We show that a continuous range of nonclassical states of light can be generated using conditional measurements on the idler mode of an optical parametric amplifier. The output state is prepared by introducing a coherent state in the signal mode of the amplifier with a single photon in the idler mode, followed by a conditional measurement of a single photon in the output idler mode. By varying the gain of the amplifier, this approach can produce a coherent state, a photon-added state, a displaced number state, or a continuous range of other nonclassical states with intermediate properties. We note that this approach can generate a photon-added state even though the postselected amplifier does not add any photons to the signal or idler modes. The ability to generate a continuous range of nonclassical states may have practical applications in quantum information processing.

Diffraction-free Bessel beams have attracted major interest because of their stability even in regimes of nonlinear propagation and filamentation. However, Kerr nonlinear couplings are known to induce significant longitudinal intensity modulation, detrimental to the generation of uniform plasma or for applications in the processing of transparent materials. These nonlinear instabilities arise from the generation of new spatiospectral components through an initial stage of continuous spectral broadening followed by four-wave mixing. In this paper, we investigate these processes analytically and numerically and show that nonlinear instabilities can be controlled through shaping the spatial spectral phase of the input beam. This opens new routes for suppressing the nonlinear growth of new frequencies and controlling ultrashort pulse propagation in dielectrics.

We consider multiple-period states in systems of periodically modulated qubits. In such states the discrete time-translation symmetry imposed by the modulation is broken. We explicitly show how multiple-period states emerge in the simplest quantum system, a single qubit subjected to a pulsed resonant modulation and/or a pulsed modulation of the transition frequency. We also show that a qubit chain with the qubit coupling modulated at twice the qubit frequency has symmetry that allows mapping it on the Kitaev chain and thus provides an example of a topologically nontrivial Floquet system. An explicit solution for a two-qubit system illustrates the effect of resonant period doubling for coupled qubits, whereas in a long chain period doubling is topologically protected.

In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules. This method allows us to display quantum correlations (entanglement) between spin and spatial degrees of freedom (spin-orbit coupling) and between spin degrees of freedom, as well as more complex combinations of spin and spatial entanglement. This is important as there is growing recognition that such properties affect the physical characteristics, and chemistry, of atoms and molecules. Our visualizations are sufficiently accessible that, with some preparation, those with a nontechnical background can gain an appreciation of subtle quantum properties of atomic and other systems. By providing insights and modeling capability, our phase-space representation will be of great utility in understanding aspects of atomic physics and chemistry not available with current techniques.

If the time evolution of a quantum system can be understood classically, then there must exist an underlying probability distribution for the variables describing the system at a sequence of times. It is well known that for systems described by a single time-evolving dichotomic variable $Q$ and for which a given set of temporal correlation functions are specified, a necessary set of conditions for the existence of such a probability are provided by the Leggett-Garg (LG) inequalities. Fine's theorem in this context is the nontrivial result that a suitably augmented set of LG inequalities are both necessary and sufficient conditions for the existence of an underlying probability. We present a proof of Fine's theorem for the case of measurements on a dichotomic variable at an arbitrary number of times, thereby generalizing the familiar proofs for three and four times. We demonstrate how the LG framework and Fine's theorem can be extended to the case in which all possible two-time correlation functions are measured (instead of the partial set of two-time correlators normally studied). We examine the limit of a large number of measurements for both of the above cases.

Upper bounds for private communication over quantum channels can be derived by adopting channel simulation, protocol stretching, and relative entropy of entanglement. All these ingredients have led to single-letter upper bounds to the secret-key capacity which can be directly computed over suitable resource states. For bosonic Gaussian channels, the tightest upper bounds have been derived by employing teleportation simulation over asymptotic resource states, namely, the asymptotic Choi matrices of these channels. In this work, we adopt a different approach. We show that teleporting over an analytical class of finite-energy resource states allows us to closely approximate the ultimate bounds for increasing energy, so as to provide increasingly tight upper bounds to the secret-key capacity of one-mode phase-insensitive Gaussian channels. We then show that an optimization over the same class of resource states can be used to bound the maximum secret-key rates that are achievable in a finite number of channel uses.

We previously predicted [P. A. Hervieux et al., Phys. Rev. A 95, 020701(R) (2017)] that, owing to predominant electron capture by incoming positrons from the molecular shell, ${\mathrm{C}}_{60}$ acts like a spherical diffractor inducing resonances in the positronium (Ps) formation as a function of the positron impact energy. By extending the study for a larger ${\mathrm{C}}_{240}$ fullerene target, we now demonstrate that the diffraction resonances compactify in energy in analogy to the shrinking fringe separation for larger slit size in classical single-slit experiment. The result provides further impetus for conducting Ps spectroscopic experiments with fullerene targets, including target- and/or captured-level differential measurements. The ground states of the fullerenes are modeled in a spherical jellium frame of the local-density approximation method with the exchange-correlation functional based on the van Leeuwen-Baerends model potential [R. van Leeuwen and E. J. Baerends, Phys. Rev. A 49, 2421 (1994)], while the positron impact and Ps formation are treated in the continuum distorted-wave final-state approximation.

We address the implementation of the positive-operator-valued measure (POVM) describing the optimal $M$-outcome discrimination of the polarization state of a single photon. Initially, the POVM elements are extended to projective operators by the Naimark theorem; then the resulting projective measure is implemented by a Knill-Laflamme-Milburn scheme involving an optical network and photon counters. We find the analytical expression of the Naimark extension and the detection scheme that realizes it for an arbitrary number of outcomes $M=2^N$.

In our recent work, we examined various fermion-to-qubit mappings in the context of quantum simulation including the original Bravyi-Kitaev superfast encoding (OSE) as well as a generalized version (GSE). We return to OSE and compare it against the Jordan-Wigner (JW) transform for quantum chemistry considering the number of qubits required, the Pauli weight of terms in the transformed Hamiltonians, and the $L_1$ norm of the Hamiltonian. We considered a test set of molecular systems known as the Atomization Energy 6 (AE6) as well as hydrogen lattices. Our results showed that the resource efficiency of OSE is strongly affected by the spatial locality of the underlying single-particle basis. We find that OSE is outperformed by JW when the orbitals in the underlying single-particle basis are highly overlapping, which limits its applicability to near-term quantum chemistry simulations utilizing standard basis sets. In contrast, when orbitals are overlapping with only few others, as is the case of hydrogen lattices with very tight orbitals, OSE fares comparatively better. Our results illustrate the importance of choosing the right combination of basis sets and fermion-to-qubit mapping to get the most out of a quantum device when simulating physical systems.

Scalar and spin-dependent relativistic effects can influence the geometries and wave functions of the ground and excited states of molecular systems in a way that is not always trivial. However, it is still common for researchers, in particular within the quantum chemistry community, to neglect the spin-dependent effects while discussing the binding between atoms in heavy-element systems. Within multiconfigurational self-consistent field frameworks, the binding in diatomic molecules can be derived from the occupation of the natural orbitals, which by definition form a basis that diagonalizes the one-body density matrix. This does not fully prevent arbitrariness, and the first objective of the present paper will be to review the concept of effective bond order, in particular with respect to the rounding up rule. Then, the respective roles of the scalar and the spin-dependent relativistic effects on the bond lengths are investigated by means of state-of-the-art nonrelativistic, scalar-relativistic, and exact two-component coupled-cluster calculations, providing reference molecular geometries for the whole $\mathrm{At}X$ ($X$ = At – F) series. A diagnostic of relevance for defining effective bond orders in heterodiatomic molecules is introduced and applied to this series, showing that the more dissymmetric the system, the less defined the effective bond order is. Finally, the role of the spin-orbit coupling on the effective bond orders is discussed. AtI appears as a key intermediate in the series in terms of the ground-state $\pi$ bonding or antibonding character. Although emphasis will be put on ground states, the present methodology is readily applicable to the description of excited states.

We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading ${\alpha }^{5}m$ and the next-to-leading ${\alpha }^{6}m$ orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavelength between rovibrational levels achieve accuracy of the order of ${10}^{-3}$–${10}^{-7}{\mathrm{cm}}^{-1}$, and are provided by simple to use computer code.

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an ${}^{27}\mathrm{Al}^{+}$ clock to enable a total fractional systematic uncertainty below ${10}^{-18}$. For this clock, with 38(19) nPa of room-temperature ${\mathrm{H}}_2$ background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order ${10}^{-16}$ at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be $-0.6\left(2.4\right)\times {10}^{-19}$, where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case $\pm \pi /2$ bound used for collisional phase shift of the ${}^{27}\mathrm{Al}^{+}$ superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

We present a scheme to control circularly polarized high-order harmonic generation (HHG) in molecules, the source of extreme ultraviolet and x-ray pulses, by multiple frequency co- and counter-rotating circularly polarized laser pulses. Simulations are performed on the oriented single electron molecular ions with cyclic equilateral geometry, ${\mathrm{H}}_3^{2+}\text{and}{\mathrm{H}}_4^{3+}$, as benchmark models, by numerically solving time-dependent Schrödinger equations. Results show that circularly polarized HHG can be produced with extended harmonic order cutoffs, which depend on the intensity ratio of fields and the field-molecule symmetry. We describe the laser induced electron dynamics in a rotating frame to examine recollision dynamics and Coriolis effects. The resulting modulation of HHG spectra arises from a combination of two bicircular fields with counter-rotating and co-rotating components. It is also found that harmonic polarization is a function of the pulse frequencies and helicities, illustrating the importance of matching the field-molecule symmetry. The results in principle illustrate a method for controlling circular polarization properties of harmonics in molecules.

We present a method for the creation and control of cold molecules that involves coherently combining Feshbach resonances and stimulated Raman adiabatic passage. We present analytical and numerical results showing how to optimize this process that can be implemented using techniques readily available in standard experimental setups. This will provide a link in the chain from atoms to ground-state molecules and can serve as a building block towards more complex processes in coherent ultracold chemistry.

Single photon detection generally consists of several stages: the photon has to interact with one or more charged particles, its excitation energy will be converted into other forms of energy, and amplification to a macroscopic signal must occur, thus leading to a “click.” We focus here on the part of the detection process before amplification (which we have studied in a separate publication). We discuss how networks consisting of coupled discrete quantum states and structured continua (e.g., band gaps) provide generic models for that first part of the detection process. The input to the network is a single continuum (the continuum of single photon states); the output is again a single continuum describing the next irreversible step. The process of a single photon entering the network, its energy propagating through that network, and finally exiting into another output continuum of modes can be described by a single dimensionless complex transmission amplitude, $T\left(\omega \right)$. We discuss how to obtain from $T\left(\omega \right)$ the photodetection efficiency, how to find sets of parameters that maximize this efficiency, as well as expressions for other input-independent quantities such as the frequency-dependent group delay and spectral bandwidth. We then study a variety of networks, discuss how to engineer different transmission functions $T\left(\omega \right)$ amenable to photodetection, and discuss implications for single photon detection technology.

We present a time-domain Schmidt-mode analysis of a broadband continuous-variable entanglement of photon pairs generated via a vectorial four-wave mixing (FWM) of ultrashort laser pulses in a highly nonlinear birefringent optical fiber. We demonstrate that the time-domain eigenmodes of high-purity two-photon states generated through vectorial FWM can be steered, by varying the pump wavelength and FWM polarization geometry, from a high-purity entangled ket to a high-entropy entangled state in a space of a very high dimensionality. Moreover, this pulse-mode analysis is shown to provide a clear physical perspective on how the entanglement structure of two-photon states builds up as a result of short-pulse FWM dynamics. This insight reveals a correspondence-type relation between the quantum and classical pictures of photon-pair generation. With an eye on practical applications, a clear understanding of the temporal profile of pulse modes representing high-purity two-photon states is central to a meaningful shaping of ultrashort photon-packet waveforms for super-resolving microscopy and multiphoton spectroscopy using quantum states of light.

We report the role of $\mathcal{PT}$ symmetry in switching characteristics of a highly nonlinear fiber Bragg grating (FBG) with cubic-quintic-septimal nonlinearities. We demonstrate that the device shows bistable (multistable) states in the broken regime as a direct consequence of the shift in the photonic band gap influenced by both $\mathcal{PT}$ symmetry and higher-order nonlinearities. We also numerically depict that such FBGs provide a productive test bed where the broken $\mathcal{PT}$-symmetric regime can be exploited to set up all-optical applications such as binary switches, multilevel signal processing, and optical computing. Unlike optical bistability (OB) in the traditional and unbroken $\mathcal{PT}$-symmetric FBG, it exhibits many peculiar features such as flat-top stable states and ramplike input-output characteristics before the onset of OB phenomenon in the broken regime. The gain-loss parameter plays a dual role in controlling the switching intensities between the stable states which are facilitated by reversing the direction of light incidence. We also find that the gain-loss parameter tailors the formation of gap solitons pertaining to transmission resonances which clearly indicate that it can be employed to set up optical storage devices. Moreover, the interplay between gain and loss and higher-order nonlinearities brings notable changes in the nonlinear reflection spectra of the system under constant pump powers. The influence of each control parameter on the switching operation is also presented in a nutshell to validate that FBG offers more degrees of freedom in controlling light with light.