We obtain the multiple-parameter quantum Cramér-Rao bound for estimating the transverse Cartesian components of the centroid and separation of two incoherent optical point sources using an imaging system with finite spatial bandwidth. Under quite general and realistic assumptions on the point-spread function of the imaging system, and for weak source strengths, we show that the Cramér-Rao bounds for the $x$ and $y$ components of the separation are independent of the values of those components, which may be well below the conventional Rayleigh resolution limit. We also propose two linear-optics-based measurement methods that approach the quantum bound for the estimation of the Cartesian components of the separation once the centroid has been located. One of the methods is an interferometric scheme that approaches the quantum bound for sub-Rayleigh separations. The other method using fiber coupling can, in principle, attain the bound regardless of the distance between the two sources.

We propose an approach to simultaneously excite two atoms by using a cavity-assisted Raman process in combination with a cavity-photon-mediated interaction. The system consists of a two-level atom and a $\mathrm{\Lambda }$-type or $\mathsf{V}$-type three-level atom, which are coupled together with a cavity mode. Having derived the effective Hamiltonian, we find that under certain circumstances a single photon can simultaneously excite two atoms. In addition, multiple photons and even a classical field can also simultaneously excite two atoms. As an example, we show a scheme to realize our proposal in a circuit QED setup, which is artificial atoms coupled with a cavity. The dynamics and the quantum-statistical properties of the process are investigated with experimentally feasible parameters.

We show how analogs of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and annihilated, an effective deterministic coupling between two states of such a system can be created. In this way, analogs of three-wave mixing, four-wave mixing, higher-harmonic and -subharmonic generation (i.e., up- and down-conversion), multiphoton absorption, parametric amplification, Raman and hyper-Raman scattering, the Kerr effect, and other nonlinear processes can be realized. In contrast to most conventional implementations of nonlinear optics, these analogs can reach unit efficiency, only use a minimal number of photons (they do not require any strong external drive), and do not require more than two atomic levels. The strength of the effective coupling in our proposed setups becomes weaker the more intermediate transition steps are needed. However, given the recent experimental progress in ultrastrong light-matter coupling and improvement of coherence times for engineered quantum systems, especially in the field of circuit quantum electrodynamics, we estimate that many of these nonlinear-optics analogs can be realized with currently available technology.

Conventional theories of electromagnetic waves in a medium assume that the energy propagating with the light pulse in the medium is entirely carried by the field. Thus, the possibility that the optical force field of the light pulse would drive forward an atomic mass density wave (MDW) and the related kinetic and elastic energies is neglected. In this work, we present foundations of a covariant theory of light propagation in a medium by considering a light wave simultaneously with the dynamics of the medium atoms driven by optoelastic forces between the induced dipoles and the electromagnetic field. We show that a light pulse having a total electromagnetic energy $\hslash \omega$ propagating in a nondispersive medium transfers a mass equal to $\delta m=(n^2-1)\hslash \omega /c^2$, where $n$ is the refractive index. MDW, which carries this mass, consists of atoms, which are more densely spaced inside the light pulse as a result of the field-dipole interaction. We also prove that the transfer of mass with the light pulse, the photon mass drag effect, gives an essential contribution to the total momentum of the light pulse, which becomes equal to the Minkowski momentum $p_{\mathrm{M}}=n\hslash \omega /c$. The field's share of the momentum is the Abraham momentum $p_{\mathrm{A}}=\hslash \omega /\left(nc\right)$, while the difference $p_{\mathrm{M}}-p_{\mathrm{A}}$ is carried by MDW. Due to the coupling of the field and matter, only the total momentum of the light pulse and the transferred mass $\delta m$ can be directly measured. Thus, our theory gives an unambiguous physical meaning to the Abraham and Minkowski momenta. We also show that to solve the centenary Abraham-Minkowski controversy of the momentum of light in a nondispersive medium in a way that is consistent with Newton's first law, one must account for the mass transfer effect. We derive the photon mass drag effect using two independent but complementary covariant models. In the mass-polariton (MP) quasiparticle approach, we consider the light pulse as a coupled state between the photon and matter, isolated from the rest of the medium. The momentum and the transferred mass of MP follow unambiguously from the Lorentz invariance and the fundamental conservation laws of nature. To enable the calculation of the mass and momentum distribution of a light pulse, we have also generalized the electrodynamics of continuous media to account for the space- and time-dependent optoelastic dynamics of the medium driven by the field-dipole forces. In this optoelastic continuum dynamics (OCD) approach, we obtain with an appropriate space-time discretization a numerically accurate solution of the Newtonian continuum dynamics of the medium when the light pulse is propagating in it. The OCD simulations of a Gaussian light pulse propagating in a diamond crystal give the same momentum $p_{\mathrm{M}}$ and the transferred mass $\delta m$ for the light pulse as the MP quasiparticle approach. Our simulations also show that, after photon transmission, some nonequilibrium of the mass distribution is left in the medium. Since the elastic forces are included in our simulations on equal footing with the optical forces, our simulations also depict how the mass and thermal equilibria are reestablished by elastic waves. In the relaxation process, a small amount of photon energy is dissipated into lattice heat. We finally discuss a possibility of an optical waveguide setup for experimental measurement of the transferred mass of the light pulse. Our main result that a light pulse is inevitably associated with an experimentally measurable mass is a fundamental change in our understanding of light propagation in a medium.

In this paper, we study the effect of $\mathcal{PT}$-symmetric complex potentials on the transport properties of one non-Hermitian system, which is formed by the coupling between a triple-quantum-dot molecule and two semi-infinite leads. As a result, it is found that the $\mathcal{PT}$-symmetric imaginary potentials have pronounced effects on the transport properties of such a system, including changes from antiresonance to resonance, shift of antiresonance, and occurrence of new antiresonance, which are determined by the interdot and dot-lead coupling manners. This paper can be helpful in understanding the quantum transport behaviors modified by the $\mathcal{P}T$ symmetry in non-Hermitian discrete systems.

Modeling and simulation are essential for predicting and verifying the behavior of fabricated quantum circuits, but existing simulation methods are either impractically costly or require an unrealistic simplification of error processes. We present a method of simulating noisy Clifford circuits that is both accurate and practical in experimentally relevant regimes. In particular, the cost is weakly exponential in the size and the degree of non-Cliffordness of the circuit. Our approach is based on the construction of exact representations of quantum channels as quasiprobability distributions over stabilizer operations, which are then sampled, simulated, and weighted to yield unbiased statistical estimates of circuit outputs and other observables. As a demonstration of these techniques, we simulate a Steane [[7,1,3]]-encoded logical operation with non-Clifford errors and compute its fault tolerance error threshold. We expect that the method presented here will enable studies of much larger and more realistic quantum circuits than was previously possible.

A many-body Green's-function method employing an infinite order summation of ring and exchange-ring contributions to the self-energy is presented. The individual correlation and relaxation contributions to the quasiparticle energies are calculated using an iterative scheme which utilizes density fitting of the particle-hole, particle-particle and hole-hole densities. It is shown that the ionization energies and electron affinities of this approach agree better with highly accurate coupled-cluster singles and doubles with perturbative triples energy difference results than those obtained with second-order Green's-function approaches. An analysis of the correlation and relaxation terms of the self-energy for the direct- and exchange–random-phase-approximation (RPA) Green's-function methods shows that the inclusion of exchange interactions leads to a reduction of the two contributions in magnitude. These differences, however, strongly cancel each other when summing the individual terms to the quasiparticle energies. Due to this, the direct- and exchange-RPA methods perform similarly for the description of ionization energies (IPs) and electron affinities (EAs). The coupled-cluster reference IPs and EAs, if corrected to the adiabatic energy differences between the neutral and charged molecules, were shown to be in very good agreement with experimental measurements.

A theoretical justification of the empirical surface hopping method for the laser-driven molecular dynamics is given by utilizing the formalism of the exact factorization of the molecular wave function [Abedi et al., Phys. Rev. Lett. 105, 123002 (2010)] in its quantum-classical limit. Employing an exactly solvable ${\mathrm{H}}_2^{+}$-like model system, it is shown that the deterministic classical nuclear motion on a single time-dependent surface in this approach describes the same physics as stochastic (hopping-induced) motion on several surfaces, provided Floquet surfaces are applied. Both quantum-classical methods do describe reasonably well the exact nuclear wave-packet dynamics for extremely different dissociation scenarios. Hopping schemes using Born-Oppenheimer surfaces or instantaneous Born-Oppenheimer surfaces fail completely.

We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approximation. Our variational wave function displays no signature of the FFLO state in the densities of the two fermion species. Nonetheless, the oscillations of the order parameter appear in density-density correlations, both in situ and after free expansion. Furthermore, above a critical polarization, the value of which depends on the interaction, we find the unpaired Fermi-gas state to be energetically more favorable.

We present an ionization mechanism for use in a cold atom electron source with the goal of producing highly monochromatic electron beams. We experimentally produce a map of the Stark states of ${}^{85}\mathrm{Rb}$ below the ionization threshold and identify states that undergo selective field ionization. The properties of an electron beam produced by field-assisted ionization of such states are quantified. A theoretical framework is established to predict the improvement to beam quality when ionization is conducted above the ionization threshold, where ionization conditions are typically more favorable than below the threshold. Calculations suggest that selective ionization of Rydberg states may offer a pathway to the production of high-brightness, highly monochromatic ion and electron beams.

Griffiths [Phys. Rev. A 94, 032115 (2016)] analyzed, in the framework of a consistent histories interpretation, the controversy regarding the approach to the past of a quantum particle introduced by Vaidman [Phys. Rev. A 87, 052104 (2013)]. I argue that Griffith's criticism of my approach using an analysis of experiments with weak probes is unfounded.

The correctness of the consistent histories analysis of weakly interacting probes, related to the path of a particle, is maintained against the criticisms in the Comment, and against the alternative approach described there, which receives no support from standard (textbook) quantum mechanics.

Recent numerical and analytical results have been obtained for the dynamics of a $V$-type system, and of a model molecular system, interacting with the thermal states of a cavity with a single mode or with a few discrete modes [D. Avisar and A. D. Wilson-Gordon, Phys. Rev. A 93, 033843 (2016)]. The authors speculate that these results may be relevant to excitation with natural incoherent radiation, such as sunlight, which has a continuous spectrum. We claim that this is incorrect, as are their comments about prior work on natural incoherent radiation that does properly deal with a continuous spectrum. Specifically, while their results obtained for the Jaynes-Cummings systems may be of interest for excitation by thermal states of cavities with a few modes, the discrete nature of their field modes produces dynamics that are fundamentally different from those induced by natural sunlight. Hence, we show here that the criticisms leveled in their paper regarding prior treatments that dealt with the continuous spectrum of natural incoherent radiation, as well as their speculation that excitation with continuous-mode thermal radiation can induce long-lived molecular coherences, are incorrect.

We recently presented an extended Jaynes-Cummings model for the interaction of a realistic molecular system of two Born-Oppenheimer potential energy surfaces and a quantized electromagnetic field [Avisar and Wilson-Gordon, Phys. Rev. A 93, 033843 (2016)]. We studied the interaction of this molecular model, and also a prototype $V$-type system, with single-mode and multimode thermal states of the field, characterized by low and high average photon number $\overline{n}$. Among our results, we showed that the three-mode thermal state of the field induces excited-state material coherence and that a thermal state of high $\overline{n}$ can induce “coherentlike” collapse and revival patterns. The preceding Comment by Dodin and Brumer [Phys. Rev. A 95, 067801 (2017)] criticizes our work for allegedly drawing conclusions regarding sunlight-induced dynamics from our results, and for unjustified citation of previous work. However, we think the Comment fails to represent the contents of our paper, and we therefore reply to it. We show it is based on misinterpretation of our paper.

A nonadiabatic and robust method of excitation transfer in a non-Hermitian tight-binding linear chain, assisted by an imaginary gauge field, is theoretically proposed. The gauge field undergoes a linear gradient in time, from a negative to a positive value, which results in an effective transfer of excitation between the two edge sites of the chain. An imaginary (gain or loss) gradient of site energy potentials is introduced to exactly cancel nonadiabatic effects, thus providing an effective shortcut to adiabaticity and pseudo-Hermitian dynamics. Numerical simulations indicate that the non-Hermitian excitation transfer method is very robust against disorder in hopping rates and site energy of the chain.

We present a protocol for interleaved randomized benchmarking of arbitrary quantum gates using Monte Carlo sampling of quantum states. It is generally applicable, including non-Clifford gates while preserving key advantages of randomized benchmarking such as error amplification as well as independence from state preparation and measurement errors. This property is crucial for implementations in many contemporary systems. Although the protocol scales exponentially in the number of qubits, it is superior to direct Monte Carlo sampling of the average gate fidelity in both the total number of experiments by orders of magnitude and savings in classical preprocessing, that are exponential.

Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we provide a fast and reliable algorithm for maximum-likelihood reconstruction that avoids this slow convergence. Our method utilizes the state-of-the-art convex optimization scheme, an accelerated projected-gradient method, that allows one to accommodate the quantum nature of the problem in a different way than in the standard methods. We demonstrate the power of our approach by comparing its performance with other algorithms for $n$-qubit state tomography. In particular, an eight-qubit situation that purportedly took weeks of computation time in 2005 can now be completed in under a minute for a single set of data, with far higher accuracy than previously possible. This refutes the common claim that MLE reconstruction is slow and reduces the need for alternative methods that often come with difficult-to-verify assumptions. In fact, recent methods assuming Gaussian statistics or relying on compressed sensing ideas are demonstrably inapplicable for the situation under consideration here. Our algorithm can be applied to general optimization problems over the quantum state space; the philosophy of projected gradients can further be utilized for optimization contexts with general constraints.

We critically examine the current status of theoretical calculations of the energies, the fine structure, and the isotope shift of the lowest-lying states of helium, searching for unresolved discrepancies with experiments. Calculations are performed within the quantum electrodynamics expansion in powers of the fine structure constant $\alpha$ and the electron-to-nucleus mass ratio $m/M$. For energies, theoretical results are complete through orders ${\alpha }^{6}m$ and ${\alpha }^6{m}^2/M$, with the resulting accuracy ranging from 0.5 to 2 MHz for the $n=2$ states. The fine-structure splitting of the $2{}^{3}P$ state is predicted with a much better accuracy, 1.7 kHz, as a consequence of a calculation of the next-order ${\alpha }^{7}m$ effect. An excellent agreement of the theoretical predictions with the recent measurements of the fine structure provides one of the best tests of the bound-state QED in few-electron systems. The isotope shift between ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ is treated with a subkilohertz accuracy, which allows for a high-precision determination of the differences of the nuclear charge radii $\delta r^2$. Several such determinations, however, yield results that are in a $4\sigma$ disagreement with each other, which remains unexplained. Apart from this, we find no significant discrepancies between theory and experiment for the helium atom. A further calculation of the yet unknown ${\alpha }^{7}m$ correction to energy levels will provide a sensitive test of universality in electromagnetic interactions of leptons by comparison of nuclear charge radii obtained by the helium and muonic helium spectroscopy.

We investigate electron-correlation effects in the $g$ factor of the ground state of Li-like ions. Our calculations are performed within the nonrelativistic quantum electrodynamics (NRQED) expansion up to two leading orders in the fine-structure constant $\alpha , {\alpha }^2$, and ${\alpha }^3$. The dependence of the NRQED results on the nuclear charge number $Z$ is studied and the individual $1/Z$-expansion contributions are identified. Combining the obtained data with the results of the all-order (in $Z\alpha$) calculations performed within the $1/Z$ expansion, we derive unified theoretical predictions for the $g$ factor of light Li-like ions.