Download Transitions between quantum levels in room temperature Rb vapor Physics Department

Physics Department
Ben Gurion University of the Negev
M.Sc. Research Proposal
April 2014
Transitions between quantum levels in room
temperature 87Rb vapor
Orr Be’er
ID:065966152
Supervisor: Prof. Ron Folman
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Introduction
Ever since the foundations of quantum mechanics were laid down early in the twentieth
century, the notion that atoms have discrete energy spectrum became common knowledge.
Therefore, an atom can absorb or emit only a discrete amount of energy. In quantum optics
(the branch of quantum mechanics that involves light-matter interactions), this fact is used
to manipulate the internal and external degrees of freedom of an atomic ensemble. These
manipulations play an important role in studying the foundations of physics as well as in
developing various technological applications.
Optical transitions are governed by selection rules. These rules are based on the
transition matrix elements (e.g. the electric or magnetic dipole or quadrupole): transitions
are only allowed for nonzero matrix elements. For example, for electric dipole transitions,
only transition amplitudes for which ∆F = 0, ±1 and ∆mF = 0, ±1 are non-zero. (F is
the total atomic angular momentum and mF is its projection on the quantum axis).
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Transitions in room temperature atomic vapor
An alkali vapor cell is a sealed high-vacuum glass cell containing a drop of an alkali metal.
Due to the high vapor pressure of the alkali metals at room temperature, the cell is filled
with the alkali vapor. Each atom in this ensemble has the simple energy levels of an
isolated atom, in contrast with a solid sample, where atoms strongly interact with each
other and with the environment resulting in a much more complex energy scheme. The
main drawback of using vapor cells is the high thermal velocity of the atoms. The mean
velocity is on the order of hundreds of meters per second, causing considerable Doppler
broadening of the energy levels.
Using such vapor cells, macroscopic entanglement was demonstrated [1] with cesium;
storing pulses of light, as well as images, was performed in rubidium vapor cells [2, 3];
rubidium vapor cells serve as the basis for chip-scale atomic clocks [4]; potassium, cesium and rubidium vapor cells are used for high sensitivity optical magnetometry [5, 6].
Additional applications can be found in Refs. [7–10].
One of the most the desireable charateristic for the vapor cells used in this study is
the atomic coherence time, i.e. the averaged time that an atom can preserve its quantum
state. There are several mechanisms that reduce the coherence time, such as collisions of
Rb atom with the vapor cell wall and Rb-Rb collisions.
Some cell manufacturing methods increase the coherence time dramatically. Coating
the cell’s inner wall with paraffin wax reduces the effect of Rb-wall collisions by up to four
orders of magnitude [11]. Filling a vapor cell with inert buffer gas [12] reduces the atom’s
mean free path and therefore reduces the probability of Rb-wall and Rb-Rb collisions.
For a properly selected buffer gas, Rb-buffer gas collisions are less likely to cause loss of
coherence.
The state of alkali vapor can be represented and studied using atomic polarization
moments (PM). The PM of a particular hyper-fine level F are defined as [10]:
ρκq =
F
X
(−1)F −m1 hF, m2 , F, −m1 |κ, qiρm1 ,m2
(1)
m1 ,m2 =−F
where κ = 0...2F , q = −κ...κ, m1 and m2 are the magnetic quantum numbers, ρm1 ,m2 are
the density matrix elements and hF, m2 , F, −m1 |κ, qi are the Clebsch-Gordan coefficients.
The ρκq elements having the same κ are typically marked ρκ , each ρκ representing a physical
quantity
of the alkali vapor. ρ0 is the population of the relevant F state divided by
√
2F + 1, ρ1 is the dipole moment (also known as orientation), ρ2 is the quadrupole
moment (also known as alignment), and so on. Recently, several works [13–15] addressed
high-rank (κ > 0) PM.
It has been recently shown that for an alkali vapor there is a “magic frequency” [16], at
which the absorption of linearly polarized light by the vapor depends only on the hyperfine
population and not on the orientations of the light and of the magnetic moments of atoms,
e.g. the angle between the direction of the light and the direction of the magnetic field.
This allows us to make robust population measurements.
In the proposed research we will investigate light-matter interaction in room temperature Rb vapor cell, focusing on the following:
√
• Improving the measurement method of the hyperfine population ρ0 × 2F + 1 using
the magic frequency method. Measuring the hyperfine population will help us understand the interaction of atoms with light as a function of the light polarization,
light frequency and the magnetic field.
• Study the effect of RF radiation on the population distribution amongst the Zeeman
sublevels.
• Investigating possible upgrades for technological applications of vapor cells, such as
magnetometers.
• Improving the quality of rubidium and cesium vapor cells as well as methods and
tools to characterize them using laser light.
References
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[2] D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Physical
Review Letters 86, 783 (2001).
[3] M. Shuker, O. Firstenberg, R. Pugatch, A. Ron, and N. Davidson, Physical Review
Letters 100, 223601 (2008).
[4] S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A. Liew, and
J. Moreland, Applied Physics Letters 85, 1460 (2004).
[5] I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, Nature 422, 596
(2003).
[6] D. Budker and M. Romalis, Nature Physics 3, 227 (2007).
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[8] W. Demtröder, Laser spectroscopy: basic concepts and instrumentation (Springer
Verlag, Berlin, New york, 2003), 3rd ed.
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[9] J. Kitching, S. Knappe, M. Vukicevic, L. Hollberg, R. Wynands, and W. Weidmann,
IEEE Transactions on Instrumentation and Measurement 49, 1313 (2000).
[10] M. Auzinsh, D. Budker, and S. Rochester, Optically Polarized Atoms: Understanding
light-atom interactions (Oxford U. Press, 2010).
[11] M. A. Bouchiat and J. Brossel, Physical Review 147, 41 (1966).
[12] W. Franzen, Physical Review 115, 850 (1959).
[13] D. Budker, W. Gawlik, D. F. Kimball, S. M. Rochester, V. V. Yashchuk, and A. Weis,
Reviews of Modern Physics 74, 1153 (2002).
[14] V. V. Yashchuk, D. Budker, W. Gawlik, D. F. Kimball, Y. P. Malakyan, and S. M.
Rochester, Physical Review Letters 90, 253001 (2003).
[15] M. T. Graf, D. F. Kimball, S. M. Rochester, K. Kerner, C. Wong, D. Budker, E. B.
Alexandrov, M. V. Balabas, and V. V. Yashchuk, Physical Review A 72, 14 (2005).
[16] M. Givon, Y. Margalit, A. Waxman, T. David, D. Groswasser, Y. Japha, and R. Folman, Physical Review Letters 111, 053004 (2013).
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