Optical tweezers are highly versatile laser traps for neutral microparticles, with fundamental applications in physics and in single molecule cell biology. Force measurements are performed by converting the stiffness response to displacement of trapped transparent microspheres, employed as force transducers. Usually, calibration is indirect, by comparison with fluid drag forces. This can lead to discrepancies by sizable factors. Progress achieved in a program aiming at absolute calibration, conducted over the past 15 years, is briefly reviewed. Here we overcome its last major obstacle, a theoretical overestimation of the peak stiffness, within the most employed range for applications, and we perform experimental validation. The discrepancy is traced to the effect of primary aberrations of the optical system, which are now included in the theory. All required experimental parameters are readily accessible. Astigmatism, the dominant effect, is measured by analyzing reflected images of the focused laser spot, adapting frequently employed video microscopy techniques. Combined with interface spherical aberration, it reveals a previously unknown window of instability for trapping. Comparison with experimental data leads to an overall agreement within error bars, with no fitting, for a broad range of microsphere radii, from the Rayleigh regime to the ray optics one, for different polarizations and trapping heights, including all commonly employed parameter domains. Besides signaling full first-principles theoretical understanding of optical tweezers operation, the results may lead to improved instrument design and control over experiments, as well as to an extended domain of applicability, allowing reliable force measurements, in principle, from femtonewtons to nanonewtons.

We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical motion via spontaneous emission of photons, as well as internal heat generation. Universal relations are derived for the radiated energy and angular momentum as trace formulas involving the object's scattering matrix. We also compute the quantum noise by deriving the full statistics of the radiated photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy generation is quantified and the total entropy is shown to be always increasing. Furthermore, we derive a Fokker-Planck equation governing the stochastic angular motion resulting from the fluctuating backreaction frictional torque. As a result, we find a quantum limit on the uncertainty of the object's angular velocity in steady rotation. Finally, we show in some detail that a rotating object drags nearby objects, making them spin parallel to its axis of rotation. A scalar toy model is introduced to simplify the technicalities and ease the conceptual complexities and then a detailed discussion of quantum electrodynamics is presented.

In this work, we give a comprehensive derivation of an exact and numerically feasible method to perform ab initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierarchy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, nonlinear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals, we present the appropriate Kohn-Sham construction. In the nonrelativistic limit, this density-functional-type theory of quantum electrodynamics reduces to the density-functional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g., restricting the allowed modes of the photon field, we derive further density-functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the appropriate effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system.

We revisit the one-dimensional discrete time quantum walk with three states and the Grover coin, the simplest model that exhibits localization in a quantum walk. We derive analytic expressions for the localization and a long-time approximation for the entire probability density function (PDF). We find the possibility for asymmetric localization to the extreme that it vanishes completely on one site of the initial conditions. We also connect the time-averaged approximation of the PDF found by Inui et al. [Phys. Rev. E 72, 056112 (2005)] to a spatial average of the walk. We show that this smoothed approximation predicts moments of the real PDF accurately.

We analyze general laws of continuous-variable entanglement dynamics during the deterministic attenuation and amplification of the physical signal carrying the entanglement. These processes are inevitably accompanied by noises, so we find fundamental limitations on noise intensities that destroy entanglement of Gaussian and non-Gaussian input states. The phase-insensitive amplification ${\Phi }_1\otimes {\Phi }_2\otimes \cdots {\Phi }_N$ with the power gain ${\kappa }_i\ge 2$ ($\approx 3$ dB, $i=1,...,N$) is shown to destroy entanglement of any $N$-mode Gaussian state even in the case of quantum-limited performance. In contrast, we demonstrate non-Gaussian states with the energy of a few photons such that their entanglement survives within a wide range of noises beyond quantum-limited performance for any degree of attenuation or gain. We detect entanglement preservation properties of the channel ${\Phi }_1\otimes {\Phi }_2$, where each mode is deterministically attenuated or amplified. Gaussian states of high energy are shown to be robust to very asymmetric attenuations, whereas non-Gaussian states are at an advantage in the case of symmetric attenuation and general amplification. If ${\Phi }_1={\Phi }_2$, the total noise should not exceed $\frac{1}{2}\sqrt{{\kappa }^2+1}$ to guarantee entanglement preservation.

Laser Doppler velocimetry is a technique used to measure linear velocity, ranging from that of exhaust gases to blood flow. A rotational analog of laser Doppler velocimetry was recently demonstrated, using a rotationally symmetric interference pattern to probe the angular velocity of a spinning object. In this work, we demonstrate the use of a diffraction-limited structured illumination pattern to measure the angular velocity of a micron-sized particle trapped and spinning at tens of Hz in an optical trap. The technique requires no detailed knowledge of the shape of the particle, or the distribution of scatterers within it, and is independent of the particle's chirality, transparency, and birefringence. The particle is also subjected to Brownian motion, which complicates the signal by affecting the rotation rate and the rotation axis. By careful consideration of these influences, we show how the measurement is robust to both, representing a technique with which to probe the rotational motion of microscale particles.

We investigate which pure states of $n$ photons in $d$ modes can be transformed into each other via passive linear optics, without postselection. In other words, we study the local unitary (LU) equivalence classes of symmetric many-qudit states. Writing our state as $f^{†}|\Omega \rangle$, with $f^{†}$ a homogeneous polynomial in the mode creation operators, we propose two sets of LU invariants: spectral invariants, which are the eigenvalues of the operator $f{f}^{†}$, and moments, each given by the norm of the symmetric component of a tensor power of the initial state, which can be computed as vacuum expectation values of $f^k{\left(f^{†}\right)}^k$. We provide a scheme for experimental measurement of the later, as related to the postselection probability of creating state $f^{†k}|\Omega \rangle$ from $k$ copies of $f^{†}|\Omega \rangle$.

In 1994, Reck et al. showed how to realize any unitary transformation on a single photon using a product of beam splitters and phase shifters. Here we show that any single beam splitter that nontrivially mixes two modes also densely generates the set of unitary transformations (or orthogonal transformations, in the real case) on the single-photon subspace with $m\ge 3$ modes. (We prove the same result for any two-mode real optical gate, and for any two-mode optical gate combined with a generic phase shifter.) Experimentally, this means that one does not need tunable beam splitters or phase shifters for universality: any nontrivial beam splitter is universal for linear optics. Theoretically, it means that one cannot produce “intermediate” models of linear optical computation (analogous to the Clifford group for qubits) by restricting the allowed beam splitters and phase shifters: there is a dichotomy; one either gets a trivial set or else a universal set. No similar classification theorem for gates acting on qubits is currently known. We leave open the problem of classifying optical gates that act on three or more modes.

Collision-induced dissociation (CID) has been studied for protonated water clusters ${\mathrm{H}}^{+}{(\mathrm{H}}_2{\mathrm{O})}_n,$ with $n$ = 2–8, colliding with argon atoms at a laboratory energy of 8 keV. The experimental data have been taken with an apparatus (Device for Irradiation of Molecular Clusters, ‘Dispositif d’Irradiation d’Agrégats Moléculaire,’ DIAM) that has been recently constructed at the Institut de Physique Nucléaire de Lyon. It includes an event-by-event mass spectrometry detection technique, COINTOF (correlated ion and neutral fragment time of flight). The latter device allows, for each collision event, to detect and identify in a correlated manner all produced neutral and charged fragments. For all the studied cluster ions, it has allowed us to identify branching ratios for the loss of $i$ = 1 to $i$ = $n$ water molecules, leading to fragment ions ranging from ${\mathrm{H}}^{+}{\left({\mathrm{H}}_2\mathrm{O}\right)}_{i=n-1}$ all the way down to the production of protons. Using a corresponding calibration technique we determine total charged fragment production cross sections for incident protonated water clusters ${\mathrm{H}}^{+}{(\mathrm{H}}_2{\mathrm{O})}_n,$ with $n$ = 2–7. Observed trends for branching ratios and cross sections, and a comparison with earlier data on measured attenuation cross sections for water clusters colliding with other noble gases (He and Xe), give insight into the underlying dissociation mechanisms.

We introduce a class of mixed multiqubit states, that corresponds to a randomized version of graph states. Such states arise when a graph state is prepared with noisy or imperfect controlled-$Z$ gates. We study the entanglement features of these states by investigating both bipartite and genuine multipartite entanglement. Bipartite entanglement is studied via the concepts of connectedness and persistency, which are related to measurement based quantum computation. The presence of multipartite entanglement is instead revealed by the use of witness operators which are subsequently adapted to study nonlocal properties through the violation of suitable Bell inequalities. We also present results on the entanglement detection of particular randomized graph states, by deriving explicit thresholds for entanglement and nonlocality in terms of the noise parameter that characterizes the controlled-$Z$ gates exploited for their generation. Finally, we propose a method to further improve the detection of genuine multipartite entanglement in this class of states.

Ionization by an attosecond pulse launches an electron wave packet in the continuum which contains rich information about the pulse, the parent system, and the ionization dynamics. This emission process is not instantaneous in the sense that the electrons take a finite time to leave the potential. This time is closely related to the Wigner time. In this paper we introduce the stereo Wigner time delay, which measures the relative delay between electrons emitted to the left and right in an asymmetric system. We present a theoretical study of the delay in photoemission for a small asymmetric molecular system using the streaking technique. The stereo Wigner time delay shows advantages compared to previous schemes. Our numerical calculation shows that such a measurement removes the infrared laser-Coulomb coupling, which has been problematic in the interpretation of the measured delay in photoemission from atomic systems.

We explore the possibility of using an optomechanical resonator to induce a conditional phase gate for single photons. The problem provides an illustration of the application to optomechanical systems of a recently developed input-output formalism for single- (or few-) photon states of the radiation field. At the two-photon level, we find significant departures from expectations based on a semiclassical treatment. We also find a tradeoff between the maximum achievable conditional phase and the fidelity of the final state, consistent with other multimode studies of conditional phases based on optical nonlinearities.

We present a detailed analysis of the multimode quantum state embedded in an optical frequency comb generated by a synchronously pumped optical parametric oscillator (SPOPO) [J. Roslund, R. Medeiros de Araújo, S. Jiang, C. Fabre, and N. Treps, Nat. Photon. 8, 109 (2014)]. The full covariance matrix of the state is obtained with homodyne detection where the local oscillator is spectrally controlled with pulse-shaping techniques. The resulting matrix reveals genuine multipartite entanglement. Additionally, the beam is comprised of several independent eigenmodes that correspond to specific pulse shapes. The experimental data is confirmed with numerical simulations. Finally, the potential to create continuous-variable cluster states from the quantum comb is analyzed. Multiple cluster states are shown to be simultaneously embedded in the SPOPO state, and these states can be revealed by a suitable basis change applied to the measured covariance matrix.

The persistent $a_{\mu }\equiv (g-2)/2$ anomaly in the muon sector could be due to new physics visible in the electron sector through a sub-ppb (parts per ${10}^9$) measurement of the anomalous magnetic moment of the electron $a_e$. Driven by recent results on the electron mass [S. Sturm et al., Nature 506, 467 (2014)], we reconsider the sources of uncertainties that limit our knowledge of $a_e$ including current advances in atom interferometry. We demonstrate that it is possible to attain the level of precision needed to test $a_{\mu }$ in the naive scaling hypothesis on a time scale similar to next-generation $g-2$ muon experiments at Fermilab and JPARC. In order to achieve this level of precision, knowledge of the quotient $h/M$, i.e., the ratio between the Planck constant and the mass of the atom employed in the interferometer, will play a crucial role. We identify the most favorable isotopes to achieve an overall relative precision below ${10}^{-10}$.

We present a simple, experimentally realizable method to make coherent three-body interactions dominate the physics of an ultracold lattice gas. Our scheme employs either lattice modulation or laser-induced tunneling to reduce or turn off two-body interactions in a rotating frame, promoting three-body interactions arising from multiorbital physics to leading-order processes. This approach provides a route to strongly correlated phases of lattice gases that are beyond the reach of previously proposed dissipative three-body interactions. In particular, we study the mean-field phase diagram for spinless bosons with three- and two- body interactions and provide a roadmap to dimer states of varying character in one dimension. This toolkit should be immediately applicable in state-of-the-art cold-atom experiments.

We propose a stereographical-visualization scheme for a polarization state by two-dimensional imaging of a weak value with a single setup. The key idea is to employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in weak measurement. Our scheme has the advantage that we can extract information on the polarization state from the single image in which the zero-intensity point of the optical vortex beam corresponds to a stereographic projection point of the Poincaré sphere. We experimentally perform single-setup weak measurement to validate the stereographical relationship between the polarization state on the Poincaré sphere and the location of the zero-intensity point.

We present a quantum theory of ion-atom interactions that is applicable at energies comparable to or smaller than the atomic hyperfine splitting and takes proper account of the effects of identical nuclei. The theory reveals the subtlety and the complexity of cold ion-atom interactions including the change of threshold behavior due to hyperfine splitting and the existence of a large number and a variety of scattering resonances between hyperfine thresholds. We show how this complexity is described, efficiently and at a quantitative level, using a multichannel quantum-defect theory that we present here for ion-atom interactions. Such an efficient description is a key enabling element to understand few-body and many-body quantum systems involving ions.

We use a microscopic quantum optical model to compute the spectrum of quantum vacuum emission from strong laser pulses propagating in nonlinear optical media. Similarities and differences with respect to the emission of analog white holes as predicted by quantum field theory in curved spacetime are highlighted. Conceptual issues related to the role played by the material dispersion and to the presence or absence of the horizon are clarified. Critical comparison with available experimental data is made.

We demonstrate and analyze a strongly driven quantum pendulum in the angular motion of state-selected and laser-aligned carbonyl sulfide molecules. Raman couplings during the rising edge of a 50-ps laser pulse create a wave packet of pendular states, which propagates in the confining potential formed by the polarizability interaction between the molecule and the laser field. This wave-packet dynamics manifests itself as pronounced oscillations in the degree of alignment with a laser-intensity-dependent period.

Highly elongated quasi-one-dimensional cold-atom samples have been studied extensively over the past years experimentally and theoretically. This work determines the energy spectrum of two identical fermions and a third distinguishable particle as functions of the mass ratio $\kappa$ and the free-space $s$-wave scattering length $a_{3\text{D}}$ between the identical fermions and the distinguishable third particle in a cylindrically symmetric waveguide whose symmetry axis is chosen to be along the $z$ axis. We focus on the regime where the mass of the identical fermions is equal to or larger than that of the third distinguishable particle. Our theoretical framework accounts explicitly for the motion along the transverse confinement direction. In the regime where excitations in the transverse direction are absent (i.e., for states with projection quantum number $M_{\text{rel}}=0$), we determine the binding energies for states with odd parity in $z$. These full three-dimensional energies deviate significantly from those obtained within a strictly one-dimensional framework when the $s$-wave scattering length is of the order of or smaller than the oscillator length in the confinement direction. If transverse excitations are present, we predict the existence of a class of universal three-body bound states with $|M_{\text{rel}}|=1$ and positive parity in $z$. These bound states arise on the positive $s$-wave scattering length side if the mass ratio $\kappa$ is sufficiently large. Implications of our results for ongoing cold-atom experiments are discussed.