Single-Photon Atomic Cooling - Raizen Lab - The University of ...

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dition to driving an internal transition, it also imparts a momentum kick. The magnitude of momentum transfered from photon to atom is given by the de Broglie relation |p| = k (1.1) where k = w/c is the magnitude of the wavevector of the resonant light. This landmark experiment demonstrated the possibility of using light to control atomic external degrees of freedom, namely position and momentum. Progress in this field effectively stopped after this observation and further advancement would have to await the invention of the laser. Interest was revitalized 40 years later with a series of proposals to cool and trap both ions and neutral atoms using the Doppler effect [2, 3]. The proposed idea is quite ingenious and is worth quickly revisiting here. It involves directing a laser beam tuned slightly below the resonance frequency (red detuned) at an atomic ensemble. The effect of such an arrangement can be deduced by considering what happens to an atom in the ensemble in the following two cases: when the atom travels toward the laser beam and when the atom travels away from it. In the first case, the atom will be brought closer into resonance by the Doppler effect and therefore its scattering rate will increase. In the latter case the motion of the atom will cause it to be further out of resonance with the laser beam, reducing the scattering rate. Note that the absorption of each photon is directional, while the direction of the subsequent spontaneous emission is random. After a large number of scattering events the momentum kicks due to spontaneous emission will average to zero, while 2
the momentum kicks due to absorption will sum. The result is that atoms traveling towards the red detuned beam will be slowed by momentum transfer from scattered photons. This arrangement does more than simply slow the center-of-mass motion of an ensemble, it also cools it because the red detuned beam affects atoms in a velocity dependent way. Quickly moving atoms are Doppler shifted to the blue more than slowly moving atoms (assuming both are traveling toward the laser source), causing them to scatter at a greater rate which in turn decelerates them more quickly than more slowly moving atoms. This compresses the velocity spread of the ensemble, thereby cooling it. Experiments applying this cooling scheme to electromagnetically trapped ions were successfully performed in 1978 [4, 5]. Then in 1985 the first experiments demonstrating slowing of neutral atomic beams were published [6, 7]. That same year, trapping in velocity space with counter propagating red detuned beams, an arrangement known as optical molasses, was demonstrated at Bell Labs by a group led by S. Chu [8]. The spatial confinement of sodium atoms using a magnetic field was also demonstrated in Gaithersburg by the group of W. Phillips [9] in that very productive year of 1985. Two years later, the combination of ideas utilized in these two experiments were used to both confine and cool atoms in a technique known as magneto-optical trapping (MOT) [10]. Shortly after this achievement, groups began to observe and report a troubling, or perhaps welcome, disagreement between experiment and theory. In particular, the group of W. Phillips reported temperatures of atomic sam- 3
Page 1 and 2: Copyright by Gabriel Noam Price 200
Page 3 and 4: Single-Photon Atomic Cooling by Gab
Page 5 and 6: Acknowledgments First, I would like
Page 7 and 8: Rubidium group when I first joined.
Page 9 and 10: Single-Photon Atomic Cooling Public
Page 11 and 12: 2.5.2.4 Magneto-Optical Trap . . .
Page 13 and 14: List of Tables 2.1 87 Rb Physical P
Page 15 and 16: 3.1 Vacuum Chamber . . . . . . . .
Page 17: Chapter 1 Introduction This chapter
Page 21 and 22: samples by allowing for very long i
Page 23 and 24: Figure 1.2: The energy level struct
Page 25 and 26: quency regime [19]. This then led t
Page 27 and 28: Figure 1.4: Depiction of a simple,
Page 29 and 30: demonstrates the cooling power of a
Page 31 and 32: a) b) c) external potential one-way
Page 33 and 34: worked on by Brillouin [27-29], ide
Page 35 and 36: the atomic ensemble. Not surprising
Page 37 and 38: are untrappable. The SI unit for en
Page 39 and 40: the atomic transition and is called
Page 41 and 42: 2.1 Rubidium Rubidium (Rb) is an al
Page 43 and 44: constant which is given by α = e2
Page 45 and 46: only one value of J is possible fro
Page 47 and 48: the latter of which only applies to
Page 49 and 50: Figure 2.1: 87 Rb D2 Transition Hyp
Page 51 and 52: Pluging Eq. 2.18 into this Hamilton
Page 53 and 54: Following the same logic leads to a
Page 55 and 56: gF = −1/2 using the approximate e
Page 57 and 58: mize their energy in high magnetic
Page 59 and 60: If we now consider the field from t
Page 61 and 62: where P is in torr. The lifetime of
Page 63 and 64: component of the dipole oscillation
Page 65 and 66: maxima. Our experiment makes extens
Page 67 and 68: atoms its wavefunction Ψ(t) is typ
Page 69 and 70:
In this equation we let H = H0 + Hc
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The significance of Isat is that at
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Δ ω =ω−Δ ω =ω−Δ Δ
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where I/Isat ≪ 1 has been assumed
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λ λ Figure 2.9: The Sisyphus cool
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process repeats. If however, it dec
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σ σ σ Figure 2.10: Geomet
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to vary linearly with position alon
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0, ±1 and ∆mF = 0, ±1, allow ex
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this figure only the relevant hyper
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D2 transition in 87 Rb has a natura
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2.7.2 Saturation Absorption Spectro
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ground state depletion due to the p
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oadened background can be removed f
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where n is the number density of at
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where σ 2 c = σ 2 2 kBTt n + m .
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Chapter 3 Experimental Apparatus Th
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Figure 3.1: The vacuum chamber duri
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Nor-Cal Products Inc. (AMV-1502-CF)
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and monitor the necessary vacuum le
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3.1.3 Lower Chamber The lower chamb
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a) top ridge 1 cm b) metal jacket h
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to the appropriate frequency throug
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plexiglass cover piezo U stack grat
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λ Figure 3
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Voltage a b c d e f Frequency Figur
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eams. For example the MOT and optic
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λ Figure 3.12: The slave lasers
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λ λ λ
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λ λ λ λ
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needed when forming a MOT or optica
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master laser is dithered at 20 kHz.
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λ λ
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Output Power > 10 W Wavelength 532
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labeled 1, 2 and 3 in the Fig. 3.21
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λ λ λ λ
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process. The two coils are arranged
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19) connected in parallel. This arr
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3.4.2 Horizontal Imaging The horizo
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Chapter 4 Single-Photon Atomic Cool
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1 s, after which time ∼ 10 8 87 R
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(a) x z magnetically trapped atoms
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h x z magnetically trapped atoms y
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z y x magnetically trapped atoms cr
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Figure 4.5: The effective potential
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depopulation present and it indicat
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numbers sufficiently large to quant
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μ μ μ
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the potential landscape due to the
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Figure 4.12: The number of atoms lo
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Figure 4.13: Incremental atom captu
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netic trap and transfer into the op
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temperature TB of atoms loaded into
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used to construct it into the remai
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μ μ μ Figure 4.18: Side view of
Page 179 and 180:
Figure 4.20: Geometry of the optica
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could potentially have undergone th
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detunings. The result of scattering
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are switched off causing non-optica
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Figure 4.25: Number (■) and tempe
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traps. If we model the ensembles in
Page 191 and 192:
Figure 4.26: Radius of the atomic c
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atoms were removed from the magneti
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trappable |F = 1,mF = −1〉 state
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the short lived 2p state. Atoms whi
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Bibliography [1] R. Frisch, “Expe
Page 201 and 202:
[15] C. C. Bradley, C. A. Sackett,
Page 203 and 204:
[31] E.T. Jaynes, “Information th
Page 205 and 206:
[49] J. Ye, S. Swartz, P. Jungner,
Page 207 and 208:
[66] J.P. Gordon and A. Ashkin, “
Page 209 and 210:
[85] C.-S. Chuu, Direct Study of Qu
Page 211 and 212:
adicals,” Phys. Rev. Lett. 94, 02
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