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

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Chapter 1 Introduction Atomic physics is the study of the atomic energy level structure and of atomic interactions with other particles, external magnetic fields, and external electric fields. It has also been a testing ground for theories of quantum mechanics. As such, it is a research field with a long tradition. One could argue that modern atomic physics started with J.J. Thomson’s discovery of the electron [1]. Ernest Rutherford, and the discovery of atomic structure consisting of a nucleus surrounded by a cloud of orbiting electrons, was the next step only a few years later [2]. Max Planck’s postulate of energy quantization of oscillators in a black body, and Niels Bohr’s model of the atomic nucleus surrounded by electrons moving in circular orbits were the first attempts to explain quantum phenoma such as the spectral emission lines of hydrogen in terms of the underlying atomic structure [3, 4]. In the following years of the early 20th century many exciting discoveries were made and theories developed, including work by Einstein and deBroglie, ultimately leading to the development of quantum mechanics by Heisenberg, Schrödinger and others. Even though much progress in the understanding of atomic structure was made during the mid 20th century, the experimental techniques used in this dissertation were not developed until the 1980s, when William Phillips, Harold Metcalf and co-workers developed the Zeeman slower to reduce the velocity of an effusive atomic beam [5–7]. Following this development was the experimental realization of optical molasses and magneto-optical trapping in 1987 [8], work for which Steven Chu was awarded the nobel prize in 1997, together with Claude Cohen-Tannoudji and William Phillips. These are still the standard techniques used today to cool and trap neutral atoms, and they have led to the realization of Bose-Einstein condensates [9–11] and degenerate Fermi gases [12–14]. 1
The development of techniques to laser-cool atoms has enabled many interesting studies based on the ability to control temperature and internal states of trapped atomic ensembles. Their applicability, however, is restriced to a limited number of atoms, mostly the alkaline atoms. By gaining a similar amount of control over all atomic species new fundamental research relying on properties specific to each atom becomes feasible. For example, measuring the isotopic shifts in hydrogen with an increased precision would provide further testing ground for theories of nuclear few-body systems. Cooled atomic ensembles of deuterium and tritium could potentially lead to such improved measure- ments. Moreover, in general, the number of atoms in an atomic ensemble is subject to Poissonian fluctuations and is not controllable in standard cold gases experiments. The atom number, however, is an important parameter in many interesting quantum- mechanical systems. Precise control of the number is required for studying phenomena like quantum entanglement and for understanding the physics of cold atomic collisions. Control of the atom number is therefore mandatory for quantum simulation and quantum computing experiments. This dissertation presents two techniques that allow for general control of phase- space density and atom number in cold atomic gases; single-photon cooling and laser culling. Chapter 2 summarizes the basic theory of atomic interactions with external fields and introduces standard atomic physics techniques as far as they pertain to the experiments described in this dissertation. Chapters 3, 4, and 5 describe the technique of single-photon cooling, the experimental apparatus used for the implementation using rubidium, and the results of the proof-of-principle experiment. The method of laser culling paves the way towards studying trapped samples with a defined number of atoms by offering the ability to control the number of atoms down to a single atom level. Chapter 6 introduces the general idea of laser culling. Chapter 7 summarizes the experimental apparatus built for a laser culling experiment of a trapped sample of fermionic lithium, and chapter 8 outlines the progress made towards creating Fock states of neutral atoms. 2
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: 7.39 Future vertical axis optics .
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
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5 2 P 3/2 5 2 S 1/2 384. 230 484 46
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distribution of the MOT master lase
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shifts. First a frequency shift of
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transition. However, the laser freq
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4.3.1.4 Upper MOT Horizontal Slave
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provides the beam for the upper MOT
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demon beam λ λ horizontal MOT bea
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scholar, Florian Schreck. It is wri
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Atoms are then optically pumped to
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ferred into the |F = 1,mF = 0〉 or
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5.2 Branching Ratios and Population
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effect of the reflected beam at zer
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y the repulsive trough beams, gaini
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Figure 5.9: Atom number as a functi
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Figure 5.10: Radius of the magnetic
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on the collision rate of atoms insi
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ferred via the single-photon coolin
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By comparison an atomic Fock state
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of atoms in the two hyperfine groun
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difference in the lifetimes is dete
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Chapter 7 Lithium Apparatus Creatin
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angle valve rotary feedthrough ion
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an ion gauge controller (Granville
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viewports (MDC, 450002) are attache
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not trapped by the MOT impinge on t
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Should contamination of the vacuum
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Figure 7.12: The assembled Zeeman s
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7.2.2 MOT Coils A second set of coi
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BGauss 250 200 150 100 50 30 20 10
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are required to create the high mag
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The coils are then checked for shor
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+ B A Figure 7.23: Feshbach coil H-
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ensure that no particulates build u
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118 Figure 7.26: Optical layout of
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The error signal shows three lines,
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into the CO2 laser. The optical lay
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Thorlabs PDA10A Coupler ZDC-10-1 to
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Imaging ber Imaging ber from Imagin
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Table 7.4 summarizes the beam power
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CO2 laser 40 MHz AOM f=2 in f=2 in
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132 Figure 7.38: Optical layout aro
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Feshbach coil objective lenses atom
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MOT beams are no longer traveling a
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The second card (NI6733) offers eig
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Averaging over the magnetic subleve
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2 2 P 3/2 D 2=670.977nm 2 2 S 1/2 m
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The right hand side of equation 7.1
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= E0 1 −n2 √2 exp σ0 ± iE0
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esidual potentials besides gravitat
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Figure 8.1: MOT loading. Typical lo
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A linear ramp typically changes the
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A typical MOT is density-limited at
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ubidium [113-115] and cesium[116].
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that most of the noise is due to th
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(a) (c) y . x z X=0.0mm Z=2.5mm 1)
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Figure 8.11: Different shapes of MO
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ZnSe lens f=5 in knife edge ZnSe wi
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shown in figure 8.13. By matching t
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Figure 8.15: Atom number and temper
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275 Hz. Using these values the beam
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system. Maybe the easiest way to ac
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Appendix A Magic Wavelength of Hydr
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transitions for the excited state p
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Bibliography [1] J.J. Thomson. Cath
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[22] C.J. Foot. Atomic Physics. Oxf
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[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.
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