Combining the differential-quadrature-phase-shift (DQPS) quantum key distribution (QKD) protocol and the recently proposed round-robin-differential-phase-shift (RRDPS), the round-robin-differential-quadrature-phase-shift (RRDQPS) protocol has been proposed. However, a security proof of the RRDQPS QKD protocol is still missing and its advantage over the original RRDPS protocol is also unknown. Here, we give the security proof of single-photon RRDQPS protocol, by which we clearly show that, if a single photon source is applied, RRDQPS protocol will overwhelm the original RRDPS protocol in terms of tolerable error rate. More interestingly, our proof gives a unified theory covering the well-known Bennett-Brassard 1984 (BB84) protocol and RRDQPS protocol. Thus, it is confirmed that BB84 protocol is indeed a special case of the RRDQPS protocol.

We define a summoning task to require propagating an unknown quantum state to a point in space-time belonging to a set determined by classical inputs at points in space-time. We consider the classical analog, in which a known classical state must be returned at precisely one allowed point. We show that, when the inputs are unconstrained, any summoning task that is possible in the classical case is also possible in the quantum case.

We perform a high-resolution Fourier-transform spectroscopic study of the $\left(4\right){}^1\mathrm{\Pi }$ state of the RbCs molecule by applying two-step $\left(4\right){}^1\mathrm{\Pi }\leftarrow A{}^1{\mathrm{\Sigma }}^{+}\sim b{}^3\mathrm{\Pi }\leftarrow X{}^1{\mathrm{\Sigma }}^{+}$ optical excitation followed by observation of the $\left(4\right){}^1\mathrm{\Pi }\to X{}^1{\mathrm{\Sigma }}^{+}$ laser-induced fluorescence (LIF) spectra. In many LIF progressions the collision-induced satellite rotational lines are observed, thus increasing the amount of term values and allowing us to estimate the $\mathrm{\Lambda }$-doubling effect in the $\left(4\right){}^1\mathrm{\Pi }$ state. The direct potential fit (DPF) of experimental term values of 777 rovibronic levels of both ${}^{85}\mathrm{RbCs}$ and ${}^{87}\mathrm{RbCs}$ isotopologues is performed by means of the robust weighted nonlinear least-squares method. The DPF analysis based on the adiabatic approximation and analytical expanded Morse oscillator potential reveals numerous regular shifts in the measured level positions. The spectroscopic studies of the $\left(4\right){}^1\mathrm{\Pi }$ state are supported by the electronic structure calculations including the potential energy curves of the singlet- and triplet-state manifold and spin-allowed transition dipole moments. The subsequent estimates of radiative lifetimes and corresponding vibronic branching ratios elucidate a dominant contribution of the $\left(4\right){}^1\mathrm{\Pi }\to A\sim b$ channel into the total radiative decay of the $\left(4\right){}^1\mathrm{\Pi }$ state. The relative intensity distributions simulated for $\left(4\right){}^1\mathrm{\Pi }\to X{}^1{\mathrm{\Sigma }}^{+}$ LIF progressions agree well with their observed counterparts even for the profoundly shifted levels of the entirely perturbed $\left(4\right){}^1\mathrm{\Pi }$ state. To get insight into the origin of the intramolecular perturbations, the relevant spin-orbit- and $L$-uncoupling electronic matrix elements are evaluated.

We use a multistage Zeeman decelerator to generate slow beams ($v\simeq 100\mathrm{m}/\mathrm{s}$) of translationally cold, spin-polarized metastable $a{}^3\mathrm{\Sigma }_u^{+}{\mathrm{He}}_2$ molecules and perform a precision measurement of their spin-rotation fine structure. The spin polarization results from the elimination of the high-field-seeking $J=N$ spin-rotational component of each rotational level (rotational quantum number $N$) by the Zeeman deceleration process. By repopulating the $J=N$ component from the $J=N\pm 1$ low-field-seeking components using radio-frequency radiation, we measured the spin-rotation fine structure of 13 rovibrational levels with $v=0$, 1 and $N=1\text{–}21$. The low beam velocity and the resulting long interaction times with the radio-frequency radiation were exploited to determine the transition frequencies with a precision of 300 Hz.

We consider one-loop light-by-light-scattering contributions to the Lamb shift of the $1s,2s,2p$ states in light muonic hydrogenlike atoms at $Z\le 10$. The contributions are of the order ${\alpha }^5{m}_{\mu }$ (with diverse dependence on the nuclear charge $Z$). Those include the contributions of the so-called Wichmann-Kroll potential $\left[\alpha {\left(Z\alpha \right)}^4{m}_{\mu }\right]$, the virtual Delbrück scattering $\left[{\alpha }^2{\left(Z\alpha \right)}^3{m}_{\mu }\right]$, etc. The results are obtained in a nonrelativistic approximation. For the calculation of the virtual-Delbrück-scattering contribution, we have constructed an effective potential in the coordinate space which may be applied to other calculations in muonic atoms.

Vacuum-ultraviolet-transparent crystals have been proposed as host lattice for the coherent driving of the unusually low-lying isomer excitation in ${}^{229}\mathrm{Th}$ for metrology and quantum optics applications. Here the possible collective effects occurring for the coherent pulse propagation in the crystal system are investigated theoretically. We consider the effect of possible doping sites, quantization axis orientation, and pulse configurations on the scattered light intensity and signatures of nuclear excitation. Our results show that for narrow-pulse driving, the rather complicated quadrupole splitting of the level scheme is significantly simplified. Furthermore, we investigate complex driving schemes with a combination of pulsed fields and investigate the occurring interference process. Our theoretical results support experimental attempts for first direct driving of the nuclear transition with coherent light.

We performed a kinematically complete experiment on double ionization accompanied by single capture in 30 keV/amu ${\mathrm{He}}^{2+}$ + Ar collisions. The data were systematically analyzed using three different techniques, namely, fully differential cross sections as a function of the electron emission angle of each electron, the correlation function, and four-particle Dalitz plots. The data can to a large extent be explained within the independent electron model. However, the correlation function reveals small but significant effects from correlations in the initial target state. These correlations strongly depend on the interaction between the nuclei of the collision partners. Furthermore, a surprisingly strong correlation between the electron momenta with the momentum transfer, reported earlier, was confirmed.

We present a detailed study of the scattering properties of ultracold mixtures of bosonic potassium atoms. We locate 20 previously unobserved Feshbach resonances in isotopic ${}^{39}\mathrm{K}\text{−}{}^{41}\mathrm{K}$ mixtures. These are assigned to $s$-wave molecular channels by comparison to an asymptotic bound state model and coupled-channel calculations. Additional Feshbach resonances are studied in spin mixtures of a single potassium isotope, both in ${}^{39}\mathrm{K}$ and ${}^{41}\mathrm{K}$. In particular, we characterize the parameters of a selected ${}^{39}\mathrm{K}$ Feshbach resonance by radio-frequency association of Feshbach molecules. Our results could be exploited to refine the model potentials for potassium scattering. Furthermore, these new Feshbach resonances enlarge the range of experiments possible with degenerate Bose-Bose mixtures.

Atoms excited into high-lying Rydberg states and under strong dipole-dipole interactions exhibit phenomena associated with highly correlated and complex systems. We perform first-principles numerical simulations on the dynamics of such systems. The emergence of a roton minimum in the excitation spectrum, as expected in strongly correlated gases and accurately described by Feynman's theory of liquid helium, is shown to significantly inhibit particle transport, with a strong suppression of the diffusion coefficient, due to the emerging spatial order. We also demonstrate how the ability to temporally tune the interaction strength among Rydberg atoms can be used in order to overcome the effects of disorder-induced heating, allowing the study of unprecedented highly coupled regimes.

We study the spectral and temporal properties of high-order harmonic generation (HHG) from aligned molecules in orthogonal two-color laser fields consisting of a strong fundamental field and its second harmonic. Numerical simulations show that the HHG depends strongly on the relative phase between these two colors and the molecular alignment. In particular, for some cases, HHG differs remarkably in consecutive half cycles of the fundamental field. As the emission of harmonics is very strong in a half laser cycle, it is weak in the following half. A simple model related to the molecular structure is proposed to explain these phenomena. Our results suggest a potential approach for generating trains of attosecond pulses with only one pulse per cycle over a wide energy region.

By using the Floquet eigenstates, we derive a formula to calculate the high-order harmonic components of the electric current (HHC) in the setup where a monochromatic laser field is turned on at some time. On the basis of this formulation, we study the HHC spectrum of electrons on a one-dimensional chain with a staggered potential to study the effect of multiple sites in the unit cell such as the systems with charge density wave order. With the help of the solution for the Floquet eigenstates, we analytically show that two plateaus of different origins emerge in the HHC spectrum. The widths of these plateaus are both proportional to the field amplitude, but inversely proportional to the laser frequency and its square, respectively. We also show numerically that multistep plateaus appear when both the field amplitude and the staggered potential are strong.

The low-energy photoelectron spectra from strong-field ionization of ${\mathrm{C}}_{60}$ fullerenes and noble gases (xenon and krypton) with $3\mu \mathrm{m}$ laser pulses are measured and compared. It is found that the low-energy structure (LES), a universal spikelike feature in the strong-field limit of atoms and small molecules, is significantly suppressed in the ${\mathrm{C}}_{60}$ photoelectron distribution. We propose that the large polarizability of the ${\mathrm{C}}_{60}$ core disrupts the corresponding electron trajectories. In particular, the induced dipole force repels the electron, which opposes the focusing and bunching due to the Coulomb potential that is responsible for the LES, thus leading to its reduction.

We present a unified description of several methods of chiral discrimination based exclusively on electric-dipole interactions. It includes photoelectron circular dichroism (PECD), enantiosensitive microwave spectroscopy (EMWS), photoexcitation circular dichroism (PXCD), and photoelectron-photoexcitation circular dichroism (PXECD). We show that, in spite of the fact that the physics underlying the appearance of a chiral response is very different in all these methods, the enantiosensitive and dichroic observable in all cases has a unique form. It is a polar vector given by the product of (i) a molecular pseudoscalar and (ii) a field pseudovector specified by the configuration of the electric fields interacting with the isotropic ensemble of chiral molecules. The molecular pseudoscalar is a rotationally invariant property, which is composed from different molecule-specific vectors and in the simplest case is a triple product of such vectors. The key property that enables the chiral response is the noncoplanarity of the vectors forming such triple product. The key property that enables chiral detection without relying on the chirality of the electromagnetic fields is the vectorial nature of the enantiosensitive observable. Our compact and general expression for this observable shows what ultimately determines the efficiency of the chiral signal and if, or when, it can reach 100%. We also discuss the differences between the two phenomena, which rely on the bound states, PXCD and EMWS, and the two phenomena using the continuum states, PECD and PXECD. Finally, we extend these methods to arbitrary polarizations of the electric fields used to induce and probe the chiral response.

We study the propagation of dispersive waves in superfluid Fermi gases in the BEC-BCS crossover. Unlike in other superfluid systems where dispersive waves have already been studied and observed, Fermi gases can exhibit a subsonic dispersion relation for which the dispersive wave pattern appears at the tail of the wave front. We show that this property can be used to distinguish between a subsonic and a supersonic dispersion relation at unitarity.

We study a three-component fermionic fluid in an optical lattice in a regime of intermediate to strong interactions allowing for optical processes connecting the different components, similar to those used to create artificial gauge fields. Using dynamical mean-field theory, we show that the combined effect of interactions and the external field induces a variety of anomalous phases in which different components of the fermionic fluid display qualitative differences, i.e., the physics is flavor selective. Remarkably, the different components can display huge differences in the correlation effects, measured by their effective masses and nonmonotonic behavior of their occupation number as a function of the chemical potential, signaling a sort of selective instability of the overall stable quantum fluid.

We propose a real-space probe that is based on density measurements to extract distinct signatures of quasihole-like states of bosons experiencing a synthetic magnetic field in a two-dimensional lattice. We numerically show that certain ratios of the mean square radii of the particle cloud, obtainable through the density profile, quickly approach the continuum values expected from Laughlin's ansatz wave functions as the magnetic flux quanta per unit cell of the lattice decreases, even in a small lattice with few particles. This method can equally be used in both ultracold atomic and photonic systems.

We study the dynamics of an impurity embedded in a trapped Bose-Einstein condensate, i.e., the Bose polaron problem. This problem is treated by recalling open quantum systems techniques: the impurity corresponds to a particle performing quantum Brownian motion, while the excitation modes of the gas play the role of the environment. It is crucial that the model considers a parabolic trapping potential to resemble the experimental conditions. Thus, we detail here how the formal derivation changes due to the gas trap, in comparison to the homogeneous gas. More importantly, we elucidate all aspects in which the gas trap plays a relevant role, with an emphasis on the enhancement of the non-Markovian character of the dynamics. We first find that the presence of a gas trap leads to a new form of the bath-impurity coupling constant and a larger degree in the super-Ohmicity of the spectral density. We then solve the quantum Langevin equation to derive the position and momentum variances of the impurity, where the former is a measurable quantity. For the particular case of an untrapped impurity, the asymptotic behavior of this quantity is found to be motion superdiffusive. When the impurity is trapped, we find position squeezing, casting the system suitable for implementing quantum metrology and sensing protocols. We detail how both superdiffusion and squeezing can be enhanced or inhibited by tuning the Bose-Einstein condensate trap frequency. Compared to the homogeneous gas case, the form of the bath-impurity coupling constant changes, and this is manifested as a different dependence of the system dynamics on the past history. To quantify this, we introduce several techniques to compare the different amount of memory effects arising in the homogeneous and inhomogeneous gas. We find that it is higher in the second case. This analysis paves the way to the study of non-Markovianity in ultracold gases, and the possibility to exploit such a property in the realization of new quantum devices.

We theoretically investigate the role of multiple impurity atoms on the ground-state properties of Bose polarons. The Bogoliubov approximation is applied for the description of the condensate resulting in a Hamiltonian containing terms beyond the Fröhlich approximation. The many-body nature of the impurity atoms is taken into account by extending the many-body description for multiple Fröhlich polarons, revealing the static structure factor of the impurities as the key quantity. Within this formalism various experimentally accessible polaronic properties are calculated such as the energy and the effective mass. These results are examined for system parameters corresponding to two recent experimental realizations of the Bose polaron, one with fermionic impurities and one with bosonic impurities.

We present an analytical description of the tunneling dynamics between two coupled Bose-Einstein condensates in the Josephson regime. The model relies on the classical analogy with a rigid pendulum and focuses on two dynamical modes of this system: Josephson oscillations and macroscopic quantum self-trapping. The analogy is extended to include an energy difference between the two superfluids caused by an asymmetry in the trapping potential. The model is compatible with the mean-field predictions of the two-mode Bose-Hubbard model. It gives insights on the mean-field model by involving experimentally measurable parameters with reduced correlations. For agreement with recent experimental observations, we establish heuristic formulas including a dissipation. We conclude with a convincing application of the model to several sets of experimental results.

The scaling of the largest eigenvalue ${\lambda }_0$ of the one-body density matrix of a system with respect to its particle number $N$ defines an exponent $\mathcal{C}$ and a coefficient $\mathcal{B}$ via the asymptotic relation ${\lambda }_0\sim \mathcal{B}{N}^{\mathcal{C}}$. The case $\mathcal{C}=1$ corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a well-known result also confirmed by bosonization gives instead $\mathcal{C}=1/2$. Here we investigate the inhomogeneous case, initially addressing the behavior of $\mathcal{C}$ in the presence of a general external trapping potential $V$. We argue that the value $\mathcal{C}=1/2$ characterizes the hard-core system independently of the nature of the potential $V$. We then define the exponents $\gamma$ and $\beta$, which describe the scaling of the peak of the momentum distribution with $N$ and the natural orbital corresponding to ${\lambda }_0$, respectively, and we derive the scaling relation $\gamma +2\beta =\mathcal{C}$. Taking as a specific case the power-law potential $V\left(x\right)\propto x^{2n}$, we give analytical formulas for $\gamma$ and $\beta$ as functions of $n$. Analytical predictions for the coefficient $\mathcal{B}$ are also obtained. These formulas are derived by exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent.