Experiments to Control Atom Number and Phase-Space Density in ...

More documents

Recommendations

Info

the optical trough geometry mixes the velocity distributions along the y and z direc- tions. Because of the orientation of the optical sheet at 45 ◦ , it is reasonable to expect the measured temperature of T ′ y = 5.2 µK to be only half of the trap depth along the y direction. Figure 5.11 shows fairly good agreement between the model and experimental data. At higher magnetic trap temperatures, the experiment systematically exceeds the value predicted by the model. This can be explained by collisions occuring inside the magnetic trap, that are neglected in the model. The demon beam truncates the temperature distribution during the single-photon cooling sequence, and collisions between the remaining atoms in the magnetic trap lead to rethermalization. Even though the time scale for rethermalization is larger than the single-photon cooling sequence, partial thermalization occurs, as shown in figure 5.12. Figure 5.12: Rethermalization of the remaining atoms in the magnetic trap. In the presence of the demon beam the magnetic trap temperature decreases as the singlephoton cooling process develops. This partial rethermalization process provides additional cooling and thus phase- space compression, so that the measured transfer efficencies can surpass efficiencies predicted by the model. Obviously the strength of this rethermalization process depends 81
on the collision rate of atoms inside the quadrupole magnetic trap. The inset in figure 5.11 shows the calculated collision rates as a function of temperature. At higher temperatures the collision rate increases, leading to a faster thermalization time and thus additional phase-space compression. The transfer efficiency can trivially be increased by increasing the spatial overlap between the optical trough and magnetic trap distributions, or by increasing the trap depth (or equivalently lowering the magnetic trap temperature). However, typically the amount of phase-space compression is important for cooling experiments. As discussed before, phase-space compression can be translated to a reduced temperature of the atomic ensemble. The simple adiabatic model predicts the phase-space compression in a non- interacting ensemble to be ρ ′ ρ σ = σ ′ z T T ′ . z (5.8) For a given optical trap geometry and trap depth, the amount of phase-space compression will thus increase with an increase in the magnetic trap temperature, despite a decreasing transfer efficiency. If collisions lead to (partial) rethermalization of the magnetically trapped atoms, the amount of phase-space compression achieved in the experiment will surpass the values predicted by the simple model. 5.6 Monte-Carlo Simulations A series of Monte-Carlo simulations, written during the course of the experiment, give further insight into the single-photon cooling process and the trap dynamics. A Box- Mueller-algorithm creates random Gaussian distributions in velocity and position space, giving the initial conditions for the simulated magnetically trapped atoms. These initial coordinates evolve following the equation of motion inside the magnetic trap. (To ensure that this describes the situation in the experiment adequately, i.e. as long as collisions can be neglected, the spatial and velocity distributions are followed in time.) The potentials of the optical beams are added to the overall potential, and the optical trap is defined as a subspace within the overall space. When an atom of the 82
Page 1 and 2:
Copyright by Kirsten Viering 2012
Page 3 and 4:
Experiments to Control Atom Number
Page 5 and 6:
Acknowledgments First of all, I wou
Page 7 and 8:
Experiments to Control Atom Number
Page 9 and 10:
Table of Contents Acknowledgments v
Page 11 and 12:
Chapter 7. Lithium Apparatus 92 7.1
Page 13 and 14:
List of Tables 2.1 Physical propert
Page 15 and 16:
4.1 Vacuum chamber . . . . . . . .
Page 17 and 18:
7.39 Future vertical axis optics .
Page 19 and 20:
The development of techniques to la
Page 21 and 22:
Ptorr 10 5 10 6 10 7 10 8 10 9 260
Page 23 and 24:
Property Symbol Value Reference Ato
Page 25 and 26:
2.3.2 Hyperfine Structure So far th
Page 27 and 28:
The Wigner-Eckhart theorem can be u
Page 29 and 30:
The total magnetic moment of an ato
Page 31 and 32:
interaction. The shift in the energ
Page 33 and 34:
(a) (b) scattering length a 0 Energ
Page 35 and 36:
a laser field with frequency ω. Th
Page 37 and 38:
Here ω0 is the resonance frequency
Page 39 and 40:
Optical molasses do not provide a s
Page 41 and 42:
J=1 J=0 -1 Δ σ + σ - σ - 0 +1 -
Page 43 and 44:
phase-space density is defined as
Page 45 and 46:
which maintains a constant η = U/k
Page 47 and 48: 2.12.1 Saturated Absorption Spectro
Page 49 and 50: Figure 2.22: Saturation absorption
Page 51 and 52: Signal 0 Signal (a) (b) Signal Freq
Page 53 and 54: (a) (b) (c) (d) Figure 2.24: Absorp
Page 55 and 56: y more complex energy level structu
Page 57 and 58: ight side of the box. An irreversib
Page 59 and 60: time (a) (b) (c) Figure 3.3: Single
Page 61 and 62: them to move from B to A, but close
Page 63 and 64: Figure 4.1: Vacuum chamber. Photogr
Page 65 and 66: ( ( Figure 4.3: Helicoflex seal. (a
Page 67 and 68: 88 mm 4.2.3 Auxiliary Coils 62 mm Q
Page 69 and 70: 5 2 P 3/2 5 2 S 1/2 384. 230 484 46
Page 71 and 72: distribution of the MOT master lase
Page 73 and 74: shifts. First a frequency shift of
Page 75 and 76: transition. However, the laser freq
Page 77 and 78: 4.3.1.4 Upper MOT Horizontal Slave
Page 79 and 80: provides the beam for the upper MOT
Page 81 and 82: demon beam λ λ horizontal MOT bea
Page 83 and 84: scholar, Florian Schreck. It is wri
Page 85 and 86: Atoms are then optically pumped to
Page 87 and 88: ferred into the |F = 1,mF = 0〉 or
Page 89 and 90: 5.2 Branching Ratios and Population
Page 91 and 92: effect of the reflected beam at zer
Page 93 and 94: y the repulsive trough beams, gaini
Page 95 and 96: Figure 5.9: Atom number as a functi
Page 97: Figure 5.10: Radius of the magnetic
Page 101 and 102: ferred via the single-photon coolin
Page 103 and 104: By comparison an atomic Fock state
Page 105 and 106: of atoms in the two hyperfine groun
Page 107 and 108: difference in the lifetimes is dete
Page 109 and 110: Chapter 7 Lithium Apparatus Creatin
Page 111 and 112: angle valve rotary feedthrough ion
Page 113 and 114: an ion gauge controller (Granville
Page 115 and 116: viewports (MDC, 450002) are attache
Page 117 and 118: not trapped by the MOT impinge on t
Page 119 and 120: Should contamination of the vacuum
Page 121 and 122: Figure 7.12: The assembled Zeeman s
Page 123 and 124: 7.2.2 MOT Coils A second set of coi
Page 125 and 126: BGauss 250 200 150 100 50 30 20 10
Page 127 and 128: are required to create the high mag
Page 129 and 130: The coils are then checked for shor
Page 131 and 132: + B A Figure 7.23: Feshbach coil H-
Page 133 and 134: ensure that no particulates build u
Page 135 and 136: 118 Figure 7.26: Optical layout of
Page 137 and 138: The error signal shows three lines,
Page 139 and 140: into the CO2 laser. The optical lay
Page 141 and 142: Thorlabs PDA10A Coupler ZDC-10-1 to
Page 143 and 144: Imaging ber Imaging ber from Imagin
Page 145 and 146: Table 7.4 summarizes the beam power
Page 147 and 148: CO2 laser 40 MHz AOM f=2 in f=2 in
Page 149 and 150:
132 Figure 7.38: Optical layout aro
Page 151 and 152:
Feshbach coil objective lenses atom
Page 153 and 154:
MOT beams are no longer traveling a
Page 155 and 156:
The second card (NI6733) offers eig
Page 157 and 158:
Averaging over the magnetic subleve
Page 159 and 160:
2 2 P 3/2 D 2=670.977nm 2 2 S 1/2 m
Page 161 and 162:
The right hand side of equation 7.1
Page 163 and 164:
= E0 1 −n2 √2 exp σ0 ± iE0
Page 165 and 166:
esidual potentials besides gravitat
Page 167 and 168:
Figure 8.1: MOT loading. Typical lo
Page 169 and 170:
A linear ramp typically changes the
Page 171 and 172:
A typical MOT is density-limited at
Page 173 and 174:
ubidium [113-115] and cesium[116].
Page 175 and 176:
that most of the noise is due to th
Page 177 and 178:
(a) (c) y . x z X=0.0mm Z=2.5mm 1)
Page 179 and 180:
Figure 8.11: Different shapes of MO
Page 181 and 182:
ZnSe lens f=5 in knife edge ZnSe wi
Page 183 and 184:
shown in figure 8.13. By matching t
Page 185 and 186:
Figure 8.15: Atom number and temper
Page 187 and 188:
275 Hz. Using these values the beam
Page 189 and 190:
system. Maybe the easiest way to ac
Page 191 and 192:
Appendix A Magic Wavelength of Hydr
Page 193 and 194:
transitions for the excited state p
Page 195 and 196:
Bibliography [1] J.J. Thomson. Cath
Page 197 and 198:
[22] C.J. Foot. Atomic Physics. Oxf
Page 199 and 200:
[46] E.D. Black. An introduction to
Page 201 and 202:
[67] J.L. Hanssen. Controlling Atom
Page 203 and 204:
[88] D.S. Naik, C.G. Peterson, A.G.
Page 205 and 206:
[110] J.W. Goodman. Introduction to
Page 207:
[132] C. Degenhardt, H. Stoehr, U.
show all

Experiments to Control Atom Number and Phase-Space Density in ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?