Parity violation detection in a cesium cell: strategy and preliminary results

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Parity violation detection in a cesium cell: strategy and preliminary results

In this chapter we describe the Paris experiment setup with its latest modifications, which should allow to measure the atomic Parity Violation (PV) of Cesium in a vapour cell with high precision: the ultimate purpose is to reduce to 1% the error on the final result. We report our experimental advances, which consented to perform a first measurement of the parity violation detected by stimulated emission, with a 8.4% relative statistical precision [24]. This preliminary result demonstrates the validity of this new method, and outlines the road map to reach the 1% precise experimental PV value.

Principle

As we have already seen, this experiment, performed on the 6S1/2-7S1/2-6P3/2 tran-sition in a dense cesium vapour, is of the pump-probe kind. The way to reach the pump energy necessary to achieve a significant amplification of the probe laser is to operate in a pulse mode. The applied longitudinal electric field makes the transition slightly allowed, in addition it provides a valuable signature for the PV detection.

Experimental setup

The lasers
The probe laser @1.47 µm This laser is used to probe the 7S1/2 → 6P3/2 transition, after pumping from 6S1/2 to 7S1/2 with our pulsed green laser @539 nm. It is a color-center laser (NaCl crystal doped with OH−, irradiated by UV light), pumped by a Nd:YAG. Usually we have about 100 mW continuous power, single mode radiation, with a jitter reduced to 1 MHz thanks to a short term stabilization on an external Fabry-Perot cavity.
A dedicated servo-lock system with a separate Cesium cell allows to stabilize the laser on the hyperfine atomic lines. In practice we always use the F =4→F =4 or the F =4→F =5 transitions, for reasons developed in the next paragraphs (2.1.2 and 2.1.3). The efficiency of the stabilization is of the order of a few megahertz.
In order to obtain short-time 20 ns square pulses from this continuous laser, the probe beam is gated by a very fast (sub ns) optical switch (LiNbO3 electro-optic modulator), which is driven by low voltage (about 15 V) pulses. The 20 ns value comes from the importance to restrict our detection to the lifetime of the 7S excited state, during which there is amplification of the probe1. The extinction ratio is better than 10−3, whereas the transmission when the switch is open is 8%. The number of photons detected at each outgoing pulse is about 5 × 107 in typical conditions.
The excitation laser @539 nm
In order to produce a 539 nm continuous-wave light beam, we use a tunable ring dye laser (Rhodamine 560) pumped by an Ar+ laser @514 nm. The dye laser system can produce 200 mW continuous single-mode radiation with a jitter below 1 MHz. This beam is then amplified in a pulsed mode by three dye cells (Coumarine 540) pumped by UV pulses, delivered by a XeCl excimer laser. By this way we obtain 15 ns long pulses @539 nm, with an energy of typically 1.5-2 mJ, in the range 90-200 Hz. Due to the appearance of geometrical instabilities, it was not possible during this thesis work to operate at more than 150 Hz2. The spectral bandwidth of the pulses is close to the Fourier transform limit (30 MHz FWHM).
The polarizations
In the fig. 2.1 it is possible to see the essential optical elements of the heart of the PV experiment. The polarization of the incoming beams is first defined by two Glan prisms, one for each beam. Then, a set of switchable half-wave plates allows to rotate the excitation and probe polarizations by 45◦, 90◦ or 135◦, before and after the passage in the cell. We will see that this feature is very useful to check the rotational symmetry of our apparatus.
It is possible to insert a quarter-wave plate into the path of each beam in order to produce circular polarization, which can be useful for some control measurements.
A Faraday rotator is used to perform tiny polarization tilts of the incoming exci-tation light. We will see that this is essential for the calibration of the PV effect.
Whole-wave plates with adjustable orientation compensate the birefringence pro-duced on the path of the beam, essentially by the entrance cell window, and so cancel the helicity of the beams inside the cell.
The electric field
In order to assist the forbidden excitation transition 6S → 7S, we apply a longitudi-nal electric field. The use of a cell made of alumina, a dielectric insulating material, made it possible to use external electrodes to apply the field. The set of eleven annular electrodes is inserted inside an “internal” oven which is used to hold and heat the body of the cell (see fig. 2.2) [27].
A numerical simulation was performed by M.A. Bouchiat for the field map. Fig. 2.3 represents the equipotential lines of the field calculated on a 600 × 600 points grid for a quarter of the cell. The sapphire ring extends the alumina tube over the window and makes the electric field more homogeneous near the end of the cell. The variation of Ez along the axis of the cell does not exceed one percent; all over the interaction region, the standard deviation of Ez is 3 × 10−4 and the standard deviation of the radial field is 8 × 10−4.
The electric field in the cell cannot be kept for too long, in order not to create discharges in the vapour. Hence, we have to use a pulsed high voltage (HV) (τ < 0.2 µs) which is applied by a system formed by a HV supply (10 kV maximum), two HV switches for the two ends of the cell and two decoupling capacities. A resistance bridge distributes the voltage over the eleven annular electrodes, the central one being connected to ground. By this way we can produce trapezoidal pulses of both signs, with a constant amplitude plateau over a time much longer than the duration of the laser pulses (usually 150 ns), so that the electric field can be considered static for the excitation process.
During the measurements, we use to apply ±8100 V, which, according to the sim-ulation, correspond to an electric field of about 1730 V/cm.
Moreover, in E. Jahier’s thesis [28], a procedure was developed which allows to calibrate the E field seen by the atoms thanks to atomic signals analysis (para-graph 2.3.5). The typical 5% difference with respect to the previous nominal value comes from the appearance of a space charge in the cell (cf. next paragraph).
The cell
As we already said, our experiment is performed on a cesium vapour contained in a cylindrical cell, 8 cm long (see fig. 2.4). The advantage with respect to an atomic beam or a trap is the high atomic density and the high number of atoms interacting with the lasers. The typical atomic density in our cell is 2 × 1014 atoms/cm 3, i.e. 2×1013 atoms in the interaction region. About 1012 atoms have such a velocity to be resonant on their 6S-7S transition with the excitation pulsed beam (30 MHz spectral width). At this density the 7S state is nearly unperturbed by Cs-Cs collisions. The 7S-6P transition dipole begins to be damped but the typical damping rate 1/(14 ns) is not prejudicial to good resolution of the 6P3/2 hyperfine structure. The cylindrical shape of the cell allows to respect the revolution symmetry as far as possible: the latter is broken only by the tube in which the cesium is collected, and by the wires which bring the voltage to the annular electrodes. Nevertheless, the reflection symmetry with respect to the vertical plane is totally preserved.
In the first years of this PV experiment, glass cells with internal electrodes were used. In the required experimental conditions, these cells give rise to serious prob-lems. In particular, with intense green laser pulses and a large applied electric field, the glass windows in contact with the cesium vapour show the appearance of dark spots, and lose their good transparency much too fast to allow for long measurement times. The other problems associated with this kind of cells are developed in [28] and [29].
A good alternative to the glass cells is to use another material: alumina. Our new cells are made of an alumina tube, at the end of which two sapphire windows have been glued (sapphire is the monocrystalline form of alumina)3.
A complete study of the improvements and limits obtained by using sapphire cells in the current PV setup was done in E. Jahier’s thesis [28]. In particular, the windows did not show any damage after many hours of measurements. Another important feature is that the resistivity of alumina is very high, even with cesium inside the cell, so that currents around the body of the cell are very small. We will see that this kind of currents could generate magnetic fields which mimic the parity violation effect.
On the other hand, an important problem which arose with the use of alumina cells was the emission of electrons from the windows hit by the intense green laser pulses. It was shown in ref. [30] that these primary electrons are amplified by secondary emission when they hit the alumina tube. This effect generates large space charge effects, which prevent serious PV data acquisition. We will see in this thesis that a good remedy for this problem has been to groove the inner surface of the alumina tube (see fig. 2.5) [30]. Indeed, the cross-section for secondary electronic emission is particularly large at grazing incidence. In the “saw tooth” alumina tube, the primarily electrons hit the alumina surface at quasi normal incidence, hence the most part of them are stopped inside the material, thus hindering multiplication.

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The internal and external ovens

In order to reach the desired density of atoms, we have to heat cesium to increase the vapour pressure. Actually, it is very important to be able to keep the temperature of the cell body higher than that of the side-arm, in order to thermally destroy the cesium dimers, which are always present for chemical equilibrium reasons (Cs+Cs Cs2), and could be harmful for the PV measurements (cf. paragraph 2.4.2) [31]. Then, the temperature of the side-arm (which can be considered the “cold” finger of the cell, where the liquid part of cesium accumulates), defines the cesium vapour density. For the separate control of the two temperatures, the heating system is composed of two ovens, called “internal” and “external”. The internal oven (fig. 2.2) contains the set of eleven annular electrodes and the body of the cell, and let the side-arm out thanks to a proper small hole. The typical operating temperature, for a good suppression of dimers, is 220◦C (for a side-arm temperature of about 140◦C). Really, the internal oven itself is divided into two halves, each one having an independent heating thermocoax wire, in order to be able to create longitudinal temperature gradients. The purpose is to separately control the temperatures of the entrance and exit windows of the cell: we will see in paragraph 2.3.2 how this temperature tuning allows to reach, for each window, very high transmissions of the excitation laser beam, thanks to Fabry-Perot interference effects.
The internal oven is then placed inside a bigger structure, the external oven, which has been thermally insulated from outside. The external oven allows to control the side-arm temperature, kept around 140◦C, and to preheat the internal oven.

The magnetic field

The stray magnetic field is compensated with the fields produced by three pairs of Helmholtz coils along the three cartesian axes x,ˆ y,ˆ zˆ, the last one being the axis of the cell. Other coils are used to compensate the gradient of the field along zˆ. The residual magnetic field variations over the length of the cell are of the order of 1 mG.
In order to perform control measurements about electric and magnetic fields, we must be able to apply substantial magnetic fields (of the order of 2 gauss). This is carried out by three extra pairs of coils.

Table of contents :

Introduction 
1 Elements of parity violation theory in atoms 
1.1 Weak interactions in atoms
1.2 Manifestation of the parity violating weak interaction
1.3 Choice of the PV observable
1.3.1 Effective transition dipole
1.3.2 Atomic anisotropy after excitation
1.3.3 Detection of the alignment by stimulated emission
2 Parity violation detection in a cesium cell: strategy and preliminary results 
2.1 Principle
2.1.1 Experimental setup
2.1.2 Detection of the alignment of the cesium atoms by the stimulated emission process
2.1.3 Main systematic effects arising from electric and magnetic fields
2.2 History and organization of the experimental work
2.2.1 Experimental background
2.2.2 Our grooved cells
2.3 First tests: characterization and optimization of the experimental conditions
2.3.1 Alignment of the PV setup
2.3.2 Cell windows: tilt and temperature
2.3.3 First examples of asymmetry
2.3.4 The transverse fields
2.3.5 The measurement of the applied longitudinal electric field
2.3.6 The longitudinal magnetic field Bz(Ez-odd)
2.4 Improvements of the experimental setup
2.4.1 Stabilization of the excitation laser frequency
2.4.2 Reducing the absorption of the probe beam
2.4.3 Use of a polarization magnifier: the dichroic cube
2.5 Parity violationmeasurements and analysis
2.5.1 Organization of the PV acquisition
2.5.2 Noisy data rejection
2.5.3 Anisotropies
2.5.4 Isotropic contribution of γ1 and α2
2.5.5 Measurements with and without the use of the polarization magnifier: considerations about the noise
2.5.6 Conclusion
3 The first steps for a parity violation experiment with radioactive francium: production and trapping
3.1 Considerations for a PVmeasurement with cold francium
3.1.1 Cold beam
3.1.2 Prospects for forbidden-transition spectroscopy and parity violation measurements using a beam of cold stable or radioactive atoms
3.1.3 Dipole trap
3.2 The present Francium experiment at Legnaro laboratories: from production to trapping
3.2.1 Franciumproduction and extraction
3.2.2 The secondary beamline
3.2.3 The neutralizer
3.2.4 The magneto-optical trap
3.2.5 Conclusion
Conclusion 
A Important quantities for parity violation experiments in cesium and francium
A.1 The case of cesiumatoms
A.1.1 Mhf
A.1.2 M1: experimental measurement of Mhf
A.1.3 The vector polarizability β
A.1.4 m(EPV
A.1.5 kPV from atomic calculations
A.1.6 The weak charge QW
A.1.7 The electric quadrupole amplitude E2
A.2 The case of franciumatoms
A.2.1 The magnetic dipole amplitude M1
A.2.2 The scalar and vector polarizabilities α and β
A.2.3 m(EPV
A.3 Summary table
Acknowledgements
List of Figures
References

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