An EIT-based memory for nanofiber guided light 

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The vacuum system and the transfer of a nanofiber into vacuum

The central element of the cold-atom-physics experiment is the main vacuum chamber. A set of anti-reflection coated windows provides optical access to its center, enabling light mediated atomic manipulation. The chamber is connected with pipes and valves to the pumping system and to the other components.
The quality of a vacuum system is quantified usually with its residual pressure. Here, the goal is to work in the so-called ultra-high vacuum regime (UHV), where the residual pressure is smaller than 10−8 mbar or Torr1. This is possible using an ion pump which ionizes and collects the molecules of the residual gas. However this type of pump cannot work with sufficient lifetime at ambient pressure. This is why a first pumping stage is performed using a turbo-molecular pump2 based on a high speed and oil-free rotor ejecting the molecules from the vacuum system. This first pumping stage allows to reach pressures lower than 10−6 mbar. Once this pressure is reached, a valve is closed in order to isolate hermetically the vacuum system and the ion pump is then started.
The main limiting factor of high-vacuum systems is the gas emitted continuously by all the components (outgassing). When designing the parts, any trapped air volume (e.g. a screw in a dead-end threaded hole) should be avoided. The total surface exposed to vacuum should be as small as possible and the components cleaned carefully.
The standard cleaning procedure is done using ultrasound baths in different solvents: soapy water, normal water, acetone and high-purity isopropyl alcohol3. They are then stored in oil-free aluminum foils. Ideally, the components are also baked: they are heated in a vacuum environment such that most of the outgassing occurs at a higher rate, diminishing the outgassing rate when going back to room temperature. Some materials, such as stainless steel, are preferred because of their lower outgassing rate, the possibility to clean them efficiently and to bake them at high temperature. They should be used with smooth surface quality to reduce the effective surface area. Other materials might be chosen for magnetic-field-sensitive experiments, or when nonconducting materials are required (e.g. Teflon or ceramics). The standard high-vacuum components are hermetically connected with the so-called CF flanges (ConFlat): a circular copper gasket is squeezed evenly between the « knife edges » of the two CF components.

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.

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. A particular example of both regimes is the interaction between an atom and the many unexcited modes of the quantum electro-magnetic field. This coupling is responsible for the instability of the excited states. They decay to lower energy levels and emit photons with a rate often noted 􀀀: the spontaneous emission rate. It is also associated with a shift of the energy levels, called Lamb shift for a single atom in an infinite space, or more generally the van der Waals or Casimir-Polder shifts in the presence of matter (such as mirrors, dielectric media, or other atoms). This section will start from a practical and now very common application of these interactions: Doppler cooling of atoms, and magneto-optical trap (MOT). I will give a brief description of the cesium atom structure, and then describe how we implemented a MOT in our nanofiber experiment. Another paragraph will focus on a short description of the laser system we have developed for resonant interaction with cesium.

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A magneto-optical trap for cesium

In our experiment, cesium atoms are cooled and gathered around the nanofiber using a magneto-optical trap (MOT) visible in Figure 2.6. The cooling and trapping originates from the radiation pressure from laser beams coming from six orthogonal directions. Because of the Doppler effect, the radiation pressure is velocity dependent. Cooling occurs when the laser beams are red-detuned relative to an atomic transition. The radiation pressure is also position-dependent thanks to a position-dependent magnetic field and the resulting Zeeman shifts. The proper choice of rotating polarizations for the laser beams results in a trapping potential.
The magnetic field is produced by a pair of identical coils symmetrically placed on both sides of the vacuum chamber, with currents rotating in opposite directions. This « anti-Helmholtz » configuration leads to a null magnetic field in the center and gradients in all directions. Details about the coils design are given in section B.2. We use rectangular coils, elongated in a direction parallel the fiber, in order to obtain a cigar shaped cloud with larger overlap with the nanofiber. This will be important for our memory experiments (chapter 3).
The spectroscopic structure of the cesium D2 line [Steck98] is shown in Figure 2.7. In our experiment, only this line is used for resonant or close to resonance interaction. The two 6S1/2 states are long lived, while the excited states decay via spontaneous emission at the rate 􀀀/2 = 5.23 MHz. Another resonance (the D1 line) occurs at 894.6 nm.

First guided-light/atom cloud interaction evidence

After having detailed how a cold atom cloud was prepared around a nanofiber, I will now describe the first observations and measurements obtained when overlapping a nanofiber and a cold cesium cloud released from a magneto-optical trap.
The results here were obtained with the first nanofiber successfully placed in our vacuum chamber. This was done in March 2014, soon followed by the overlap of a cold atomic cloud with the nanofiber, and by measurements of absorption of resonant light propagating through the fiber and cesium atoms. These first experiments led to the observation of electromagnetically induced transparency and a memory for light in May 2014. After studying different parameters of this setup the detailed results were published in 2015 [Gouraud15].
The nanofiber used here has a diameter of approximately 400 nm over a length of 0.9 cm and was made from Thorlabs SM800-5.6-125 fiber. The symmetric tapered regions have a constant angle shape with 3.1 mrad opening angle. The tapered regions and the nanofiber are 9 cm long overall and thus fit into the vacuum chamber. 11.5% losses for light guided through the fiber was induced by fabrication of the nanofiber and 1.8% more losses were recorded during the transfer into vacuum (they occurred when over-tightening one of the swagelok fiber feedthrough).

Overlapping the MOT and the nanofiber

Atoms in the magneto-optical trap (MOT) can be overlapped with the nanofiber in two different ways. The first (and easiest in a first step) possibility is to use 3 pairs of bias coils in the three orthogonal directions to modify the magnetic field gradient of the MOT, in particular the position where the field cancels. The other possibility is to misalign the MOT laser beams. Both of the methods allow to displace the MOT, though the second method will be preferred since it offers better flexibility on magnetic field manipulation or cancellation for further experiments. The MOT overlap with the fiber is first established while monitoring with cameras in 3 different directions. It is then further optimized by monitoring the absorption of a laser beam through the fiber as described in the next paragraph and illustrated in Figure 2.12. Note that the MOT cloud is typically a few millimeters long, thus a little shorter here than the nanofiber waist.

Table of contents :

Introduction
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
Conclusion
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
Bibliography 

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