The magnesium ramsey interferometer: Applications and prospects

In this paper it will be shown that an atom interferometer, based on the coherent splitting of the atomic wavefunction by four travelling waves (Ramsey interferometer), may be explained by a purely mechanical interpretation. As our first application of this Ramsey interferometer we have measured the phase shifts respectively optical length changes in a magnesium atomic beam caused by the acceleration of the partial atomic wave in one arm of the interferometer. This acceleration was achieved by the dipole force exerted by an off-resonant crossing laser beam which interacted with the ground state part of the wavefunction only. Further applications of this interferometer and improvements due to laser cooling will be discussed.     

Interferometry with Ca atoms

Separated field excitation of a calcium atomic beam using four traveling laser fields represents two distinct atom interferometers utilizing the internal degrees of freedom of the atoms. Phase shifts between the atomic partial waves have been realized by phase shifts of the laser wave fields, by the ac-Stark shift, and by rotation of the interferometer (Sagnac effect). One particular interferometer can be selected by interaction of the atomic waves with extra laser fields. We furthermore report on the preparation of a laser cooled and deflected calcium atomic beam that can be utilized to largely increase the sensitivity of the interferometer.     

Measure of the tunnelling time of a single photon through a Fabry-Perot cavity

The displacement of the peak of a wavepacket that crosses an empty Fabry-Perot cavity is measured by using photon pairs generated by parametric down conversion, a Hong-Ou-Mandel (HOM) interferometer and coincidence detection. The Fabry-Perot cavity distorts the photon wavepacket. The HOM interferometer is a good tool to map this distortion. We discuss the corrections which must be made in the two-photon inteference results, in order to achieve the true data researched. Even in the absence of active absorbers media or media with inverted atomic populations, superluminal-like effects connected with the tunnelling phenomena are observed. An interpretation of the experimental results in the causality frame is given.     

Step-selective measurement by grating-based lateral shearing interferometry for segmented telescopes

We present an original step-selective mode which allows to measure only the steps and not the slowly varying aberrations of a wave front. This mode can be implemented when measuring segmented wave front by a diffraction-grating-based lateral shearing interferometer. This set-up rests on the different chromatic response of these interferometers depending on the rate of change of the impinging wave front: for smooth defects, the response is classically achromatic whereas it is chromatic for a step variation, which was to our knowledge overlooked. The interest of this mode for astronomical measurements is highlighted. First we present theoretical considerations to show how this mode of measure is possible; then a numerical simulation illustrates them.     

Atom interferometry measurement of the electric polarizability of lithium

Using an atom interferometer, we have measured the static electric polarizability of ⁷Li α=(24.33 ±0.16)×10^-30 m³ = 164.2±1.1 atomic units with a 0.66% uncertainty. Our experiment, which is similar to an experiment done on sodium in 1995 by Pritchard and co-workers, consists in applying an electric field on one of the two interfering beams and measuring the resulting phase-shift. With respect to Pritchard's experiment, we have made several improvements which are described in detail in this paper: the capacitor design is such that the electric field can be calculated analytically; the phase sensitivity of our interferometer is substantially better, near 16 mrad/ ; finally our interferometer is species selective so that impurities present in our atomic beam (other alkali atoms or lithium dimers) do not perturb our measurement. The extreme sensitivity of atom interferometry is well illustrated by our experiment: our measurement amounts to measuring a slight increase Δv of the atom velocity v when it enters the electric field region and our present sensitivity is sufficient to detect a variation Δv/v ≈6 ×10^-13.     

Compact and portable holographic camera using photorefractive crystals. Application in various metrological problems

We present a compact holographic interferometer that uses a photorefractive crystal of the sillenite family as a holographic recording medium. Its development is based on a previous prototype that showed lack of flexibility and portability. We briefly discuss the main improvements leading to a compact device. Applications of this instrument in various metrological problems are shown, among which are two that were not already considered using holography, namely measurement of a thermal expansion coefficient and detection of fingerprints. Received: 20 December 2000 / Revised version: 8 February 2001 / Published online: 20 April 2001     

Atom interferometers manipulated through the toroidal trap realized by the interference patterns of Laguerre-Gaussian beams

In this paper, we proposed new constructions of atom interferometers manipulated through the toroidal trap formed by the interference patterns of two co-propagation Laguerre-Gaussian (LG) beams. The coherent splitting and merging of the atomic ensemble, which is essential for the atom interferometer, is realized by the interference pattern of two LG beams. Along the beam propagation direction, a single-well trap is evolved into a double-well trap and then recombined back into a single-well trap, which can be used to form an atom interferometer.     

Density-density correlation of ultracold atomic gases released from a series of attractive potentials

The purpose of this paper is to explore the density-density correlation for the ultracold atomic gases released from a series of attractive potentials. It is found that the interference fringes in the density-density correlation reflect in a unique way the arrangement of these attractive potentials, which is similar to the Hanbury-Brown-Twiss stellar interferometer. To clearly show this, after a general theoretical study, we study in detail the situations for a series of attractive potentials arranged along the circumferences of an ellipse and a circle. An experimental scheme to observe this theoretical predication is discussed.     

Theoretical analysis of a large momentum beamsplitter using Bloch oscillations

In this paper, we present the implementation of Bloch oscillations in an atomic interferometer to increase the separation of the two interfering paths. A numerical model, in very good agreement with the experiment, is developed. The contrast of the interferometer and its sensitivity to phase fluctuations and to intensity fluctuations are also calculated. We demonstrate that the sensitivity to phase fluctuations can be significantly reduced by using a suitable arrangement of Bloch oscillations pulses.     

Optical pumping and modulation techniques with a molecular Ramsey–Bordé interferometer

Using the example of a matter-wave interferometer with K₂ molecules, we present different methods to simplify the observed interference structures within a hyperfine pattern for improving phase measurements of the interference structure. We consider optical pumping for depletion of specific components to simplify the observed spectra. In connection with a lock-in amplifier, amplitude modulation as well as frequency modulation of laser beams in the interferometer are investigated for better detection of the interference pattern. As a follow-up treatment, digital filtering is demonstrated. Received: 22 December 2000 / Revised version: 30 April 2001 / Published online: 18 July 2001     

Atom interferometry based on light pulses: Application to the high precision measurement of the ratio <Emphasis Type="Italic">h</Emphasis>/<Emphasis Type="Italic">m</Emphasis> and the determination of the fine structure constant

In this paper we present a short overview of atom interferometry based on light pulses. We discuss different implementations and their applications for high precision measurements. We will focus on the determination of the ratio h/m of the Planck constant to an atomic mass. The measurement of this quantity is performed by combining Bloch oscillations of atoms in a moving optical lattice with a Ramsey-Bordé interferometer.     

Direct measurement of dispersion of the group refractive indices of quartz crystal by white-light spectral interferometry

We present a white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the dispersion of the ordinary and extraordinary group refractive indices of a quartz crystal over the wavelength range approximately from 480 to 860 nm. The technique utilizes a dispersive Michelson interferometer with the quartz crystal of known thickness to record a series of spectral interferograms and to measure the equalization wavelength as a function of the displacement of the interferometer mirror from the reference position, which corresponds to a balanced non-dispersive Michelson interferometer. We confirm that the measured group dispersion agrees well with that described by the dispersion equation proposed by Ghosh. We also show that the measured mirror displacement depends, in accordance with the theory, linearly on the theoretical group refractive index and that the slope of the corresponding straight line gives precisely the thickness of the quartz crystal.     

Rashba interferometers: Spin-dependent single- and two-electron interference

Quantum transport in semiconductor nanostructures can be described theoretically in terms of the propagation and scattering of electron probability waves. Within this approach, elements of a phase-coherent electric circuit play a role similar to quantum-optical devices that can be characterised by scattering matrices. Electronic analogues of well-know optical interferometers have been fabricated and used to study special features of charge carriers in solids. We present results from our theoretical investigation into the interplay between spin precession and quantum interference in an electronic Mach-Zehnder interferometer with spin-orbit coupling of the Rashba type. Intriguing spin-dependent transport effects occur, which can be the basis for novel spintronic devices such as a magnet-less spin-controlled field-effect transistor and a variety of single-qubit gates. Their functionality arises entirely from spin-dependent interference of each single-input electron with itself. We have also studied two-electron interference effects for the spin-dependent Mach-Zehnder interferometer, obtaining analytical expressions for its two-fermion-state scattering matrix. Using this result, we consider ways to generate two-electron output states for which the Rashba spin-subband quantum number and the output arm index are entangled. Combining spin-dependent interference in our proposed Mach-Zehnder interferometer with a projective charge measurement at the output enables entanglement generation. As our particular scheme involves tuneable spin precession, electric-field control of entanglement production can be achieved.     

Multiple atomic wave interferometry with standing-waves of light

Fringe shapes in a multiple-beam de Broglie-wave interferometer based on the atomic Kapitza-Dirac effect are studied. An all-optical implementation of such a device is proposed. A realization in the time-domain, using Bose-Einstein condensates released from a trap, seems viable within the present state of the art. Received 5 April 2000 and Received in final form 14 July 2000     

Topological phase shift in a cold-atom interferometer

Matter-wave interferences in a four-pulse version of a Ramsey-Bordé atom interferometer have been utilized to study phase shifts. A topological phase shift analogous to the scalar Aharonov-Bohm effect proposed for charged-particle interferences in the presence of a pulsed electrostatic potential has been investigated. The time-dependent potential has been generated by the interaction of a laser field with an induced atomic dipole without spatial variation along the interferometer arms. The atom interferometer has been run with laser-cooled magnesium atoms stored in a magneto-optical trap.Dedicated to H. Walther on the occasion of his 60th birthday     

A calibrated atomic force microscope using an orthogonal scanner and a calibrated laser interferometer

A compact and two-dimensional atomic force microscope (AFM) using an orthogonal sample scanner, a calibrated homodyne laser interferometer and a commercial AFM head was developed for use in the nano-metrology field. The x and y position of the sample with respect to the tip are acquired by using the laser interferometer in the open-loop state, when each z data point of the AFM head is taken. The sample scanner, which has a motion amplifying mechanism was designed to move a sample up to 100 μm × 100 μm in orthogonal way, which means less crosstalk between axes. Moreover, the rotational errors between axes are measured to ensure the accuracy of the calibrated AFM within the full scanning range. The conventional homodyne laser interferometer was used to measure the x and y displacements of the sample and compensated via an X-ray interferometer to reduce the nonlinearity of the optical interferometer. The repeatability of the calibrated AFM was measured to sub-nanometers within a few hundred nanometers scanning range.     

Adaptive interferometers with no external field using reflection gratings in CdTe:Ge at 1550 nm

We demonstrate experimentally the operation of an adaptive two-wave mixing interferometer with no field applied to a photorefractive crystal in which the quadrature condition is introduced by an external π/2 phase step. To achieve high signal to noise ratio the counter-propagating geometry for grating recording is used with a CdTe:Ge crystal, ensuring effective recording of reflection holograms. It is demonstrated that the interferometer with a photorefractive semiconductor crystal provides good sensitivity without the adverse effects that are normally associated with an applied field.     

Initial wavefunction dependence on atom interferometry phases

In this paper we present a mathematical procedure to analytically calculate the output signal of a pulsed atom interferometer in an inertial field. Using the well-known ABCDξ method we take into account the full wave dynamics of the atoms with a first order treatment of the wavefront distortion by the laser pulses. Using a numerical example we study the effect of both the length of the beam splitting laser pulses and of the width of the initial spatial distribution of the atoms. First, we find that in a general inertial field the interferometer only has a limited window in terms of the initial width (centered around 100 μm in the example calculation) in which interference fringes are visible at all. This effect is caused by the inevitable statistical spread in atomic parameters, such as initial position and momentum, and the dependence of the interferometer phase on these. In the optimum case, the useful range of the initial width is formed by the range in which both the spatial distribution and the diffraction limited momentum spread are small enough to avoid large phase differences over the atomic wavefunction. As a second result we find that the interferometer phase depends strongly on the length of the laser pulses and, to a smaller extent, on the initial width of the atomic cloud. This spatial dependency is relatively small (～10^?5 rad) and justifies semiclassical approximations, as used in other calculations, for most experiments. New high-accuracy experiments, however, will come in the range where this effect is no longer negligible.     

Multi-color XUV interferometry using high-order harmonics

We present a novel interferometric setup operating in the XUV spectral range. The interferometer consists of a combination of a double pinhole (similar to Young’s double slit) and a transmission grating. In the case of a light source consisting of discrete spectral lines, it allows recording interferograms for multi-colors simultaneously. We present two experiments in which high-order harmonics generated by a titanium sapphire laser were used as the light source for the interferometer. First, the temporal coherence lengths of the single harmonics were determined, and second, the index of refraction and the absorption of a thin beryllium foil were measured simultaneously in the range of 17–25 nm.     

Single-mode hollow optical fibres for atom guiding

We present a novel design for a single-mode, hollow optical fibre, which is suitable for use as a waveguide for atomic de Broglie waves. The design, development and characterisation of such a fibre are discussed, as well as an optimised method for coupling light into the fibre. Received: 22 May 2001 / Revised version: 5 September 2001 / Published online: 29 November 2001