged tetra-atomic aluminum clusters have been measured for photon energies between 1.8 and 2.7 eV. The experiment used the depletion technique in combination with an electrostatic ion-beam trap, in which ${{\mathrm{Al}}_4}^{-}$ ions produced in a sputter ion source were stored for 90 ms before being subjected to a short laser pulse. Moreover, the competition between one-atom fragmentation and electron emission of the laser-excited ${{\mathrm{Al}}_4}^{-}$ has been measured. These measurements show that fragmentation dominates electron emission at all photon energies below the electron attachment energy of $\sim 2.2$ eV, even though the fragmentation energy is expected to be 10%–20% higher than the electron attachment energy. These findings, when taken together with the delayed-electron and fragmentation yields observed in a previous measurement [O. Aviv et al., Phys. Rev. A 83, 023201 (2011)], can be well explained within the statistical phase-space theory for unimolecular decays assuming the ${{\mathrm{Al}}_4}^{-}$ ions to be rotationally hot. The analysis permits the determination of the adiabatic electron detachment energy of ${{\mathrm{Al}}_4}^{-}$ to be $E_{\text{ad}}=(2.18\pm 0.02)$ eV and the one-atom fragmentation energy to be $D_0=(2.34\pm 0.05)$ eV. Moreover, two direct $s$-wave ionization channels are observed with threshold energies of $(2.18\pm 0.02)$ eV and $(2.45\pm 0.02)$ eV.

A frequency-offset separated-oscillatory-field technique is presented. The technique is a modification of the Ramsey method of separated oscillatory fields [Phys. Rev. 76, 996 (1949)], in which the frequencies of the two separated oscillatory fields are slightly offset from each other, so that the relative phase of the two fields varies continuously with time. With this technique, the detection signal oscillates in time at the offset frequency, and the resonance frequency is obtained by using a simple straight-line fit of the phase of this signal. The technique has the advantages of being insensitive to the frequency response of the experimental system, of being sensitive only to noise at the offset frequency, and of allowing systematic effects to be more cleanly resolved due to the simple lineshape.

A systematic study of angle-integrated cross sections for electron scattering from neutral aluminum is presented. The calculations cover elastic scattering, excitation of the 14 states $\left(3s^{2}np\right){}^{2}P^o (n=3,4,5,6), \left(3s^{2}ns\right){}^{2}S (n=4,5,6), \left(3s^{2}nd\right){}^{2}D (n=3,4), \left(3s3p^2\right){}^{4,2}P,{}^{2}D,{}^{2}S$, and $\left(3s^{2}4f\right){}^{2}F^o$, as well as electron impact ionization. The sensitivity of the results to changes in the theoretical model is checked by comparing predictions from a variety of approximations, including a large-scale model with over 500 continuum pseudostates. The current results are believed to be accurate at the few-percent level and should represent a sufficiently extensive set of electron collision data for most modeling applications involving neutral aluminum.

We present an analytical solution of the single-photon quantum feedback in a cavity quantum electrodynamics system based on a half-cavity setup coupled to a structured continuum. Our exact analytical expression constitutes an important benchmark for quantum-feedback models and allows us to unravel the necessary conditions for the previously reported numerical result that a single-emitter-cavity system, which is initially in the weak-coupling regime, can be driven into the strong-coupling regime via the proposed quantum-feedback mechanism [A. Carmele et al., Phys. Rev. Lett. 110, 013601 (2013)]. We specify the phase relations between the cavity mode and the delay time and state explicitly the theoretical limit for a feedback effect in the single-photon regime. Via the photon-path representation, we prove that the stabilization phenomenon relies on a destructive interference effect and we discuss the stabilization time in the weak- and strong-coupling limits.

The semiconductor double-quantum-dot (DQD) micromaser generates photons through single-electron tunneling events. Charge noise couples to the DQD energy levels, resulting in a maser linewidth that is 100 times larger than the Schawlow-Townes prediction. We demonstrate linewidth narrowing by more than a factor of 10 using injection locking. The injection locking range is measured as a function of input power and is shown to be in excellent agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models.

We report measurements of the time-dependent phases of the leak and retrieved pulses obtained in electromagnetically-induced-transparency storage experiments with metastable helium vapor at room temperature. In particular, we investigate the influence of the optical detuning at two-photon resonance and provide numerical simulations of the full dynamical Maxwell-Bloch equations, which allow us to account for the experimental results.

In a recent paper [Phys. Rev. A 91, 053844 (2015)], Mukamel and Dorfman compare spectroscopies performed with classical vs quantum light and conclude that nonlinear quantum-spectroscopy signals cannot be obtained from averaging their classical-spectroscopy counterparts over the Glauber-Sudarshan quasiprobability distribution of the quantum field. In this Comment, we show that this interpretation is correct only when classical spectroscopy is perceived as a theoretical description which neglects quantum fluctuations of light altogether. While such an assumption can be a good approximation and useful for comparing theoretical results, it is never realized exactly in laser-spectroscopy experiments that typically use coherent states. Even though coherent states represent the most classical form of light, their quantumness must be considered to fully understand laser-spectroscopy experiments and their connection to quantum spectroscopy, performed with true quantum sources, such as Schrödinger's cat states. Thus, instead of using a classical approximation, the connection between coherent states and true quantum states of light must be considered. We rigorously show that quantum spectroscopy can always be projected from the experimentally realized coherent-state spectroscopy regardless how nonlinear the system response is.

We discuss the proper definition of the term “quantum spectroscopy.” Since the response of matter to coherent states of the field is not necessarily classical, positivity of the Glauber-Sudarshan $P$ representation as used by Kira et al. [Nat. Phys. 7, 799 (2011)] does not imply that the response is classical. We show that classical and quantum spectroscopies may be unambiguously distinguished by formulating the signals in terms of multipoint field correlation functions.

Reconstructions of quantum theory usually implicitly assume that experimental events are ordered within a global causal structure. The process matrix framework accommodates quantum correlations that violate an inequality verified by all causally ordered correlations. Using a generalized probabilistic framework, we propose three principles constraining bipartite correlations to the quantum bound. Our approach highlights the role of a measure of dependence other than mutual information for an information-theoretic reconstruction of causal structures in quantum theory.

Randomized benchmarking allows one to efficiently and scalably characterize the average error of a unitary 2-design such as the Clifford group $\mathcal{C}$ on a physical candidate for quantum computation, as long as there are no noncomputational leakage levels in the system. We investigate the effect of leakage errors on randomized benchmarking induced from an additional level per physical qubit and provide a modified protocol that allows us to derive reliable estimates for the error per gate in their presence. We assess the variance of the sequence fidelity corresponding to the number of random sequences needed for valid fidelity estimation. Our protocol allows for gate-dependent error channels without being restricted to perturbations. We show that our protocol is compatible with interleaved randomized benchmarking and expand to benchmarking of arbitrary gates. This setting is relevant for superconducting transmon qubits, among other systems.

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Rényi entropy of a partial observation to a subsystem consisting of contiguous sites in the limit of large size. The present work generalizes similar results due to Its, Jin, and Korepin [Fields Institute Communications, Universality and Renormalization, Vol. 50, p. 151, 2007] and Its, Mezzadri, and Mo [Commun. Math. Phys. 284, 117 (2008)]. A striking feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size. This logarithmic behavior originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyze the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long-range pairing.

We demonstrate the importance of considering the shape of field-dressed molecular orbitals in interpreting angle-dependent measures of strong-field ionization from excited states. Our calculations of angle-dependent ionization for three homologous polyatomic molecules with very similar valence orbitals show that one has to take into account the shape of the field-dressed orbitals rather than the field-free orbitals in order to rationalize the experimental measurements.

We have recently examined electron-impact ionization of molecules that have one large atom at the center, surrounded by H nuclei (${\mathrm{H}}_2\mathrm{O}, \mathrm{N}{\mathrm{H}}_3, \mathrm{C}{\mathrm{H}}_4$). All of these molecules have ten electrons; however, they vary in their molecular symmetry. We found that the triple-differential cross sections (TDCSs) for the highest occupied molecular orbitals (HOMOs) were similar, as was the character of the HOMO orbitals which had a $p$-type “peanut” shape. In this work, we examine ethane (${\mathrm{C}}_2{\mathrm{H}}_6$) which is a molecule that has two large atoms surrounded by H nuclei, so that its HOMO has a double-peanut shape. The experiment was performed using a coplanar symmetric geometry (equal final-state energies and angles). We find the TDCS for ethane is similar to the single-center molecules at higher energies, and is similar to a diatomic molecule at lower energies.

The vibrational transition frequencies of a ${{\mathrm{N}}_2}^{+}$ molecular ion are advantageous for precise measurement because the Stark shift is much smaller than that of heteronuclear diatomic molecules. The ${}^{14}{{\mathrm{N}}_2}^{+}$ S(0) transition has been observed by a group in Basel. For most transitions, the Zeeman shift limits the attainable accuracy. This paper reports the quadrupole transitions (observed with simpler apparatus than that required for the Raman transition) for which the Zeeman shift is less than 100 Hz at a magnetic field of 1 G. $\mathrm{Q}\left(N\right)$ transitions ($N$: even) of the molecular ion with $I=0$ are advantageous for measurement within an uncertainty of ${10}^{-16}$. The transition frequencies of molecular ions with $I\ne 0$ are difficult to measure within an uncertainty of ${10}^{-12}$ because $J$-mixing makes the linear Zeeman coefficient in the Q transitions large and narrow hyperfine splitting makes the quadratic Zeeman coefficient large.

We theoretically study homogeneously trapped atomic Bose-Einstein condensates where all three-momentum components couple to a pseudo-spin-$\frac{1}{2}$ degree of freedom. Tuning the anisotropies of spin-orbit coupling and the spin-dependent interactions is shown to provide access to a rich phase diagram with a tetracritical point, first-order phase transitions, and multiple metastable phases of stripe and plane-wave character. The elementary excitation spectrum of the axial plane-wave phase features an anisotropic roton feature and can be used to probe the phase diagram. In addition to providing a versatile laboratory for studying fundamental concepts in statistical physics, the emergence of metastable phases creates new opportunities for observing false-vacuum decay and bubble nucleation in ultracold-atom experiments.

We study the nonequilibrium dynamics of two-component bosonic atoms in a one-dimensional optical lattice in the presence of spin-orbit coupling. In the Mott-insulating regime, the two-component bosonic system at unity filling can be described by the quantum spin $XXZ$ model. The atoms are initially prepared in their lower spin states. The system becomes out of equilibrium by suddenly introducing spin-orbit coupling to the atoms. The system shows the relaxation and nonstationary dynamics, respectively, in the different interaction regimes. We find that the time average of magnetization is useful to characterize the many-body dynamics. The effects of even and odd numbers of sites are discussed. Our result sheds light on nonequilibrium dynamics due to the interplay between spin-orbit coupling and atomic interactions.

By using a full many-body approach, we calculate the excitation energy, the effective mass, and the density profile of soliton states in a three-dimensional Bose gas of hard spheres at zero temperature. The many-body wave function used to describe the soliton contains a one-body term, derived from the solution of the Gross-Pitaevskii equation, and a two-body Jastrow term, which accounts for the repulsive correlations between atoms. We optimize the parameters in the many-body wave function via a variational Monte Carlo procedure, calculating the grand-canonical energy and the canonical momentum of the system in a moving reference frame where the soliton is stationary. As the density of the gas is increased, significant deviations from the mean-field predictions are found for the excitation energy and the density profile of both dark and gray solitons. In particular, the soliton effective mass $m^{*}$ and the mass $m\mathrm{\Delta }N$ of missing particles in the region of the density depression are smaller than the result from the Gross-Pitaevskii equation, their ratio, however, being well reproduced by this theory up to large values of the gas parameter. We also calculate the profile of the condensate density around the soliton notch, finding good agreement with the prediction of the local-density approximation.