The propagation of light in nonlinear media is well described by a two-dimensional nonlinear Schrödinger equation (NLSE) within the paraxial approximation, which is equivalent to the Gross-Pitaevskii equation, the mean-field description for the dynamics of Bose-Einstein condensates (BECs). Due to this similarity, many theoretical and experimental investigations of phenomena which have already been studied and realized in BECs have been recently analyzed in alternative experimental platforms such as hot atomic vapors. In this work we study the formation of droplets of light in these media, attempting to establish a mapping between the experimental parameters normally used in BEC experiments and those needed to observe the analogous phenomenon in hot atomic vapors. We obtain the energy functional for the susceptibility of the medium in the ${\chi }^{\left(3\right)}, {\chi }^{\left(3\right)}+{\chi }^{\left(5\right)}$, and saturating regimes for a two-level atomic configuration considering the focusing (attractive) regime. We apply a Gaussian variational approach and check its predictions through numerical simulations of the NLSE for each regime. Finally, we study the real-time dynamics of the system for both the ${\chi }^{\left(3\right)}+{\chi }^{\left(5\right)}$ and saturating nonlinearities, focusing our attention on the behavior of the breathing mode and on the analysis of droplet formation for realistic experimental conditions.

Bose-Einstein condensation happens as a gas of bosons is cooled below its transition temperature, and the ground state becomes macroscopically occupied. The phase transition occurs in the thermodynamic limit of many particles. However, recent experimental progress has made it possible to assemble quantum many-body systems from the bottom up, for example, by adding single atoms to an optical lattice one at a time. Here, we show how one can predict the condensation temperature of a Bose gas from the energy fluctuations of a small number of bosons. To this end, we make use of recent advances in Lee-Yang theories of phase transitions, which allow us to determine the zeros and the poles of the partition function in the complex plane of the inverse temperature from the high cumulants of the energy fluctuations. By increasing the number of bosons in the trapping potential, we can predict the convergence point of the partition-function zeros in the thermodynamic limit, where they reach the inverse critical temperature on the real axis. Using fewer than 100 bosons, we can estimate the condensation temperature for a Bose gas in a harmonic potential in two and three dimensions, and we also find that there is no phase transition in one dimension as one would expect.

With rapid progress in control and manipulation of ultracold magnetic atoms and dipolar molecules, the quantum simulation of lattice models with strongly interacting dipole-dipole interactions (DDIs) and high densities is now within experimental reach. This rapid development raises the issue about the validity of quantum simulation in such regimes. In this study, we address this question by performing a full quantitative comparison between the continuum description of a one-dimensional gas of dipolar bosons in an optical lattice and the single-band Bose-Hubbard lattice model that it quantum simulates. By comparing energies and density distributions and calculating direct overlaps between the continuum and lattice many-body wave functions, we demonstrate that in regimes of strong DDIs and high densities the continuum system fails to recreate the desired lattice model. Two-band Hubbard models become necessary to reduce the discrepancy observed between continuum and lattice descriptions, but appreciable deviations in the density profile still remain. Our study elucidates the role of strong DDIs in generating physics beyond lowest-band descriptions and should offer a guideline for the calibration of near-term dipolar quantum simulators.

We consider plane wave modes in ultracold, but not quantum degenerate, dipolar Fermi gases in the hydrodynamic limit. Longitudinal waves present anisotropies in both the speed of sound and their damping, and experience a small, undulatory effect in their flow velocity. Two distinct types of shear waves appear, a “familiar” one, and another that is accompanied by nontrivial density and temperature modulations. We propose these shear modes as an experimental means to measure the viscosity coefficients, including their anisotropies.

The theory of optimal quantum control serves to identify time-dependent control Hamiltonians that efficiently produce desired target states. As such, it plays an essential role in the successful design and development of quantum technologies. However, often the delivered control pulses are exceedingly sensitive to small perturbations, which can make it hard if not impossible to reliably deploy these in experiments. Robust quantum control aims at mitigating this issue by finding control pulses that uphold their capacity to reproduce the target states even in the presence of pulse perturbations. However, finding such robust control pulses is generically hard, since the assessment of control pulses requires the inclusion of all possible distorted versions in the evaluation. Here we show that robust control pulses can be identified based on disorder-dressed evolution equations. The latter capture the effect of disorder, which here stands for the pulse perturbations, in terms of quantum master equations describing the evolution of the disorder-averaged density matrix. In this approach to robust control, the purities of the final states indicate the robustness of the underlying control pulses, and robust control pulses are singled out if the final states are pure (and coincide with the target states). We show that this principle can be successfully employed to find robust control pulses. To this end, we adapt Krotov's method for disorder-dressed evolution and demonstrate its application with several single-qubit control tasks.

Resonance energy transfer between chiral molecules can be used to discriminate between different enantiomers. The transfer rate between chiral molecules consists of nondiscriminatory and discriminatory parts. We derive these two rate contributions in the framework of macroscopic quantum electrodynamics. We show that their ratio is usually larger in the retarded regime or far zone of large separation distances and that the degree of discrimination can be modified when considering a surrounding medium. We highlight the importance of local field effects onto the degree of discrimination and predict for general identical chiral molecules the optimum dielectric medium for discrimination. We apply our results to 3-methylcyclopentanone and show that exotic media can even invert the discriminatory effect.

In most theories of diffraction by a diaphragm, the amplitude of the diffracted wave, and hence the position wave function of the associated particle, is calculated directly without prior calculation of the quantum state. Few models express the state of the particle to then deduce the position and momentum wave functions related to the diffracted wave. We present a model of this type for Fraunhofer diffraction. The diaphragm is assumed to be a device for measuring the three spatial coordinates of the particles passing through the aperture. A matrix similar to the $S$ matrix of the scattering theory describes the process, which turns out to be more complex than a simple position measurement. Some predictions can be tested. The wavelet emission involved in the Huygens-Fresnel principle occurs from several neighboring wavefronts instead of just one, causing typical damping of the diffracted wave intensity. An angular factor plausibly accounts for the decrease in intensity at large diffraction angles, unlike the obliquity factors of the wave optics theories. The position measurement modifies the polarization states and for an incident photon in an elliptically polarized pure state, the ellipse axes can undergo a rotation which depends on the diffraction angles.

Attosecond four-wave mixing (FWM) spectroscopy using an extreme ultraviolet (XUV) pulse and two noncollinear near-infrared (NIR) pulses is employed to measure Rydberg wave packet dynamics resulting from XUV excitation of a $3s$ electron in atomic argon into a series of autoionizing $3s^{-1}np$ Rydberg states $\sim 29$ eV. The emitted signals from individual Rydberg states exhibit oscillatory structure and persist well beyond the expected lifetimes of the emitting Rydberg states. These results reflect substantial contributions of longer-lived Rydberg states to the FWM emission signals of each individually detected state. A wave packet decomposition analysis reveals that coherent amplitude transfer occurs predominantly from photoexcited $3s^{-1}\left(n+1\right)p$ states to the observed $3s^{-1}np$ Rydberg states. The experimental observations are reproduced by time-dependent Schrödinger equation simulations using electronic structure and transition moment calculations. The theory highlights that coherent amplitude transfer is driven nonresonantly to the $3s^{-1}np$ states by the NIR light through $3s^{-1}\left(n+1\right)s$ and $3s^{-1}\left(n-1\right)d$ dark states during the FWM process.

Several plasmonic nanoparticles supporting dipolar resonances can couple to form normal modes. Here, we develop an analytical model to explain the formation of nonradiative “dark” and radiative “bright” modes through radiative coupling in bilayers consisting of dipolar nanoantenna arrays that are separated by a subwavelength distance. We also include near-field contributions in our model and show that the absorption and reflectance spectra obtained from our model agree reasonably well with the respective finite-difference time-domain simulation results for both perfectly aligned and misaligned bilayers. The ability to vary the reflection and absorption spectra of these bilayers by changing the material and geometrical parameters has potential applications in the design of efficient spectral filters. We also show that we can selectively excite these modes by adjusting the phase between two counterpropagating normally incident fields, which has applications in all-optical modulators and switches based on purely linear interferometric effects.

Time-bin qudits have emerged as a promising encoding platform in many quantum photonic applications. However, the requirement for efficient single-shot measurement of time-bin qudits instead of reconstructive detection has restricted their widespread use in experiments. Here, we propose an efficient method to measure arbitrary superposition states of time-bin qudits and confirm it up to dimension 4. This method is based on encoding time bins at the picosecond timescale, also known as ultrafast time bins. By doing so, we enable the use of robust and phase-stable single spatial mode temporal interferometers to measure time-bin qudit in different measurement bases.

The opportunity to manipulate small-scale objects pushes us to the limits of our understanding of physics. Particularly promising in this regard is the interdisciplinary field of levitation, in which light fields can be harnessed to isolate nanoparticles from their environment by levitating them optically. When cooled towards their motional quantum ground state, levitated systems offer the tantalizing prospect of displaying mesoscopic quantum properties. While the interest in levitation has so far been focused mainly on manipulating individual objects with simple shapes, the field is currently moving towards the control of more complex structures, such as those featuring multiple particles or different degrees of freedom. Unfortunately, current cooling techniques are mostly designed for single objects and thus cannot easily be multiplexed to address such coupled many-body systems. Here we present an approach based on the spatial modulation of light in the far field to cool multiple nano-objects in parallel. Our procedure is based on the experimentally measurable scattering matrix and on its changes with time. We demonstrate how to compose from these ingredients a linear energy-shift operator, whose eigenstates are identified as the incoming wavefronts that implement the most efficient cooling of complex moving ensembles of levitated particles. Submitted in parallel with Hüpfl et al. [Phys. Rev. Lett. 130, 083203 (2023)], this article provides a theoretical and numerical study of the expected cooling performance as well as of the robustness of the method against environmental parameters.

We investigate experimentally and theoretically the collective coupling between atoms with multilevel ground-state manifolds and an optical cavity mode. In our setup the cavity field optically pumps populations among the ground states. The ensuing dynamics can be conveniently described by means of an effective dynamical atom-cavity coupling strength that depends on the occupation of the individual states and their coupling strengths with the cavity mode. This leads to a dynamical backaction of the atomic populations on the atom-cavity coupling strength which results in a nonexponential relaxation dynamics. We experimentally observe this effect with laser-cooled ${}^{87}\mathrm{Rb}$ atoms, for which we monitor the collective normal-mode splitting in real time. Our results show that the multilevel structure of electronic ground states can significantly alter the relaxation behavior in atom-cavity settings as compared to ensembles of two-level atoms.

It is known that by probabilistically mixing an arbitrary pair of pure quantum states, one of which is entangled and the other product, in any bipartite quantum system, one always obtains an entangled state, provided the entangled state of the pair appears with a nonzero probability. On the other hand, if we consider any superposition of the same pair, with a nonzero amplitude for the entangled state of the pair, the output state may not always be entangled. Motivated by this fact, in this work we study the superpositions of a pure entangled state and a pure product state, when the amplitudes corresponding to the states appearing in any superposition are nonzero. We show, in particular, that all such superpositions produce only entangled states if the initial entangled state has Schmidt rank 3 or higher. Again, superposing a pure entangled state and a product state cannot lead to product states only, in any bipartite quantum system. These lead us to define conditional and unconditional inseparabilities of superpositions. These concepts in turn are useful in quantum communication protocols. We find that conditional inseparability of superpositions help in identifying strategies for conclusive local discrimination of shared quantum ensembles. We also find that the unconditional variety leads to systematic methods for spotting ensembles exhibiting the phenomenon of more nonlocality with less entanglement and two-element ensembles of conclusively and locally indistinguishable shared quantum states.

Recent experimental advances in positronium (Ps) physics have made it possible to produce dense Ps ensembles in which Ps-Ps interactions may occur, leading to the production of ${\mathrm{Ps}}_2$ molecules and paving the way to the realization of a Ps Bose-Einstein condensate (BEC). In order to achieve this latter goal it would be advantageous to develop new methods to measure Ps densities in real time. Here we describe a possible approach to do this using polaritonic methods: Using realistic experimental parameters, we demonstrate that a dense Ps gas can be strongly coupled to the photonic field of a distributed Bragg reflector microcavity. In this strongly coupled regime, the optical spectrum of the system is composed of two hybrid positronium-polariton resonances separated by the vacuum Rabi splitting, which is proportional to the square root of the Ps density. Given that polaritons can be created on a subcycle timescale, a spectroscopic measurement of the vacuum Rabi splitting could be used as an ultrafast Ps density measurement in regimes relevant to Ps BEC formation. Moreover, we show how positronium polaritons could potentially enter the ultrastrong light-matter coupling regime, introducing a platform to explore its nonperturbative phenomenology.

Alkali-metal dimers, ${\mathrm{Ak}}_2$, residing on the surface of He nanodroplets, are doubly ionized due to multiphoton absorption from an intense 50-fs laser pulse leading to fragmentation into a pair of alkali-metal cations. Based on the measured kinetic energy distributions $P\left(E_{\text{kin}}\right)$ of the ${\mathrm{Ak}}^{+}$ fragment ions, we retrieve the distribution of internuclear distances $P\left(R\right)$ via the ${\mathrm{Ak}}_2^{2+}$ potential curve. Results are obtained for ${\mathrm{Na}}_2, {\mathrm{K}}_2, {\mathrm{Rb}}_2$, and ${\mathrm{Cs}}_2$ in both the $1{}^1{\mathrm{\Sigma }}_g{}^{+}$ ground state and the lowest-lying triplet state $1{}^3{\mathrm{\Sigma }}_u{}^{+}$ and for ${\mathrm{Li}}_2$ in the $1{}^3{\mathrm{\Sigma }}_u{}^{+}$ state. For ${\mathrm{Li}}_2, {\mathrm{K}}_2$, and ${\mathrm{Rb}}_2$, the center of the measured $P\left(R\right)$ is close to the center of the wave function $\mathrm{\Psi }\left(R\right)$ of the vibrational ground state in the $1{}^1{\mathrm{\Sigma }}_g{}^{+}$ and $1{}^3{\mathrm{\Sigma }}_u{}^{+}$ states, whereas for ${\mathrm{Na}}_2$ and ${\mathrm{Cs}}_2$ small shifts are observed. For all the ${\mathrm{Ak}}_2$, the width of the measured $P\left(R\right)$ is broader than ${\left|\mathrm{\Psi }\left(R\right)\right|}^2$ by a factor of 2–4. We discuss that resonance effects in the multiphoton ionization and interaction of the ${\mathrm{Ak}}^{+}$ ion with the He droplet give rise to the observed deviations of $P\left(R\right)$ from ${\left|\mathrm{\Psi }\left(R\right)\right|}^2$. Despite these deviations, we deem that timed Coulomb explosion will allow imaging of vibrational wave packets in alkali-metal dimers on He droplets surfaces.

The production of pairs of correlated Lyman-$\alpha$ photons upon XUV excitation of molecular hydrogen is studied using coincidence measurements to evaluate at which level the entanglement is transferred from atoms to photons. By referencing the timing of fluorescence photon detection to the synchrotron light pulse, we were able to determine branching ratios for the $2p+2p$ and $2p+3\ell$ (with $\ell =s,d$) channels separately. Time-dependent analysis of the spectral signature recorded around 33.6 eV and close examination of the doubly excited states lying in the Franck-Condon window confirm prior assignments of the $2p+2p$ being the main dissociation channel of the $Q_2{}^1\mathrm{\Pi }_u$ (1) molecular state. The angular dependence of the two-photon detection probability measured with respect to the polarization axis is found to be in agreement with earlier measurements [Y. Torizuka et al., Phys. Rev. A 99, 063426 (2019)]. A simple model, assuming a transition from Hund's case (a) to Hund's case (c), reproduces the measured angular distributions satisfactorily.

The intensity peak of a “flying” focus travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an accurate description of the electromagnetic fields. Here we present exact analytical solutions to Maxwells equations for the electromagnetic fields of a constant-velocity flying focus, generalized for arbitrary polarization and orbital angular momentum. The approach combines the complex source-point method, which transforms multipole solutions into beamlike solutions, with the Lorentz invariance of Maxwell's equations. Propagating the fields backward in space reveals the space-time profile that an optical assembly must produce to realize these fields in the laboratory. Comparisons with simpler paraxial solutions provide conditions for their reliable use when modeling a flying focus.

The evaluation of the interaction between objects arranged on a lattice requires the computation of lattice sums. A scenario frequently encountered involves systems governed by the Helmholtz equation in the context of electromagnetic scattering in an array of particles forming a metamaterial, a metasurface, or a photonic crystal. While the convergence of direct lattice sums for such translation coefficients is notoriously slow, the application of Ewald's method converts the direct sums into exponentially convergent series. We present a derivation of such series for the two-dimensional (2D) and three-dimensional (3D) solutions of the Helmholtz equation, namely, spherical and cylindrical solutions. When compared to prior research, our expressions are especially aimed at computing the lattice sums for several interacting sublattices in one-dimensional lattices (chains), 2D lattices (gratings), and 3D lattices. The presented approach establishes a unified framework to derive efficient expressions for lattice sums. Besides reproducing previously known formulas in a more accessible manner the approach results in expressions for interacting sublattices of a chain in three dimensions. Furthermore, the derived formulas are not limited to the dipolar case but are applicable to arbitrary multipolar orders. We verify our results by comparison with the direct computation of the lattice sums.

We demonstrate an intense, continuous cold atomic beam generated via post-nozzle seeding of a supersonic ${}^4\mathrm{He}$ jet with ${}^7\mathrm{Li}$ atoms. The nozzle is cooled to about 4.4 K to reduce the forward velocity of the atoms. The atomic beam is brought to a focus 176 cm from the nozzle by a 10 cm bore diameter magnetic hexapole lens. Absorption and fluorescence imaging of the focus show a flux of $2.3\left(4\right)\times {10}^{12}{\text{s}}^{-1}$, brightness of $1.8\left(6\right)\times {10}^{19}{\text{m}}^{-2}{\text{s}}^{-1}{\text{sr}}^{-1}$, forward velocity of 211(2) m/s, and longitudinal temperature of 7(3) mK. Results agree with a Monte Carlo simulation of the seeding dynamics and a particle-tracing simulation of the atom lens. We predict that 10 times higher flux would be possible with improved vacuum system design. Our method should provide a useful high-brightness source for atom-optical and other atomic and molecular physics applications.

Setting the minimal-time bound for a quantum system to evolve between two distinguishable states, the quantum speed limit (QSL) characterizes the latent capability in speeding up of the system. It has found applications in determining the quantum superiority in many quantum technologies. However, previous results showed that such a speedup capability is generally destroyed by the environment induced decoherence in the Born-Markovian approximate dynamics. We here propose a scheme to recover the speedup capability in a dissipative continuous-variable system within the exact non-Markovian framework. It is found that the formation of a bound state in the energy spectrum of the total system consisting of the system and its environment can be used to restore the QSL to its noiseless performance. Giving an intrinsic mechanism in preserving the QSL, our scheme supplies a guideline to speed up certain quantum tasks in practical continuous-variable systems.