We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of near-threshold four-body bound states, systematically studying the effects of molecular properties, such as interaction strength, interaction range, and atomic mass. It is found that the adiabatic potential's nearest-neighbor energy level distribution transitions from significant level repulsion characteristic of chaos (Brody distribution) to nonchaotic (Poisson distribution) as the two molecules are separated. For the near-threshold four-atom bound states, the case where all atoms have equal masses shows a Poissonian spacing distribution, while the unequal-mass system exhibits significant level repulsion characterized by a nonzero Brody parameter. We derive a semiclassical formula for the density of states and extract from it simple scaling laws with potential depth and range. We find good agreement between the semiclassical predictions for the density of states and the full quantum mechanical calculations.

Standard optical potentials use an off-resonant laser standing-wave-induced ac Stark shift. In a recent development [Łącki et al., Phys. Rev. Lett. 117, 233001 (2016)] a three-level scheme in a $\mathrm{\Lambda }$ configuration coupled coherently by resonant laser fields was introduced, leading to an effective lattice with subwavelength potential peaks. Here, as an extension of that work, a four-level atomic setup in the tripod configuration is used to create spin-$\frac{1}{2}$-like two-dimensional dark space with one-dimensional motion and the presence of external gauge fields. Most interestingly for possible applications, the lifetime for a dark subspace motion is up to two orders of magnitude longer than for a similar $\mathrm{\Lambda }$ system. The model is quite flexible, leading to lattices with significant nearest, next-nearest, or next-to-next-nearest hopping amplitudes $J_1, J_2$, and $J_3$ offering intriguing possibilities to study, e.g., frustrated systems. The characteristic Wannier functions lead also to a type of intersite interaction not realizable in typical optical lattices.

Levitated optomechanical systems are rapidly becoming leading tools for precision sensing, enabling a high level of control over the sensor's center-of-mass motion, rotation, and electric charge state. Higher-order multipole moments in the charge distribution, however, remain a major source of backgrounds. By applying controlled precessive torques to the dipole moment of a levitated microsphere in vacuum, we demonstrate cancellation of dipole-induced backgrounds by 2 orders of magnitude. We measure the dipole moments of nanogram-mass spheres and determine their scaling with sphere size, finding that the dominant torques arise from induced dipole moments related to dielectric-loss properties of the ${\mathrm{SiO}}_2$ spheres. Control of multipole moments in the charge distribution of levitated sensors is a key requirement to sufficiently reduce background sources in future applications.

We study the collective emission of a beam of atomic dipoles into an optical cavity. Our focus lies on the effect of a finite detuning between the atomic transition frequency and the cavity resonance frequency. By developing a theoretical description of the coupled atom-cavity dynamics we analyze the stationary atomic configurations including a superradiant phase where the atoms undergo continuous monochromatic collective emission. In addition, we derive an analytical formula for the cavity pulling coefficient which characterizes the displacement of the emission frequency towards the cavity frequency. We find that the pulling is small if the cavity linewidth is much larger than the collective linewidth of the atomic beam. This regime is desired for building stable lasers because the emission frequency is robust against cavity length fluctuations. Furthermore, we investigate the stability of the atomic phases and compare our theoretical predictions with numerical results. Remarkably, we also find polychromatic emission regimes, where the spectrum has several frequency components while the light output is still superradiant.

We demonstrate how to create maximal entanglement between two qubits that are encoded in two spectrally distinct solid-state quantum emitters embedded in a waveguide interferometer. The optical probe is provided by readily accessible squeezed light, generated by parametric down-conversion. By continuously illuminating the emitters, the photon scattering and incremental path-erasure builds up entanglement. Our method does not require perfectly identical emitters, and accommodates spectral variations due to the fabrication process. Furthermore, for some linewidth and energy ratios, the entanglement buildup can be significantly faster than for more similar emitters. It is also robust enough to create entanglement with a concurrence above 99% in the event of scattering losses and detector inefficiencies and can form the basis for practical entangled networks.

We present a theoretical investigation to understand the connection between the formation of different rotational alignment echoes and the underlying excitation pathways induced by temporally delayed laser pulses. The fractional and multiple imaginary alignment echoes are predicted and demonstrated in the linear polar molecule carbonyl sulfide. We also use a two-dimensional spectrum obtained from higher-order alignment echo signals to identify the underlying quantum coherence. This work deepens our understanding of the alignment echo phenomenon. It provides a way to gain insight into the relationship between the echo signal and the underlying pathway with potential applications in rotational echo spectroscopy.

The Dicke model and the Rabi model can undergo phase transitions from the normal phase to the superradiant phase at the same boundary, which can be accurately determined using some approximated approaches. The underlying mechanism for this coincidence is still unclear, and the universality class of these two models is elusive. Here we prove this phase transition exactly using the path-integral approach based on the faithful Schwinger fermion representation, and give a unified phase boundary condition for these models. We demonstrate that at the phase boundary, the fluctuation of the bosonic field is vanished, thus, it can be treated as a classical field, based on which a much simplified method to determine the phase boundary is developed. This explains why the approximated theories by treating the operators as classical variables can yield the exact boundary. We use this method to study several similar spin and boson models, showing its much wider applicability than the previously used approaches. Our results demonstrate that these phase transitions belong to the same universality by the classical Landau theory of phase transition from a more general way, which can be confirmed using the platforms in the recent experiments.

We perform an analysis of the supercooled state in an analog of an early universe phase transition based on a one-dimensional, two-component Bose gas with time-dependent interactions. We demonstrate that the system behaves in the same way as a thermal, relativistic Bose gas undergoing a first-order phase transition. We propose a way to prepare the state of the system in the metastable phase as an analog to supercooling in the early universe. We show that parametric resonances in the system can be suppressed by thermal damping if the damping rate is similar to some of the higher rates previously used for modeling nonequilibrium experiments. However, the theoretically predicted damping rate for equilibrium systems within our model is too weak to suppress the resonances.

When a photon interferes with itself while traversing a Mach-Zehnder interferometer, the output port where it emerges is influenced by the phase difference between the interferometer arms. This allows for highly precise estimation of the path length difference (delay) but is extremely sensitive to phase noise. By contrast, a delay between the arms of the two-photon Hong-Ou-Mandel interferometer directly affects the relative indistinguishability of the photon pair, affecting the rate of recorded coincidences. This likewise allows for delay estimation, notably less precise but with the advantage of being less sensitive to perturbations of the photons' phase. Focusing on two-photon input states, we here investigate to what degree of noise Mach-Zehnder interferometry retains its edge over Hong-Ou-Mandel interferometry. We also explore the competing benefits of different two-photon inputs for a Mach-Zehnder interferometer and under what parameter regimes each input performs best.

We find that a bipartite quantum state is entangled if and only if it is quantum coherent with respect to complete bases of states in the corresponding system that are distinguishable under local quantum operations and classical communication. The corresponding minimal quantum coherence is the entanglement of formation. Connections to the relative entropy of entanglement and quantum coherence, and generalizations to the multiparty case are also considered.

We investigate the effects of non-Hermitian driving potential on quantum coherence in a bipartite system. The results show that the dynamical localization will revive after being destroyed by the Hermitian interaction, which provides evidence of the restoration of quantum coherence by a non-Hermitian driving potential. Besides, the entanglement between the two subsystems also decays with the boosting of non-Hermitian driving strength, which gives more evidence that non-Hermitian driving potential will protect quantum coherence. The physics behind this phenomenon is the domination of the quasieigenstate with maximum imaginary value of the quasieigenvalue over the dynamics of the non-Hermitian system. Our discovery establishes a restoration mechanism of quantum coherence in interacting and dissipative quantum systems which is highly expectable in updated experiments from many-body physics to quantum information.

The simulation of adiabatic evolution has deep connections with adiabatic quantum computation, the quantum approximate optimization algorithm, and adiabatic state preparation. Here we address the error analysis problem in quantum simulation of adiabatic process using Trotter formulas. We show that with additional conditions, the circuit depth can be linear in simulation time $T$. The improvement comes from the observation that the fidelity error here can't be estimated by the norm distance between evolution operators. This phenomenon is termed the robustness of discretization in digital adiabatic simulation. It can be explained in three steps, from analytical and numerical evidence: (1) The fidelity error should be estimated by applying adiabatic theorem on the effective Hamiltonian instead. (2) Because of the specialty of Riemann-Lebesgue lemma, most adiabatic process is naturally robust against discretization. (3) As the Trotter step gets larger, the spectral gap of effective Hamiltonian tends to close, which results in the failure of digital adiabatic simulation.

We derive the second-order approximation (PT2) for the ensemble correlation energy functional by applying the Görling-Levy perturbation theory to the ensemble density-functional theory. Its performance is checked by calculating excitation energies with the direct ensemble correction method in one-dimensional (1D) model systems and three-dimensional atoms using numerically exact Kohn-Sham orbitals and potentials. Compared with the exchange-only approximation, the inclusion of the ensemble PT2 correlation improves the excitation energies in 1D model systems in most cases, including double excitations and charge-transfer excitations. However, the excitation energies for atoms are generally worse with PT2. We find that the failure of PT2 in atoms is due to the two contributions of an orbital-dependent functional to excitation energies being inconsistent in the calculations. We also analyze the convergence of PT2 excitation energies with respect to the number of unoccupied orbitals.

A four-body coincident measurement of carbonyl sulfide dimers is conducted using a femtosecond laser-induced Coulomb explosion. Sequential and concerted processes that occur during the Coulomb explosion are distinguished. Four isomers of carbonyl sulfide dimer are resolved, and their structures are retrieved from the measured coincident momenta of the fragment ions generated in the concerted process, with the help of a classical trajectory simulation. As a result of our study, we can resolve the isomers of a weakly bound molecular cluster and determine their stereo configuration by using the Coulomb explosion. There is also the potential in femtosecond time-resolved imaging for structural evolution of molecular complexes in dissociation.

We present a theoretical analysis of the dynamics of a one-dimensional spin-1/2 fermionic gas subject to weak two-body losses. Our approach highlights the crucial role played by spin conservation in the determination of the full time evolution. We focus in particular on the dynamics of a gas that is initially prepared in a Dicke state with a fully symmetric spin wave function, in a band insulator, or in a Mott insulator. In the latter case, we investigate the emergence of a steady symmetry-resolved purification of the gas. Our results could help with the modelization and understanding of recent experiments with alkaline-earth(-like) gases like ytterbium and fermionic molecules.

We compute the fluctuations of the number of bosons with a given momentum for the Tonks-Girardeau gas at zero and finite temperature in a harmonic trap. We show that correlations between opposite momentum states $p$, which is an important fingerprint of long-range order in weakly interacting Bose systems, are suppressed. Nontrivial correlations, including negative correlations, are observed for momenta smaller than or of the order of the inverse radius of the gas. The full distribution of the number of bosons with momentum $p$ exhibits an interesting crossover from a nontrivial distribution at zero momentum to an exponential distribution. The distribution of the quasicondensate occupation is also studied. The experimental relevance of our findings for recent cold-atom experiments is discussed.

We examine the one-dimensional Gross-Pitaevskii lattice at zero temperature in the presence of uncorrelated disorder. We obtain analytical expressions for the thermodynamic properties of the ground state field and compare them with numerical simulations both in the low- and high-density regimes. We analyze weak excitations above the ground state and compute the localization properties of Bogoliubov–de Gennes modes. In the long-wavelength limit, these modes delocalize in accordance with the extended nature of the ground state. For high densities, we observe and derive a divergence of their localization length at finite energy due to an effective correlated disorder induced by the weak ground state field fluctuations. We derive effective high-density field equations for the excitations and generalize to higher dimensions.

Electric field measurement based on electric-field-induced second-harmonic generation (E-FISHG) of gas molecules is a promising method that enables noninvasive field measurement in gases. Although the probing laser beam is focused on the target area by a lens, the signal detected by the E-FISHG method is affected by the electric field along the probing laser path. The influencing path spans many tens of times the Rayleigh length of the front and rear of the focused spot. The E-FISHG signal has been frequently calibrated under uniform electric fields. However, this can yield a significantly incorrect calibrated value if the difference between the electric-field profiles in the measurement and calibration is not considered. In this paper, we propose a method to calibrate and furthermore restore the electric-field profile along a probing optical path by measuring a series of E-FISHG signals by changing the focusing spot position. The electric-field profile along the probing laser path is successfully restored from the measured E-FISHG signal sequence, which is verified by an experiment.