We report on experimental measurements and theoretical calculations of Rabi oscillation distortion during rubidium clock transition in a compact cold-atom clock. The distortion of the Rabi oscillations of the clock transition caused by the magnetically sensitive transitions between magnetic sublevels is related to the duration and amplitude of the microwave pulse, the density distribution of cold atoms, and the biased magnetic field inside the microwave cavity. The theoretical calculations agreed well with the experimental results. The Rabi oscillation measurements are beneficial for determining the optimal parameters of a cold-atom clock and identifying the uniformity of the microwave field inside the cavity. This measurement can be extended to the atomic fountain clock and the vapor-cell atomic clock.

We propose a class of spectral singularities that are sensitive to the direction of excitation and arise in nonlinear systems with broken parity symmetry. These spectral singularities are sensitive to the direction of the incident beam and result in diverging transmission and reflection for the left (right) incident, while the transmission and reflection of the right (left) side of the system remain finite. For the pedagogical reason, first we review the scattering formalism in nonlinear systems using an abstract $\delta$-function model. Then, using a parity symmetry broken nonlinear system consisting of two $\delta$ functions, one linear and the other nonlinear, we prove the existence of our proposed spectral singularities. Finally, we use an experimentally feasible realistic model based on coupled disk resonators to demonstrate the spectral singularity with directional sensitivity (SSDS). Our proposed SSDS might have applications in the design of nonlinear sensors and might provide a solution for the hole-burning problem in pumped laser ring resonators.

We study theoretically the second-order correlation function $g^{\left(2\right)}\left(t\right)$ for photons transmitted through a periodic Bragg-spaced array of superconducting qubits, coupled to a waveguide. We demonstrate that photon bunching and antibunching persist much longer than both radiative and nonradiative lifetimes of a single qubit. Due to the Borrmann effect, that is a strongly non-Markovian collective feature of light-qubit coupling inherent to the Bragg regime, the photon-photon correlations become immune to nonradiative dissipation. This persistence of quantum correlations opens new avenues for enhancing the performance of setups of waveguide quantum electrodynamics.

We investigate the multiphoton quantum dynamics of a leaking single-mode quantized cavity field coupled with a resonantly driven two-level system possessing permanent dipoles. The frequencies of the interacting subsystems being considered are very different, e.g., the microwave range for the cavity and the optical domain for the frequency of the two-level emitter, respectively. In this way, the emitter couples to the resonator mode only via its diagonal dipole moments. Furthermore, the generalized Rabi frequency resulting from the external coherent driving of the two-level subsystem is also assumed to be different from the resonator's frequency or its multiples. As a consequence, this highly dispersive interaction regime is responsible for the cavity multiphoton quantum dynamics and photon conversion from the optical to microwave range, respectively.

We investigate the quantum state generated by optical parametric down-conversion in a ${\chi }^{\left(2\right)}$ medium driven by two noncollinear light modes. The analysis shows the emergence of multimode, namely, three- or four-mode, entangled states in a subset of the spatiotemporal modes generated by the process. These appear as bright spots against the background fluorescence, providing an interesting analogy with the phenomenology recently observed in two-dimensional nonlinear photonic crystals. We study two realistic setups. (1) Noncritical phase matching in a periodically poled lithium tantalate slab, characterized by a three-mode entangled state. (2) A type I setup in a beta-barium borate crystal, where the spatial walk-off between the two pumps can be exploited to make a transition to a four-mode entangled state. In both cases, we show that the properties of the state can be controlled by modulating the relative intensity of two pump waves, making the device a versatile tool for quantum state engineering.

State-of-the-art linear sensors of force, motion, and magnetic fields have reached the sensitivity where the quantum noise of the meter is significant or even dominant. In particular, the sensitivity of the best optomechanical devices has reached the standard quantum limit (SQL), which directly follows from the Heisenberg uncertainty relation and corresponds to balancing the measurement imprecision and the perturbation of the probe by the quantum back-action of the meter. The SQL is not truly fundamental and several methods for its overcoming have been proposed and demonstrated. At the same time, two quantum sensitivity constraints which are more fundamental are known. The first limit arises from the finiteness of the probing strength (in the case of optical interferometers—of the circulating optical power) and is known as the energetic quantum limit or, in a more general context, as the quantum Cramér-Rao bound (QCRB). The second limit arises from the dissipative dynamics of the probe, which prevents full efficacy of the quantum back-action evasion techniques developed for overcoming the SQL. No particular name has been assigned to this limit; we propose the term dissipative quantum limit (DQL) for it. Here we develop a unified theory of these two fundamental limits by deriving the general sensitivity constraint for stationary, linear systems from which they follow as particular cases. Our analysis reveals a phase transition occurring at the boundary between the QCRB-dominated and the DQL regimes, manifested by the discontinuous derivatives of the optimal spectral densities of the meter quantum noise. This leads to the counterintuitive (but favorable) finding that quantum-limited sensitivity can be achieved with meter noise cross-correlations having a nonzero imaginary component, a feature arising in lossy meter systems. Finally, we show that the DQL originates from the nonautocommutativity of the internal thermal noise of the probe and that it can be overcome in nonstationary measurements.

Quantum nonlocality and quantum steering are fundamental correlations of quantum systems which cannot be created using classical resources only. Nonlocality describes the ability to influence the possible results of measurements carried out in distant systems, in quantum steering where Alice remotely steers Bob's state. Research in nonlocality and steering is of fundamental interest for the development of quantum information and in many applications requiring nonlocal resources like quantum key distribution. On the other hand, the Stern-Gerlach experiment holds an important place in the history, development, and teaching of quantum mechanics and quantum information. In particular, the thought experiment of consecutive Stern-Gerlach experiments is commonly used to exemplify the concept of noncommutativity between quantum operators. However, to the best of our knowledge, the consecutive Stern-Gerlach experiments have not been treated in a fully fledged quantum manner yet, and it is a widely accepted idea that atoms crossing consecutive Stern-Gerlach experiments follow classical paths. Here we demonstrate that two consecutive Stern-Gerlach experiments generate nonlocality and steering, and these nonlocal effects strongly modify our usual understanding of this experiment. Also, we discuss the implications of this result and its relation with entanglement. This suggests the use of quantum correlations, of particles possessing mass, to generate nonlocal tasks using this experiment.

We give an operational meaning to the min-entropy of a quantum state as a resource measure for various interconnected tasks. In particular, we show that the min-entropy without smoothing measures the amount of quantum information that can be hidden or encoded perfectly in the one-shot setting when the quantum state is used as a randomness or correlation source. First, we show that the min-entropy of entanglement of a pure bipartite state is the maximum number of qubits privately transferable when the state is used as a quantum one-time pad. Then, through the equivalence of quantum secret sharing–like protocols, it is also shown that the min-entropy of a quantum state is the maximum number of qubits that can be masked when the state is used as a randomness source for a quantum masking process. Consequently, we show that the min-entropy of a quantum state is half the size of the quantum state it can catalytically dephase. This gives a necessary and sufficient condition for catalysts for state transition processes.

Coherence of a quantum state (with respect to a fixed incoherent basis) is usually quantified by distancelike quantities, among which a particularly convenient and intuitive quantifier of coherence is based on the Hilbert-Schmidt distance between the quantum state and its dephased counterpart. This quantifier has a simple structure and many nice properties, although it is not a coherence monotone in the conventional resource-theoretic framework of coherence. Here we reveal its information-theoretic significance by showing that it coincides with uncertainty, as quantified by the variance of the state in the incoherent basis. The key point here is to regard the state as an observable, and to regard the incoherent basis as an ensemble of states rather than as measurement operators. Our result provides a natural decomposition of coherence into components along the incoherent basis. Furthermore, in terms of the Tsallis 2-entropy, which is also a measure of uncertainty, we provide two alternative interpretations of coherence: as increase of uncertainty caused by decoherence and as the conditional Tsallis 2-entropy in the context of purification. An intrinsic relation between the maximal coherence and the Brukner-Zeilinger invariant information is also established. These identifications of coherence with increase of uncertainty lead us to interpret coherence as a manifestation of quantum uncertainty, which may have implications for both quantum foundations and applications.

Sufficiently strong intersite interactions in extended-Hubbard and XXZ spin models result in dynamically bound clusters at neighboring sites. We show that the dynamics of these clusters in two-dimensional lattices is remarkably different and richer than that of repulsively bound on-site clusters in gases without intersite interactions. Whereas on-site pairs move in the same lattice as individual particles, nearest-neighbor dimers perform an interacting quantum walk in a different lattice geometry, leading to a peculiar dynamics characterized by multiple timescales. Although this is generally true, it is especially relevant in some lattices, including triangular and diamond lattices for hard-core bosons, and square lattices for soft-core bosons, where dimers move resonantly in either a kagome or a Lieb lattice. As a result, dimers show two very different transport velocities—a fast one comparable to the motion of individual particles, and a very slow one associated to flatband quasilocalization. Moreover, these lattices permit the resonant motion of longer clusters, and, remarkably, trimers move faster than quasi-flatband dimers for sufficiently strong optical lattices. This rich interplay between multiscaled quantum walk dynamics, quasilocalization, and flatband physics may be readily observed in experiments with lanthanide atoms.

Noise-induced phase transition between chaos and ordered states plays an important role in the self-organization of dissipative structures. Here, we numerically simulate the phase transitions between statistically stationary regimes in a laser cavity by using a stochastic complex cubic-quintic Ginzburg-Landau equation with a phase-diffusion model. Depending on the linear and nonlinear gains, the dissipative system converges from the initial noise floor to different regimes, including continuous wave, phase turbulence, amplitude turbulence (AT), and stable soliton structure. Around the regime boundaries, we found that only certain phase noise can cause the instability of phase turbulence. The defects formed due to the noise will continue to spread out and self-organize to form AT or stabilize the soliton structure in the defect area. Our results are helpful in understanding the dynamics of the buildup of mode locking and noiselike pulses in passively mode-locked lasers.

Fourier-transform ghost imaging (FGI) enables us to realize diffraction imaging within the Fresnel region by calculating the second-order correlations of light fields. Existing FGI schemes reconstruct the Fourier frequency spectrum via correlation or sparsity constraints, which generally require object-arm detection values with relatively high signal-to-noise ratio. In this paper, we propose a correspondence FGI scheme, which reconstructs the object's Fourier spectrum by averaging partial reference patterns corresponding to object-arm detection values of high fluctuations. This conditional-averaging method is theoretically demonstrated and then explored and verified by both simulation and experiment. Moreover, an information-theory-based explanation of the simulation results is performed by studying the Fisher information of detection signals. The proposed scheme improves the sampling efficiency and is expected to expand the application of FGI by combining it with other reconstruction techniques.

Spontaneous collapse models are proposed modifications to quantum mechanics which aim to solve the measurement problem. In this article, we will consider models which attempt to extend a specific spontaneous collapse model, the Ghirardi-Rimini-Weber model (GRW), to be consistent with special relativity. We will present a condition that a relativistic GRW model must meet for three cases: for a single particle, for $N$ distinguishable particles, and for indistinguishable particles. We will then show that this relativistic condition implies that one can have a relativistic GRW model for a single particles or for distinguishable noninteracting, nonentangled particles but not otherwise.

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than $10000$ with errors below ${10}^{-12}$.

Quantum communication channels benefit from nonbinary entanglement-assisted stabilizer codes using preshared entangled states for achieving better error correction capability compared to those that do not use preshared entanglement, making them indispensable for realizing large-scale quantum computing and communication systems over qudits. We provide a previously unreported design architecture of the syndrome computation unit for qudit stabilizer codes based on classical additive codes using discrete Fourier transform gates, $\mathrm{ADD}$ gates, and multiplication gates. The proposed syndrome computation circuit architectures are necessary toward the implementable realization of such entanglement-assisted and -unassisted qudit stabilizer codes within the quantum transceiver system. We further provide an equivalent design architecture of the syndrome computation unit that decomposes into two syndrome computation units based on X errors and Z errors separately for entanglement-assisted and -unassisted qudit CSS codes. The proposed quantum error correction architectures are useful for building high-density coded quantum memories for archival quantum storage.

Relativistic four-component electronic structure calculations at the density functional level have been carried out to describe parity-violation (PV) energy shifts to the total electronic energy for the chiral molecule CHFClBr. An $n$-mode ($n=3,4$) expansion of the complete potential energy surface at the explicitly correlated coupled-cluster level has been used for the vibrational analysis of PV effects for CHFClBr and CDFClBr. The vibrational spectrum and corresponding absolute intensities for fundamental, overtone, and combination band transitions obtained from a variational configuration interaction treatment are in excellent agreement with experimental data and the most accurate so far obtained. The results show that a 3-mode expansion is sufficient for the vibrational analysis. The PV energy shifts for the fundamental, overtone, and combination bands are all in the mHz region. The data provided will be useful for future detection of PV in chiral molecules.

Spin-exchange collisions among alkali-metal atoms affect the coherence time and gyromagnetic ratio of atoms by redistributing the ground-state population. We theoretically study the interactions between magnetic fields and atoms in the presence of spin-exchange collisions. Using the modified Bloch equations derived from the density-matrix equation in a low spin-polarization limit, we obtain explicit formulas describing the role of spin-exchange collisions in the interactions between atoms and magnetic fields, especially the nonresonant radio-frequency fields, which are widely used to manipulate atoms. The results derived from these equations agree well with density-matrix simulations and previous experimental results, and provide a simple and precise way to quantitatively analyze the effect of spin-exchange collisions on atoms. Our paper is helpful to gain physical insight into the spin-exchange collisions and optimize the performance of atom-based precision measurement instruments.

High-order harmonic generation (HHG) is responsible for high-energy photons and isolated attosecond pulses. The plasmonic fields excited by nanostructures exhibit both field enhancement and spatial dependence. And two-dimensional (2D) materials exhibit attractive features for coherent HHG. Here, by using ab initio simulations, we explore the possibility of combining 2D materials and plasmonic fields generated by nanoscale dimers to produce efficient HHG. In our scheme, we find the spatial inhomogeneity of plasmonic fields plays a key role for HHG enhancement in a wide range of the high-energy region, which enables the production of isolated attosecond pulses. By the classical trajectory simulation based on the single-electron approximation, we further analyze and confirm the role of the spatial inhomogeneity. We also investigate the HHG enhancement in bilayer 2D materials and analyze the influences of the stacking forms between two layers. According to our simulation results, different stacking forms will induce distinctive interlayer plasmons which cause significant differences in low-energy harmonics. Our exploration supplies a scheme to generate high-energy photons and ultrashort isolated pulses.