The Transverse Stern–gerlach Experiment

Bloom, Myer; Erdman, K. L.

doi:10.1139/p62-016

Cited by 28 publications

(20 citation statements)

References 2 publications

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“…The interaction-picture Hamiltonian is of the form //int = ~~ /BefT Irot (3) with B e ff an effective field as seen in a reference frame rotating about z with unit angular velocity. The rotatingframe spin I ro t is defined by I = [z®z + cosO)(l-z®z) + sinO)z*]I r (4) Here z* is the antisymmetric matrix (f *) y * =£,•£/,*. Henceforth we work exclusively in the rotating frame, and drop the subscript from I ro t. It is convenient to parametrize B e fr in Eq.…”

Section: H-t(p 2 + Q 2 )-Yb C -L-ybt'lco*(t)-yqn'g-imentioning

confidence: 99%

Folded Stern-Gerlach experiment as a means for detecting nuclear magnetic resonance in individual nuclei

1992

Phys. Rev. Lett.

135

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In a Stern-Gerlach experiment, the spatial trajectory of a particle traversing a magnetic-field gradient serves as a detector of its spin state. This paper considers the implications of adding a harmonic restoring potential to the Stern-Gerlach experiment. The behavior of such systems is shown to resemble that of a "folded" Stern-Gerlach experiment, in that the linear spatial trajectory of the Stern-Gerlach experiment becomes folded into the cyclic phase-space trajectory of the oscillator. Under appropriate circumstances, the coupling between the spin and the oscillator is shown to be sufficiently strong that it might find practical application as the basis of a magnetic resonance imaging device. : 33.25.-j, 35.80.+S, 61.16.Hn PACS numbersConsider a system made up of three elements: (1) a harmonic oscillator, (2) a spin-y particle (nominally a proton) mounted on the oscillator, and (3) an externally applied magnetic field. The magnetic moment of the particle will create a coupling between the field and the oscillator. How strong is the coupling? What is the dynamic behavior of the coupled system? This paper shows that, under the proper conditions, the coupling is sufficiently strong that magnetic resonance imaging of a single nucleus may be feasible, by monitoring the excitation of an oscillator coupled to the nucleus.Let (o be the resonant frequency of the mechanical oscillator, and m the oscillator mass. We adopt units h ^co-m = 1. The external magnetic field B(x,f) is assumed to have a uniform component, a time-dependent component, and a gradient component;

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Section: H-t(p 2 + Q 2 )-Yb C -L-ybt'lco*(t)-yqn'g-imentioning

confidence: 99%

Folded Stern-Gerlach experiment as a means for detecting nuclear magnetic resonance in individual nuclei

1992

Phys. Rev. Lett.

135

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“…1(a) an atom, localized to less than a wavelength of the oscillatory field, passes through the two separated interaction zones in Ramsey spectroscopy at t 1 and t 2 . The spatial variations of the dipole energy in the resonant microwave (or optical) standing waves deliver impulses to the dressed-state wave functions [11][12][13][14][15][16][17][18]. In a clock the temporal phase of the second Ramsey interaction at t 2 is shifted by χ = ±π/2 for the detected transition probability in Fig.…”

mentioning

confidence: 99%

“…1(a) [11,12,[16][17][18]. After the first Ramsey interaction, the dressed states propagate freely [ ( r,z) = 0] to the second interaction.…”

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confidence: 99%

Ramsey spectroscopy, matter-wave interferometry, and the microwave-lensing frequency shift

Gibble

2014

Phys. Rev. A

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We derive the general frequency shift of a microwave atomic clock due to resonant dipole forces acting on the atomic wave functions during the Ramsey interactions. We explicitly demonstrate that only dressed-state populations in position space contribute significantly to the frequency shift and that the de Broglie phases of the dressed-state wave functions do not contribute. In addition, we show that momentum changes in the second Ramsey interaction normally produce negligible frequency shifts in comparison to those from the first Ramsey interaction.Laser-cooled microwave atomic-fountain clocks currently provide the most accurate contributions to International Atomic Time (TAI) [1][2][3][4][5]. The accuracy of these standards continues to improve [1], with several clocks reporting accuracies of order 2×10 −16 [2,4,5]. Significant recent advances have come from properly treating first-order Doppler shifts [2][3][4][5][6][7][8], reducing the uncertainty of frequency shifts from cold collisions [2,4,9,10], and theoretically evaluating the microwave-lensing frequency shift [2][3][4][5]11,12].The scale of the microwave-lensing frequency shift is of order of the recoil shift [13] for a microwave photon, fractionally 1.5×10 −16 [11,14]. Several clocks have corrected for this bias, using calculated shifts that range from 0.6×10 −16 to 0.9×10 −16 [2][3][4]. This shift is the largest bias applied to clocks that has not yet been experimentally observed. One group recently questioned the behavior and size of the microwave-lensing shift and reported a significantly smaller bias that they neglected [5,12]. To clarify the behavior of this shift, here we explicitly expand our previous treatment [11] and present a concise and intuitive calculation of this frequency shift, which agrees with [2][3][4]11].Viewing a clock as a matter-wave interferometer [15] facilitates insight into the microwave lensing shift. In Fig. 1(a) an atom, localized to less than a wavelength of the oscillatory field, passes through the two separated interaction zones in Ramsey spectroscopy at t 1 and t 2 . The spatial variations of the dipole energy in the resonant microwave (or optical) standing waves deliver impulses to the dressed-state wave functions [11][12][13][14][15][16][17][18]. In a clock the temporal phase of the second Ramsey interaction at t 2 is shifted by χ = ±π/2 for the detected transition probability in Fig. 1(b) to be most sensitive to the phase of the coherent superposition of the two clock states [1]. The second interaction for χ = + (−) π/2 transfers dressed state |2(1) to the excited state [11], which is subsequently detected. Thus, because more of dressed state |2 passes through apertures in the clock, more excited-state atoms are detected for χ = +π/2 than −π/2, producing a positive frequency shift of the clock's Ramsey fringe [11].We begin with an interaction Hamiltonian H int = ωσ 3 / 2 + ( r,z)cos(ωt)σ 1 , which couples the ground and excited states of the clock transition, |g and |e , in each Ramsey interaction in Fig. 1(a). Her...

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“…[2][3][4] In this Letter we show that a gas of atoms can be trapped using forces derived from the gradient of a microwave radiation field on resonance with an atomic transition. 5 The principal difference between microwave and optical traps is the virtual absence of microwave spontaneous emission. This changes the nature of the trap potential and eliminates the spontaneous emission heating of the atoms.…”

mentioning

confidence: 99%

“…(5). For £=0 the dressed states are equal admixtures of \e,N -\) and \g,N) so that the time spent in each state is equal, thus the force is zero.…”

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confidence: 99%

Trapping of neutral atoms with resonant microwave radiation

et al. 1989

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We discuss a resonant microwave trap for neutral atoms. Because of the long spontaneous radiation time this trap is remarkably different from the optical trap. It also has advantages over static magnetic traps that trap the excited spin state of the lowest electronic level, in that atoms predominantly in the spin ground state can be trapped. We analyze the relaxation-ejection lifetime of atoms in such a trap using the formalism of dressed atomic states. Results are applied to atomic hydrogen and the possibility of Bose-Einstein condensation is considered.

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The Transverse Stern–gerlach Experiment

Cited by 28 publications

References 2 publications

Folded Stern-Gerlach experiment as a means for detecting nuclear magnetic resonance in individual nuclei

Folded Stern-Gerlach experiment as a means for detecting nuclear magnetic resonance in individual nuclei

Ramsey spectroscopy, matter-wave interferometry, and the microwave-lensing frequency shift

Trapping of neutral atoms with resonant microwave radiation

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