We investigate the gravitational Aharonov-Bohm effect by placing a quantum system in free fall around a gravitating body, e.g., a satellite orbiting the Earth. Since the system is in free fall, by the equivalence principle, the quantum system is local in flat, gravity free space-time---it is screened from the gravitational field. For a slightly elliptical orbit, the gravitational potential will change with time. This leads to the energy levels of the quantum system developing sidebands which is the signature for this version of the Aharonov-Bohm effect. This contrasts with the normal signature of the Aharonov-Bohm effect of shifting of interference fringes. 

Gravitational Aharonov-Bohm effect

The flight model of the laser cooled cesium atomic clock, PHARAO, has been qualified for operation in space. The clock has passed the vibration, thermal and electromagnetic compatibility tests required to fly in low Earth orbit (400 km). On ground, the clock realized a typical frequency stability of 3.0x10-13 t-1/2 with an estimated accuracy of 2.3x10-15. Frequency comparisons with the SYRTE primary frequency standard FOM agree within their stated accuracies. Because PHARAO is optimized for the longer interaction times possible in microgravity, we expect a frequency stability of 1.1x10-13 t-1/2 and a frequency accuracy of 1.1x10-16 for operation in space. The clock has been delivered to the European Space Agency for the assembly of the ACES payload and is scheduled to be launched into space in 2021.

Qualification and frequency accuracy of the space based primary frequency standard PHARAO

This thesis presents the experimental results obtained during the development and the ground tests of the flight model of the cold atoms space clock PHARAO. PHARAO, the first Primary Frequency Standard (PFS) for space applications, is developed by the French space agency CNES. It is a main instrument of the ESA space mission ACES: Atomic Clock Ensemble in Space with a launch scheduled on 2016. The mission is based on high performances time and frequency comparisons between a payload including PHARAO and ground based clocks to perform tests in fundamental physics. The payload will be installed on an external pallet of the International Space Station. After an introduction on atomic clocks and a summary on the ACES mission, the PHARAO architecture, optimized for microgravity environment, and its operation is described. It is followed by the measurements and the analysis of the frequency stability. On ground the frequency stability is measured at a level of 3.1 10-13 t-1/2. This value is in agreement with the different sources of noise. In space the frequency stability will reach 10-13 t-1/2. Finally the main frequency shifts are analyzed. A detailed study is given on magnetic shield properties, hysteresis and the design of the active magnetic compensation. The objective is to reduce the uncertainty of the second order Zeeman effect within few 10-17. The temperature determination of the atomic environment is also detailed and the goal is to reach an uncertainty on the blackbody frequency shift in the 10-17 range. A preliminary budget on the frequency accuracy of PHARAO on ground is evaluated at 1.1 10-15. This value is compatible with the expected accuracy budget of 3x10-16 when the clock will operate in microgravity. In the next step all the ACES instruments will be assembled for a launch scheduled on 2016.

On-ground characterization of the cold atoms space clock PHARAO

In optical lattice clocks, an ensemble of cold neutral atoms confined in a lattice-shaped dipole trap are probed by an ultrastable laser. They have recently become the best frequency references, because they combine a narrow atomic resonance in the optical domain – hence a large quality factor – and a large number of simultaneously probed atoms. In this paper, we present the latest developments of these clocks, both in terms of frequency stability and accuracy, by focusing on two strontium optical lattice clocks under operation at LNE-SYRTE.

/pdf/horloges-a-reseau-optique-au-strontium-59sv3nqppd.pdf

Horloges à réseau optique au strontium

A frequency standard based on an atomic fountain of cesium atoms may have an accuracy of 10(exp -16) due to longer interaction times and smaller anticipated systematic errors. All of the known systematic effects that now limit the accuracy of the Cs frequency standard increase either linearly or as some higher power of the atom's velocity. The one systematic frequency shift which is dramatically different is the frequency shift due to the collisions between the laser cooled atoms. At a temperature of a few micro-K, the de Broglie wavelength (lambda(sub deB) = h/p, where h is Planck's constant and p is the momentum of the atom) is much larger than the scale of the interatomic potential. Under these conditions the collision cross sections can be as large as (lambda(sub deB)(sup 2))/Pi and the frequency shift due to these collisions was recently calculated. In our Cs atomic fountain, we laser cooled and trapped 10(exp 10) Cs atoms in 0.4 s. By shifting the frequencies of the laser beams, the atoms were launched upwards at 2.5 m/s and a fraction of the atoms were optically pumped into the F=3 ground state. The unwanted atoms in the F=4 ground state were removed from the fountain with radiation pressure from a laser beam tuned to excite only those atoms. The Cs atoms in the F=3 state traveled ballistically upwards, were excited by the microwave cavity, and then returned back through the same cavity in the atomic fountain configuration. By varying the cold atom density, a density dependent shift of -12.9 +/- 0.7 mHz or -1.4 x 10-12 for an average fountain density of (2.7 +/- 1.5) 10(exp 9) atoms/cm(sup 3) was measured.

A Laser-cooled Cesium Fountain Frequency Standard and a Measurement of the Frequency Shift due to Ultra-cold Collisions

CNES, LKB and SYRTE are developing a primary frequency standard, called PHARAO, which is specially designed for space applications. The clock signal is referenced on the frequency measurement of the hyperfine transition performed on a cloud of cold cesium PHARAO : LE PREMIER ETALON PRIMAIRE DE FREQUENCE, A ATOMES FROIDS, SPATIAL 3 atoms (∼1 μK). The transition is induced by an external field feeding a Ramsey cavity. In microgravity the interaction time inside the cavity can be adjusted over two orders of magnitude by changing the atomic velocity (5 cm·s−1–5 m·s−1) in order to study the ultimate performances of the clock. An engineering model has been assembled to validate the architecture of the clock. This model has been fully tested on ground for operation faults. Of course the clock performances are reduced by the effect of the gravity on the moving atoms. The main results are a frequency stability of 3.3× 10−13t−1/2. The main systematic effects have been analyzed and their frequency uncertainties contribution is 1.6 × 10−15. The clock has been compared with the primary frequency standard, the mobile fountain of SYRTE. The mean frequency shift is lower than 2 × 10−15. The mechanical and thermal space qualifications have been carried out by testing a representative mechanical model of the clock and by using refined calculations. The design of the clock has been improved and now the flight model is being assembled. The PHARAO clock is a key instrument of the European ESA space mission called ACES. This mission is dedicated to perform space-time measurements in order to test some fundamental physics aspects.

PHARAO : le premier étalon primaire de fréquence, à atomes froids, spatial

PHARAO (Projet d'Horloge Atomique par Refroidissement d'Atomes en Orbite), which has been developed by CNES, is the first primary frequency standard specially designed for operation in space. PHARAO is the main instrument of the ESA mission ACES (Atomic Clock Ensemble in Space). ACES payload will be installed on-board the International Space Station (ISS) to perform fundamental physics experiments. All the sub-systems of the Flight Model (FM) have now passed the qualification process and the whole FM of the cold cesium clock, PHARAO, is being assembled and will undergo extensive tests. The expected performances in space are frequency accuracy less than 3.10-16 (with a final goal at 10-16) and frequency stability of 10-13 τ-1/2. In this paper, we focus on the laser source performances and the main results on the cold atom manipulation.

/pdf/pharao-flight-model-optical-on-ground-performance-tests-1spt2t87sm.pdf

PHARAO flight model: optical on ground performance tests

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Qualification and frequency accuracy of the space based primary frequency standard PHARAO

PHARAO : le premier étalon primaire de fréquence, à atomes froids, spatial

PHARAO flight model: optical on ground performance tests