Polarizabilities of rubidium (9-10)S 1/2 and 8D 3/2, 5/2 states

Polarizabilities of several rubidium states were determined by measuring stark shifts of transitions using an electro-optically modulated laser beam to excite an atomic beam. The voltage required for atoms excited by the laser beam in an electric field to be simultaneously in resonance as atoms excited by a frequency sideband of the laser in a field free region was measured. The scalar α and tensor α ₂ polarizabilities were found to be: α (9 S _1/2 ) = 103.77±0.09, α (10 S _1/2 ) = 272.54±0.16, α (8 D _3/2 ) = 230.68±0.25 and α ₂ (8 D _3/2 ) = 26.55±0.10, α (8 D _5/2 ) = 222.68±0.14 and α ₂ (8 D _5/2 ) = 51.91±0.10 MHz/(kV/cm)². The results are 100 times more accurate than previous measurements and are within 1% of those found theoretically using a Coulomb approximation calculation. Received 7 September 2000 and Received in final form 6 December 2000     

Interaction of a supersonic beam of toluene with a resonant RF electric field

Deflection of a cold supersonic toluene beam seeded in He has been observed when these molecules interact with both a static and a resonant oscillating electric field. The toluene beam splits into two beams each one peaking at a deflection angle of 1 degree towards the positive and negative direction of the Stark field when the employed resonant frequency between the two Stark levels of the toluene molecule is 1411 kHz. This deflection angle is about four orders of magnitude higher than the value one would expect from the toluene dipole moment and the employed RF field gradient. Different hypothesis are suggested to explain the observed strong beam splitting including the possibility of transverse beam interferences induced by both the resonant RF field and the transverse uniform electric field. A theoretical model is presented based on molecular beam interferences induced by the resonant RF field which seems to account satisfactorily for the present observations.     

Interaction of polar molecules with a resonant RF electric field: strong deflection of a NO molecular beam

Deflection of a cold supersonic NO beam seeded in He has been observed when these molecules interact with both static and a resonant oscillating electric field. The NO beam splits into two beams each one deflecting about 0.5° towards the positive and negative direction of the Stark field when the employed resonant frequency between the two Stark levels of the NO molecule is 1515 kHz. This deflection angle is about four orders of magnitude higher than the value one would expect from the NO dipole moment and the employed RF field gradient. This phenomenon suggests the possibility of a significant translational motion perpendicular to the beam axis, which is induced by the resonant RF electric field on the cold and high-density supersonic beam.     

Alignment-orientation conversion in molecules in an external magnetic field caused by a hyperfine structure

The paper presents a discussion on the problem of alignment-orientation conversion in an excited state of molecules. It is shown that a rather strong alignment-orientation conversion effect in the excited molecular state can be caused by a joint action of an external magnetic field and hyperfine interaction. The orientation thus created is transverse, i.e. perpendicular to the direction of the external magnetic field. The magnitude of this effect is analyzed as dependent on molecular parameters. Received 15 July 1999 and Received in final form 17 November 1999     

Precise - and -factor measurements of Ba+ isotopes

Laser-microwave double and triple resonance experiments were performed on clouds of Ba⁺ ions confined in a Penning ion trap to induce and detect electronic and nuclear spin flip transitions. Collisions with buffer gas molecules in the trap was used to reduce the lifetime of a long lived metastable state of the ions, in which population trapping might occur, and to cool the ions to the ambient temperature. Loss of ions from the trap by collisions were prevented by coupling the magnetron and reduced cyclotron motions by an additional r.f. field at the sum frequency of the two motions. Electronic Zeeman transitions in ¹³⁸Ba⁺ and ¹³⁵Ba⁺ were observed at a full width of about 3 kHz at a transition frequency of 80 GHz. The uncertainty of the line center was . From the magnetic field calibration by the cyclotron resonance of electrons stored in the same trap the g_J-factor for both isotopes could be determined to . From radiofrequency induced transitions of ¹³⁵Ba⁺ the nuclear g-factor could be determined . Both measurements improve earlier results by about one order of magnitude. Received: 9 July 1998 / Accepted: 14 July 1998     

Light-pulse atom interferometry in microgravity

We describe the operation of a light pulse interferometer using cold ⁸⁷Rb atoms in reduced gravity. Using a series of two Raman transitions induced by light pulses, we have obtained Ramsey fringes in the low gravity environment achieved during parabolic flights. With our compact apparatus, we have operated in a regime which is not accessible on ground. In the much lower gravity environment and lower vibration level of a satellite, our cold atom interferometer could measure accelerations with a sensitivity orders of magnitude better than the best ground based accelerometers and close to proven spaced-based ones.     

Magnetic trapping of strongly-magnetized Rydberg atoms

Effective magnetic moments of drift Rydberg atoms in strong magnetic fields are obtained for different energy and angular-momentum states. Classical two-body trajectory calculations and quantum-mechanical one-body calculations are employed. For heavy atoms such as rubidium, the trapping dynamics can largely be explained by the net magnetic moment due to the cyclotron and the magnetron motion of the Rydberg electron. In light Rydberg atoms such as hydrogen, the intrinsic two-body nature of the dynamics becomes manifest in that the ionic motion significantly contributes to the effective magnetic moment. Also, light drift Rydberg atoms exhibit an anisotropic response to field-inhomogeneities parallel and transverse to the magnetic-field lines. The results are relevant to magnetic trapping of Rydberg atoms in strong-magnetic-field atom traps.     

Demonstration of a Sagnac-Type Cold Atom Interferometer with Stimulated Raman Transitions

Cbld-matter-wave Sagnac interferometers possess many advantages over their thermal atomic beam counterparts when they are used as precise inertial sensors. We report a realization of a Sagnac-type interferometer with cold atoms. Cold rubidium atoms are prepared in a magneto-optical trap and are pushed by resonant laser pulse to form slow atomic beam. In the interference region, atomic wave packets are coherently manipulated using π/2 -π - π/2 Raman pulse sequences. Interference fringes with maximum contrast of 37% are observed experimentally.     

Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G

We developed a gravity-gradiometer based on atom interferometry for the determination of the Newtonian gravitational constant G. The apparatus, combining a Rb fountain, Raman interferometry and a juggling scheme for fast launch of two atomic clouds, was specifically designed to reduce possible systematic effects. We present instrument performances and preliminary results for the measurement of G with a relative uncertainty of 1%. A discussion of projected accuracy for G measurement using this new scheme shows that the results of the experiment will be significant to discriminate between previous inconsistent values.     

Atomic reflection from a magnetic mirror: Beyond the adiabatic approximation

We present theoretical calculations for the reflection of atoms from a magnetic surface with a sinusoidal magnetization. A fully quantum mechanical treatment is possible because the problem may be reduced to an effective one-dimensional one. Results of numerical wave-packet calculations are presented and compared with an analytical model in which the atoms separate into different internal state components which follow classical paths in different potentials. Received 21 October 1999 and Received in final form 18 January 2000     

Stark shifts and fine structure of the Li 3 D states

⁶Li 3²D _{3/2, 5/2} states were studied using a diode laser to first excite the 2P _3/2 state and a dye laser to populate the 3²D _{3/2, 5/2} states. The dye laser was modulated by an electro-optic modulator and intersected an atomic beam that passed through a field free region and subsequently through a uniform electric field. A value of 1084.24±0.20 MHz was found for the 3²D fine structure splitting. The scalar and tensor polarizabilities were determined to be α (3D _3/2 ) = - 3.753±0.015, α ₂ (3D _3/2 ) = 2.893±0.017, α (3D _5/2 ) = - 3.772±0.008 and α ₂ (3D _5/2 ) = 4.058±0.013 MHz/(kV/cm)². Received 26 September 2002 / Received in final form 22 January 2003 Published online 11 March 2003 RID="a" ID="a"e-mail: wlaser@yorku.ca     

Measurement of the three-dimensional velocity distribution of Stark-decelerated Rydberg atoms

The full three-dimensional velocity distributions of decelerated and accelerated particles in a Stark decelerator for Rydberg atoms and molecules have been measured. In the experiment, argon atoms in a supersonic beam are excited to low-field and high-field seeking Stark states with principal quantum number in the range n=15 to 25 and are decelerated in a 3 mm long decelerator consisting of four electrodes on which time-dependent voltages are applied. The time dependence of the resulting inhomogeneous electric field is chosen such that the decelerating force acting on the high-field seeking states is maximized at each point along the trajectories. The three-dimensional velocity distribution of the atoms before and after the deceleration is determined by measuring times of flight and two-dimensional images of the atomic cloud on the detector. Under optimal deceleration conditions, the decrease in kinetic energy in the longitudinal dimension amounts to 1.0×10^-21 J and the increase in mean kinetic energy in the transverse dimensions is only 1.0×10^-23 J. The corresponding temperatures of 100 mK and 300 mK in the two transverse dimensions are sufficiently low that trapping can be envisaged. The possibility of focusing a Rydberg atom beam is demonstrated experimentally.     

Net polarization of a molecular beam by strong electrostatic or radiative fields

We present a simple analytic approximation for evaluating the ensemble-averaged orientation or alignment of a beam of molecules subjected to a strong static or radiative field. This approximation is based on the eigenproperties which polar or polarizable molecules exhibit in the strong-field, harmonic-librator limit, and on the Boltzmann statistics of the free rotor states which adiabatically correlate with the harmonic librator states. For either the permanent or induced dipole case, the resultant formula involves just two dimensionless parameters which characterize the strength of the molecule-field interaction and the rotational temperature. The net polarization of a molecular beam thus obtained is shown to be in an excellent agreement with the exact values computed numerically from first principles. The validity range of the approximation includes the large-interaction, high temperature regions of the parameter space where first-principle calculations are onerous.     

Stern Gerlach interferometry with metastable argon atoms: an immaterial mask modulating the profile of a supersonic beam

A new Stern Gerlach interferometer operating with a nozzle beam of metastable argon atoms Ar^* (3p⁵ 4s, ³ P ₂) is described. The selection of incoming (polarisation) and outgoing (analysis) Zeeman sublevels is achieved by use of laser induced transitions at two wavelengths, 811.5 nm (closed J = 2 → J = 3 transition) and 801.5 nm (open J = 2 → J = 2 transition). Linear superpositions of Zeeman sublevels, just beyond the polariser and just before the analyser, are prepared by means of two zones where Majorana transitions take place. In between, a controlled magnetic field configuration (the phase object) is produced within a triple μ-metal shielding. Standard interference patterns are obtained by scanning the field and detecting the atoms by secondary electron emission from a Faraday cup. When a static radial magnetic gradient is used, the beam profile is modulated by interference. The transverse pattern, which can be translated at will by adding a homogeneous field, is observed for the first time using a multi-channel electron multiplier followed by a phosphor screen and a CCD camera. The results satisfactorily agree with all theoretical predictions. Received 27 June 2002 / Received in final form 20 September 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: perales@lpl.univ-paris13.fr RID="b" ID="b"UMR 7538 du CNRS     

Interferometry with entangled atoms

A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser beam. The laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two, motion-sensitive, phase shifts, which allow the measurement of the average acceleration of each ensemble, and, via simple differencing, of the acceleration gradient. Here we propose entangling the quantum states of atoms from the two ensembles prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase which can be measured directly, with no need for differencing. Received 6 June 2002 / Received in final form 25 October 2002 Published online 28 January 2003     

Photodetachment of H- in a static electric field

We derive a formula using closed-orbit theory for the photodetachment cross-section of H^- in the presence of a static electric field when there is an arbitrary angle θ_L between the laser polarization direction and the static electric field. This formula generalizes the previous result for laser polarization parallel to the static electric field, the effect of laser polarization direction appears as a factor cos²(θ_L) in the amplitude of the oscillation. A photodetachment cross-section formula valid above and below detachment threshold is proposed.     

Non perturbative approach for a polar and polarizable linear molecule in an inhomogeneous electric field: Application to molecular beam deviation experiments

A non perturbative approach is used to solve the problem of a rigid linear molecule with both a permanent dipole moment and a static dipole polarizability, in a static electric field. Eigenenergies are obtained and compared to perturbative low field and high field approximations. Analytical expressions for the orientation parameters and for the gradient of the energy are given. This non perturbative approach is applied to the simulation of beam deviation experiments in strong electric field. Results of simulations are given for inhomogeneous alkali dimers. For LiNa, the simulations are compared to experimental data. For LiK, deviation profiles have been simulated in order to prepare future experiments on this molecule. Received 21 July 1999 and Received in final form 22 September 1999     

Photoionization of atoms in parallel electric and magnetic fields: Cross-section calculations using the Lanczos algorithm and the complex coordinate method in a discrete variable representation

A combination of the complex-coordinate method and the Lanczos recursion scheme is implemented in the discrete variable representation (DVR) to obtain total photoionization cross-sections using an iterative procedure. Applications to photoionization of hydrogen atoms in electric fields and sodium atoms in electric and parallel electric and magnetic fields are presented and discussed. Received 15 May 2000 and Received in final form 4 October 2000     

On the interaction of a beam of polar molecules with a static and a resonant RF field as a source of molecular interferences

A molecular beam interference model is presented based on a two-state interaction between a polar molecule and a resonant RF field as it occurs in the so-called C-field of a typical molecular beam electric resonant spectrometer. The treatment shows the onset of interferences in the beam transmission spectra as well as in its transverse profile. It is demonstrated how the molecular interferences are originated by the wavefunction phase shift introduced by the resonant RF field. Furthermore it is shown that for a given beam velocity and oscillating field frequency the fringes’ visibility depends on the strength of the RF field, i.e. the Rabi frequency, in the transmission spectra. Likewise the presence of a RF field gradient in the perpendicular beam direction gives rise to a peak structure in the transverse beam profile. The theoretical model was applied to simulate a variety of beam transmission spectra under resonant conditions as well as some experimental data already published by our group showing a satisfactory agreement between experimental and simulated data. Finally, the potentiality of this internal state molecular interferometer to carry out studies in matter-wave interferometry is remarked.     

Bright optical lattices in a longitudinal magnetic field. Experimental study of the oscillating and jumping regimes

All the bright optical lattices studied so far have been designed to obtain a circularly polarized light at the bottom of the optical potential wells. This condition minimizes the departure rate of the atoms from the fundamental adiabatic surface and permits an oscillating regime in a large range of parameters. We present here an experimental study of cesium atoms in a three-dimensional optical lattice, where the light is linearly polarized at the bottom of the potential wells. Temperature measurements and pump-probe spectroscopy give similar results for this lattice and for the conventional lin lin lattice (which have circular polarizations at the bottom of the wells) despite the fact that one lattice operates in the jumping regime and the other in the oscillating regime. We study the behaviour of the two types of lattices in a longitudinal magnetic field, with particular emphasis on the zero field and strong field regimes. The strong field situation is very simple because the eigenstates are then almost pure Zeeman substates and the adiabatic and diabatic potential surfaces are identical. The comparison between the zero-field and the high-field situations shows that the diabatic potentials are more appropriate to account for experimental observations in the novel lattice. Received: 9 October 1997 / Accepted: 6 November 1997