The set of all electronic states that can be expressed as a single Slater determinant forms a submanifold, isomorphic to the Grassmannian, of the projective Hilbert space of wave functions. We explored this fact by using tools of Riemannian geometry of Grassmannians as described by [Absil et al., Acta Appl. Math. 80, 199 (2004)] to propose an algorithm that converges to a Slater determinant that is a critical point of the overlap function with a correlated wave function. This algorithm can be applied to quantify the entanglement or correlation of a wave function. We show that this algorithm is equivalent to the Newton method using the standard parametrization of Slater determinants by orbital rotations, but it can be more efficiently implemented because the orbital basis used to express the correlated wave function is kept fixed throughout the iterations. We present the equations of this method for a general configuration interaction wave function and for a wave function with up to double excitations over a reference determinant. Applications of this algorithm to selected electronic systems are also presented and discussed.

Ozone formation and depletion play a key role in various physical and chemical atmospheric processes which remain to be understood in more detail. The modeling of such phenomena based on ozone dynamics calculations requires a detailed knowledge of quantum states, transition probabilities, and ozone potential energy surface (PES) near the dissociation threshold $D_0$. Knowledge of highly excited rovibrational states with energies approaching $D_0$ is necessary for a reliable interpretation of satellite measurements of the ozone absorption or emission in the upper atmosphere in nonlocal thermodynamic equilibrium conditions. In addition, these states provide an ideal probe of PESs computed by ab initio methods but their detection by absorption spectroscopy is particularly challenging due to the sharp decrease of the intensity with the energy of the corresponding vibrational combination and overtone bands. In this work, two very high-energy vibrational bands are detected by high sensitivity cavity ring-down spectroscopy providing a noise equivalent absorption ${\alpha }_{\min }$ on the order of a few ${10}^{-11}\mathrm{c}{\mathrm{m}}^{-1}$. The corresponding cold bands, assigned as ${\nu }_1+6{\nu }_2+3{\nu }_3$ and $6{\nu }_1+{\nu }_2+{\nu }_3$ centered at 7969 and $7993\mathrm{c}{\mathrm{m}}^{-1}$, respectively, are about nine orders of magnitude less intense than the well-known ${\nu }_3$ fundamental band near 10 µm. The spectrum analysis allowed for the experimental determination of 240 rovibrational energy levels of the upper vibrational states. The corresponding rotational patterns, located between 93.1% and 96.7% of the dissociation threshold, are the most excited ones measured so far by absorption spectroscopy. The values of the band centers and rotational constants derived from the spectrum analysis provide further confirmation of the absence of an activation barrier on the minimum-energy path towards the dissociation threshold [Tyuterev et al., Phys. Rev. Lett. 113, 143002 (2014)]. The vibrational dynamics is discussed in the context of the radiative transition probabilities and related Einstein coefficients for the observed bands. Another important question in the context of the nuclear dynamics concerns the interaction among the three identical potential wells of the ozone molecule in the ground electronic state, which appears to be due to the Jahn-Teller effect. Recent theoretical results accounting for the three potential wells in a full symmetry approach predicted that vibration states should exhibit deviations from the conventional one-potential-well ab initio calculations, near the dissociation threshold. In the present work, we observe a better agreement of the experimentally determined energy value with the three-wells prediction for the (1,6,3) vibrational state involving a large simultaneous excitation of both bending (${\upsilon }_2=6$) and asymmetric stretch (${\upsilon }_3=3$) vibrations pointing towards a nearby well. This could be tentatively interpreted as a manifestation of the three-wells effect.

We investigate the two-photon double ionization of atomic magnesium induced by ultrashort pulses. Though the initial and final state symmetries are comparable to the same process in helium, in stark contrast the range of photon energies for which nonsequential ionization is the only open pathway is narrow (less than 1 eV) in magnesium. Thus several sequential ionization pathways feature heavily in these processes. Nonetheless, it is found that for pulse durations between 0.25 and 2.0 fs, the joint angular dependence of the ejected electrons can depend sensitively on pulse length, varying between the strictly back-to-back ejection characteristic of nonsequential ionization to other distributions. The significance of excited-state correlating configurations in representing the initial state of magnesium is discussed in the light of their consequences for the resulting angular distributions at photon energies where sequential ionization can access intermediate states that lie nearby in energy, particularly for longer pulses.

We propose a powerful and convenient method to systematically design flat-band lattice models, which overcomes the difficulties underlying the previous method. Especially, our method requires no elaborate calculations, applies to arbitrary spatial dimensions, and guarantees to result in a completely flat ground band. We use this method to generate several classes of lattice models, including models with both short- and long-range hoppings, both topologically trivial and nontrivial flat bands. Some of these models were previously known. Our method, however, provides important insight. For example, we have reproduced and generalized the Kapit-Mueller model [Kapit and Mueller, Phys. Rev. Lett. 105, 215303 (2010)] and demonstrated a universal scaling rule between the flat-band degeneracy and the magnetic flux that was not noticed in previous studies. We show that the flat band of this model results from the (over-)completeness properties of coherent states.

We determine the incoherent spectrum, squeezing properties, and second-order correlation function of the collective atomic degrees of freedom in absorptive optical bistability. This is accomplished via a linearized Fokker-Planck equation in the positive $P$ representation, guided by the analysis of H. J. Carmichael [Phys. Rev. A 33, 3262 (1986)] which does not resort to adiabatic elimination. We focus on the regimes of weak and strong intracavity excitation, addressing the good-cavity and bad-cavity limits as well as the limit of collective strong coupling. Adiabatic elimination of the intracavity field sustained by an auxiliary resonator coupled to the ensemble is used to probe the atomic correlations via the formation of a collective emission channel. We compare to the corresponding expressions for the forward-scattered light with reference to experimental results, discussing key differences between the lower and upper branch of the steady-state semiclassical bistability curve. Our analysis is carried out around the stable states situated far away from the turning points, where analytical expressions can be obtained self-consistently, demonstrating a clear departure from classical behavior.

We consider a toy model for nonlocal quantum correlations in which nature resorts to some form of hidden signaling (i.e., signaling between boxes but not available to the users) to generate correlations. We show that if such a model also had memory, the parties would be able to exploit the hidden signaling and use it to send a message, achieving faster-than-light communication. Given that memory is a resource easily available for any physical system, our results add evidence against hidden signaling as the mechanism behind nature's nonlocal behavior.

Identifying which master equation is preferable for the description of a multipartite open quantum system is not trivial and has led in recent years to the local vs global debate in the context of Markovian dissipation. We treat here a paradigmatic scenario in which the system is composed of two interacting harmonic oscillators A and B, with only A interacting with a thermal bath—collection of other harmonic oscillators—and we study the equilibration process of the system initially in the ground state with the bath finite temperature. We show that the completely positive version of the Redfield equation obtained using coarse-grain and an appropriate time-dependent convex mixture of the local and global solutions give rise to the most accurate approximations of the whole exact system dynamics, i.e., both at short and at long timescales, outperforming the local and global approaches.

Enhancing the precision of a measurement requires maximizing the information that can be gained about the quantity of interest from probing a system. For optical-based measurements, such an enhancement can be achieved through two approaches, increasing the number of photons used to interrogate the system and using quantum states of light to increase the amount of quantum Fisher information gained per photon. Here we consider the use of quantum states of light with a large number of photons, namely the bright single-mode squeezed state and the bright two-mode squeezed state, which take advantage of both of these approaches for the problem of transmission estimation. We show that, in the limit of large squeezing, these states approach the maximum possible quantum Fisher information per photon for transmission estimation that is achieved with the Fock state and the vacuum two-mode squeezed state. Since the bright states we consider can be generated at powers much higher than those of the quantum states that achieve the maximum quantum Fisher information per photon, they can achieve a much higher absolute precision as quantified by the quantum Cramér-Rao bound. We discuss the effects of losses external to the system on the precision of transmission estimation and identify simple measurement techniques that can saturate the quantum Cramér-Rao bound for the bright squeezed states even in the presence of such external losses.

We report high-precision measurements on the thallium fluoride $\tilde{J}=1$ hyperfine manifold of the $B{}^3\mathrm{\Pi }_1$ ($v=0$) state. This state is of special interest because it is central to an optical cycling scheme that is envisioned to play an important role in enhancing the sensitivity of the CeNTREX nuclear Schiff-moment experiment presently under construction. The measurements are made by monitoring the fluorescence induced by narrow-band laser excitation of a cryogenic molecular beam. We use a multipass arrangement of the laser beam to enhance fluorescence. When viewed with a camera, we can spatially resolve images from adjacent passes that approach the molecules from opposing directions. These images yield a sensitive visual method to identify the central frequency of a transition. Coupling these line-center determinations with frequency calibration from an acousto-optic modulator has allowed a more precise determination of the $\tilde{J}=1$ manifold of hyperfine level splittings. We observe Stark shifts of the $\tilde{J}=1$ levels and infer a permanent electric dipole moment of 2.28(7) D and Λ-doublet splittings for the ${F_1}^{\prime }=1/2$ and ${F_1}^{\prime }=3/2$ manifolds of 14.4(9) and 17.4(11) MHz, respectively.

The problem of Freeman resonances [Freeman et al., Phys. Rev. Lett. 59, 1092 (1987)] when strong-field ionization is enhanced due to transient population of excited Rydberg states during ionization is revisited. An intuitive model is put forward which explains the mechanism of intermediate population of excited states during nonadiabatic tunneling ionization via under-the-barrier recollision and recombination. The theoretical model is based on perturbative strong-field approximation (SFA), where the sub-barrier bound-continuum-bound pathway is described in the second-order SFA, with further ionization from the excited state by an additional perturbative step. The enhancement of ionization is shown to arise due to constructive interference of contributions into the excitation amplitudes originating from different laser cycles. The applied model provides an intuitive understanding of the electron dynamics during a Freeman resonance in strong-field ionization, as well as a means of enhancing the process and possible applications to related processes.

I consider general interacting systems of quantum particles in one spatial dimension. These consist of bosons or fermions, which can have any number of components, arbitrary spin, or a combination thereof, featuring low-energy two- and multiparticle interactions. The single-particle dispersion can be Galilean (nonrelativistic), relativistic, or have any other form that may be relevant for the continuum limit of lattice theories. Using an algebra of generalized functions, statistical transmutation operators that are genuinely unitary are obtained, putting bosons and fermions in a one-to-one correspondence without the need for a short-distance hard core. In the nonrelativistic case, low-energy interactions for bosons yield, order by order, fermionic dual interactions that correspond to the standard low-energy expansion for fermions. In this way, interacting fermions and bosons are fully equivalent to each other at low energies. While the Bose-Fermi mappings do not depend on microscopic details, the resulting statistical interactions heavily depend on the kinetic energy structure of the respective Hamiltonians. These statistical interactions are obtained explicitly for a variety of models, and regularized and renormalized in the momentum representation, which allows for theoretically and computationally feasible implementations of the dual theories. The mapping is rewritten as a gauge interaction, and one-dimensional anyons are also considered.

We experimentally investigate a mechanical squeezed state realized in a parametrically modulated membrane resonator embedded in an optical cavity. We demonstrate that a quantum characteristic of the squeezed dynamics can be revealed and quantified even in a moderately warm oscillator, through the analysis of motional sidebands. We provide a theoretical framework for quantitatively interpreting the observations and present an extended comparison with the experiment. A notable result is that the spectral shape of each motional sideband provides a clear signature of a quantum mechanical squeezed state without the necessity of absolute calibrations, in particular in the regime where residual fluctuations in the squeezed quadrature are reduced below the zero-point level.

The optical resonance problem is similar to but different from the time-steady Schrödinger equation to the point that eigenfunctions in resonance problems are exponentially growing. We introduce the perfectly-matched-layer method and the complex stretching technique to transform eigenfunctions from exponential growth to exponential decay. Accordingly, we construct a Hamiltonian operator to calculate eigenstates of optical resonance systems. We successfully apply our method to calculate the eigenvalues for whispering-gallery modes and the results perfectly agree with existing theory that is developed only for regularly shaped cavities. We also apply the method to investigate the mode evolution near exceptional points—a special phenomenon that only happens in non-Hermitian systems. The presenting method is applicable to optical resonance systems with arbitrary dielectric distributions.

Non-Hermitian, one-dimensional potentials which are also nonlocal, allow for scattering asymmetries, namely, asymmetric transmission or reflection responses to the incidence of a particle from left or right. The symmetries of the potential imply selection rules for transmission and reflection. In particular, parity-time (PT) symmetry or the symmetry of any local potential do not allow for asymmetric transmission. We put forward a feasible quantum-optical implementation of non-Hermitian, nonlocal, non-PT potentials to implement different scattering asymmetries, including transmission asymmetries.

We study the dynamical properties of a driven-dissipative Bose-Hubbard model in the strongly interacting regime through a quantum trajectory approach with a cluster Gutzwiller Ansatz for the wave function. This allows us to take classical and quantum correlations into account. By studying the dynamical hysteresis surface that arises by sweeping through the coherent driving strength we show that the phase diagram for this system is in qualitative correspondence with the Gutzwiller mean-field result. However, quantitative differences are present and the inclusion of classical and quantum correlations causes a significant shift of the critical parameters. Additionally, we show that approximation techniques relying on a unimodal distribution such as the mean field and $1/z$ expansion drastically underestimate the particle number fluctuations. Finally, we show that a proposed mapping of the driven-dissipative many-body Bose-Hubbard model onto a single driven-dissipative Kerr model is not accurate for parameters in the hysteresis regime.

Pivotal within quantum physics, the concept of quantum incompatibility is generally related to algebraic aspects of the formalism, such as commutation relations and unbiasedness of bases. Recently, the concept was identified as a resource in tasks involving quantum state discrimination and quantum programmability. Here, we link quantum incompatibility with the amount of information that can be extracted from a system upon successive measurements of noncommuting observables, a scenario related to communication tasks. This approach leads us to characterize incompatibility as a resource encoded in a physical context, which involves both the quantum state and observables. Moreover, starting with a measure of context incompatibility we derive a measurement-incompatibility quantifier that is easily computable, admits a geometrical interpretation, and is maximum only if the eigenbases of the involved observables are mutually unbiased.

Adiabatic passage is a standard tool for achieving robust transfer in quantum systems. We show that in driven nonlinear quantum systems adiabatic passage becomes highly nonrobust when the target is unstable. This occurs for a generic (1:2) resonance, for which the complete transfer corresponds to a hyperbolic fixed point featuring an adiabatic connectivity strongly sensitive to small perturbations of the model. By inverse engineering, we devise high-fidelity and robust partially nonadiabatic trajectories. They localize at the approach of the target near the stable manifold of the separatrix, which drives the dynamics towards the target in a robust way. These results can be applicable to atom-molecule Bose-Einstein condensate conversion and to nonlinear optics.

The evolution of the discrete Wigner function is formally similar to a probabilistic process, but the transition probabilities, like the discrete Wigner function itself, can be negative. We investigate these transition probabilities, as well as the transition rates for a continuous process, aiming particularly to give simple criteria for deciding when a set of such quantities corresponds to a legitimate quantum process. We also show how the transition rates for any Hamiltonian evolution can be worked out by expanding the Hamiltonian as a linear combination of displacement operators in the discrete phase space.