Polarization of the fields and atomic angular momentum in EIT

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A « breakable » vacuum system

The whole vacuum setup should be designed properly before assembling. All the necessary tools and components should be gathered and cleaned and all decisions should be made in order to lower the risk of mistake or contamination. far from the central chamber and shielded with μ-metal5 in order the minimize the effects of its strong magnetic field on the experiment. However this distance makes more difficult the efficient pumping of the vacuum system6. Here, the whole setup is clamped on a vibration damped optical table. The ion pump is actually under this table. The clamping is also something that should be thought carefully before assembling, especially because the whole vacuum system is rather heavy and uneasy to handle.
This particular setup was designed with the idea that we should be able to transfer a nanofiber in the main chamber easily, and ideally to change the nanofiber on a regular basis. This means that the vacuum has to be « broken » and « rebuilt » efficiently. Because of this, two valves are used. One is separating the main chamber from the ion pump, as close to the chamber as possible, such that a volume including the ion pump can be isolated from the rest, and stay under high-vacuum conditions even when the main chamber is under ambient pressure. The other valve is separating the chamber from a connection used for two different reasons. It is first used as a nitrogen input: when « breaking » the vacuum, a constant and clean nitrogen flow is maintained at this input such that ideally nothing else than nitrogen enters the chamber. It is thus kept as clean as possible, and is more easily re-pumped to high-vacuum conditions. The other use of this connection is for the turbo-pump during the first pumping stage. Once a nanofiber is ready in high-vacuum conditions, this second valve is closed and the ion pump valve re-opened.

The vacuum fiber holder

The nanofiber can be seen in the center of Figure 2.3. After the tapered region, on the acrylate coated part, its two tails are glued on the vacuum fiber holder. This holder was designed such that there is optical access for a light beam propagating in free-space along an axis as parallel as possible12 to the nanofiber. After fabrication, the nanofiber is glued on the holder outside the chamber with UVH compatible ultraviolet curing glue13. It is then transfered in the center of the vacuum chamber.

The vacuum fiber feedthroughs

The two tails are fed outside vacuum with a very convenient technique involving Swagelok gas connectors14. One of the two metallic rings of the connector is replaced with a home-made Teflon part in which a hole slightly larger than the coated fiber has been drilled. After having passed the fiber through this hole the Teflon is squeezed around the fiber using the Swagelok nut. This system has been described in [Abraham98] and is used in many experiments involving optical fibers and vacuum.
In our setup, the Teflon parts have been designed and tested by Kevin Makles (optomechanics team) and fabricated by Arnaud Leclercq (LKB’s mechanical workshop). The result is a leak-free system working well enough in UVH conditions. Images and dimensions of the feedthrough are shown in Figure 2.4. Note that the elasticity of Teflon leads to significant fabrication imprecision on the dimensions, although this has never induced leaks in our nanofiber setup. Starting the nut rotation on the thread remains tricky and requires some training in our setup. The nut usually has to be pushed in order to pre-squeeze the Teflon part, which is risky and uneasy (recall there is also an optical fiber that you cannot afford to break). For now, we do this using an adjustable wrench and a fixed pivot point on the table. The next step is to tighten the nut. This is done with a wrench, of about 10 cm length. The nut has to be tightened for a few turns to avoid leaks: a very small torque is needed and the tightening should be stopped when the nut starts to resist against the imposed rotation. Screwing it further would induce optical loss in the fiber.

Transferring a nanofiber into vacuum

Producing a nanofiber and transferring it into vacuum is something that has to be prepared carefully. The full protocol is written beforehand and discussed with the whole team taking part in the task (ideally three persons). A stripped copy of the protocol we have been using is given in Appendix C. I will summarize here the main ideas. It has been used in the team repeatedly since 2014 and proved to be efficient and rather fast ( half a day) after some training. There are a few tricky points remaining, but the only cause of failure in our group until now (summer 2015) seems to come from the nanofiber fabrication process as mentioned in paragraph 1.2.415.


Some general ideas on atom/electro-magnetic field interaction

The properties of an isolated atom are well described by the electro-magnetic interaction between its nucleus and its electrons. The Hamiltonian of the system gives rise to a set of bounded and unbounded eigenstates with well defined wave-functions and energies. The probability amplitudes of an atom in a superposition of these eigenstates oscillate relative to each other at the Bohr frequencies: the energy differences between two levels divided by the universal Planck’s constant h. Much of atom physics can then be understood as electromagnetic perturbations of those eigenstates.
There are two main regimes. In the first regime the perturbation is oscillating resonantly with these frequencies. This resonant perturbation will induce variations in the populations of the atomic eigenstates. Most of section 2.3 and chapter 3 will focus on this kind of interaction between atoms and nanofiber guided light. In the second regime, the perturbation is static or off-resonance. The main result here is a perturbation to both the eigenstates wave-functions and to their energies. The latter is called a level shift and has many different appellations depending on the nature of the perturbation. The Stark shifts correspond to perturbations induced by a static electric field while the Zeeman shift is the counterpart for a static magnetic field. Oscillating fields lead to the ac Stark19 or Zeeman shifts. When the perturbation field is spatially varying, the atom experiences a spatially dependent energy, or in other words a conservative force. An off-resonance electric field can thus be used as an atomic trap: the so-called optical dipole trap. The last chapter of this thesis will focus on such a trap based on the off-resonance fields propagating in a nanofiber.

Table of contents :

1 Subwavelength optical fibers 
1.1 Propagation in optical nanofibers
1.1.1 Step-index fiber: Derivation of the guided mode properties
1.1.2 Properties of the fundamental HE11 mode in a nanofiber
1.2 Producing optical nanofibers
1.2.1 Hydrogen/Oxygen flame
1.2.2 Cleaning and preparing the fiber for pulling
1.2.3 Controlling the pulling stages
1.2.4 Monitoring and characterizing the process
1.3 Setting the polarization of a nanofiber-guided light beam
2 A nanofiber in a cold atom physics experiment 
2.1 The vacuum system and the transfer of a nanofiber into vacuum
2.1.1 A « breakable » vacuum system
2.1.2 The cesium dispensers
2.1.3 The vacuum fiber holder
2.1.4 The vacuum fiber feedthroughs
2.1.5 Transferring a nanofiber into vacuum
2.1.6 Detecting leaks
2.2 Manipulating atoms with lasers
2.2.1 Some general ideas on atom/electro-magnetic field interaction
2.2.2 A magneto-optical trap for cesium
2.2.3 Laser system
2.3 First guided-light/atom cloud interaction evidence
2.3.1 Overlapping the MOT and the nanofiber
2.3.2 Absorption measurements
3 An EIT-based memory for nanofiber guided light 
3.1 Theoretical basis for a -type 3-level atom
3.1.1 Schrödinger equation and dark state
3.1.2 Optical Bloch equations
3.1.3 Polarization of the fields and atomic angular momentum in EIT
3.1.4 Dynamic EIT and the classical dark-state polariton
3.1.5 The quantum dark-state polariton
3.2 Experimental evidence of EIT for a nanofiber guided probe
3.2.1 Some experimental parameters
3.2.2 Transparency
3.2.3 Slow light
3.2.4 Implementation of the memory protocol
3.2.5 Memory lifetime and controlled revivals
4 A nanofiber-trapped ensemble of atoms 
4.1 A two-color dipole trap in the evanescent field of a nanofiber
4.1.1 Basic ideas of two-color trapping
4.1.2 Dynamical (ac) Stark shifts for a real alkali atom
4.1.3 Back to the trap: ground-state coherence
4.1.4 Driving optical transitions in a dipole trap: magic wavelengths .
4.1.5 The chosen nanofiber trap
4.1.6 Collisional blockade
4.1.7 Loading the trap
4.2 Experimental realization
4.2.1 Optical system
4.2.2 Loading the trap
4.2.3 Characterizing the trap
A Experiment control 
A.1 Interfacing the experiment
A.2 FPGAs as a tool for synchronization and time-stamp acquisition
A.2.1 Different possible choices
A.2.2 FPGA programming
B Magnetic fields 
B.1 Measuring magnetic fields with Zeeman structure spectroscopy
B.1.1 Method for Zeeman-sublevel spectroscopy
B.1.2 Canceling residual magnetic field offset and gradients in our experiment
B.2 Magnetic field coil design
B.2.1 Helmholtz and anti-Helmholtz configurations
B.2.2 Coils arrangement for an elongated MOT
B.2.3 Criteria considered for coil design
B.2.4 Final design
C Transferring a nanofiber into vacuum protocol 
C.1 Parts needed during operation
C.2 To be prepared days before operation
C.3 Protocol
C.3.1 Getting ready
C.3.2 First stage
C.3.3 Second stage
C.3.4 Third and last stage


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