Exploration de la physique à deux dimensions avec des gaz de Bose dans des potentiels à fond plat
overv iew of a cold atom exper iment
General features
Electronic structure of 87Rb Rubidium belongs to the alkali group and has a simple electronic structure. Lasers addressing its electronic transitions are easy to access, enabling cooling schemes as well as optical trapping methods. All these advantages make this atom a widely-spread tool in the cold atoms community. The electronic ground state of the atom is 2S1/2 and its first excited state has two fine levels: 2P1/2 and 2P3/2 . The transition 2S1/2 → 2P1/2 (resp. 2S1/2 → 2P3/2 ) is called the D1 (resp. D2) line and has a wavelength of 795 nm (resp. 780 nm). We are only interested here in the 2S1/2 and 2P3/2 states, that we use for our cooling scheme. Each of these levels experiences hyperfine splitting due to the coupling between the electron and the spin of the nucleus: the 2S1/2 level splits splits into four levels labelled from F 0 = 0 to F 0 = 3. The two hyperfine states of 2S1/2 are the ones in which we perform the interesting physics. They experience Zeeman splitting in the presence of a magnetic field B: the F = 1 state splits into three levels, labelled with mF = −1, 0, 1, and the F = 2 state splits into five levels, labelled with mF = −2, −1, 0, 1, 2. In the low magnetic field regime where the quadratic Zeeman shift is negligible, the displacement of the energy of each level is ∆E = µBgF mF B, with µB the Bohr magneton, and gF the Landé factor of the hyperfine state of interest. For F = 1 (resp. F = 2), we have gF = −1/2 (resp. 1/2). For magnetic fields around a few gauss, these displacements correspond to frequencies on the order of a few megahertz. All these features of the electronic structure of rubidium are summarized on Fig. 2.1, where only the relevant states are depicted.
Lasers
We use lasers with four different optical wavelengths to reach the quantum regime from a metallic sample, to trap them in a controlled geometry and to probe the properties of 2D samples.: • Two lasers at 780 nm to address the D2 line. They are used for the cooling schemes summarized in 2.2.1, and for the imaging of the cloud explained in 2.1.2. We use saturated absorption on a vapour of rubidium to lock the frequency of these lasers with a precision of a few hundreds of kilohertz
- Two lasers at 1064 nm, red-detuned with respect to the D1 and D2 lines, to create conservative attractive potentials (see 2.2.1), referred to as optical dipole traps. • A laser at 532 nm, blue-detuned with respect to the D1 and D2 lines, to create conservative repulsive potentials and shape the final geometry of the cloud (see 2.2.2 and 2.2.3). • A laser at 790 nm, between the D1 and D2 lines, to perform Raman transfers between the two lowest hyperfine states of the atom, as developed in Chapter 3.
Vacuum system
The experiments are performed in a compact vacuum system where a high vacuum is maintained. All experimental steps are performed in a single rectangular glass cell with high optical access and dimensions 25 × 25 × 105 mm. In particular, the early cooling steps to prepare the atomic sample and the experiments performed on it are done at the same position, which prevents any technical difficulty due to the transport of the cloud between different regions of space. Using a glass cell also allows to have coils and optical elements very near the atoms and outside the cell. Having these tools near the atoms permits to reach higher magnetic fields and optical numerical apertures, and not having them in the vacuum cell is technically easier to develop. The glass cell is represented seen from three sides on Fig. 2.2, and as many elements as possible that are described in this chapter are depicted on these drawings.
Magnetic fields
The magnetic field in the glass cell has to be well-controlled in order to implement some of the cooling stages (see 2.2.1) and to control the energy splitting between Zeeman states of the atoms (see 2.3.1) and reliably address transitions between these states. There are several pairs of coils to achieve these tasks: • A pair of water-cooled coils in anti-Helmholtz configuration along the vertical (z) axis. They produce a quadrupolar field for our quadrupole magnetic trap with a maximal vertical gradient of 240 G/cm. • A pair of water-cooled coils in anti-Helmholtz configuration along the y axis. They produce a quadrupolar field for our magneto-optical trap (MOT) with a maximal gradient of 22 G/cm. • Three pairs of coils in Helmholtz configuration along the three axes, to create bias fields. The pair on the vertical axis (resp. horizontal axes) creates a maximum bias field of 2 G (resp. 1 G). These coils are located around the glass cell, but they are not represented on Fig. 2.2. The intensity is provided by power supplies (Delta Elektronika ES 030-5) with a relative intensity noise of 10−4 , which corresponds to a fluctuation of magnetic field of 0.2 (resp. 0.1) mG
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