Measurements of interactions between cold molecules and ultracold atoms can allow for a detailed understanding of fundamental collision processes. These measurements can be done using various experimental geometries, including where both species are in a beam, where one species is trapped, or when both species are trapped. Simultaneous trapping offers significantly longer interaction times and an associated increased sensitivity to rare collision events. However, there are significant practical challenges associated with combining atomic and molecular systems, which often have competing experimental requirements. Here, we describe in detail an experimental system that allows for studies of cold collisions between ultracold atoms and cold molecules in a dual trap, where the atoms and molecules are trapped using static magnetic and electric fields, respectively. As a demonstration of the system's capabilities, we study cold collisions between ammonia (${}^{14}\mathrm{ND}_3$ and ${}^{15}\mathrm{ND}_3$) molecules and rubidium (${}^{87}\mathrm{Rb}$ and ${}^{85}\mathrm{Rb}$) atoms.

We explore the sensitivity of the photon echo technique for achieving precise measurements of atomic lifetimes. Using short-pulse excitation of atomic rubidium vapor, we report the most statistically precise measurement of ($26.11\pm 0.03$) ns for the $5{}^2{P}_{3/2}$ lifetime. This statistical uncertainty of 0.11% was achieved in a total data acquisition time of 4 h over several weeks and rivals the most precise measurements in this atomic system. The experiment primarily relies on heterodyne detection and exploits the signal-to-noise ratio of the coherent release of energy along the direction of excitation, which is an exponential decay as a function of pulse separation $T$, as well as large repetition rates that are feasible in a gently heated vapor cell. We have developed an understanding of the technical limitations responsible for lifetime measurement instabilities on the basis of a simple model, which also enables us to propose a feedback scheme to limit these effects. Studies of the fractional uncertainty of the lifetime suggest that the statistical precision of this technique can be extended to the level of 0.03% in 10 min of data acquisition if the technical limitations are addressed. This level of precision has so far been exceeded by only one other lifetime measurement. Under these conditions, a rigorous investigation of systematic effects could potentially allow the echo technique to achieve the most accurate measurement of atomic lifetimes.

We theoretically investigate the photoelectron spectra of fluorine anions by a few-cycle linearly polarized laser pulse for different atomic orbitals, which are calculated by an exact solution to the time-dependent Schrödinger equation and by the strong-field approximation, respectively. Through the comparison of results by both methods, we show that the initial orbital symmetry strongly affects the main shape of the photoelectron spectra. Based on the saddle-point method, we find that the orbital symmetry only affects the intracycle interference for the low-energy electron spectra. More importantly, it is found that the elastic scattering differential cross section leaves different fingerprints in the photoelectron spectra for atomic orbitals with different magnetic quantum numbers.

We study strongly interacting ultracold spin-$1/2$ fermions in a honeycomb lattice in the presence of a harmonic trap. Tuning the strength of the harmonic trap we show that it is possible to confine the fermions in artificial structures reminiscent of graphene nanoflakes in solid state. The confinement on small structures induces magnetic effects which are absent in a large graphene sheet. Increasing the strength of the harmonic potential we are able to induce different magnetic states, such as a Néel-like antiferromagnetic or ferromagnetic state, as well as mixtures of these basic states. The realization of different magnetic patterns is associated with the terminations of the artificial structures, in turn controlled by the confining potential.

We study the dissipative dynamics of neutral atoms in anisotropic harmonic potentials, immersed in a reservoir species that is not trapped by the harmonic potential. Considering initial motional excitation of the atoms along one direction, we explore the resulting spontaneous emission of reservoir excitations, across a range of trap parameters from strong to weak radial confinement. In different limits these processes are useful as a basis for analogies to laser cooling, or as a means to introduce controlled dissipation to many-body dynamics. For realistic experimental parameters, we analyze the distribution of the atoms during the decay and determine the effects of heating arising from a finite temperature reservoir.

In this article we perform the quantization of graphene plasmons using both a macroscopic approach, based on the classical expression for the average electromagnetic energy in a dielectric medium, and a quantum hydrodynamic model, in which graphene electrons are modeled as a charged fluid. Both models allow one to take into account the dispersion in the optical response, with the hydrodynamic model also allowing for the inclusion of the momentum dependence of the optical response (nonlocal effects). Using both methods, the electromagnetic field mode functions, and the respective frequencies, are determined for two different graphene structures. We show how to quantize graphene plasmons, considering that graphene is a dispersive medium, within the local and nonlocal descriptions. It is found that the dispersion of graphene's optical response leads to a nontrivial normalization condition for the mode functions. The obtained mode functions are then used to calculate the decay of an emitter, represented by a dipole, via the excitation of graphene surface plasmon polaritons. The obtained results are compared with the total spontaneous decay rate of the emitter and a near perfect match is found in the relevant spectral range. It is found that nonlocal effects in graphene's conductivity become relevant for the emission rate for small Fermi energies and small distances between the dipole and the graphene sheet.

We employ complex index modulation to manipulate light scattering in a waveguide and achieve different kinds of singularities in the system. The singularities refer to poles or zeros in the scattering and transfer matrices. By using spatially complex index modulation, we realize unidirectional zero-reflection singularities, which can be manipulated by adjusting the modulation phase difference between the real and imaginary parts. Laser-coherent perfect absorber singularities with both diverging reflectance and transmittance are also achieved by cascading two waveguides with different modulation phases. Meanwhile, bidirectional zero-reflection singularities with reflectionless light transporting on both sides of the waveguides are also demonstrated. In addition, we utilize temporally complex modulation to obtain transfer matrix singularities and achieve nonreciprocal light transmission. The study may find great applications in light amplification, attenuation, and absorption, as well as constructing nonreciprocal optical devices.

Lots of digital devices were widely used in computational ghost imaging (CGI) to serve as optical sources and detectors. These digital devices greatly affect the statistical behaviors of the CGI system. In this paper, we attribute all the influence of these digital devices to the discrete probability density functions of the optical sources. We investigate CGI with three discrete optical sources, which emit intensities fulfilling Bernoulli, binomial, and Poisson distributions. We clarify the inner relation between the bucket signals and the reference signals by using their joint density probability functions. In correlation measurement, the visibility and signal-to-noise ratio of the ghost images greatly depend on the probability statistics of the sources. We find that CGI with discrete sources can surpass the classical visibility limit one-third in the thermal-light case. The simulation results confirm our theoretical predictions. Thus, the utility of the digital devices makes CGI manipulable and applicable in practice.

We employ the intertwining operator technique to synthesize a supersymmetric (SUSY) array of arbitrary size $N$. The synthesized SUSY system is equivalent to a spin $(N-1)/2$ under an effective magnetic field. By considering an additional imaginary magnetic field, we obtain a generalized parity-time-symmetric non-Hermitian Hamiltonian that describes a SUSY array of coupled resonators or waveguides under a gradient gain and loss; all the $N$ energy levels coalesce at an exceptional point (EP), forming an isotropic high-order EP with $N$ states coalescence (EPN). Near the EPN, the scaling exponent of phase rigidity for each eigenstate is $(N-1)/2$; the eigenfrequency response to the perturbation $\epsilon$ acting on the resonator or waveguide couplings is ${\epsilon }^{1/N}$. Our findings reveal the importance of the intertwining operator technique for spectral engineering and exemplify the practical application in non-Hermitian physics.

We demonstrate time-domain sampling of mid-infrared electric field transients and their conjugate counterparts exploiting the dynamical Pockels effect. To this end, the complete polarization change of few-femtosecond probe pulses is studied. An intuitive picture based on a phasor representation is established before gaining quantitative understanding in experiment and theory. In the standard version of electro-optic sampling, the electric field is determined by analyzing the change of ellipticity of the probe polarization. Beyond this, we find that a temporal gradient of the input electric field manifests itself in a rotation of the polarization ellipsoid of the probe. The relative contribution of sum- and difference-frequency mixing processes and their spectral distribution over the near-infrared probe bandwidth are identified as key aspects. If one of these processes dominates, detecting ellipticity changes and polarization rotation as a function of time delay results in two wave forms which are Hilbert transforms of each other. Such conditions may be achieved by angle phase matching in birefringent materials or spectral filtering of the probe after the nonlinear interaction. In this case, a static phase introduced by birefringence or reflection at metallic mirrors results in a specific phase shift of both time traces with respect to the input electric field. Contributions from sum- and difference-frequency generation are found to be equivalent when using electro-optic sensors with isotropic refractive index. Polarization rotations in the low- and high-frequency parts of the probe then tend to cancel out. In this limit, spurious additional phase shifts do not change the phase of the detected transients. This fact leads to a robust recovery of the carrier-envelope phase of the input wave form. Clarifying the role of imperfections of superachromatic phase retarders completes our survey on proper determination of the electric field and its conjugate variable.

We develop an analytic formalism to describe dipole radiation near the Dirac cone of a two-dimensional photonic crystal slab. In contrast to earlier work, we account for all polarization effects and derive a closed-form expression for the dyadic Green's function of the geometry. Using this analytic Green's function, we demonstrate that the dipolar interaction mediated by the slab exhibits winding phases, which are key ingredients for engineering topological systems for quantum emitters. As an example, we study the coherent atomic interactions mediated by the Dirac cone, which were recently shown to be unusually long range with no exponential attenuation. These results pave the way for further, rigorous analysis of emitters interacting in photonic crystals via photonic Dirac cones.

In the context of Fock states, demonstrating multiphoton quantum interference, e.g., the generalized Hong-Ou-Mandel (HOM) interference, is at the core of many applications of quantum technologies. However, it is difficult to demonstrate high-visibility quantum interference for a large number of photons. Here, we introduce an experimentally feasible proposal to achieve this goal using phase-randomized weak coherent states and practical photon-number-resolving detectors. Our method can be used to obtain analytically tight bounds of the generalized HOM dip in a beam splitter, and it is robust against practical errors. The simulation shows that for an ideal detector that can resolve any number of photons without an upper bound, the proposed method can bound the generalize HOM interference for a large number of photons, e.g., 100 photons; for a practical detector that can resolve up to 29 photons, the proposed method can bound the generalized HOM interference for 56 photons with visibility $99.4\%$. Our proposal is a general approach for multiphoton quantum interference in optical networks with multiple inputs and outputs.

The interaction of a single-photon pulse of radiation with an atom or an ensemble of atoms is studied using a source-field approach. The atom-field interaction is weak insofar as it can be treated in lowest, nonvanishing order of perturbation theory. The output field intensity and second-order correlation function of the field are calculated. It is shown that, even when any modification of the atomic dynamics produced by the incident field is neglected, as a function of the time delay $\tau$ between the incident field pulse and the field radiated by the atom(s), there is a “bump” in the time-integrated second-order correlation at $\tau =0$. The increase in coincidence counts for $\tau =0$ can be interpreted in terms of Hanbury Brown and Twiss–type interference. By looking at the field intensity, we show that the bump has no direct relation with stimulated emission—it occurs even when the input field is attenuated. In recent down conversion experiments, an increase in coincidence counts has been attributed to stimulated emission—we comment on the validity of such an interpretation in light of our results.

Nonlinear magneto-optical rotation is studied under nonequilibrium conditions. The polarization rotation of linearly polarized light, traversing a room-temperature rubidium vapor, is observed versus the time-dependent (swept) longitudinal magnetic field in the presence of static transverse magnetic fields. Presence of the transverse fields modifies the character of the observed signals. In particular, for the weaker fields, the longitudinal-field sweep leads to a two-frequency oscillation of the polarization rotation while crossing zero. Unlike the steady state, this was observed independent of the transverse-field direction. For the stronger transverse fields, the oscillations deteriorate eventually reaching a situation when a nonoscillating dynamic signal, with a distinct minimum close to the zero longitudinal field, is observed. The presented experimental results are supported with theoretical analysis based on the density-matrix formalism. The analysis confirms all the features of experimental results while providing an intuitive explanation of the observed behavior based on angular-momentum probability surfaces used for density-matrix visualization.

Quantum information theory has shown strong connections with classical statistical physics. For example, quantum error correcting codes like the surface and the color code present a tolerance to qubit loss that is related to the classical percolation threshold of the lattices where the codes are defined. Here we explore such connection to study analytically the tolerance of the color code when the protocol introduced in Vodola et al. [Phys. Rev. Lett. 121, 060501 (2018)] to correct qubit losses is applied. This protocol is based on the removal of the lost qubit from the code, a neighboring qubit, and the lattice edges where these two qubits reside. We first obtain analytically the average fraction of edges $r\left(p\right)$ that the protocol erases from the lattice to correct a fraction $p$ of qubit losses. Then, the threshold $p_c$ below which the logical information is protected corresponds to the value of $p$ at which $r\left(p\right)$ equals the bond-percolation threshold of the lattice. Moreover, we prove that the logical information is protected if and only if the set of lost qubits does not include the entire support of any logical operator. The results presented here open a route to an analytical understanding of the effects of qubit losses in topological quantum error codes.

Majorana stars, the $2j$ spin coherent states that are orthogonal to a spin-$j$ state, offer a visualization of general quantum states and may disclose deep structures in quantum states and their evolutions. In particular, the genuine tripartite entanglement—the three-tangle of a symmetric three-qubit state, which can be mapped to a spin-3/2 state—is measured by the normalized product of the distance between the Majorana stars. However, the Majorana representation cannot be applied to general nonsymmetric $n$-qubit states. We show that, after a series of $\mathrm{SL}(2,\mathbb{C})$ transformations, nonsymmetric three-qubit states can be transformed to symmetric three-qubit states, while at the same time the three-tangle is unchanged. Thus the genuine tripartite entanglement of general three-qubit states has the geometric representation of the associated Majorana stars. The symmetrization and hence the Majorana star representation of certain genuine high-order entanglement for more qubits are possible for some special states. In general cases, however, the constraints on the symmetrization may prevent the Majorana star representation of the genuine entanglement.

Stability and robustness are important criteria to evaluate the performance of a quantum-key-distribution (QKD) system in real-life applications. However, the inherent birefringence effect of the fiber channel and disturbance caused by the variation of the deployment environment of the QKD system tremendously decrease its performance. To eliminate this adverse impact, we propose a polarization-insensitive phase-coding QKD system based on Sagnac–Mach-Zehnder interferometers. Verified by theoretical analysis and experimental tests, this QKD system is robust against channel polarization disturbance. The robustness and long-term stability of the QKD system is confirmed with a 10-day continuous operation over a 12.6-dB channel, which consists of a 50-km fiber spool and a polarization scrambler (2 rad/s). As a result, an average quantum bit error rate of $0.958\%$ and a sustained secure key rate of 3.68 kbps are obtained. Moreover, the secure key rate of the QKD system for a typical channel loss of 10 dB reaches 6.89 kbps, and the achievable maximum transmission distance exceeds 125 km.

We study the fluctuation-induced dissipative dynamics of the quantized center-of-mass motion of a polarizable dielectric particle trapped near a surface. The particle's center of mass is treated as an open quantum system coupled to the electromagnetic field acting as its environment, with the resulting system dynamics described by a quantum Brownian motion master equation. The dissipation and decoherence of the particle's center of mass are characterized by the modified spectral density of the electromagnetic field that depends on surface losses and the strength of the classical trap field. Our results are relevant to experiments with levitated dielectric particles near surfaces, illustrating potential ways of mitigating fluctuation-induced decoherence while preparing such systems in macroscopic quantum states.

The effects of atom numbers on the miscibility-immiscibility transition of a harmonically trapped population imbalanced binary Bose-Einstein condensate are investigated. In two-dimensional parameter space expanded by the strength of interspecies interaction and the ratio of atom numbers between two components, we have mapped out the ground-state phase diagrams for the ideal model without intraspecies interactions, and for the ${}^{23}\mathrm{Na}\text{−}{}^{23}\mathrm{Na}$ mixture and the ${}^{87}\mathrm{Rb}\text{−}{}^{87}\mathrm{Rb}$ mixture with experimentally accessible intraspecies scattering lengths, respectively. It is found that all the phase diagrams include the miscible, symmetric immiscible, and asymmetric immiscible phases, and there exists a tricritical point where those three different phases merge. Furthermore, the phase boundaries among those three phases show a strong dependence on the atom numbers of two components. These results can be observed in current experiments.

We introduce the concept of hypergraphs to describe quantum optical experiments with probabilistic multiphoton sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such a general graph description provides new insights for producing complex high-dimensional multiphoton quantum entangled states, which go beyond limitations imposed by pair creation via spontaneous parametric down-conversion. Furthermore, the properties of hypergraphs can be investigated experimentally. For example, the NP-complete problem of deciding whether a hypergraph has a perfect matching can be answered by experimentally detecting multiphoton events in quantum experiments. By introducing complex weights in hypergraphs, we show a general many-particle quantum interference and manipulating entanglement in a pictorial way. Our work paves the path for the development of multiphoton high-dimensional state generation and might inspire new applications of quantum computations using hypergraph mappings.