Experiments to Control Atom Number and Phase-Space Density in ...
Experiments to Control Atom Number and Phase-Space Density in ...
Experiments to Control Atom Number and Phase-Space Density in ...
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Chapter 6<br />
Fock States <strong>and</strong> Laser Cull<strong>in</strong>g<br />
In typical cold a<strong>to</strong>m experiments, the number of a<strong>to</strong>ms of the ensemble is un-<br />
known, <strong>and</strong> is usually determ<strong>in</strong>ed after the experimental sequence via absorption or<br />
fluorescence imag<strong>in</strong>g. Furthermore, repeat<strong>in</strong>g the experiment will lead <strong>to</strong> a different<br />
a<strong>to</strong>m number, <strong>and</strong> the distribution will <strong>in</strong> general follow Poissonian statistics. <strong>Control</strong>-<br />
l<strong>in</strong>g the particle number precisely is a first step <strong>to</strong>wards study<strong>in</strong>g quantum entanglement<br />
<strong>and</strong> quantum collision on the few particle level, without resort<strong>in</strong>g <strong>to</strong> ensemble averaged<br />
measurements, were even small variations from the average can have a large <strong>in</strong>fluence<br />
on the experimental result.<br />
6.1 A<strong>to</strong>mic Fock States<br />
In general a Fock state is a quantum state with a well-def<strong>in</strong>ed number of particles,<br />
e.g. pho<strong>to</strong>ns or phonons, <strong>in</strong> a s<strong>in</strong>gle mode. They are also frequently referred <strong>to</strong> as<br />
number states. Fock states are most commonly encountered when solv<strong>in</strong>g the quantum<br />
harmonic oscilla<strong>to</strong>r. In this case the energy levels are equally spaced, <strong>and</strong> the energy<br />
eigenstates are also the eigenstates of the number of phonons with energy equal <strong>to</strong> the<br />
energy splitt<strong>in</strong>g.<br />
An N-pho<strong>to</strong>n Fock state <strong>in</strong> a cavity is def<strong>in</strong>ed as hav<strong>in</strong>g N pho<strong>to</strong>ns <strong>in</strong> a partic-<br />
ular cavity mode. Pho<strong>to</strong>n Fock states have been realized experimentally us<strong>in</strong>g several<br />
different approaches, for example pho<strong>to</strong>n down-conversion [81], us<strong>in</strong>g a high-Q cavity<br />
[82], us<strong>in</strong>g a s<strong>in</strong>gle a<strong>to</strong>m trapped <strong>in</strong> a cavity [83], <strong>and</strong> by controll<strong>in</strong>g emission from a<br />
s<strong>in</strong>gle molecule [84]. Properties of pho<strong>to</strong>n Fock states have been studied <strong>in</strong> a number<br />
of experiments [85, 86], <strong>and</strong> the application of these pho<strong>to</strong>n Fock states <strong>to</strong> quantum<br />
comput<strong>in</strong>g <strong>and</strong> quantum cryp<strong>to</strong>graphy has been considered [87, 88].<br />
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