We investigate the quantum optical properties of Maxwell's two-dimensional fish eye lens at the single-photon and single-atom level. We show that such a system mediates effectively infinite-range dipole-dipole interactions between atomic qubits, which can be used to entangle multiple pairs of distant qubits. We find that the rate of the photon exchange between two atoms, which are detuned from the cavity resonances, is well described by a model where the photon is focused to a diffraction-limited area during absorption. We consider the effect of losses on the system and study the fidelity of the entangling operation via dipole-dipole interaction. We derive our results analytically using perturbation theory and the Born-Markov approximation and then confirm their validity by numerical simulations. We also discuss how the two-dimensional Maxwell's fish eye lens could be realized experimentally using transformational plasmon optics.

We develop a general framework to assess capabilities and limitations of the Gaussian toolbox in continuous-variable quantum information theory. Our framework allows us to characterize the structure and properties of quantum resource theories specialized to Gaussian states and Gaussian operations, establishing rigorous methods for their description and yielding a unified approach to their quantification. We show in particular that, under a few intuitive and physically motivated assumptions on the set of free states, no Gaussian quantum resource can be distilled with free Gaussian operations, even when an unlimited supply of the resource state is available. This places fundamental constraints on state manipulations in all such Gaussian resource theories. We discuss in particular the applications to quantum entanglement, where we extend previously known results by showing that Gaussian entanglement cannot be distilled even with Gaussian operations preserving the positivity of the partial transpose, as well as to other Gaussian resources such as steering and optical nonclassicality. A comprehensive semidefinite programming representation of all these resources is explicitly provided.

The physics of highly excited Rydberg atoms is governed by blockade or exclusion interactions that hinder the excitation of atoms in the proximity of a previously excited one. This leads to cooperative effects and a relaxation dynamics displaying space-time heterogeneity similar to what is observed in the relaxation of glass-forming systems. Here, we establish theoretically the existence of a glassy dynamical regime in an open Rydberg gas, associated with phase coexistence at a first-order transition in dynamical large deviation functions. This transition occurs between an active phase of low density in which dynamical processes take place on short timescales, and an inactive phase in which excited atoms are dense and the dynamics is highly arrested. We perform a numerically exact study and develop a mean-field approach that allows us to understand the mechanics of this phase transition. We show that radiative decay—which becomes experimentally relevant for long times—moves the system away from dynamical phase coexistence. Nevertheless, the dynamical phase transition persists and causes strong fluctuations in the observed dynamics.

We consider the application of a basic principle of quantum theory, the tracelessness of a certain class of Hamiltonians, to the precision spectroscopy of the molecular hydrogen ions. We show that it is possible to obtain the spin-averaged transition frequencies between states from a simple weighted sum of experimentally accessible spin-dependent transition frequencies. We discuss the cases ${\mathrm{H}}_2{}^{+}$ and ${\mathrm{HD}}^{+}$, which are distinct in the multipole character of their rovibrational transitions. Inclusion of additional frequencies permits canceling also the electric quadrupole shift, the Zeeman shift, and partially the Stark shift. In this context, we find that measuring electric quadrupole transitions in the heteronuclear molecule ${\mathrm{HD}}^{+}$ is advantageous. The required experimental effort appears reasonable.

We measure the complete quantum state for six modes of the electromagnetic field produced by an optical parametric oscillator. The investigation involves the sidebands of the intense pump, signal, and idler fields generated by stimulated parametric down-conversion inside a triply resonant optical resonator. We develop a theoretical model to successfully interpret the experimental results. The model takes into account the coupling of the field modes to the phonon bath of the nonlinear crystal, clearly showing the roles of different physical effects in shaping the structure of the quantum correlations between the six optical modes.

We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the computable cross-norm or realignment criterion based on local orthogonal observables. As an illustration, we demonstrate the enhanced entanglement detection power in simple systems of qubit and qutrit pairs. This observation highlights the significance of SIC POVMs for entanglement detection.

The mean-field steady states of a generalized model of $N$ two-state systems interacting with one mode of the radiation field in the presence of external driving and dissipation are surveyed as a function of three control parameters: one governs the interaction strength relative to the resonance frequency, thus accessing the Dicke quantum phase transition, a second the relative strength of counter-rotating to rotating-wave interactions, and a third the amplitude of an external field driving the cavity mode. We unify the dissipative extension of the Dicke quantum phase transition with the recently reported breakdown of photon blockade [H. J. Carmichael, Phys. Rev. X 5, 031028 (2015)]; key to the unification is a previously unreported phase of the Dicke model and a renormalized critical drive strength in the breakdown of photon blockade. For the simplest case of one two-state system, we complement mean-field results with a full quantum treatment: we derive quasienergies to recover the renormalized critical drive strength, extend the multiphoton resonances of a photon blockade to a counter-rotating interaction, and explore quantum fluctuations through quantum trajectory simulations.

We optically trap a nanoparticle in a laser beam strongly focused on a dielectric membrane in vacuum. By investigating the motion of the trapped particle, we map the position-dependent optical potential in front of the membrane while interferometrically measuring the distance between the particle and the membrane surface. Furthermore, we demonstrate feedback cooling of the particle's motion in subwavelength proximity to the dielectric surface. The demonstrated optomechanical control of a levitated nanoparticle in close proximity of an interface at low gas pressures is an integral requirement to investigate short-range interactions in yet unexplored parameter regimes.

The problem of closing the detection loophole in Bell tests is investigated in the presence of a limited number of efficient detectors using emblematic multipartite quantum states. To this end, a family of multipartite Bell inequalities is introduced based on local projective measurements conducted by $N-k$ parties and applying a $k$-party Bell inequality on the remaining parties. Surprisingly, we find that most of the studied pure multipartite states involving, e.g., cluster states, the Dicke states, and the Greenberger-Horne-Zeilinger states can violate our inequalities with only the use of two efficient detectors, whereas the remaining detectors may have arbitrary small efficiencies. We believe that our inequalities are useful in Bell experiments and device-independent applications if only a small number of highly efficient detectors are at our disposal or our physical system is asymmetric, e.g., atom-photon.

Optical antennas have been widely used to control the absorption and emission properties of dipole emitters. Understanding the relationship between the absorption and emission processes of such dipole emitters in the presence of optical antennas is therefore of fundamental importance. Here we provide an in-depth analysis of the relationship between the absorption and emission directivities of dipoles coupling to optical antennas. We show that, for reciprocal systems, the absorption and emission directivities are identical for a single dipole emitter, and also in the case of multiple dipole emitters when one considers incoherent emission from the emitters. On the other hand, in general, the coherent emission directivities of the dipoles are always different from the absorption directivities in the multiple-dipole case. But there are special situations in the multiple-dipole case where the coherent emission has directivities that are approximately the same as the absorption directivity. This study clarifies the relation between absorption and emission directivities for emitters coupled with optical antennas and may provide useful insights into the design and characterization of optical antennas for various applications.

Laser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that noninteracting photons can thermalize with the atoms to a grand canonical ensemble with a nonzero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser-cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential nearly equal to the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare-earth atoms. With the addition of photon-photon interactions, this system could provide a platform for exploring many-body physics.

Motivated by recent experiments with ultracold polar molecules trapped in deep optical lattices, we study ground-state properties of the site-diluted long-ranged XXZ model. Site dilution results in off-diagonal disorder. We map the spin model to a hard-core Bose–Hubbard model and perform large-scale Monte Carlo simulations by the worm algorithm. In absence of site dilution, we find that, for large enough interaction, three phases are stabilized: a superfluid phase, a checkerboard solid phase, only present at density $m=0.5$, and a checkerboard supersolid phase which can be reached by doping the CB phase away from half filling. In the presence site-dilution and at fixed density $m=0.5$, we find that, unlike what observed in the case of short-range hopping, localization never occurs even for site dilution larger than the percolation threshold, and off-diagonal order, although strongly suppressed, persists for arbitrarily large values of site dilution.

The subtraction or addition of a prescribed number of photons to a field mode does not, in general, simply shift the probability distribution by the number of subtracted or added photons. Subtraction of a photon from an initial coherent state, for example, leaves the photon statistics unchanged and the same process applied to an initial thermal state increases the mean photon number. We present a detailed analysis of the effects of the initial photon statistics on those of the state from which the photons have been subtracted or to which they have been added. Our approach is based on two closely related moment-generating functions, one that is well established and one that we introduce.

On-chip nanophotonic cavities will advance quantum information science and measurement because they enable efficient interaction between photons and long-lived solid-state spins, such as those associated with rare-earth ions in crystals. The enhanced photon-ion interaction creates new opportunities for all-optical control using the ac Stark shift. Toward this end, we characterize the ac Stark interaction between off-resonant optical fields and ${\mathrm{Nd}}^{3+}$-ion dopants in a photonic crystal resonator fabricated from yttrium orthovanadate (${\mathrm{YVO}}_4$). Using photon echo techniques, at a detuning of 160 MHz we measure a maximum ac Stark shift of $2\pi \times 12.3$ MHz per intracavity photon, which is large compared to both the homogeneous linewidth (${\mathrm{\Gamma }}_{\mathrm{h}}$= 84 kHz) and characteristic width of isolated spectral features created through optical pumping (${\mathrm{\Gamma }}_f\approx 3$ MHz). The photon-ion interaction strength in the device is sufficiently large to control the frequency and phase of the ions for quantum information processing applications. In particular, we discuss and assess the use of the cavity enhanced ac Stark shift to realize all-optical quantum memory and detection protocols. Our results establish the ac Stark shift as a powerful added control in rare-earth ion quantum technologies.

Recently, it was proposed to use cavity-optomechanical systems to test for quantum gravity corrections to quantum canonical commutation relations [I. Pikovski et al., Nat. Phys. 8, 393 (2012)]. Improving the achievable precision of such devices represents a major challenge that we address with this work. More specifically, we develop sophisticated paths in phase space of such optomechanical systems to obtain significantly improved accuracy and precision under contributions from higher-order corrections to the optomechanical Hamiltonian. An accurate estimate of the required number of experimental runs is presented based on a rigorous error analysis that accounts for mean photon-number uncertainty, which can arise from classical fluctuations or from quantum shot noise in measurement. Furthermore, we propose a method to increase precision by using squeezed states of light. Finally, we demonstrate the robustness of our scheme to experimental imperfection, thereby improving the prospects of carrying out tests of quantum gravity with near-future optomechanical technology.

We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several tens of seconds. Rayleigh scattering does not cause significant decoherence of the atomic superposition state near a magic wavelength. Among the Raman scattering processes, lattice-induced decay of the excited state $\left(5s5p\right){}^{3}P_0$ to the ground state $\left(5s^2\right){}^{1}S_0$ via the state $\left(5s5p\right){}^{3}P_1$ is particularly relevant, as it reduces the effective lifetime of the excited state and gives rise to quantum projection noise in spectroscopy. We observe this process in our experiment and find a decay rate of $556\left(15\right)\times {10}^{-6}{\mathrm{s}}^{-1}$ per photon recoil energy $E_{\mathrm{r}}$ of effective lattice depth, which agrees well with the rate we predict from atomic data. We also derive a natural lifetime $\tau =330\left(140\right)\mathrm{s}$ of the excited state ${}^{3}P_0$ from our observations. Lattice-induced decay thus exceeds spontaneous decay at typical lattice depths used by present clocks. It eventually limits interrogation times in clocks restricted to high-intensity lattices but can be largely avoided, e.g., by operating them with shallow lattice potentials.

We investigate the properties of two interacting ultracold polar molecules described as distinguishable quantum rigid rotors, trapped in a one-dimensional harmonic potential. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions including dipole-dipole interaction. The impact of external electric and magnetic fields resulting in Stark and Zeeman shifts of molecular rovibrational states is also investigated. Energy spectra and eigenstates are calculated by means of the exact diagonalization. The importance and interplay of the molecular rotational structure, anisotropic interactions, spin-rotation coupling, electric and magnetic fields, and harmonic trapping potential are examined in detail, and compared to the system of two harmonically trapped distinguishable atoms. The presented model and results may provide microscopic parameters for molecular many-body Hamiltonians, and may be useful for the development of bottom-up molecule-by-molecule assembled molecular quantum simulators.

Several distinct classes of unitary mode transformations have been known to exhibit the strict suppression of a large set of transmission events, as a consequence of totally destructive many-particle interference. In another work [C. Dittel et al., Phys. Rev. Lett. 120, 240404 (2018)] we unite these cases by identifying a general class of unitary matrices which exhibit such interferences. Here we provide a detailed theoretical analysis that substantially expands on all aspects of this generalization: We prove the suppression laws put forward in our other paper, establish how they interrelate with forbidden single-particle transitions, show how all suppression laws hitherto known can be retrieved from our general formalism, and discuss striking differences between bosons and fermions. Furthermore, beyond many-particle Fock states on input, we consider arbitrary pure initial states and derive suppression laws which stem from the wave function's permutation symmetry alone. Finally, we identify conditions for totally destructive interference to persist when the involved particles become partially distinguishable.

We present a versatile imaging scheme for fermionic ${}^6\mathrm{Li}$ atoms with single-particle sensitivity. Our method works for freely propagating particles and completely eliminates the need for confining potentials during the imaging process. We illuminate individual atoms in free space with resonant light and collect their fluorescence on an electron-multiplying CCD camera using a high-numerical-aperture imaging system. We detect approximately 20 photons per atom during an exposure of $20\mu \mathrm{s}$ and identify individual atoms with a fidelity of $(99.4\pm 0.3)\%$. By addressing different optical transitions during two exposures in rapid succession, we additionally resolve the hyperfine spin state of each particle. The position uncertainty of the imaging scheme is $4.0\mu \mathrm{m}$, given by the diffusive motion of the particles during the imaging pulse. The absence of confining potentials enables readout procedures such as the measurement of single-particle momenta in time of flight, which we demonstrate here. Our imaging scheme is technically simple and easily adapted to other atomic species.

We study analytically the Wigner function $W_N(\mathbf{x},\mathbf{p})$ of $N$ noninteracting fermions trapped in a smooth confining potential $V\left(\mathbf{x}\right)$ in $d$ dimensions. At zero temperature, $W_N(\mathbf{x},\mathbf{p})$ is constant over a finite support in the phase space $(\mathbf{x},\mathbf{p})$ and vanishes outside. Near the edge of this support, we find a universal scaling behavior of $W_N(\mathbf{x},\mathbf{p})$ for large $N$. The associated scaling function is independent of the precise shape of the potential as well as the spatial dimension $d$. We further generalize our results to finite temperature $T>0$. We show that there exists a low-temperature regime $T\sim e_N/b$, where $e_N$ is an energy scale that depends on $N$ and the confining potential $V\left(\mathbf{x}\right)$, where the Wigner function at the edge again takes a universal scaling form with a $b$-dependent scaling function. This temperature-dependent scaling function is also independent of the potential as well as the dimension $d$. Our results generalize to any $d\ge 1$ and $T\ge 0$ the $d=1$ and $T=0$ results obtained by Bettelheim and Wiegman [Phys. Rev. B 84, 085102 (2011)] (see also the earlier paper by Balazs and Zipfel [Ann. Phys. (NY) 77, 139 (1973)]).