THERMAL
4.1 Observations of spin mixing
Spinor dynamics and the dual-beam atom laser
“The world was young and I was young and the experiment was beautiful. . . These atoms in spatially quantized states—analyze them in one field, turn your focus back, and there it is. Count them! It was wonderful. There I really, really believed in the spin.
There are the states—count them!”
Isidor Isaac Rabi John S. Rigden, biographer.
T
he creation of an all-optical condensatewith resulting spinor prop- erties was the first major goal of the research described in this thesis. The second, as documented in this chapter, was the exploration of some of the phenomena made accessible through the liberation of the spin degree of freedom.The dynamics of this new system are quite rich, and the field is quite fast-moving, as documented in §1.4. Here we chronicle some of the efforts made in the past year to illuminate some of the features of the spinor condensate.
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−3 0 −2 −1 0 1 2 3
5 10 15 20 25 30 35
spin−spin energy [Hz]
distance [ µ m]
Figure 4.1: The spin-spin energy scale. The horizontal dashed line represents the typical quadratic Zeeman shift, and the parabolas represent the spin-spin energy scale 2c2n. The densities chosen are typical values at a) default power (80 mW) b) 500 mW of adiabatic compression, and c) 1.8 W.
magnetic field and the conserved magnetization M. While we made some cursory observations of the evolution of a mixed state at low densities, the majority of the spin-mixing results presented in this thesis were obtained using the technique that revealed spin mixing most clearly, namely adiabatic compression of a pure mF = 0 condensate.
4.1.1 Magnetic field issues
The quadratic Zeeman shift in87Rb (F = 1), 350 Hz/G2[78], plays a strong role in the expected spin dynamics in that it sets the energy of the mF =±1 states higher than the planned initial condition for mixing. This implies that if this shift is larger than the spin-spin energy scale the spin-relaxation collision will be energetically forbidden and no departure from the mF = 0 intial state will be observed. This concept is illustrated in more detail in Fig. 4.1.
The experimental situation is complicated by the fact that a naturally well-zeroed field was not desirable for the crucial dipole trap-loading phase; in fact, as discussed in §3, strong fields of at least the size of the earth’s field were required to properly locate the MOT such that a maximum number of atoms were transferred to the dipole trap. We thus arranged for the fields to jump from the loading values to new values after the state-preparation phase of the evaporation had finished, so that the final stages of evaporation, condensation, and later adiabatic compression could all occur at a known (low) field.
Given density estimates for ourmF = 0 condensates of 4–8×1013cm−3, a magnetic field well below 100 mG was desired (2c2n ∼ 4Hz∼ νB2). Absolute zeroing was not desired due to reports of rapid (<100 ms) Zeeman sublevel population redistribution due to stray AC magnetic fields at main fields of order 10 mG [78].
To measure magnetic fields we implemented a simple radiofrequency spectroscopy experiment, whereby condensed or near-condensed mF = 0 clouds were exposed to radiation from a simple loop antenna placed outside the vacuum chamber; this oc- curred after the current values in the bucking coils had been shifted away from the trap-loading values to the low-field values.
The Zeeman resonance of the |F = 1, mF = 0,±1i manifold is known to be 700 kHz/G [137]; the typical signals sent through the loop through the calibration process were in the range ωrf = 50–500kHz. The measurement itself was a comparison of the fractional population of the variousmF states at the end of runs whereωrf had been applied for the duration of the low-field/final evaporation phase; near resonance, the Stern-Gerlach separation technique would reveal redistribution of themF states away from the low-power/off-resonant limit of the pure mF = 0 state. This redistribution was of course a brute-force approach, as the radiation was present for up to a second and the resonance appeared quite power-broadened. We used a HP3325A synthesizer to drive the shorted loop, which while crude by radiofrequency engineering stan- dards was sufficient for our needs. Typical powers used were 30 dBm, although when searching for low magnetic fields lower powers were used in an attempt to reduce
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the linewidth of the Zeeman redistribution. The technique yielded final resonance frequencies around 60 kHz, corresponding to a field of around 85±10 mG, with the spread caused by inherent linewidth and signal-to-noise from low atom number. It should be noted that while we were satisfied with this range (due to concern that stray AC magnetic noise would cause trouble at lower fields) further zeroing proved difficult, as the linewidth of the process combined with possible issues with the an- tenna efficiency appeared to limit the technique’s calibration potential. An obviously better path to take would be microwave spectroscopy at 6.8 GHz, which would yield the same observables [78]. This resonance process was repeated several times between spin-mixing experiments—in some cases merely for confirmation, and in others to ac- tively troubleshoot for reasons why spin mixing was not occurring at a particular time, which usually was the fault of the switching electronics. Regardless, even when the fields were totally reset, the 60 kHz resonances were readily reachievable.
4.1.2 Density, adiabatic compression, and spin mixing
As shown in §1.1.2, the peak condensate density is determined by the chemical po- tential, itself found in Eq. 1.1.13, as nc,0 =µm/4π~2a. This yields an expression of the peak density in term of the trap frequencies:
nc,0 = 152/5~4/5m1/5a2/5
2 Nc2/5ω¯6/5 (4.1.1)
If we wish to increase this peak density, the parameter we have access to is the mean trap frequency, controlled via laser power as ¯ω ∝ √
P. Thus, more succinctly, we have the simple relation that peak condensate density is simply related to condensate number and trap depth asnc,0 ∝Nc2/5U02/5.
Visually pure mF = 0 states were first created using techniques described in
§3. Adiabatic compression was then performed using power-vs.-time paths such as shown in Fig. 4.2. Adiabaticity was ensured through the use of a gentle quadratic