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Institut
We derive the quantum-mechanical master equation (generalized optical Bloch equation) for an atom in the vicinity of a flat dielectric surface. This equation gives access to the semiclassical radiation pressure force and the atomic momentum diffusion tensor, that are expressed in terms of the vacuum field correlation function (electromagnetic field susceptibility). It is demonstrated that the atomic center-of-mass motion provides a nonlocal probe of the electromagnetic vacuum fluctuations. We show in particular that in a circularly polarized evanescent wave, the radiation pressure force experienced by the atoms is not colinear with the evanescent wave's propagation vector. In a linearly polarized evanescent wave, the recoil per fluorescence cycle leads to a net magnetization for a Jg = 1/2 ground state atom.
We present an analytical approach to the calculation of the linewidth and lineshift of an atom or molecule in the near field of a structured dielectric surface. For soft surface corrugations with amplitude lambda/50, we find variations of the linewidth in the ten percent region. More strikingly, the shift of the molecular resonance can reach several natural linewidths. We demonstrate that the lateral resolution is of the order of the molecule-surface distance. We give a semiquantitative explanation of the outcome of our calculations that is based on simple intuitive models.
New physics with evanescent wave atomic mirrors : the van der Waals force and atomic diffraction
(1998)
After a brief introduction to the field of atom optics and to atomic mirrors, we present experimental results obtained in our group during the last two years while studying the reflection of rubidium atoms by an evanescent wave. These involve the first measurement of the van der Waals force between an atom in its ground state and a dielectric wall, as well as the demonstration of a reflection grating for atoms at normal incidence. We also consider the influence of quantum reflection and tunnelling phenomena. Further studies using the atomic mirror as a probe of the van der Waals interaction, and of very small surface roughness are briefly discussed.
We study the electromagnetic coupling and concomitant heating of a particle in a miniaturized trap close to a solid surface. Two dominant heating mechanisms are identified: proximity fields generated by thermally exicted currents in the absorbing solid and timedependent image potentials due to elastic surfaces distortions (Rayleigh phonons. Estimates for the lifetime of the trap ground state are given. Ions are paricularly sinsitive to electric proximity fields: for a silver substrate, we find a lifetime below one second at distrances closer than some ten 10^-6m to the surfaces. Neutral atoms may approach the surface more closely: if they have a magnetic moment, a minimum distance of one 10^-6m is estimatied in tight traps, the heat being transferred via magnetic proximity fields. For spinless atoms, heat is transferred by inelastic scattering of virtual photons off sorface phonons. The corresponding lifetime, however, is estimated to be extremely long compared to the timescale of typical experiments.
We derive the time and loss rate for a trapped atom that is coupled to fluctuating fields in the vicinity of a room-temperature metallic and/or dielectric surface. Our results indicate a clear predominance of near-field effects over ordinary blackbody radiation. We develop a theoretical framework for both charged ions and neutral atoms with and without spin. Loss processes that are due to a transition to an untrapped internal state are included.
We discuss heating and decoherencw in traps fpr ions and neutral paricles close to metallic surfaces. We focus on simple trap geometries and compute noise spectra of thermally excited electromagnetic fields. If the trap is located in the near field of the substrate, the field fluctuations are largely increased compared to the level of the blackbody field, leading to much shorter coherence and life times of the trapped atoms. The correspinding time constants are computed for ion traps and magnetic traps. Analytical estimates for the size dependence of the noise spectrum are given. We finally discuss prospects for the coherent transport of matter waves in integrated surface waveguides.
We analyze the spatial coherence of the electromagnetic field emitted by a half-space at temperature T close to the interface. An asymptotic analysis allows to identify three different contributions to the cross-spectral density tensor in the near-field regime. It is shown that the coherence length can be either much larger or much shorter than the wavelength depending on the dominant contribution.
A transport theory for atomic matter waves in low-dimensional waveguides is outlined. The thermal fluctuation spectrum of magnetic near fields leaking out of metallic microstructures is estimated. The corresponding scattering rate for paramagnetic atoms turns out to be quite large in micrometer-sized waveguides (approx. 100/s). Analytical estimate for the heating and decoherence of a cold atom cloud are given. We finally discuss numerical and analytical results for the scattering from static potential imperfections and the ensuing spatial diffusion process.
Coherent transport
(2001)
We discuss the transport of matter waves in low-dimensional waveguides. Due to scattering from uncontrollable noise fields, the spatial coherence gets reduced and eventually lost. We develop a description of this decoherence process in terms of transport equations for the atomic Wigner function. We outline its derivation and discuss the special case of white noise where an analytical solution can be found.
Coherence properties of thermal near fields : implications for nanometer-scale radiative transfer
(2001)
With the recent development of local (optical and thermal) probe microscopy and the advent of nanotechnology, it seems necessary to revisit the old subject of coherence properies of thermal sources of light. Concerning temporal coherence, we show that thermal sources may produce quasi-monochromatic near fields. In light of this result, the possibility of perfoming near-field solid-state spectroscopy and of designing near-field infrared sources is discussed. The problem of radiative transfer between two thermal sources held at subwavelength distance is studied. The radiative flux may be enhanced by several orders of magnitude due to the excitation of resonant surface waves, and this may occur at particular frequencies. Finally, we study the spatial coherence of thermal sources and the substantial influence of the near field. Surface waves may induce long-range spatial correlation, on a scale much larger than the wavelength. Conversely, quasi-static contributions, as well as skin-layer currents, induce arbitary small correlations. With the recent development of local (optical and thermal) probe microscopy and the advent of nanotechnology, it seems necessary to revisit the old subject of coherence of thermal fields.
We review the 10 year long journey into the miniaturization and integration of matter wave optics resulting in devices mounted on surfaces, so called atom chips. The first experiments started with the guiding of atoms with free standing wires and investigated the trapping potentials in simple geometries. Atom optical elements can now be micro fabricated down to 1 um size on atom chips. The creation of a Bose-Einstein condensate miniaturized in surface traps was recently achieved, and the first attempts to integrate light optics are in progress. In this review, we describe microscopic atom optics elements using current carrying and charged structures. Experiments with free standing structures (atom wires)are reviewed, investigating the basic principles of microscopic atom optics. We then discuss the miniaturization on the atom chip. One of the open central questions is dealt with: what happens with cold atoms close to a warm surface, how fast will they heat up or lose their coherence? The review concludes with an outlook of what we believe the future directions to be, and what can be hoped for.
We study the optical forces due to the radiation of a thermal source. Our model consists of a particle modelled by a dipole above a half-space at temperature T. The fluctuating fields are computed using the Lifshitz model. We find two contributions to the force: a repulsive "wind" component and a dispersive force mainly due to the contribution of thermally excited surface waves. It is found that for SIC material, the latter is repulsive in the very near field. The usual van der Waals force is larger by a factor of approximately ten for submicron size particles.
We discuss the dynamics of a condensate in a miniaturized electromagnetic trap formed above a microstructured substrate. Recent experiments have found that trap lifetimes get reduced when approaching the substrate because atoms couple to thermally excited near fields. The data agree quantitatively with our theory [Appl. Phys. B 69, 379 (1999)]. We focus on the decoherence of a quantum degenerate gas in a quasi-one-dimensional trap. Monte Carlo simulations indicate that atom interactions reduce the condensate decoherence rate. This is explained by a simple theory in terms of the suppression of long-wavelength excitations. We present preliminary simulation results for the adiabatic generation of dark solitons
Spontaneous emission in a subwavelength environment characterized by boundary integral equations
(2004)
We discuss the impact of a dielectric nanoparticle on the fluorescence light from an emitter embedded in the particle. Numerical and analytical calculations predict a slower radiative decay compared to a bulk dielectric due to electrostatic screening. We assess the relevance of the nanoparticle shape and size and the position and orientation of the molecule. The numerical results are obtained from a rigorous solution of the Maxwell equations, formulated as boundary integral equations
We discuss the impact of thermally excited near fields on the coherent expansion of a condensate in a miniaturized electromagnetic trap. Monte Carlo simulations are compared with a kinetic two-component theory and indicate that atom interactions can slow down decoherence. This is explained by a simple theory in terms of the condensate dynamic structure factor
We study the dynamics of Bose-Einstein condensates in time-dependent microtraps for the purpose of understanding the influence of the mean field interaction on the performance of interferometers. We identify conditions where the nonlinearity due to atom interactions increases the sensitivity of interferometers to a phase shift. This feature is connected with the adiabatic generation of a dark soliton. We analyse the robustness of this phenomenon with respect to thermal fluctuations, due to excited near fields in an electromagnetic surface trap
The Casimir force between metallic plates made of realistic materials is evaluated for distances in the nanometer range. A spectrum over real frequencies is introduced and shows narrow peaks due to surface resonances (plasmon polaritons or phonon polaritons) that are coupled across the vacuum gap. We demonstrate that the Casimir force originates from the attraction (repulsion) due to the corresponding symmetric (antisymmetric) eigenmodes, respectively. This picture is used to derive a simple analytical estimate of the Casimir force at short distances. We recover the result known for Drude metals without absorption and compute the correction for weakly absorbing materials
We propose an optical ring interferometer to observe environment-induced spatial decoherence of massive objects. The object is held in a harmonic trap and scatters light between degenerate modes of a ring cavity. The output signal of the interferometer permits to monitor the spatial width of the object's wave function. It shows oscillations that arise from coherences between energy eigenstates and that reveal the difference between pure spatial decoherence and that coinciding with energy transfer and heating. Our method is designed to work with a wide variety of masses, ranging from the atomic scale to nanofabricated structures. We give a thorough discussion of its experimental feasibility
We discuss the influence of the material type in metal wires to the electromagnetic fluctuations in magnetic microtraps close to the surface of an atom chip. We show that significant reduction of the magnetic noise can be achieved by replacing the pure noble metal wires with their dilute alloys. The alloy composition provides an additional degree of freedom which enables a, controlled reduction of both magnetic noise and resistivity if the atom chip is cooled. In addition, we provide a careful re-analysis of the magnetically induced trap loss observed by Yu-Ju Lin et al. [Phys. Rev. Lett. 92 050404 (2004)] and find good agreement with an improved theory
We investigate the lifetime of magnetically trapped atoms above a planar, layered atom chip structure. Numerical calculations of the thermal magnetic noise spectrum are performed, based on the exact magnetic Green function and multi layer reflection coefficients. We have performed lifetime measurements where the center of a side guide trap is laterally shifted with respect to the current carrying wire using additional bias fields. Comparing the experiment to theory, we find a fair agreement and demonstrate that for a chip whose topmost layer is metallic, the magnetic noise depends essentially on the thickness of that layer, as long as the layers below have a, much smaller conductivity; essentially the same magnetic noise would be obtained with a metallic membrane suspended in vacuum. Based on our theory we give general scaling laws of how to reduce the effect of surface magnetic noise on the trapped atoms
The existing optical microscopes form an image by collecting photons emitted from an object. Here we report on the experimental realization of microscopy without the need for direct optical communication with the sample. To achieve this, we have scanned a single gold nanoparticle acting as a nanoantenna in the near field of a sample and have studied the modification of its intrinsic radiative properties by monitoring its plasmon spectrum
We develop an effective low-frequency theory of the electromagnetic field in equilibrium with thermal objects. The aim is to compute thermal magnetic noise spectra close to metallic microstructures. We focus on the limit where the material response is characterised by the electric conductivity. At the boundary between empty space and metallic microstructures, a large jump occurs in the dielectric function which leads to a partial screening of low-frequency magnetic fields generated by thermal current fluctuations. We resolve a, discrepancy between two approaches used in the past to compute magnetic field noise spectra close to microstructured materials
We establish strict upper limits for the Casimir interaction between multilayered structures of arbitrary dielectric or diamagnetic materials. We discuss the appearance of different power laws due to frequency-dependent material constants. Simple analytical expressions are in good agreement with numerical calculations based on Lifshitz theory. We discuss the improvements required for current ( meta) materials to achieve a repulsive Casimir force
We present a theoretical framework for the analysis of the statistical properties of thermal fluctuations on a lossy transmission line. A quantization scheme of the electrical signals in the transmission line is formulated. We discuss two applications in detail. Noise spectra at finite temperature for voltage and current are shown to deviate significantly from the Johnson-Nyquist limit, and they depend on the position on the transmission line. We analyze the spontaneous emission, at low temperature, of a Rydberg atom and its resonant enhancement due to vacuum fluctuations in a capacitively coupled transmission line. The theory can also be applied to study the performance of microscale and nanoscale devices, including high-resolution sensors and quantum information processors
The coherence length of the thermal electromagnetic field near a planar surface has a minimum value related to the nonlocal dielectric response of the material. We perform two model calculations of the electric energy density and the field's degree of spatial coherence. Above a polar crystal, the lattice constant gives the minimum coherence length. It also gives the upper limit to the near field energy density, cutting off its 1/z(3) divergence. Near an electron plasma described by the semiclassical Lindhard dielectric function, the corresponding length scale is fixed by plasma screening to the Thomas-Fermi length. The electron mean free path, however, sets a larger scale where significant deviations from the local description are visible
We study the spontaneous emission of a single emitter close to a metallic nanoparticle, with the aim to clarify the distance dependence of the radiative and non-radiative decay rates. We derive analytical formulas based on a dipole- dipole model, and show that the nonradiative decay rate follows a R-6 dependence at short distance, where R is the distance between the emitter and the center of the nanoparticle, as in Forster's energy transfer. The distance dependence of the radiative decay rate is more subtle. It is chiefly dominated by a R-3 dependence, a R-6 dependence being visible at plasmon resonance. The latter is a consequence of radiative damping in the effective dipole polarizability of the nanoparticle. The different distance behavior of the radiative and non-radiative decay rates implies that the apparent quantum yield always vanishes at short distance. Moreover, non-radiative decay is strongly enhanced when the emitter radiates at the plasmon-resonance frequency of the nanoparticle.
Le rayonnement électromagnétique produit par un corps à température T est généralement considéré comme l'exemple type du rayonnement incohérent que l'on oppose au rayonnement laser. L'un est quasi isotrope tandis que l'autre est très directionnel, l'un a un large spectre tandis que l'autre est quasi-monochromatique. Aussi surprenant que cela puisse paraître, le rayonnement thermique de bon nombre de corps est cohérent lorsque l'on se place à une distance inférieure à la longueur d'onde de la surface émettrice. Nous verrons que ces effets peuvent être prédits à l'aide d'une approche électromagnétique du rayonnement thermique. Plusieurs expériences récentes ont confirmé ces propriétés inattendues.
Nous évaluons la force de Casimir entre deux surfaces planes métalliques constituées d'argent. Nous prenons, pour effectuer cette évaluation, des propriétés optiques de l'argent à différentes températures [1]. Nous montrons que cette dépendance en température modifie la force de Casimir (de 0.2%) y compris à des distances inférieures à la longueur d'onde thermique.
We present experimental results showing the diffuse reflection of a Bose Einstein condensate from a rough mirror, consisting of a dielectric substrate supporting a blue-detuned evanescent wave. The scattering is anisotropic, more pronounced in the direction of the surface propagation of the evanescent wave. These results agree very well with theoretical predictions.
We compute the local spectrum of the magnetic field near a metallic microstructure at finite temperature. Our main focus is on deviations from a plane-layered geometry for which we review the main properties. Arbitrary geometries are handled with the help of numerical calculations based on surface integral equations. The magnetic noise shows a significant polarization anisotropy above flat wires with finite lateral width, in stark contrast to an infinitely wide wire. Within the limits of a two-dimensional setting, our results provide accurate estimates for loss and dephasing rates in so-called `atom chip traps' based on metallic wires. A simple approximation based on the incoherent summation of local current elements gives qualitative agreement with the numerics, but fails to describe current correlations among neighboring objects.
In this paper we study the role of surface plasmon modes in the Casimir effect. The Casimir energy can be written as a sum over the modes of a real cavity and one may identify two sorts of modes, two evanescent surface plasmon modes and propagative modes. As one of the surface plasmon modes becomes propagative for some choice of parameters we adopt an adiabatic mode definition where we follow this mode into the propagative sector and count it together with the surface plasmon contribution, calling this contribution ``plasmonic''. We evaluate analytically the contribution of the plasmonic modes to the Casimir energy. Surprisingly we find that this becomes repulsive for intermediate and large mirror separations. The contribution of surface plasmons to the Casimir energy plays a fundamental role not only at short but also at large distances. This suggests possibilities to taylor the Casimir force via a manipulation of the surface plasmon properties.
Coherent thermal radiation
(2007)
The radiation emitted by a heated body is generally quoted as a typical example of incoherent radiation, in distinction to laser radiation. One is nearly isotropic, the other highly directional; one is spectrally broad, the other quasi-monochromatic. It may come as a surprise that the thermal radiation of a large number of substances is coherent, both in space and time, when it is observed at a distance from the body that is shorter than the wavelength. This behaviour can be understood within an electromagnetic approach to thermal emission. Several recent experiments have confirmed these unexpected properties.
We discuss the laser theory for a single-mode laser with nonlinear gain. We focus in particular on a micromaser which is pumped with a dilute beam of excited atoms crossing the laser cavity. In the weak-coupling regime, an expansion in the coupling strength is developed that preserves the Lindblad form of the master equation, securing the positivity of the density matrix. This can be improved with an alternative approach, not restricted to weak coupling: the Lindblad operators are expanded in orthogonal polynomials adapted to the probability distribution for the atom-laser interaction time. Results for the photon statistics and the laser linewidth illustrate the theory.
Superconductors are considered in view of applications to atom chip devices. The main features of magnetic traps based on superconducting wires in the Meissner and mixed states are discussed. The former state may mainly be interesting for improved atom optics, while in the latter, cold atoms may provide a probe of superconductor phenomena. The properties of a magnetic side guide based on a single superconducting strip wire placed in an external magnetic field are calculated analytically and numerically. In the mixed state of type II superconductors, inhomogeneous trapped magnetic flux, relaxation processes and noise caused by vortex motion are posing specific challenges for atom trapping.
We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps, we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studies and the analysis of all important elements, relevant for the experimental stage. On the theoretical side, we discuss different methods to couple electron qubits. We estimate the relevant qubit coherence times and draw implications for the experimental setting. A critical assessment of quantum information processing with trapped electrons concludes the paper.
We study the quantum and thermal fluctuations of eddy (Foucault) currents in thick metallic plates. A Casimir interaction between two plates arises from the coupling via quasistatic magnetic fields. As a function of distance, the relevant eddy current modes cross over from a quantum to a thermal regime. These modes alone reproduce previously discussed thermal anomalies of the electromagnetic Casimir interaction between good conductors. In particular, they provide a physical picture for the Casimir entropy whose nonzero value at zero temperature arises from a correlated, glassy state.
Considering the Casimir effect due to phononic excitations of a weakly interacting dilute Bose-Einstein condensate ( BEC), we derive a renormalized expression for the zero-temperature Casimir energy E-C of a BEC confined to a parallel plate geometry with periodic boundary conditions. Our expression is formally equivalent to the free energy of a bosonic field at finite temperature, with a nontrivial density of modes that we compute analytically. As a function of the interaction strength, E-C smoothly describes the transition from the weakly interacting Bogoliubov regime to the non- interacting ideal BEC. For the weakly interacting case, E-C reduces to leading order to the Casimir energy due to zero- point fluctuations of massless phonon modes. In the limit of an ideal Bose gas, our result correctly describes the Casimir energy going to zero.
We characterize the entanglement in position and momentum of photon pairs generated in type-II parametric down- conversion. Coincidence maps of the photon positions in the near-field and far-field planes are observed in two transverse dimensions using scanning fiber probes. We estimate the covariance matrix of an effective two-mode system and apply criteria for entanglement based on covariance matrices to certify space-momentum entanglement. The role of higher- order spatial modes for observing spatial entanglement between the two photons is discussed.
We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and ac conductivity of a homogeneous superconductor with an arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers-Kronig transforms. A number of applications illustrate its efficiency: a simplified low-frequency expansion of the conductivity, the electromagnetic bulk self-energy due to longitudinal plasma oscillations, and the Casimir free energy of a superconducting cavity.
We investigate the role of surface plasmons in the electromagnetic Casimir effect at finite temperature, including situations out of global thermal equilibrium. The free energy is calculated analytically and expanded for different regimes of distances and temperatures. Similar to the zero-temperature case, the interaction changes from attraction to repulsion with distance. Thermal effects are shown to be negligible for small plate separations and at room temperature but become dominant and repulsive at large values of these parameters. In configurations out of global thermal equilibrium, we show that the selective excitation of surface plasmons can create a repulsive Casimir force between metal plates.