We report the observation of resonancelike loss in the trap population of ultracold dysprosium as a function of magnetic field, which we attribute to anisotropy-induced Fano-Feshbach resonances arising from Dy's large magnetic dipole moment and nonzero electronic orbital angular momentum. We recorded these resonances for four different isotopes, three bosonic and one fermionic, over a field range of 0–6 G and show that the number of resonances changes significantly as a function of temperature, even in the nK regime. Most of the observed resonances are of very narrow width. The fermionic isotope, unlike its bosonic counterparts, possesses nonzero nuclear spin and exhibits a much higher density of resonances.

Using a recently developed strong-coupling method, we present a comprehensive theory for doublon production processes in modulation spectroscopy of a three-dimensional system of ultracold fermionic atoms in an optical lattice with a trap. The theoretical predictions compare well to the experimental time traces of doublon production. For experimentally feasible conditions, we provide a quantitative prediction for the presence of a nonlinear “two-photon” excitation at strong modulation amplitudes.

Recently we calculated relativistic recoil corrections to the energy levels of the low-lying states in muonic hydrogen induced by electron vacuum polarization effects. The results were obtained by Breit-type and Grotch-type calculations. The former were described in our previous papers in detail, and here we present the latter. The Grotch equation was originally developed for pure Coulomb systems and allowed to express the relativistic recoil correction to order ${\left(Z\alpha \right)}^4{m}^2/M$ in terms of the relativistic nonrecoil contribution ${\left(Z\alpha \right)}^{4}m$. Certain attempts to adjust the method to electronic vacuum polarization took place in the past, however, the consideration was incomplete and the results were incorrect. Here we present a Grotch-type approach to the problem and in a series of papers consider relativistic recoil effects in order $\alpha {\left(Z\alpha \right)}^4{m}^2/M$ and ${\alpha }^2{\left(Z\alpha \right)}^4{m}^2/M$. That is the first paper of the series and it presents a general approach, while two other papers present results of calculations of the $\alpha {\left(Z\alpha \right)}^4{m}^2/M$ and ${\alpha }^2{\left(Z\alpha \right)}^4{m}^2/M$ contributions in detail. In contrast to our previous calculation, we address now a variety of states in muonic atoms with a certain range of the nuclear charge $Z$.

We continue our account of relativistic recoil effects in muonic atoms and present explicitly analytic results at first order in electron-vacuum-polarization effects. The results are obtained within a Grotch-type approach based on an effective Dirac equation. Some expressions are cumbersome and we investigate their asymptotic behavior. Previously, relativistic two-body effects due to the one-loop electron vacuum polarization were studied by several groups. Our results found here are consistent with the previous result derived within a Breit-type approach (including ours) and disagree with a recent attempt to apply a Grotch-type approach.

The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a method based on the concept of data mining. We demonstrate that the proposed method can more accurately detect small erroneous deviations in reconstructed density matrices, which contain intrinsic fluctuations due to the limited number of samples, than a naive method of checking the trace distance from the average of the given density matrices. This method has the potential to be a key tool in broad areas of physics where the detection of small deviations of quantum states reconstructed using a limited number of samples is essential.

The QED cascade induced by the two counterpropagating lasers is studied. It is demonstrated that the probability of a seed photon to create a pair is much larger than that of a seed electron. By analyzing the dynamic characteristics of the electron and positron created by the seed photon, it is found that the created particles are more likely to emit photons than the seed electron. With these results, furthermore, we demonstrate that the QED cascade can be more easily triggered by the seed photon than by the seed electron with the same incident energy and the same laser.

We revisit the definitions of error and disturbance recently used in error-disturbance inequalities derived by Ozawa and others by expressing them in the reduced system space. The interpretation of the definitions as mean-squared deviations relies on an implicit assumption that is generally incompatible with the Bell-Kochen-Specker-Spekkens contextuality theorems, and which results in averaging the deviations over a non-positive-semidefinite joint quasiprobability distribution. For unbiased measurements, the error admits a concrete interpretation as the dispersion in the estimation of the mean induced by the measurement ambiguity. We demonstrate how to directly measure not only this dispersion but also every observable moment with the same experimental data, and thus demonstrate that perfect distributional estimations can have nonzero error according to this measure. We conclude that the inequalities using these definitions do not capture the spirit of Heisenberg's eponymous inequality, but do indicate a qualitatively different relationship between dispersion and disturbance that is appropriate for ensembles being probed by all outcomes of an apparatus. To reconnect with the discussion of Heisenberg, we suggest alternative definitions of error and disturbance that are intrinsic to a single apparatus outcome. These definitions naturally involve the retrodictive and interdictive states for that outcome, and produce complementarity and error-disturbance inequalities that have the same form as the traditional Heisenberg relation.

Due to its ability to tolerate high channel loss, decoy-state quantum key distribution (QKD) has been one of the main focuses within the QKD community. Notably, several experimental groups have demonstrated that it is secure and feasible under real-world conditions. Crucially, however, the security and feasibility claims made by most of these experiments were obtained under the assumption that the eavesdropper is restricted to particular types of attacks or that the finite-key effects are neglected. Unfortunately, such assumptions are not possible to guarantee in practice. In this work, we provide concise and tight finite-key security bounds for practical decoy-state QKD that are valid against general attacks.

Every choice of an orthonormal frame in the $d$-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, to the classical statistical state space of the system; the quantum state space itself can thus be profitably viewed as an $\text{SU}\left(d\right)$ orbit of classical state spaces, one for each orthonormal frame. We exploit this connection to study the relative volume of separable states of a bipartite quantum system. While the two-qubit case is studied in considerable analytic detail, for higher-dimensional systems we fall back on Monte Carlo. Several insights seem to emerge from our study.

Quantum walk (QW) on a disordered lattice leads to a multitude of interesting phenomena, such as Anderson localization. While QW has been realized in various optical and atomic systems, its implementation with superconducting qubits still remains pending. The major challenge in simulating QW with superconducting qubits emerges from the fact that on-chip superconducting qubits cannot hop between two adjacent lattice sites. Here we overcome this barrier and develop a gate-based scheme to realize the discrete time QW by placing a pair of qubits on each site of a one-dimensional (1D) lattice and treating an excitation as a walker. It is also shown that various lattice disorders can be introduced and fully controlled by tuning the qubit parameters in our quantum walk circuit. We observe a distinct signature of transition from the ballistic regime to a localized QW with an increasing strength of disorder. Finally, an eight-qubit experiment is proposed where the signatures of such localized and delocalized regimes can be detected with existing superconducting technology. Our proposal opens up the possibility of exploring various quantum transport processes with promising superconducting qubits.

The decay of highly excited states of xenon after absorption of extreme ultraviolet light is directly tracked via attosecond transient absorption spectroscopy using a time-delayed near-infrared perturbing pulse. The lifetimes of the autoionizing 5$s$5$p^6$6$p$ and 5$s$5$p^6$7$p$ channels are determined to be (21.9 ± 1.3) fs and (48.4 ± 5.0) fs, respectively. The observed values support lifetime estimates obtained by traditional linewidth measurements. The experiment additionally obtains the temporal evolution of the decay as a function of energy detuning from the resonance center, and a quantum mechanical formalism is introduced that correctly accounts for the observed energy dependence.

Laser cooling to sub-Doppler temperatures by optical molasses is thought to be inhibited in atoms with unresolved, near-degenerate hyperfine structure in the excited state. We demonstrate that such cooling is possible in one to three dimensions, not only near the standard $D_2$ line for laser cooling, but over a wide range extending to the $D_1$ line. Via a combination of Sisyphus cooling followed by adiabatic expansion, we reach temperatures as low as 40 $\mu$K, which corresponds to atomic velocities a factor of 2.6 above the limit imposed by a single-photon recoil. Our method requires modest laser power at a frequency within reach of standard frequency-locking methods. It is largely insensitive to laser power, polarization and detuning, magnetic fields, and initial hyperfine populations. Our results suggest that optical molasses should be possible with all alkali-metal species.

The multiple Auger electron emission processes after the $2p_{3/2}^{-1}$ 4$s$ excitation in Ar have been investigated with a multielectron coincidence method. We have observed the double, triple, and quadruple Auger decays of the resonant state, where both cascade and direct processes are identified. The cascade processes in the resonant double and triple Auger decays result mostly from the spectator behavior of the Rydberg electron in the initial core-hole decay: First Auger decay produces ion states with large internal energies, and subsequent electron emission leads mainly formation of ground Ar${}^{2+}$ and Ar${}^{3+}$ states. It is revealed that spectator behavior, which is known to be the dominant path in resonant single Auger decay, is also important in the direct paths of the resonant double and triple Auger decays. In contrast, the participation of the Rydberg electron is predominant in the direct path of the resonant quadruple Auger decay.

We develop a theoretical understanding of the trapping of divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wave functions. The optical potential is proportional to the ac Stark polarizability. We find that in the independent-particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usually employed free-electron polarizability, the Rydberg contribution depends both on the laser intensity profile and on the rotational symmetry of the total electronic wave function. We focus on the $J=0$ Rydberg states of Sr and evaluate the dynamic polarizabilities of the $5sns$(${}^1{S}_0$) and $5snp$(${}^3{P}_0$) Rydberg states. We specifically chose the Sr atom for its optical-lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states [$5s^2$(${}^1{S}_0$) and $5s5p$(${}^3{P}_0$)] and the $J=0$ Rydberg states [$5sns$(${}^1{S}_0$) and $5snp$(${}^3{P}_0$)] vanishes. We tabulate these wavelengths as a function of the principal quantum number $n$ of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\sim$1000 nm are “universal” as they do not depend on the principal quantum number $n$.

We investigate the Berry phase in an ensemble of thermal ${}^{87}\mathrm{Rb}$ atoms which we prepare in a superposition state under conditions near and at electromagnetically induced transparency. The geometric phase is imprinted in the atoms by rotating the laboratory magnetic field. Phase-stabilized light fields permit us to monitor phase changes of the atomic sample in a Ramsey-type interferometer by instant probing of the absorptive response of the atoms as well as by monitoring the free-induction decay of the coherent superposition. The absolute sign of the phase is determined by reference to controllable phase shifts imposed by the experimenter. We prove that the geometric phase is independent of the rotational frequency of the magnetic field in the adiabatic regime, that the phase is additive in multiple rotations, and it is independent of the Landé factor of the atomic magnetic moment, as predicted in Berry's seminal paper. We show that the absolute sign of the phase encodes the sign of the observable angular momentum in relation to laboratory coordinates.

We study the dynamics of interacting superfluid bosons in a one-dimensional vertical optical lattice after a sudden increase of the lattice potential depth. We show that this system can be exploited to investigate the effects of strong interactions on Bloch oscillations. We perform theoretical modeling of this system, identify experimental challenges, and explore a regime of Bloch oscillations characterized by interaction-induced matter-wave collapse and revivals which modify the Bloch oscillations dynamics. In addition, we study three dephasing mechanisms: finite value of tunneling, effective three-body interactions, and a background harmonic potential. We also find that the center-of-mass motion in the presence of finite tunneling goes through collapse and revivals, giving an example of quantum transport where interaction-induced revivals are important. We quantify the effects of residual harmonic trapping on the momentum distribution dynamics and show the occurrence of an interaction-modified temporal Talbot effect. Finally, we analyze the prospects and challenges of exploiting Bloch oscillations of cold atoms in the strongly interacting regime for precision measurement of the gravitational acceleration $g$.

We evaluate the sensitivity of a dual cloud atom interferometer to the measurement of vertical gravity gradient. We study the influence of most relevant experimental parameters on noise and long term drifts. Results are also applied to the case of doubly differential measurements of the gravitational signal from local source masses. We achieve a short-term sensitivity of $3\times {10}^{-9}$ g/$\sqrt{\text{Hz}}$ to differential gravity acceleration, limited by the quantum projection noise of the instrument. Active control of the most critical parameters allows us to reach a resolution of $5\times {10}^{-11}$ g after 8000 s on the measurement of differential gravity acceleration. The long-term stability is compatible with a measurement of the gravitational constant $G$ at the level of ${10}^{-4}$ after an integration time of about 100 h.

We experimentally study spin dynamics in a sodium antiferromagnetic spinor condensate as a result of spin-dependent interactions $c$ and microwave dressing field interactions characterized by the net quadratic Zeeman effect $q_{\mathrm{net}}$. In contrast to magnetic fields, microwave dressing fields enable us to access both negative and positive values of $q_{\mathrm{net}}$. We find an experimental signature to determine the sign of $q_{\mathrm{net}}$ and observe harmonic spin population oscillations at every $q_{\mathrm{net}}$ except near each separatrix in phase space where spin oscillation period diverges. No spin domains and spatial modes are observed in our system. Our data in the negative $q_{\mathrm{net}}$ region exactly resembles what is predicted to occur in a ferromagnetic spinor condensate in the positive $q_{\mathrm{net}}$ region. This observation agrees with an important prediction derived from the mean-field theory: spin dynamics in spin-1 condensates substantially depends on the sign of $q_{\mathrm{net}}/c$. This work uses only one atomic species to reveal mean-field spin dynamics, especially the remarkably different relationship between each separatrix and the magnetization, of spin-1 antiferromagnetic and ferromagnetic spinor condensates.

The influence of group-velocity-dispersion (GVD) effects on the propagation of femtosecond laser pulses in air at different pressures is investigated by numerically solving the extended nonlinear Schrödinger equation. It is observed that GVD has a great influence on the collapse distance $L_{\mathrm{c}}$ of the self-focusing short laser pulses when the pressure is relatively high (e.g., 10 atm), in which case the semiempirical formula describing the collapse distance of self-focusing laser pulse [Dawes and Marburger, Phys. Rev. 179, 862 (1969)] is no longer applicable, while GVD has little influence on the self-focusing process of longer laser pulses. Through the results of numerical simulations as well as analytical analysis, we find that the initial duration of the laser pulse is the main factor that determines the GVD effect on the propagation and the increase of the pressure and pulse compression during the propagation enhance this effect. The spectral data show that GVD also influences the spectrum broadening in high-pressure cases.

We study the system involving mutual interaction between three qubits and an oscillator within the ultrastrong coupling regime. We apply the adiabatic approximation approach to explore two extreme regimes: (i) the oscillator's frequency is far larger than each qubit's frequency and (ii) the qubit's frequency is far larger than the oscillator's frequency, and analyze the energy-level spectrum and the ground-state property of the qubit-oscillator system under the conditions of various system parameters. For the energy-level spectrum, we concentrate on studying the degeneracy in low-energy levels. For the ground state, we focus on its nonclassical properties that are necessary for preparing the nonclassical states. We show that the minimum qubit-oscillator coupling strength needed for generating the nonclassical states of the Schrödinger-cat type in the oscillator is just one half of that in the Rabi model. We find that the qubit-qubit entanglement in the ground state vanishes if the qubit-oscillator coupling strength is strong enough, for which the entropy of three qubits remains larger than 1. We also observe the phase-transition-like behavior in the regime where the qubit's frequency is far larger than the oscillator's frequency.