Stern-Gerlach spatial separation

The method of subsequent imaging described above almost necessarily requires the atoms to be in different hyperfine manifolds, i.e. f =1 and f =2. For atoms merely in separate Zeeman states of the same hyperfine manifold, imaging one state without affecting the other one is close to impossible due to the insufficient energy separation of the levels. An alternative approach is to spatially separate the states before the image is taken, using a Stern-Gerlach magnetic field gradient. According to equation (1.46), atoms are attracted towards the position of minimal energy, which depends on the internal atomic state. Having spatially separated the two states, one can take one image of both states at the same time. The main advantage of this method compared to the subsequent imaging is that for sufficient spatial separation, atoms in one state cannot affect the image of atoms in the other state (as for example with an imperfect “blow-away” pulse). In the work in[109], we use a pulsed magnetic field gradient

3.4 Normalised two-state detection 69 for a duration of_∼3 – 4 ms to separate the states. The gradient is produced by the coils of our magnetic trap. The imaged states are again the atomic clock states|f ₌1,m_{f =}0〉and

|f =2,mf =0〉, and the separation relies on the second order Zeeman shift. Figure 3.6 is an illustration of typical two-state absorption pictures using (a) subsequent imaging and (b) Stern-Gerlach separation of the two states. The figure is presented as an illustration only, and a comparison between signal and noise on the two pictures is not sensible due to different scales and atom numbers.

Chapter 4

Interferometry with Bose-condensed

atoms

The invention of atom interferometers[2]has led to significant advances in the sensitivity of precision measurement devices. Most modern atom interferometers rely on Ramsey-type interferometry, using the method of separated oscillatory fields[38]. The most fundamental version of this technique includes two temporally or spatially separated beam splitters that couple a two-level system to an external driving field. Control of the time between the two beam splitters or the phase or the frequency of the driving field allows the observation of Ramsey fringes, an oscillation in population transfer between the two states in the interferometer. The position of the fringe pattern contains information about the relative phase accumulated by the two atomic states, enabling precision measurements with atom interferometers. So far, the most remarkable results have been achieved using thermal atoms, e.g. for the measurement of the gravitational constantG _[5, 6_], the fine structure constantα_[7, 8, 127_]and for the definition

of time in atomic clocks[3, 4, 128]. Thermal atom interferometers have been established as highly sensitive devices for inertial measurements, such as accelerations and rotations. In many cases, improved performance can be achieved by using laser-cooled atoms from a magneto-optical trap, substantially narrowing the atomic velocity distribution. Bose-Einstein condensates comprise a macroscopic number of atoms in a single momentum state and have an even narrower momentum width, making Bose-condensed sources an excellent candidate for high precision atom interferometers. A detailed analysis of the advantages and disadvantages of Bose-condensed as compared to thermal sources has been presented in chapter 2.

While the two previous chapters investigate the initial (source) and final (detection) stage involved in interferometric experiments, we will here describe the characteristics of the inter- ferometric sequence itself. The beam splitters of the interferometer are the elements relating the atomic phase to the external reference, and thereby performing the phase measurement inherent to every atom interferometer. The design and stability of the atomic state coupling scheme of the beam splitters is of crucial importance and will be described in section 4.1. Section 4.2 contains the main results and presents our free-space atom laser interferometer, operating on the|f ₌1,m_{f =}0〉 → |f ₌2,m_{f =}0〉87_{Rb hyperfine ground state transition,}

which was achieved as part of this thesis. Such an interferometer is similar in design to atomic fountain clocks and allows a strong decoupling from environmental noise influences. The device is the first atom interferometer built in our group and represents a precursor for more complicated external state interferometry schemes. We show the phase sensitivity achieved with two different beam splitter coupling setups and the quantum projection noise limited performance of the interferometric beam splitters in one of the two coupling setups. Section 4.3 contains results on a different interferometry experiment, performed on a trapped Bose-

72 Chapter 4. Interferometry with Bose-condensed atoms Einstein condensate instead of a freely propagating atom laser. In-trap measurements generally allow for longer interrogation times while at the same time being more prone to external noise sources. We compare different aspects of the two interferometers and make an analysis of the noise mechanisms contributing to a deteriorated interferometric signal in section 4.4. The results presented in this chapter are based on the work published in[86, 109, 126].

4.1 Coupling schemes

The state coupling scheme is crucial for achieving a stable interferometric signal. It is usual and convenient to differentiate between coupling of internal (hyperfine and Zeeman levels) and external (momentum) states that are coupled in the interferometer. Coupling the external states is a requirement for the measurement of spatial effects and is most frequently realised via multi-photon transitions, transferring momentum from the coupling light field to the atoms. Internal state coupling on the other hand is necessary when one wants to take advantage of differential shifts of the two levels involved in the interferometer, or for the measurement of time in atomic clocks. In addition, the internal states provide a label to the interferometer beam paths, allowing for straightforward state-selective detection. The experimental results obtained in the work presented in this thesis are solely based on internal state beam splitting, and we shall concentrate on such internal state beam splitting schemes. In many cases, the arguments can be easily transferred to the common internal plus external state Raman beam splitters and to purely external state Bragg beam splitting.