723:
Atoms after passing the first inhomogeneous field will split into 2 beams corresponding the spin up and spin down state. Select one beam (spin up state, for example) and let it pass the rotating field. If the rotating field has frequency (ω) equal to the Larmor frequency, it will produce a high
595:
434:
228:
139:
449:
302:
643:
698:
724:
intensity of the other beam (spin down state). By sweeping the frequency to obtain a maximum intensity, one can find out the Larmor frequency and the magnetic moment of the atom.
324:
720:
The experiment setup contains 3 parts: an inhomogeneous magnetic field in front, the rotating field at the middle, and another inhomogeneous magnetic field at the end.
732:
151:
778:
68:
590:{\displaystyle {\frac {d{\vec {J_{R}}}}{dt}}=\hbar {\vec {J}}\times ({\vec {B_{0}}}+{\vec {B_{R}}})-{\vec {J}}\times {\vec {\omega }}}
705:
Since the rotating field is perpendicular to the static field, the spin in rotating frame is now able to flip between up and down.
26:
for measuring the nuclear spin. The atom is placed in a static magnetic field and a perpendicular rotating magnetic field.
733:
https://web.archive.org/web/20160325004825/https://www.colorado.edu/physics/phys7550/phys7550_sp07/extras/Ramsey90_RMP.pdf
309:
The minus sign is necessary. It reflects that the J is rotating in left-hand when the thumb is pointing as the H field.
261:
605:
660:
429:{\displaystyle {\frac {d{\vec {J_{R}}}}{dt}}={\frac {d{\vec {J}}}{dt}}-{\vec {J}}\times {\vec {\omega }}}
316:), with angular frequency ω. In the rotating frame of the rotating field, the equation of motion is:
773:
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8:
243:
223:{\displaystyle {\vec {\mu }}=g{\frac {\mu _{B}}{\hbar }}{\vec {J}}=\gamma {\vec {J}}}
23:
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743:
650:
246:, which is dimensionless and reflecting the environmental effect on the spin.
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134:{\displaystyle {\frac {d{\vec {J}}}{dt}}={\vec {\mu }}\times {\vec {B}}}
748:
712:, one can obtain a maximum flipping and determine the magnetic moment.
645:, the static field is cancelled, and the spin now precesses around H
60:
According to mechanics, the equation of motion of the spin J is:
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253:) with the magnetic field pointing on z-axis:
312:when turned on the rotating magnetic field (B
53:and the corresponding angular frequency is ω
29:We present a classical treatment in here.
297:{\displaystyle \omega _{0}=-\gamma B_{0}}
638:{\displaystyle \gamma B_{0}=\omega _{0}}
727:
693:{\displaystyle \omega _{R}=\hbar B_{R}}
779:Atomic, molecular, and optical physics
761:
37:When only the static magnetic field (B
249:Solving gives the angular frequency (
16:Technique for measuring nuclear spin
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41:) is turned on, the spin will
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715:
22:is a technique developed by
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649:with angular frequency
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20:Rabi resonance method
728:References and notes
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24:Isidor Isaac Rabi
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251:Larmor frequency
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47:Larmor frequency
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237:magnetic moment
235:where μ is the
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45:around it with
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774:Atomic physics
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769:Quantum optics
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744:Rabi frequency
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651:Rabi frequency
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708:By sweeping ω
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754:Rabi problem
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763:Categories
749:Rabi cycle
716:Experiment
678:ℏ
666:ω
627:ω
610:γ
582:→
579:ω
573:×
567:→
558:−
549:→
527:→
508:×
502:→
493:ℏ
473:→
421:→
418:ω
412:×
406:→
397:−
380:→
348:→
282:γ
279:−
267:ω
215:→
206:γ
197:→
186:ℏ
177:μ
162:→
159:μ
126:→
117:×
111:→
108:μ
85:→
738:See also
244:g-factor
43:precess
33:Theory
242:g is
602:if
441:or
765::
239:.
57:.
710:R
686:R
682:B
675:=
670:R
647:R
631:0
623:=
618:0
614:B
564:J
555:)
544:R
540:B
533:+
522:0
518:B
511:(
499:J
490:=
484:t
481:d
468:R
464:J
457:d
403:J
391:t
388:d
377:J
371:d
365:=
359:t
356:d
343:R
339:J
332:d
314:R
290:0
286:B
276:=
271:0
212:J
203:=
194:J
181:B
171:g
168:=
123:B
102:=
96:t
93:d
82:J
76:d
55:0
51:0
49:ν
39:0
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