RUBIDIUM CONDENSATE AND RAMAN BEAMS

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RUBIDIUM CONDENSATE AND RAMAN BEAMS

The source of the atom laser is a Bose-Einstein condensate (BEC). The first Rb BEC achieved in our lab was in 2001 [66], before a major improvement of the experiment was undertaken in 2002 [67]. This chapter is split into 2 different sections. The first part describes the third generation of our BEC machine which allows us to repeatedly produce condensates of constant number of atoms in a very stable magnetic trap. The apparatus is based on a double Magneto-Optical Trap (MOT) structure (see figures 2.1 and 2.2) where a 3D MOT is loaded from a 2D MOT using a push beam. The system also involves a physical transport of the atoms in a strongly confining magnetic field from the 3D MOT to a quadrupole-Ioffe configuration (QUIC) magnetic trap where Bose-Einstein condensation occurs. The second part describes and discusses the optical setup used to produce the optical Raman beams.

EXPERIMENTAL SETUP TO PRODUCE BEC

In the following sections, the laser and vacuum systems are described yielding an overview of the entire experimental setup. Each step of the experiment is then briefly discussed, starting from the 2D MOT to the production of a BEC in the QUIC trap.

Atomic structure of 87Rb

Alkali atoms (Li[3], Na[2], K[68, 69], Rb[1], Cs[70]) are often used in BEC experiments due to their advantageous atomic properties. 87Rb is the most popular choice. It was the first atomic species condensed and hence expertise was built up rapidly and is now widely available. Additionally, Rb atoms have large elastic cross-sections at low temperatures which allow effi-cient evaporative cooling. Also, optical transitions from the Rb 52S1/2 ground state are easily accessible using commercially available, relatively cheap lasers.
The atomic spectroscopy of 87Rb is presented in figure 2.3 showing both the D1 and D2 op-tical transitions and the relevant optical splitting. In particular, the two hyperfine levels of the atomic ground state are split by ∼ 6.8 GHz and can be split further by the Zeeman effect in the presence of a magnetic field. Various optical frequencies are required to cool and manipulate the atoms on the path to BEC. The cooling is performed on the 52S1/2, F = 2 → 52P3/2, F′ = 3 tran-sition. However, approximately one in every thousand atoms will be excited to the 52P3/2, F′ = 2 state and one in every two of these atoms will decay to the 52S1/2, F = 1 state, taking the atoms out of resonance with the cooling laser. Consequently, in order to avoid a loss of atoms, a second laser, known as the repump, is used to repopulate the 52S1/2, F = 2 state via the 52P3/2, F′ = 2 state. Finally, an optical pumping beam driving the 52S1/2, F = 2 → 52P3/2, F′ = 2 transition is used to polarize the atoms in order to achieve an efficient transfer of the atoms from the 3D MOT into a magnetic trap (see section 2.1.6).

Laser system

The schematics of the laser system, which involves three independent diode lasers to produce the required optical beams, is shown in figure 2.4. Each laser and its function in the setup are independently described in the following points:
1. A Toptica-TA 100 provides a maximum power of 330 mW at 780 nm. A small amount of light (∼ 1 mW) is sent to a saturated-absorption locking circuit and the laser is locked to the F = 2 → F′ = 1, 3 cross-over [67] which is shown at the top of figure 2.4. Two independent acousto-optic modulators (AOM, 110 ± 20 MHz) are aligned in double-pass configuration in order to up-shift the light frequency on resonance to the F = 2 → F′ = 3 transition. One of the AOMs provides the 3D MOT beams whereas the second AOM creates the imaging light and the push beam. In addition, the 0-order of the second AOM single-passes through a 60 MHz AOM which down-shifts the light on resonance to the F = 2 → F′ = 2 transition for optical pumping. Each laser beam injects independent single-mode polarization-maintaining (SM-PM) fibers which are sent to the BEC table.
Accounting for the important losses through the AOMs and optical fibers, a total of ∼ 100 mW of light is available for the 3D trapping, imaging, optical pumping and push beams. Note that the intensity balance between the imaging and push beams can be adjusted on the BEC table using a controllable liquid-crystal half wave-plate that can shunt the light from one beam to the other.
2. A Toptica-DLX 100 provides a maximum power of 500 mW at 780 nm which is used to produce the 2D MOT beams. A small amount of the light (∼ 1 mW) is double-passed through an AOM (110 ± 20 MHz) which down-shifts its frequency. This light is sent to a saturated-absorption locking circuit and locked on the F = 2 → F′ = 1, 3 cross-over. As a result, the frequency of the 2D MOT beam is set close to resonance of the F = 2 → F′ = 3 transition. However, the frequency of the beam cannot be easily tuned without affecting the locking circuit, and the light must be switched on and off using a mechanical shut-ter. The 2D MOT beam is sent to the BEC machine in free space with a total power of approximately 480 mW onto the atoms.
3. A Toptica-DL 100 provides a maximum power of 90 mW at 780 nm which is used to produce the repump beams for both the 2D and 3D MOT. A small amount of the light is locked to the F = 1 → F′ = 2 transition which is shifted off the natural resonance by ∼ 20 MHz using a Zeeman shift on the saturated absorption cell. The repump light is sent to the BEC table using SM-PM optical fibers and is split equally to provide independent repumping beams for the 2D and 3D MOT. In particular, the 2D MOT repump is combined with the push beam whereas the 3D MOT repump is mixed with each of the 3D MOT beams.

Vacuum system

A schematic of the vacuum system is shown in figure 2.5. It consists of two vacuum cham-bers, a Creation and a Science chamber, which are connected through a differential pumping tube.
The Creation chamber is a quartz cell of 3.6 ×3.6 ×20 cm dimension with a wall thickness of approximately 4 mm. Two ‘Alvasource’ dispensers (from Alvatec), based on stable intermetallic compounds, contain the 87Rb natural isotope. Each dispenser is 115 mm long with a 4 mm diameter and has a capacity of 50 mg. The Rb metal is initially protected in a sealed stainless steel housing which makes it chemically stable under ambient air. The sealing can melt under a thermal activation process, which is done during the baking of the vacuum system. Under normal operation, the dispensers are run continuously and a heating current controls the amount of pure 87Rb released in the chamber so that the vapor cell can be filled up close to the saturated vapor pressure of rubidium (∼ 1 × 10−7 Torr at 20◦C). The only pumping of the vapor cell is achieved through a differential pumping tube, consisting of a 14 cm long stainless steel cylinder (external diameter 10 mm, internal diameter 7 mm).
The ultra-high vacuum (UHV) Science chamber consists of two parts. The first is the Collection chamber which collects the atoms from the Creation cell and holds a 3D-MOT in the center.
The frame of this chamber is a 316 stainless-steel (non-magnetic) standard hexagon. It has eight 3.5 cm diameter windows on the side providing a large optical access whereas two large diameter windows offer additional optical access in the vertical direction. This chamber is pumped by a 40 l.s−1 ion pump which is connected by a high conductance metal tube. The pump magnet is located 90 cm away from the chamber, thus avoiding any fringing field to distort the magnetic trapping field in the UHV chamber. The pumping efficiency is also enhanced by two titanium sublimation (Ti-Sub) pumps which were run three times in total to improve the pressure in the UHV chamber. The final pressure in the UHV chamber (∼ 5 × 10−11 Torr) was measured by a pressure gauge as well as from the lifetime of the 3D MOT. The second is the BEC chamber which is a quartz cell of 3.6 × 3.6 × 20 cm dimension and is directly attached to the Collection chamber. A translation stage (see section 2.1.7) transports the atoms from the Collection chamber to the end of the glass cell where the sample is transferred into a magnetic trap and condensed.

2D MOT

In the Creation chamber, the atoms released by the two dispensers are confined and cooled in a 2D MOT. A radial laser-cooling is performed by two orthogonal pairs of retro-reflected beams (2 cm diameter, ∼ 500 mW of laser power in total) with opposite polarization σ +/σ − (see figure 2.6). Four magnetic coils (see figure 2.2) provide a radial quadrupolar trapping field with the zero of the magnetic field along the axial y-direction. Consequently, a beam of atoms is created along the y-direction. The atoms are transferred to the Collection chamber through the differential pumping tube by a low power push beam (∼ 200 µ W). The tube is attached by stainless steel nuts to the gaskets. It is cut at a 45◦ angle at one end and holds a polished mirror which has a 1 mm hole in its center. Initially, this mirror was planned to retro-reflect a laser beam in order to provide additional laser-cooling along the axial x-direction. However, a single push beam is used in our experiment to transfer the atoms from the Creation to the Collection chamber. Finally, the flux of atoms is optimized by adjusting the heating current applied to the dispensers.

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3D MOT

In the Collection chamber, three orthogonal pairs of retro-reflected beams (1.4 cm diameter, ∼ 30 mW of laser power in total) with opposite polarization σ +/σ − provide a cooling in three directions. Two internally water-cooled quadrupole coils, which were operated by using 60 A currents in opposite directions, provided confinement for the atoms. These quadrupole coils are mounted on a translation stage which can be moved all the way to the end of the BEC cell (see section 2.1.7). The 3D MOT is typically loaded in 10 s with a rate of ∼ 5 × 109 atoms.s−1, resulting in approximately 5 ×1010 atoms to be trapped in the 3D MOT. Note that the laser beams of both the 2D and 3D MOTs are slightly focussed in order to account for absorption and to keep the intensity constant as the beams go through the atomic clouds. A 10 ms compressed MOT (CMOT) stage is performed by attenuating the repump beam and ramping up the current in the magnetic coils. The MOT lasers are then far-detuned from the F = 2 → F′ = 3 atomic transition by ∼ 40 MHz and the magnetic trap is abruptly switched off in ∼ 100 µ s, followed by 10 ms of Polarization Gradient Cooling (PGC) [71]

Transfer to a magnetic trap

In a magneto-optical trap, atoms are generally distributed approximately equally across all hyperfine states. In contrast, pure magnetic trapping requires the atoms to have gF mF > 0 [72]. For the two hyperfine states of 87Rb, where gF=2 = 1/2 and gF=1 = −1/2, the only magnetically trappable Zeeman sub-states are thus: |F = 2, mF = 2 , |F = 2, mF = 1 and |F = 1, mF = −1 . Consequently, in order to achieve high transfer efficiencies from a 3D MOT to a magnetic trap, the atoms must initially be spin polarized in one of these states. For that purpose, all laser beams are turned off and an optical pumping cycle, illustrated schematically in figure 2.7, is applied to the atoms. To transfer the atoms to the |F = 2, mF = 2 state (see figure 2.7a), the repump light is switched on and a σ + polarized light drives the S1/2, F = 2 → P3/2, F ′ = 2 transition. Once the atoms are pumped into the magnetically trapped |F = 2, mF = 2 dark state they are no longer interacting with the pumping laser and remain in a dark state. Alternatively, it is possible to transfer the atoms to the |F = 1, mF = −1 state (see figure 2.7b) using a σ − polarized light to drive the S1/2, F = 2 → P3/2, F′ = 2 transition and a short repump pulse. This process is less efficient than pumping the |F = 2, mF = 2 state since the |F = 1, mF = −1 state is not dark when the repump is on and other Zeeman sub-states can also be populated in this scheme. However, by choosing appropriate timing and laser power for both the optical pumping and repump beams, a transfer of up to 80% of the atoms into the |F = 1, mF = −1 state was performed experimentally.
In early experiments carried out in our group, the atoms were transferred to the |F = 2, mF = 2 dark state as the process is the most efficient and the characteristic trapping frequency is 2 larger than that for the other states, leading to higher collision rates which are advantageous for evapo-rative cooling. However, when working with atom lasers, it is more appropriate for the source of atoms to be in the |F = 1, mF = −1 state in order to increase the flux and decrease the classical noise in the atom laser beam (see chapter 5).

Transport by a Translation Stage

In order not to make any compromise on the creation of a large MOT and on the efficiency of the magnetic trapping of the condensate, the setup is designed so that the positions of the 3D MOT and the final location of the magnetic QUIC trap do not coincide (see figure 2.2). Conse-quently, the atoms are transported from the Collection to the BEC chamber using the technique developed at JILA [73]. Following the 3D MOT and optical pumping stages, all optical beams are switched off and the current in the quadrupole coils is ramped up from 0 to 360 A in 10 µ s in order to strongly confine the spin-polarized atoms. The coils, which are mounted on a computer controlled 25 cm high precision linear translation stage (PI M-521), subsequently transport the atoms all the way to the BEC cell. Figure 2.8 shows the position of the quadrupole transport coils at different locations, from their initial position around the 3D MOT (1) to their final posi-tion where the atoms are transferred to a QUIC trap (3). In order to minimize losses or heating of the atoms, a smooth transport of the magnetic coil is achieved in 7 s. The first second of transport consists of a very smooth acceleration to reach a constant velocity, whereas the last second is a very smooth deceleration to zero velocity. All magnetic coils are water-cooled and have an interlock which switches the power supplies off if any overheating is detected.

Table of contents :

CHAPTER 1: EXPERIMENTAL AND THEORETICAL BACKGROUND OF ATOM LASERS
1.1 GENERAL OVERVIEW OF ATOM LASERS
1.1.1 Background
1.1.2 An Analogy with Optical Lasers
1.1.3 Definition of an ’Atom Laser’
1.2 ATOM LASER OUT-COUPLING TECHNIQUES
1.2.1 Non-State Changing Out-coupling
1.2.2 State Changing Out-coupling
1.2.3 Radio-Frequency Output Coupling
1.2.4 Raman Output Coupling
1.3 RESONANT WIDTH OF THE CONDENSATE
1.3.1 Gravitational Sag
1.3.2 Resonant Frequency Width
1.4 RABI-FREQUENCY AND THE DIFFERENT OUT-COUPLING REGIMES
1.4.1 Output Coupling Strength
1.4.2 Pulsed and Quasi-Continuous Output Coupling
1.4.3 Out-coupling regimes
1.5 CONCLUSION
CHAPTER 2: RUBIDIUM CONDENSATE AND RAMAN BEAMS
2.1 EXPERIMENTAL SETUP TO PRODUCE BEC
2.1.1 Atomic structure of 87Rb
2.1.2 Laser system
2.1.3 Vacuum system
2.1.4 2D MOT
2.1.5 3D MOT
2.1.6 Transfer to a magnetic trap
2.1.7 Transport by a Translation Stage
2.1.8 QUIC Trap
2.1.8.1 Transfer to the QUIC Trap
2.1.8.2 Optical Imaging
2.1.8.3 Trap Frequencies
2.2 EXPERIMENTAL SETUP TO PRODUCE RAMAN BEAMS
2.2.1 Optical setup
2.2.2 Adjusting the polarization of each of the beams
2.3 CONCLUSION
CHAPTER 3: DIVERGENCE OF AN ATOM LASER
3.1 M2 QUALITY FACTOR
3.2 OUT-COUPLING FROM THE CENTER OF THE BEC
3.3 REDUCING THE DIVERGENCE OF THE ATOM LASER
3.4 THEORETICAL MODEL OF THE EXPERIMENT
3.4.1 The model
3.4.2 Data analysis
3.5 DEPENDENCE ON TRAPPING FREQUENCIES
3.6 CONCLUSION
CHAPTER 4: COHERENT ATOM BEAM SPLITTING
4.1 OVERVIEW ON BRAGG DIFFRACTION
4.2 DIFFRACTION FROM A SINGLE LASER BEAM
4.3 A VELOCITY RESONANT PROCESS
4.3.1 Theoretical Model
4.3.2 Experimental measurement
4.4 BRAGG DIFFRACTION EFFICIENCY
4.4.1 Measurement
4.4.2 Theoretical Model
4.5 CONCLUSION
CHAPTER 5: RF OUT-COUPLING FROM TWO- AND MULTI-LEVEL SYSTEMS
5.1 THEORETICAL MODEL
5.1.1 Time-dependent Gross-Pitaevskii Equations (GPE)
5.1.1.1 GPE for a condensate
5.1.1.2 GPE for a multi-level system
5.1.1.3 Dimensionality reduction
5.1.1.4 Initial conditions
5.1.2 Numerical method
5.1.2.1 The grid
5.1.2.2 Results of the simulations
5.2 EXPERIMENTAL COMPARISON OF THE MODEL
5.2.1 Bound state of an atom laser
5.2.2 Spatial structure of an atom laser
5.3 COMPARISON OF TWO- AND MULTI-STATE SYSTEMS
5.3.1 Flux of the atom laser
5.3.2 Population dynamics
5.3.2.1 Five-state system
5.3.2.2 Three- and two-state systems
5.3.3 Spatial dynamics
5.3.4 Density fluctuations
5.3.4.1 Five-state system
5.3.4.2 Three- and two-state systems
5.3.5 Flux and fluctuations trade-off
5.4 CONCLUSION
CHAPTER 6: HELIUM BEC: EXPERIMENTAL SETUP
6.1 THE METASTABLE HELIUM ATOM 4He∗
6.1.1 The metastable 23S1 triplet state
6.1.2 Penning collisions
6.2 EXPERIMENTAL SETUP
6.2.1 Vacuum system
6.2.2 Optical Setup
6.2.3 The source of atoms
6.2.4 Collimation-Deflection
6.2.5 The Zeeman Slower
6.2.6 Channel Electron Multiplier (Channeltron)
6.2.7 The MOT
6.2.8 Magnetic trap and evaporative cooling
6.3 CONCLUSION
CHAPTER 7: OPTICAL TRAPPING OF 4HE ATOMS
7.1 OPTICAL DIPOLE POTENTIALS
7.1.1 Oscillator Model
7.1.1.1 Interaction with a light field
7.1.1.2 Atomic Polarizability
7.1.1.3 Dipole Potential and Scattering Rate
7.1.2 Dressed State Picture
7.1.2.1 Two-Level Atom
7.1.2.2 Multi-Level Atom
7.2 RED-DETUNED DIPOLE TRAP FOR HE∗
7.2.1 Single Gaussian Beam
7.2.2 Crossed Dipole Trap
7.2.3 Experimental Layout
7.2.3.1 Light Source
7.2.3.2 Output Beam Waist
7.2.3.3 AOM efficiency
7.2.3.4 Lens focussing
7.2.3.5 Loading an optical dipole trap
7.3 INELASTIC COLLISION RATES IN A GAS OF SPIN-POLARIZED METASTABLE HELIUM ATOMS
7.3.1 Spin-dipole Hamiltonian
7.3.2 Spin relaxation
7.3.3 Spin relaxation towards Sf = 2
7.3.4 Spin relaxation towards Sf = 0
7.3.5 Inelastic collision rates and magnetic field dependence
7.3.6 Future experiment
7.4 CONCLUSION
CHAPTER 8: NOVEL ATOM TRAP FOR HE ATOMS IN OPTICAL LATTICES
8.1 PERIODIC LATTICE POTENTIALS
8.1.1 Overview
8.1.2 Quantum Phase Transition from a Superfluid to a Mott Insulator
8.1.2.1 Bose-Hubbard Model
8.1.2.2 Superfluid-Mott Insulator quantum phase transition
8.1.3 New insight with metastable helium atoms
8.2 NOVEL ATOM TRAP
8.2.1 Experimental challenge
8.2.2 Optical lattice requirements
8.2.3 Coil and beam geometry
8.2.4 Trap simulations
8.2.5 Electric circuitry
8.2.5.1 Wiring circuit
8.2.5.2 Water cooling
8.3 CONCLUSION
BIBLIOGRAPHY

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