Modern Physics and Quantum Mechanics

Anderson, Elmer E.; Erlichson, Herman

doi:10.1119/1.1986747

Cited by 12 publications

(13 citation statements)

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“…Itano has presented a theoretical treatment for the quadrupole moment shift for an arbitrary angular orientation between a field gradient and the quantization axis [40]. We have performed calculations using hydrogenic wave functions [41] for the 4d 2 D 5/2 level. By fitting the actual state energy to an effective hydrogenic energy level, with effective quantum number n * = 2.43, a matrix element ͗4d͉r 2 ͉4d͘ = 9.24 a o 2 was obtained where a o is the Bohr radius.…”

Section: Gallaghermentioning

confidence: 99%

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Absolute frequency of theSr+885sS1∕2
Madej
¹
,
Bernard
²
,
Dubé
³

et al. 2004
Phys. Rev. A
91
2
98
0
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A Cs referenced optical frequency comb system has been used to measure the center frequency of the 5s 2 S 1/2 -4d 2 D 5/2 transition at 445 THz in a single, trapped, and laser-cooled 88 Sr + ion. The transition frequency SD = 444 779 044 095 510 Hz± 50 Hz ͑1͒ is obtained, when corrected for systematic shifts. A detailed calculation of the estimated systematic shifts is presented which yields improved values for the various shift parameters including blackbody and electric quadrupole moment shifts. PACS number(s): 32.30.Jc, 32.80.Pj, 06.20.Fn, 06.30.Ft FIG. 1. Partial energy level diagram of 88 Sr + showing the principal transitions used in cooling, fluorescence detection, repumping, and probing of the reference 445-THz ͑674 nm͒ transition. 70 012507-1 FIG. 2. Schematic diagram of the NRC femtosecond laser frequency comb system.

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Section: Gallaghermentioning

confidence: 99%

“…By using second-order perturbation theory [41], these shifts have been determined to be ⌬ Z2 = 6 25 K; m = ± 1 2 ,…”

Section: Second-order Zeeman Shiftmentioning

confidence: 99%

Absolute frequency of theSr+885sS1∕2
Madej
¹
,
Bernard
²
,
Dubé
³

et al. 2004
Phys. Rev. A
91
2
98
0
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“…The equivalence of mass and energy only manifests in the zeromomentum frame. 17 ) In the frame of the particles where their clocks run at the proper rate, Lorentz contraction of the Earth's atmosphere makes the duration of the trip through the atmosphere shorter than it is in the frame of the Earth, thereby allowing the particles to survive the trip without decaying. The reduced ageing of the particles during their trip through the atmosphere is absolute even when acceleration is negligible or ignored.…”

Section: A Real and Ongoing Experimentsmentioning

confidence: 98%

When moving clocks run fast.

Allen¹

2013

phys essays

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An asymmetry in Lorentz contraction can be created with a pointlike object in uniform motion relative to another object that has a finite, linear, spatial extent along the line of motion (extended object). Let Dt be the time that elapses as the pointlike object flies by the extended object in the frame of the latter. Let Dt 0 be the time that elapses as the extended object flies by the pointlike object in the frame of the latter. These elapsed times depend upon the frame of reference. However, because the extended object is Lorentz contracted and the pointlike object is not, the relationship between the elapsed times is "interframe consistent" according to Dt/Dt 0 ¼ c. In the frame of the extended object, time runs slower in the moving frame, as expected. But in the frame of the pointlike object, time runs faster in the moving frame. In both frames, the duration of the flyby is shorter in the frame of the pointlike object. The twin-type paradox is eliminated without acceleration. Cosmic ray showers provide a natural example. Analogous to measurement in quantum mechanics, an experimentalist can create a pointlike object by choosing to measure the uniform motion of an extended object relative to a point in the laboratory frame. V C 2013 Physics Essays Publication. [http://dx.Résumé: Une asymétrie dans la contraction de Lorentz peut être créée avec un objet de dimension de point en déplacement uniforme par rapport à un autre objet qui a une extension spatiale linéaire finie dans la direction du mouvement (objet étendu). Soit Dt le temps qui s'écoule quand l'objet de dimension de point vole près de l'objet étendue dans le référentiel de ce dernier. Soit Dt 0 le temps qui s'écoule quand l'objet étendu vole près de l'objet de dimension de point dans le référentiel de ce dernier. Ces temps écoulés dépendent du référentiel. Toutefois, parce que l'objet étendu est contracté de Lorentz mais pas l'objet de dimension de point, la relation entre les temps la écoulés est "consistent entre les référentiels" selon l'équation Dt/Dt 0 ¼ c. Dans le référentiel de l'objet étendu, le temps s'écoule plus lentement dans le référentiel en mouvement, comme prévu. Mais dans le référentiel de l'objet de dimension de point, le temps s'écoule plus vite dans le référentiel en mouvement. Dans les deux référentiels, la durée du survol est plus courte dans le référentiel de l'objet de dimension de point. Le paradoxe des jumeaux n'a plus cours sans accélération. Un exemple naturel nous est fourni par les gerbes de rayons cosmiques. De façon analogue à une mesure en mécanique quantique, un expérimentateur peut créer un objet de dimension de point en choisissant de mesurer le déplacement uniforme d'un objet étendu par rapport à un point dans le référentiel de laboratoire.

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“…From the calculation, the statistical error of the linear Zeeman shift was 0.24 Hz. As for the second-order Zeeman shift, it can be calculated using second-order perturbation theory [29]. For our system, the average magnetic field during the measurements is 430 nT and the fluctuation of the field we measured is ∼3 nT.…”

Section: Estimation Of the Clock Transition Shiftsmentioning

confidence: 99%

Evaluation of the systematic shifts of a single-40Ca+-ion frequency standard

Huang

Cao

et al. 2011

Phys. Rev. A

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Progress on the evaluation of systematic frequency shifts is described in the development of the optical frequency standard based on single-trapped 40 Ca + with a "clock" transition at 729 nm. The overall systematic uncertainty of the 4s 2 S 1/2 -3d 2 D 5/2 clock resonance has been characterized to be 7.8 × 10 −16 . This uncertainty is at a level similar to the Cs fountain primary standard, while the potential stability for the 40 Ca + clock exceeds that of Cs.

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Modern Physics and Quantum Mechanics

Cited by 12 publications

References 0 publications

Absolute frequency of theSr+885sS1∕2
Madej
¹
,
Bernard
²
,
Dubé
³

et al. 2004
Phys. Rev. A
91
2
98
0
View full text Add to dashboard Cite

Absolute frequency of theSr+885sS1∕2
Madej
¹
,
Bernard
²
,
Dubé
³

et al. 2004
Phys. Rev. A
91
2
98
0
View full text Add to dashboard Cite

When moving clocks run fast.

Evaluation of the systematic shifts of a single-40Ca+-ion frequency standard

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Modern Physics and Quantum Mechanics

Cited by 12 publications

References 0 publications

Absolute frequency of theSr+885sS1∕2Madej1, Bernard2, Dubé3 et al. 2004Phys. Rev. A912980View full textAdd to dashboardCite

Absolute frequency of theSr+885sS1∕2Madej1, Bernard2, Dubé3 et al. 2004Phys. Rev. A912980View full textAdd to dashboardCite

When moving clocks run fast.

Evaluation of the systematic shifts of a single-40Ca+-ion frequency standard

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Product

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About

Absolute frequency of theSr+885sS1∕2
Madej
¹
,
Bernard
²
,
Dubé
³

et al. 2004
Phys. Rev. A
91
2
98
0
View full text Add to dashboard Cite

Absolute frequency of theSr+885sS1∕2
Madej
¹
,
Bernard
²
,
Dubé
³

et al. 2004
Phys. Rev. A
91
2
98
0
View full text Add to dashboard Cite