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| The '''Rabi frequency''' is the frequency of oscillation for a given [[atomic electron transition|atomic transition]] in a given light field. It is associated with the strength of the coupling between the light and the transition. [[Rabi flopping]] between the levels of a 2-level system illuminated with resonant light, will occur at the Rabi frequency. The Rabi frequency is a semiclassical concept as it is based on a [[Quantum mechanics|quantum]] [[Energy level|atomic transition]] and a [[Classical mechanics|classical]] [[Electromagnetic field|light field]].
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| In the context of a [[nuclear magnetic resonance]] experiment, the Rabi frequency is the nutation frequency of a sample's net nuclear magnetization vector about a radiofrequency field. (Note that this is distinct from the [[Larmor precession|Larmor frequency]], which characterizes the precession of a transverse nuclear magnetization about a static magnetic field.)
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| == Definition ==
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| The Rabi frequency is defined as
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| :<math> \chi_{i,j} = {\vec{d}_{i,j}\cdot\vec{E}_0 \over \hbar}</math>
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| where <math>\scriptstyle{\vec{d}_{i,j}}</math> is the [[transition dipole moment]] for the <math>\scriptstyle{i \rightarrow j}</math> transition and <math>\scriptstyle{\vec{E}_0 = \hat{\epsilon}E_0}</math> is the [[vector (geometric)|vector]] [[electric field]] [[amplitude]] which includes the [[Polarization (waves)|polarization]]. The numerator has dimensions of energy, so dividing by <math>\scriptstyle{\hbar}</math> gives an [[angular frequency]]. Although <math>\scriptstyle{\vec{d}_{i,j} = \vec{d}_{j,i}^*}</math>, one cannot assume that <math>\scriptstyle{\chi_{i,j} = \chi_{j,i}^*}</math> as <math>\scriptstyle{\hat{\epsilon}E_0}</math> may be complex, as in the case of [[circularly polarized light]].<ref name="MilonniEberly">{{cite book| title = Lasers | edition = | last = Milonni | first = Peter W. | coauthors = Eberly, Joseph H. | year = 1998| publisher = John Wiley & Sons| isbn = 0-471-62731-3| page = 191}}</ref>
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| By analogy with a [[Classical physics|classical]] [[dipole]], it is clear that an atom with a large dipole moment will be more susceptible to perturbation by [[Electric field|electric]] and [[Magnetic field|magnetic]] fields. The [[dot product]] includes a factor of <math>\cos\theta</math>, where <math>\theta</math> is the angle between the polarization of the light and the transition dipole moment. When they are parallel or antiparallel the interaction is strongest, when they are perpendicular there is no interaction at all. The vector electric field amplitude defines both the intensity and the polarization of the light.
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| In real systems, with more than two levels, the correct dipole transition matrix element for the relevant transition has to be calculated. When equating the Rabi frequency the correct [[Clebsch-Gordan coefficient]] has to be considered which is a common source of mistakes throughout scientific literature.{{Citation needed|date=November 2011}} There are also some publications that use a different definition for the Rabi frequency which is by a factor of two smaller than the one introduced here.{{Citation needed|date=November 2011}}
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| [[File:Animation of optical resonance, frequency domain.gif|Animation of optical resonance, frequency domain]]
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| == Generalized Rabi frequency ==
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| For light that is off resonance with a transition, it is common to define the ''generalized Rabi frequency'' <math>\Omega_{i,j}</math>. [[Rabi flopping]] actually occurs at the generalized Rabi frequency.
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| :<math>\Omega_{i,j} = \sqrt{|\chi_{i,j}|^2 + \Delta^2}</math>
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| where <math>\Delta = \omega_{light} - \omega_{transition}</math> is the [[laser detuning|detuning]], a measure of how far the light is off resonance with the transition.
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| ==See also==
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| *[[Rabi cycle]]
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| *[[Vacuum Rabi oscillation]]
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| *[[Rabi resonance method]]
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| ==References==
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| {{reflist|1}}
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| [[Category:Quantum optics]]
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| [[Category:Atomic physics]]
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| [[Category:Atomic, molecular, and optical physics]]
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Greetings! I am Myrtle Shroyer. California is our beginning place. For years I've been working as a payroll clerk. To gather badges is what her family members and her enjoy.
Visit my blog post blogzaa.com