Bosonic gases coupled to a particle reservoir have proven to support a regime of operation where Bose-Einstein condensation coexists with unusually large particle-number fluctuations. Experimentally, this situation has been realized with two-dimensional photon gases in a dye-filled optical microcavity. Here we investigate theoretically and experimentally the open-system dynamics of a grand canonical Bose-Einstein condensate of photons. We identify a regime with temporal oscillations of the second-order coherence function $g^{\left(2\right)}\left(\tau \right)$, even though the energy spectrum closely matches the predictions for an equilibrium Bose-Einstein distribution and the system is operated deeply in the regime of weak light-matter coupling. The observed temporal oscillations are attributed to the nonlinear, weakly driven dissipative nature of the system, which leads to time-reversal symmetry breaking.

A phase-space distribution associated with a quantum state was previously proposed, which incorporates a specific epistemic restriction parametrized by a global random variable on the order of Planck constant, transparently manifesting quantum uncertainty in phase space. Here we show that the epistemically restricted phase-space (ERPS) distribution can be determined via weak measurement of momentum followed by postselection on position. In the ERPS representation, the phase and amplitude of the wave function are neatly captured respectively by the position-dependent (conditional) average and the variance of the epistemically restricted momentum fluctuation. They are in turn respectively determined by the real and imaginary parts of the weak momentum value, permitting a reconstruction of wave function using weak momentum value measurement, and an interpretation of momentum weak value in terms of epistemically restricted momentum fluctuations. The ERPS representation thus provides a transparent and rich framework to study the deep conceptual links between quantum uncertainty embodied in epistemic restriction, quantum wave function, and weak momentum measurement with position postselection, which may offer useful insight to better understand their meaning.

Much research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians with Hamming-symmetric potentials, such as the well-studied “spike” example. Due to the large amount of symmetry in these potentials such problems are readily open to analysis both analytically and computationally. However, more realistic potentials do not have such a high degree of symmetry and may have many local minima. Here we present a somewhat more realistic class of problems consisting of many individually Hamming-symmetric potential wells. For two or three such wells we demonstrate that such a problem can be solved exactly in time polynomial in the number of qubits and wells. For greater than three wells, we present a tight-binding approach with which to efficiently analyze the performance of such Hamiltonians in an adiabatic computation. We provide several basic examples designed to highlight the usefulness of this toy model and to give insight into using the tight-binding approach to examining it, including (1) an adiabatic unstructured search with a transverse field driver and a prior guess to the marked item and (2) a scheme for adiabatically simulating the ground states of small collections of strongly interacting spins, with an explicit demonstration for an Ising-model Hamiltonian.

We propose and discuss a method to engineer stroboscopically arbitrary one-dimensional optical potentials with subwavelength resolution. Our approach is based on subwavelength optical potential barriers for atoms in the dark state in an optical $\mathrm{\Lambda }$ system, which we use as a stroboscopic drawing tool by controlling their amplitude and position by changing the amplitude and the phase of the control Rabi frequency in the $\mathrm{\Lambda }$ system. We demonstrate the ability of the method to engineer both smooth and comblike periodic potentials for atoms in the dark state, and establish the range of stroboscopic frequencies when the quasienergies of the stroboscopic Floquet system reproduce the band structure of the time-averaged potentials. In contrast to usual stroboscopic engineering which becomes increasingly accurate with increasing the stroboscopic frequency, the presence of the bright states of the $\mathrm{\Lambda }$ system results in the upper bound on the frequency, above which the dynamics strongly mixes the dark and the bright channels, and the description in terms of a time-averaged potential fails. For frequencies below this bound, the lowest Bloch band of quasienergies contains several avoided-crossing coming from the coupling to high-energy states, with widths decreasing with increasing stroboscopic frequency. We analyze the influence of these avoided crossings on the dynamics in the lowest band using Bloch oscillations as an example, and establish the parameter regimes when the population transfer from the lowest band into high bands is negligible. We also present protocols for loading atoms into the lowest band of the painted potentials starting from atoms in the lowest band of a standard optical lattice.

Recent progress in matter-wave interferometry aims to directly probe the quantum properties of matter on ever increasing scales. However, in order to perform interferometric experiments with massive mesoscopic objects, taking into account the constraints on the experimental setups, the pointlike-particle approximation needs to be cast aside. In this work, we consider near-field interferometry based on the Talbot effects with a single optical grating for large spherical particles beyond the point-particle approximation. We account for the suppression of the coherent grating effect and, at the same time, the enhancement of the decoherence effects due to scattering and absorption of grating photons.

Arrays of ultracold dipolar gases loaded in optical lattices are emerging as powerful quantum simulators of the many-body physics associated with the rich interplay between long-range dipolar interactions, contact interactions, motion, and quantum statistics. In this work we report on our investigation of the quantum many-body dynamics of a large ensemble of bosonic magnetic chromium atoms with spin $S=3$ in a three-dimensional lattice as a function of lattice depth. Using extensive theory and experimental comparisons, we study the dynamics of the population of the different Zeeman levels and the total magnetization of the gas across the superfluid to the Mott insulator transition. We are able to identify two distinct regimes. At low lattice depths, where atoms are in the superfluid regime, we observe that the spin dynamics is strongly determined by the competition between particle motion, on-site interactions, and external magnetic-field gradients. Contact spin-dependent interactions help to stabilize the collective spin length, which sets the total magnetization of the gas. On the contrary, at high lattice depths, transport is largely frozen out. In this regime, while the spin populations are mainly driven by long-range dipolar interactions, magnetic-field gradients also play a major role in the total spin demagnetization. We find that the dynamics at low lattice depth is qualitatively reproduced by mean-field calculations based on the Gutzwiller ansatz; on the contrary, only a beyond-mean-field theory can account for the dynamics at large lattice depths. While the crossover between these two regimes does not display sharp features in the observed dynamical evolution of the spin components, our simulations indicate that it would be better revealed by measurements of the collective spin length.

We theoretically investigate the collisional heating of a cold atom system subjected to time-periodic forces. We show within the Floquet framework that this heating rate due to two-body collisions has a general semiclassical expression $\mathcal{P}\propto \rho \sigma v_{\mathrm{col}}{E}_0$, depending on the kinetic energy $E_0$ associated with the shaking, particle number density $\rho$, elastic collision cross section $\sigma$, and an effective collisional velocity $v_{\mathrm{col}}$ determined by the dominant energy scale in the system. We further show that the collisional heating is suppressed by Pauli blocking in cold fermionic systems and by the modified density of states in systems in lower dimensions. Our results provide an exactly solvable example and reveal some general features of Floquet heating in interacting systems.

We propose a procedure to achieve a complete energy conversion between laser pulses carrying orbital angular momentum (OAM) in a cloud of cold atoms characterized by a double-$\mathrm{\Lambda }$ atom-light-coupling scheme. A pair of resonant spatially dependent control fields prepare atoms in a position-dependent coherent-population-trapping state, while a pair of much weaker vortex probe beams propagate in the coherently driven atomic medium. Using the adiabatic approximation we derive the propagation equations for the probe beams. We consider a situation where the second control field is absent at the entrance to the atomic cloud and the first control field goes to zero at the end of the atomic medium. In that case the incident vortex probe beam can transfer its OAM to a generated probe beam. We show that the efficiency of such an energy conversion approaches the unity under the adiabatic condition. On the other hand, by using spatially independent profiles of the control fields, the maximum conversion efficiency is only $1/2$.

Driving a many-body quantum system in a periodic manner gives access to its fundamental properties, both in terms of energy spectrum and relaxation mechanisms. It also leads to important applications, as shown by superconducting Josephson junctions (SCJJs). Thanks to the so-called Shapiro resonances that occur in the presence of a microwave drive, SCJJs constitute metrological devices relating the drive frequency to the voltage across the junction. Here we present a detailed experimental study of an atomic analog of a driven SCJJ based on a spinor Bose-Einstein condensate of sodium atoms. We analyze the short-time evolution of the system in terms of a slow Hamiltonian dynamics superimposed with a rapid micromotion. After a long-time evolution, we observe that the system may relax to a nonequilibrium steady state and exhibit a hysteretic behavior. We compare our experimental results with simple phenomenological models of dissipation that can roughly be described as amplitude or phase damping. We find that the amplitude damping model is able to reproduce quantitatively our observations, while the phase-damping model fails qualitatively in certain regimes. Our study therefore constitutes an accurate benchmark for the development of an ab initio microscopic theory of the relaxation processes in this driven many-body system.

The only known qubit states that produce maximal quantum violation of a tight Bell inequality with maximally incompatible local measurements are Bell states, Greenberger-Horne-Zeilinger states, and a recently identified three-qubit state called $|S\rangle$. Here we report the results of an experiment for preparing $|S\rangle$ and testing the maximum quantum violation of the corresponding tripartite Bell inequality. Using a heralded source of three entangled photons and three tunable polarization-dependent filters, we experimentally prepare $|S\rangle$ with 0.924 fidelity. Using maximally incompatible measurements for the three parties, we observe a value of $T_{26}=7.30\pm 0.06$, which clearly violates the tight Bell inequality $T_{26}\le 5$. In addition, we show that our setup allows preparing multipartite states that were inaccessible with previous methods and are useful for quantum information and metrology.

Laser cooling is a powerful method to control molecules for applications in precision measurement, as well as quantum information, many-body physics, and fundamental chemistry. However, many optically active metal centers in valence states which are promising for these applications, especially precision measurement, are difficult to laser cool. In order to extend the control afforded by laser cooling to a wider array of promising atoms, we consider the use of small, hypermetallic molecules that contain multiple metal centers. We provide a detailed analysis of YbCCCa and YbCCAl as prototypical examples with different spin multiplicities and consider their feasibility for precision measurements making use of the heavy Yb atom. We find that these molecules are linear and feature metal-centered valence electrons and study the complex hybridization and spin structures that are relevant to photon cycling and laser cooling. Our findings suggest that this hypermetallic approach may be a versatile tool for experimental control of metal species that do not otherwise efficiently cycle photons and could present a relevant platform for state-of-the-art precision measurements.

We consider a coherent state of light propagating through an ensemble of two-level atoms where all the atoms are initially in their ground state. In ordinary absorption, the transition of atoms to their excited state along with the absorption of a photon will remove energy from the beam and attenuate the signal. Here we show that post-selecting on those cases in which none of the atoms made a transition to the excited state can give even more attenuation than would normally occur due to absorption. The same process can also produce amplification when there is a sufficiently strong interaction between the photons and the atoms.

We study optical pulse propagation through a hollow-core fiber filled with a radially inhomogeneous cloud of cold atoms. A copropagating control field establishes electromagnetically induced transparency. In analogy to a graded index fiber, the pulse experiences microlensing and the transmission spectrum becomes distorted. Based on a two-layer model of the complex index of refraction, we can analytically understand the cause of the aberration, which is corroborated by numerical simulations for a radial Gaussian-shaped function. With these insights, we show that the spectral distortions can be rectified by choosing an optimal detuning from one-photon resonance.

The direct multiphoton ionization (MPI) of hydrogenlike ions by intense, linearly polarized, ultrashort infrared laser pulses is investigated within the framework of the strong field approximation (SFA) for laser peak intensities and angular frequencies where relativistic effects are important. We obtain an expression for the differential MPI probability using the Dirac equation and demonstrate that, for the particular case of light ions, the Dirac spin-unresolved MPI probabilities agree with those obtained using the Klein-Gordon equation as well as the relativistic Schrödinger equation. As an example, the interaction of hydrogenlike neon ions with an intense four-cycle Ti:sapphire laser pulse is considered. We show that, in contrast to the nonrelativistic regime, for ultrashort pulses in the relativistic regime, interference effects do not play a role in determining the main features of the energy-resolved photoelectron spectrum. Moreover, we find that the angle-integrated photoelectron spectrum can be obtained using the well-known nonrelativistic SFA formula, properly adjusted to account for the electron drift along the laser propagation direction.

Ergodicity and chaos play an integral role in the behavior of dynamical systems and are crucial to the formulation of statistical mechanics. Still, a general understanding of how ergodicity and chaos emerge in the dynamical evolution of closed quantum systems remains elusive. Here, we develop an experimental platform for the realization of canonical quantum chaotic Hamiltonians based on quantum simulation with synthetic lattices. We map the angular momentum projection states of an effective quantum spin onto the linear momentum states of a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate, which can be alternatively viewed as synthetic lattice sites. This synthetic lattice, with local and dynamical control of tight-binding lattice parameters, enables new capabilities related to the experimental study of quantum chaos. In particular, the capabilities of our system let us tune the effective size of our spin, allowing us to illustrate how classical chaos can emerge from a discrete quantum system. Moreover, spectroscopic control over our synthetic lattice allows us to explore unique aspects of our spin's dynamics by measuring the out-of-time-ordered correlation function and enables future investigations into new symmetry classes of chaotic kicked-top systems.

Stern-Gerlach experiments allow one to study the magnetism of isolated particles in the gas phase. However, gaining insight into the intrinsic magnetic properties of small metal clusters in beam deflection experiments is usually hampered by rotational and vibrational excitation. Here, we address this issue for the magnetic deflection of the cryogenically cooled ${\mathrm{GdSn}}_{15}$ cluster ($T=16-100\mathrm{K}$). A single-sided deflection towards high field and, in the low-temperature regime, a pronounced tailing are observed. We present a microscopic model considering spin, rotational, and vibrational degrees of freedom of the cluster which explains the experimentally observed features in the beam profiles reasonably well. This model will be a helpful tool for the interpretation of results from Stern-Gerlach experiments in future studies, especially to distinguish effects from intrinsic magnetic properties and rotationally or vibrationally excited states of the investigated cluster species.

Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another. Computing the error probability directly requires complete knowledge and diagonalization of the density matrices describing these states. Both of these fundamental requirements become impractically difficult to obtain as the dimensions of the states grow large. In this paper, we analyze quantum illumination as a quantum channel discrimination protocol and circumvent these issues by using the normalized Hilbert-Schmidt inner product as a measure of distinguishability. Using this measure, we show that the greatest advantage gained by quantum illumination over conventional illumination occurs when one uses a Bell state.

Important information for the roton-maxon spectrum of a flattened dipolar Bose-Einstein condensate is extracted by applying a static perturbation exhibiting a periodic in-plane modulation. By solving the Gross-Pitaevskii equation in the presence of the weak perturbation, we evaluate the linear density response of the system and use it, together with sum rules, to provide a Feynman-like upper-bound prediction for the excitation spectrum, finding excellent agreement with the predictions of full Bogoliubov calculations. By suddenly removing the static perturbation, while still maintaining the trap, we find that the density modulations—as well as the weights of the perturbation-induced side peaks of the momentum distribution—undergo an oscillatory behavior with double the characteristic frequency of the excitation spectrum. The measurement of the oscillation periods could provide an easy determination of dispersion relations.

We consider a nanoparticle levitated in a Paul trap in ultrahigh cryogenic vacuum, and look for the conditions which allow for a stringent noninterferometric test of spontaneous collapse models. In particular we compare different possible techniques to detect the particle motion. Key conditions which need to be achieved are extremely low residual pressure and the ability to detect the particle at ultralow power. We compare three different detection approaches based, respectively, on an optical cavity, an optical tweezer, and an electrical readout, and for each one we assess advantages, drawbacks, and technical challenges.

The formalism of quantum electrodynamics for treating the interelectronic-interaction correction of first order in $1/Z$ to the two-electron part of the nuclear recoil effect on binding energies in atoms and ions is developed. The nonperturbative (in $\alpha Z$) calculations of the corresponding contribution to the energies of the $1s^2$ state in He-like and the $1s^{2}2s$ and $1s^{2}2p_{1/2}$ states in Li-like ions are performed in the range $Z=5–100$. The behavior of the two-electron part of the nuclear recoil effect beyond the lowest-order relativistic approximation as a function of $Z$ is studied.