Solving the challenging problem of the amplification and generation of an electromagnetic field in nanostructures enables us to implement many properties of the electromagnetic field at the nanoscale in practical applications. A first-principles quantum-mechanical consideration of such a problem is sufficiently restricted by the exponentially large number of degrees of freedom and does not allow the electromagnetic-field dynamics to be described if it involves a high number of interacting atoms and modes of the electromagnetic field. Conversely, the classical description of electromagnetic fields is incorrect at the nanoscale due to the high level of quantum fluctuations connected to high dissipation and noise levels. In this paper, we develop a framework with a significantly reduced number of degrees of freedom, which describes the quantum spatial dynamics of electromagnetic fields interacting with atoms. As an example, we consider the interaction between atoms placed in a metallic subwavelength groove and demonstrate that a spontaneously excited electromagnetic pulse propagates with the group velocity. The developed approach may be exploited to describe nonuniform amplification and propagation of electromagnetic fields in arbitrary dispersive dissipative systems.
Purely azimuthal entanglement is analyzed for noncollinear frequency-degenerate biphoton states. The degree of azimuthal entanglement is found to be very high, with the Schmidt parameter K on the order of the ratio of the pump waist to its wavelength. A scheme is suggested for partial realization of this high entanglement resource in the form of a multichannel Schmidt-type decomposition.
Passive side-channel attacks in quantum key distribution (QKD) aim at obtaining information about the quantum signals without disturbing them and hence compromise real-world QKD security. Currently, there are no reliable tools for the assessment of QKD signal generation imperfections. In this work we propose a generic experimental method which allows to upper-bound QKD light-source imperfections and directly integrate them into the modern security proofs. The method relies on Hong-Ou-Mandel interference between different emitted signals: the maximum interference visibility reveals overall signal distinguishability that could lead to passive side-channel information leakage. We apply it for the standard decoy-state BB84 protocol and calculate a lower bound on the secret key rate for realistic values of interference visibility. The method can be readily implemented in practical QKD setups and is especially relevant for multiple-laser QKD systems such as the one installed on the Micius satellite.
It is shown that tailored breaking of the translational symmetry through weak scattering in waveguides and optical fibers can control chromatic dispersions of the individual modes at any order; thereby, it overcomes the problem of coherent classical and quantum signal transmission at long distances. The methodology is based on previously developed quantum control techniques and gives an analytic solution in ideal scattering conditions; it has been also extended to incorporate and correct nonunitary effects in the presence of weak backscattering. In practice, it requires scatterers able to couple different modes and carefully designed dispersion laws giving a null average quadratic distortion in the spectral vicinity of the operational frequency.
For a system of two spatially separated qubits (two-level atoms) coupled to a one-dimensional waveguide we have described the time evolution of singly or doubly excited states of the atomic subsystem. When the interatomic distance l takes special (“resonant” or “antiresonant”) values, the singly excited system of resonant atoms can form metastable (dark) states. If l slightly deviates from one of the special values or the atomic frequencies do not coincide, the dark states slowly decay and we have calculated the decay rate. Also, we have found that the doubly excited state of two resonant atoms located at the special positions does not completely decay but, with a finite probability, can evolve (with the emission of a single photon) to one of the metastable singly excited states. Metastable states of pairs of qubits may find applications (e.g., as memory elements) in information processing or as detectors sensitive to external perturbations.
A natural atom placed into a cavity with time-dependent parameters can be parametrically excited due to interaction with the quantized photon mode. One of the channels for this process is the dynamical Lamb effect, induced by a nonadiabatic modulation of the atomic-level Lamb shift. However, in experiments with natural atoms it is quite difficult to isolate this effect from other mechanisms of atom excitation. We point out that a transmission line cavity coupled with a superconducting qubit (an artificial macroscopic atom) provides a unique platform for observation of the dynamical Lamb effect. A key idea is to exploit a dynamically tunable qubit-resonator coupling, which was implemented quite recently. By varying the coupling nonadiabatically, it is possible to parametrically excite a qubit through a nonadiabatic modulation of the Lamb shift, even if the cavity was initially empty. The dynamics of such a coupled system is studied within the Rabi model with a time-dependent coupling constant and beyond the rotating-wave approximation. An efficient method to increase the effect through the periodic and nonadiabatic switching of the qubit-resonator coupling energy is proposed. © 2015 American Physical Society. ©2015 American Physical Society.
We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green’s functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form ω ∝ p^2 in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a three-dimensional weakly interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to a second-quantized Hamiltonian in which the microscopic two-body potentials in each channel are replaced by the corresponding off-shell scattering amplitudes. The superfluid drag density can be calculated by considering a mixture of phonons and magnons interacting via the effective potentials. We show that this problem is identical to the second-order perturbative treatment of a Bose polaron. In two dimensions the drag contributes to the magnon dispersion already in the first approximation. Our consideration provides a basis for systematic study of emergent phases in quantum degenerate Bose-Bose mixtures.
We study the generation of single-photon pulses with the tailored temporal shape via nonlocal spectral filtering. A shaped photon is heralded from a time-energy entangled photon pair upon spectral filtering and time-resolved detection of its entangled counterpart. We show that the temporal shape of the heralded photon is defined by the time-inverted impulse response of the spectral filter and does not depend on the heralding instant. Thus one can avoid postselection of particular heralding instants and achieve a substantially higher heralding rate of shaped photons as compared to the generation of photons via nonlocal temporal modulation. Furthermore, the method can be used to generate shaped photons with a coherence time in the ns-μ s range and is particularly suitable to produce photons with the exponentially rising temporal shape required for efficient interfacing to a single quantum emitter in free space.
The van der Waals coefficient C6(θ;nlJM) of two like Rydberg atoms in their identical Rydberg states |nlJM〉 is resolved into four irreducible components called scalar Rss, axial (vector) Raa, scalar-tensor RsT=RTs, and tensor-tensor RTT parts in analogy with the components of dipole polarizabilities. The irreducible components determine the dependence of C6(θ;nlJM) on the angle θ between the interatomic and the quantization axes of atoms. The spectral resolution for the biatomic Green's function with account of the most contributing terms is used for evaluating the components Rαβ of atoms in their Rydberg series of doublet states of the low angular momenta (2S, 2P, 2D, 2F). The polynomial presentations in powers of the Rydberg-state principal quantum number n taking into account the asymptotic dependence C6(θ;nlJM)∝n11 are derived for simplified evaluations of irreducible components. Numerical values of the polynomial coefficients are determined for Rb atoms in their n2S1/2, n2P1/2,3/2, n2D3/2,5/2, and n2F5/2,7/2 Rydberg states of arbitrary high n. The transformation of the van der Waals interaction law −C6/R6 into the dipole-dipole law C3/R3 in the case of close dipole-connected two-atomic states (the Förster resonance) is considered and the dependencies on the magnetic quantum numbers M and on the angle θ of the constant C3(θ;nlJM) are determined together with the ranges of interatomic distances R, where the transformation appears.
Using geometric means, we first consider a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled one, which contains no product state components. We show that this convex decomposition can be achieved in practice with the help of a linear programming algorithm that scales in the general case polynomially with the system dimension. We illustrate the algorithm implementation with an example of a composite system of dimension 12 that undergoes a loss of coherence due to classical noise and we trace the time evolution of its essentially entangled component. We suggest a “geometric” description of entanglement dynamics and demonstrate how it explains the well-known phenomena of sudden death and revival of multipartite entanglements. For a statistical weight loss of the essentially entangled component with time, its average entanglement content is not affected by the coherence loss.
We consider an expansion of the strongly interacting superfluid Fermi gas in a vacuum in the so-called unitary regime when the chemical potential μ ∝ h^2 n^(2/3)/m, where n is the density of the Bose-Einstein condensate 2 of Cooper pairs of fermionic atoms. At low temperatures T → 0, such an expansion can be described in the framework of the Gross-Pitaevskii equation (GPE). For such a dependence of the chemical potential on the density, the GPE has additional symmetries, resulting in the existence of the virial theorem, connecting the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at T → ∞ to the gas cloud expansion, linearly growing in time. We study such asymptotics and reveal the perfect match between the quasiclassical self-similar solution and the asymptotic expansion of the noninteracting gas. This match is governed by the virial theorem, derived through utilizing the Talanov transformation, which was first obtained for the stationary self-focusing of light in media with a cubic nonlinearity due to the Kerr effect. In the quasiclassical limit, the equations of motion coincide with three-dimensional hydrodynamics for the perfect monatomic gas with γ = 5/3. Their self-similar solution describes, within the background of the gas expansion, the angular deformities of the gas shape in the framework of the Ermakov-Ray-Reid–type system.
Adaptive measurements were recently shown to significantly improve the performance of quantum state tomography. Utilizing information about the system for the online choice of optimal measurements allows one to reach the ultimate bounds of precision for state reconstruction. In this article we generalize an adaptive Bayesian approach to the case of process tomography and experimentally show its superiority in the task of learning unknown quantum operations. Our experiments with photonic polarization qubits cover all types of single-qubit channels. We also discuss instrumental errors and the criteria for evaluation of the ultimate achievable precision in an experiment. It turns out that adaptive tomography provides a lower noise floor in the presence of strong technical noise.
We report an experimental realization of adaptive Bayesian quantum state tomography for two-qubit states. Our implementation is based on the adaptive experimental design strategy proposed in the work by Husz´ar and Houlsby [F. Husz´ar and N. M. T. Houlsby, Phys. Rev. A 85, 052120 (2012).] and provides an optimal measurement approach in terms of the information gain. We address the practical questions which one faces in any experimental application: the influence of technical noise and the behavior of the tomographic algorithm for an easy-to-implement class of factorized measurements. In an experiment with polarization states of entangled photon pairs, we observe a lower instrumental noise floor and superior reconstruction accuracy for nearly pure states of the adaptive protocol compared to a nonadaptive protocol. At the same time, we show that for the mixed states, the restriction to factorized measurements results in no advantage for adaptive measurements, so general measurements have to be used.
Isotropy parameters of truly linear (LT ) and truly circular (CT ) polarization singularities in a threedimensional monochromatic electromagnetic field are defined. It is demonstrated that these parameters characterize the distribution of polarization ellipses near the singular points in a more detailed way than a topological index. A numerical algorithm which tracks CT and LT lines and visualizes the changes of isotropy parameters along the lines is proposed. The algorithm is applied to visualize the polarization singularity lines and their properties in the vicinity of a metallic nanospheroid that is irradiated by a plane elliptically polarized wave. It is shown that both CT and LT lines appear close to the surface of the nanoparticle and they are three-dimensional closed loops or arcs that start and end at the surface of the nanospheroid. In most cases the singular lines of different types are topologically linked
The analysis of single-mode photon fluctuations and their counting statistics at the superradiant phase transition is presented. The study concerns the equilibrium Dicke model in a regime where the Rabi frequency, related to a coupling of the photon mode with a finite-number qubit environment, plays the role of the transition's control parameter. We use the effective Matsubara action formalism based on the representation of Pauli operators as bilinear forms with complex and Majorana fermions. Then, we address fluctuations of superradiant order parameter and quasiparticles. The average photon number, the fluctuational Ginzburg-Levanyuk region of the phase transition, and Fano factor are evaluated. We determine the cumulant-generating function which describes a full counting statistics of equilibrium photon number. Exact numerical simulation of the superradiant transition demonstrates quantitative agreement with analytical calculations.
Purely azimuthal entanglement is analyzed for non-collinear frequency-degenerate biphoton states. The degree of azimuthal entanglement is found to be very high, with the Schmidt parameter $K$ on the order of the ratio of the pump waist to its wavelength. A scheme is suggested for partial realization of this high entanglement resource in the form of a multichannel Schmidt-type decomposition.
An integral equation approach to the weak-field asymptotic theory (WFAT) of tunneling ionization is developed. An integral representation for the exact partial amplitudes of ionization into parabolic channels is derived. The WFAT expansion for the ionization rate follows immediately from this relation. Integral representations for the coefficients in the expansion are obtained. The integrals accumulate where the ionizing orbital has large amplitude and are not sensitive to its behavior in the asymptotic region. Hence, these formulas enable one to reliably calculate the WFAT coefficients even if the orbital is represented by an expansion in Gaussian basis, as is usually the case in standard software packages for electronic structure calculations. This development is expected to greatly simplify the implementation of the WFAT for polyatomic molecules, and thus facilitate its growing applications in strong-field physics.
The operation of a surface plasmon amplification by stimulated emission of radiation- (spaser)-based nanolaser is theoretically investigated. We find that the lasing frequency undergoes a shift as the lasing intensity increases, a result that agrees with recent experiments. We show that the mechanism of the intensity-dependent shift involves a spatial deformation of the lasing mode, which is induced by the spatial hole burning in the surrounding gain media. We develop a general analytical scheme to account for the mode deformation. Our numerical calculations demonstrate good correspondence of the lasing frequency shift with the experimental data for the simplest (spherical) geometry of the spaser.
We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks-Girardeau gas. We establish that given an initial momentum p0 the impurity relaxes to a steady state with a nonvanishing momentum p∞. The nature of the steady state is found to depend drastically on whether the masses of the impurity and the host are equal. This is due to multiple coherent scattering processes leading to a resonant interaction between the impurity and the host in the case of equal masses. The dependence of p∞ on p0 remains nontrivial even in the limit of vanishing interaction between the impurity and host particles. In this limit p∞(p0) is found explicitly.
Spontaneous emission spectra of two initially excited closely spaced identical atoms are very sensitive to the strength and the direction of the applied magnetic field. We consider the relevant schemes that ensure the determination of the mutual spatial orientation of the atoms and the distance between them by entirely optical means. A corresponding theoretical description is given accounting for the dipole-dipole interaction between the two atoms in the presence of a magnetic field and for polarizations of the quantum field interacting with magnetic sublevels of the two-atom system.
Absorption spectrum of a system of two closely spaced identical atoms displays, at certain preparation, a dip that can be much narrower than the natural linewidth. This preparation includes (i) application of a strong magnetic field at an angle α, that is very close to the magic angle α0 = arccos √(1/ 3) ≈ 54.7◦, with respect to the direction from one atom to another, and (ii) in-plane illumination by a laser light in the form of a nonresonant standing wave polarized at the same angle α. Both qualitative and quantitative arguments for the narrow dip effect are presented.