We observe bimodal fluorescence patterns from atoms in a fast atomic beam when the laser excitation occurs in the presence of a magnetic field and the atoms sample only a portion of the laser profile. The behavior is well explained by competition between the local intensity of the laser, which tends to generate a coherent-population-trapping (CPT) dark state in the $J=1$ to $J^{\prime }=0$ system, and the strength of an applied magnetic field that can frustrate the CPT process. This work is relevant for understanding and optimizing the detection process for clocks or other coherent systems utilizing these transitions and could be applicable to in situ calibration of the laser-atom interaction, such as the strength of the magnetic field or laser intensity at a specific location.

The semiconductor Bloch equations (SBEs) are routinely used for simulations of strong-field laser-matter interactions in condensed matter. In systems without inversion or time-reversal symmetries, the Berry connections and transition dipole phases (TDPs) must be included in the SBEs, which in turn requires the construction of a smooth and periodic structure gauge for the Bloch states. Here, we illustrate a general approach for such a structure-gauge construction for topologically trivial systems. Furthermore, we investigate the SBEs in the length and velocity gauges and discuss their respective advantages and shortcomings for the high-harmonic generation (HHG) process. We find that in cases where we require dephasing or separation of the currents into interband and intraband contributions, the length-gauge SBEs are computationally more efficient. In calculations without dephasing and where only the total current is needed, the velocity-gauge SBEs are structure-gauge independent and are computationally more efficient. We employ two systems as numerical examples to highlight our findings: a one-dimensional model of ZnO and the two-dimensional monolayer hexagonal boron nitride (hBN). The omittance of Berry connections or TDPs in the SBEs for hBN results in nonphysical HHG spectra. The structure- and laser-gauge considerations in the current work are not restricted to the HHG process and are applicable to all strong-field matter simulations with SBEs.

We investigate the role of the rotational excitation in the coherent and unidirectional $B{}^2{\mathrm{\Sigma }}_u^{+}\text{–}X{}^2{\mathrm{\Sigma }}_g^{+}$ emission of ${{\mathrm{N}}_2}^{+}$ at 391 nm called air lasing generated when ${\mathrm{N}}_2$ is irradiated with intense femtosecond near-infrared laser pulses at 800 nm. We simulate the time-dependent population transfer process of ${{\mathrm{N}}_2}^{+}$, which is assumed to be generated suddenly in an intense ultrashort laser pulse, by including vibrational and rotational degrees of freedom, and reveal that, when the light field intensity is below $\approx 4\times {10}^{14}{\mathrm{W}\mathrm{cm}}^{-2}$, the population inversion can be achieved in ${{\mathrm{N}}_2}^{+}$ only between rotationally highly excited levels in the vibrational ground ($v^{\prime }=0$) state of the $B{}^2{\mathrm{\Sigma }}_u^{+}$ state and those in the vibrational ground ($v^{\prime \prime }=0$) state of the $X{}^2{\mathrm{\Sigma }}_g^{+}$ state, so that the lasing at 391 nm is realized even when the total population in the $v^{\prime }=0$ state of the electronically excited $B{}^2{\mathrm{\Sigma }}_u^{+}$ state is not inverted with respect to the total population in the $v^{\prime \prime }=0$ state of the electronic ground $X{}^2{\mathrm{\Sigma }}_g^{+}$ state.

We present the structure of the ${\mathrm{H}}_3$ molecule (both quartet and doublet state) in the presence of strong magnetic fields of up to $5\hslash /\left(e{a}_0^2\right)$, equivalent to 1.175 MT. Both systems are stable molecules, adopting a triangular structure above about $1\hslash /\left(e{a}_0^2\right)$, but are oriented differently with respect to the magnetic field axis. For computing the molecular structure we implemented the unrestricted Hartree-Fock method including a strong magnetic field in the Hamiltonian. Using multiresolution analysis for the representation of the wave function the basis-set error is reduced to microhartree accuracy, giving rise to essentially gauge-origin-invariant molecular energies and properties. The method is applicable to general molecules of any structure and orientation with respect to the magnetic field axis. Nuclear gradients and current densities are readily available.

Progress in atomic optical clocks with total uncertainty of ${10}^{-18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the laser detuning and trap depth is also investigated. We find that there exists a distinctive operational magic lattice intensity of $5.33\left(2\right)E_R$ ($E_R$ is the lattice photon recoil energy) that reduces the total light shift below $1\times {10}^{-19}$ over $14\%$ of the trap depth variation, which will pave the way for the development of a new time-frequency standard of the Mg lattice clock.

We report the observation and manipulation of heteronuclear spin dynamics in a spin-1 mixture of ultracold ${}^{87}\mathrm{Rb}$ and ${}^{23}\mathrm{Na}$ atoms. The dynamics is driven by the interspecies spin-dependent interaction and shows a pronounced dependence on magnetic fields with influences from both linear and quadratic Zeeman shifts. Similar to the well-studied homonuclear cases, the interspecies spin dynamics can be controlled by tuning the quadratic Zeeman shift with far-detuned microwave fields. In addition, we successfully realize spin dynamics' control with vector light shifts which act as a species-selective effective magnetic field on ${}^{87}\mathrm{Rb}$ atoms. Both methods show negligible loss of atoms thus will be powerful techniques for investigating spin dynamics with fast temporal and high spatial resolutions.

We calculate the collective modes of ultracold trapped alkaline-earth-metal fermionic atoms, which possess an $\mathrm{SU}(N$) symmetry of the nuclear spin degree of freedom and a controllable $N$, with $N$ as large as 10. We calculate the breathing and quadrupole modes of two-dimensional and three-dimensional harmonically trapped gases in the normal phase. We particularly concentrate on two-dimensional gases, where the shift is more accessible experimentally, and the physics has special features. We present results as a function of temperature, interaction strength, density, and $N$. We include calculations across the collisionless to hydrodynamic crossover. We assume the gas is interacting weakly, such that it can be described by a Boltzmann-Vlasov equation that includes both mean-field terms and the collision integral. We solve this with an approximate scaling ansatz, taking care in two dimensions to preserve the scaling symmetry of the system. We predict the collective-mode frequency shifts and damping, showing that these are measurable in experimentally relevant regimes. We expect these results to furnish powerful tools to characterize interactions and the state of alkaline-earth-metal gases, as well as to lay the foundation for future work, for example, on strongly interacting gases and $\mathrm{SU}\left(N\right)$ spin modes.

We investigate the photon statistics of the light transmitted by a dipolariton system in interaction with a squeezed light from a degenerate optical parametric oscillator. We show that the presence of the squeezed photons in the cavity considerably increases the excitonic intensities and leads to a narrowing of the widths and a duplication of the intensity peaks. Our study reveals that the outgoing light exhibits a strong thermally resistant squeezing. Furthermore, it turns out that the weak-coupling regime is favorable to a perfect squeezing depending on the detunings and the strength of the squeezed pump. For a weak coherent driving field, the proposed system presents a bunching effect of the emitted light.

The so-called preparation uncertainty that occurs in the quantum world can be understood well in purely operational terms, and its existence in any given theory, perhaps differently than in quantum mechanics, can be verified by examining only measurement statistics. Namely, one says that uncertainty occurs in some theory when for some pair of observables, there is no preparation that would exhibit deterministic statistics for both of them. However, the right-hand side of the uncertainty relation is not operational anymore if we do not insist that it is just the minimum of the left-hand side for a given theory. For example, in quantum mechanics, it is some function of two observables that must be computed within the quantum formalism. Also, while joint nonmeasurability of observables is an operational notion, the complementarity in Bohr's sense (i.e., in terms of information needed to describe the system) has not yet been expressed in purely operational terms. Here we propose a general operational framework that provides answers to the above issues. We introduce an operational definition of complementarity and further postulate that complementary observables have to exhibit uncertainty, which means that we propose to put the (operational) complementarity as the right-hand side of the uncertainty relation. In particular, we identify two different notions of uncertainty and complementarity for which the above principle holds in the quantum-mechanical realm. We also introduce postulates for the general measures of uncertainty and complementarity. In order to define quantifiers of complementarity we first turn to the simpler notion of independence that is defined solely in terms of the statistics of two observables. Importantly, for clean and extremal observables—i.e., ones that cannot be simulated irreducibly by other observables—any measure of independence reduces to the proper complementary measure. Finally, as an application of our general framework we define a number of complementarity indicators and show that they can be used to state uncertainty relations. One of them, assuming some natural symmetries, leads to the Tsirelson bound for the Clauser-Horne-Shimony-Holt (CHSH) inequality. Lastly, we show that for a single system a variant of information causality called the information content principle, under the above symmetries, can be interpreted as an uncertainty relation in the above sense.

A thorough understanding of the structure of correlations in multipartite systems is essential for the success of most quantum information processing applications. The problem, however, quickly becomes nontrivial as the size of the multipartition increases. With this motivation in mind, in this paper, we put forth a detailed study of genuine multipartite correlations in the Dicke model of superradiance. We compute all genuine $k$-partite correlations for Dicke states with arbitrary excitations and use these results to characterize the evolution of multipartite correlations during the superradiant dynamics. Nontrivial effects in the way correlations in Dicke states are distributed between the multiple parts are found, showing strong finite-size effects. We also employ the concept of weaving to classify how multipartite correlations scale with the number of particles in the system.

The stored-program architecture is canonical in classical computing, while its power needs more investigations for the quantum case. We study quantum information processing with stored quantum program states, i.e., using qubits instead of bits to encode quantum operations. We develop a stored-program model based on Choi states, following from channel-state duality, and a symmetry-based generalization of deterministic gate teleportation, which can be employed to compose Choi states. Our model enriches the family of universal models for quantum computing, in particular the measurement-based models, and can also be employed for tasks including quantum simulation and communication.

The variations of the bound states of heteronuclear collision complexes in a static electric field are investigated. Using a prototype model, we engineer the interatomic interaction of the collision complex to have an $l$-wave bound state or quasibound state (virtual state for $s$ wave) close to the threshold. The variation of such a state with electric field is calculated to find out whether it crosses the threshold and produces a zero-energy resonance. We identify the cases in which an electric-field-induced resonance can occur at low field. The prototype model is used to interpret the calculated results with realistic potentials for heteronuclear alkali-metal collision complexes. We also calculate the probability density of the low-energy scattering state and find that the short-range probability density can still be enhanced in the absence of electric-field-induced resonance.

The rotation of two-component Fermi gases and the subsequent appearance of vortices have been the subject of numerous experimental and theoretical studies. Recent experimental advances in hyperfine state-dependent potentials and highly degenerate heteronuclear Fermi gases suggest that it would be feasible to create component-dependent rotation potentials in future experiments. In this study, we use an effective field theory for Fermi gases to consider the effects of rotating only one component of the Fermi gas. We find that the superfluid band gap in bulk exists up to higher rotation frequencies because the superfluid at rest, far away from the vortex, has to resist only half of the rotational effects. The vortex remains the energetically favorable state above a critical frequency, but exhibits a larger core size.

Estimating the quality of a single-photon source is crucial for its use in quantum technologies. The standard test for semiconductor sources is a value of the second-order correlation function of the emitted field below $1/2$ at zero time delay. This criterion alone provides no information regarding the amplitude of the single-photon contribution for general quantum states. Addressing this question requires the knowledge of additional observables. We derive an effective second-order correlation function, strongly connected to the Mandel-$Q$ parameter and given in terms of both the second-order correlation and the average photon number, that provides a lower bound on the single-to-multiphoton projection ratio. Using both observables individually allows for lower and upper bounds for the single-photon projection. Comparing the tightness of our bounds with those in the literature, we find that relative bounds may be better described using the average photon number, while absolute bounds for low excitation states are tighter using the vacuum projection. Our results show that estimating the quality of a single-photon source based on additional information is very much dependent on what aspect of the quantum state of light one is interested in.

The scattering of partially coherent radiation by a localized continuous material having parity-time ($\mathcal{PT}$) symmetry is considered under the formalism of classical coherence theory and the assumption that the Born approximation is valid. Our results suggest that the correlation-induced spectral changes are strongly dependent upon the gain and loss properties of the material. In particular, the center frequency of the scattered radiation undergoes a discontinuity as a function of the non-Hermitian parameter characterizing the physical properties of the material. The physical reason behind this abrupt behavior is that the $\mathcal{PT}$ symmetry induces the creation of two asymmetrical frequency bands inside the original Hermitian spectrum. We describe how this splitting occurs and offer possibilities to dynamically characterize the scattered spectrum.

It has been shown elsewhere that two spatially separated atoms can jointly absorb one photon, whose frequency is equal to the sum of the transition frequencies of the two atoms. We describe this process in the presence of an ensemble of many two-level atoms and show that it can be used to generate spin squeezing and entanglement. This resonant collective process allows us to create a sizable squeezing already at the single-photon limit. It represents a way to generate many-body spin-spin interactions, yielding a two-axis twisting-like interaction among the spins, which is very efficient for the generation of spin squeezing. We perform explicit calculations for ensembles of magnetic molecules coupled to a superconducting coplanar cavities. This system represents an attractive on-chip architecture for the realization of improved sensing.

We examine the existence of completely separable ground states (GS) in finite spin-$s$ arrays with anisotropic $XYZ$ couplings, immersed in a nonuniform magnetic field along one of the principal axes. The general conditions for their existence are determined. The analytic expressions for the separability curve in field space, and for the ensuing factorized state and GS energy, are then derived for alternating solutions, valid for any spin and size. They generalize results for uniform fields and show that nonuniform fields can induce GS factorization also in systems which do not exhibit this phenomenon in a uniform field. It is also shown that such a curve corresponds to a fundamental $S_z$-parity transition of the GS, present for any spin and size, and that two different types of GS parity diagrams can emerge, according to the anisotropy. The role of factorization in the magnetization and entanglement of these systems is also analyzed, and analytic expressions at the borders of the factorizing curve are provided. Illustrative examples for spin pairs and chains are as well discussed.

Effective Hamiltonian methods are utilized to model the two-qubit cross-resonance gate for both the ideal two-qubit case and when higher levels are included. Analytic expressions are obtained in the qubit case and the higher-level model is solved both perturbatively and numerically, with the solutions agreeing well in the weak-drive limit. The methods are applied to parameters from recent experiments and, accounting for classical cross-talk effects, results in good agreement between theory and experimental results.

Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum devices, parametrized quantum circuits have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a quantum circuit, which accepts a training dataset encoded in superposition or an easily preparable mixed state. We also demonstrate the ability to evaluate the gradient of the encoded cost function in a quantum state.