Introduction To Electrodynamics

Not your usual NMR

The CPT theorem implies, except for the sign of various properties such as charge, a particle and its antiparticle should be absolutely identical. The theorem is an essentially inviolable tenet of quantum field theory, and one that follows from the assumption that physics is the same in all inertial frames. The CPT theorem has been tested with baryons—composite particles made up of quarks bound by the strong interaction—by using a Penning trap to compare the masses of the proton and the antiproton to a precision better than one part in , they report the observation of spin flips of a single proton confined to a Penning trap [ 2 ].

A Penning trap confines a charged particle, in ultrahigh vacuum, using a uniform magnetic field, which causes the particle to undergo a circular cyclotron motion; and an electrostatic potential, which causes the particle to oscillate along the axis of the trap, parallel to the magnetic field (Fig.1). The magnetic moment of the particle, expressed as the dimensionless quantity known as the factor, can be measured very precisely in this setup because it is the ratio of two frequencies: the Larmor spin-precession frequency, which is the frequency of the (weak) oscillating magnetic field needed to flip the proton’s spin direction with respect to the magnetic field in the trap, and the frequency of the particle’s cyclotron motion. In essence, the cyclotron frequency measures the magnetic field. Although there are other methods for measuring the magnetic moment of the proton—after all, Larmor precession is the basis of nuclear magnetic resonance (NMR)—none of these can be readily applied to the antiproton. Using a Penning trap, the antiproton magnetic moment could be measured to better than one part in , yielding a precise test of the CPT theorem for leptons [ 5 ].

In a Penning trap, the frequencies of the cyclotron and axial motions of a charged particle can be measured by detecting, using tuned circuits and cryogenic preamplifiers, the oscillating image charges induced in the trap electrodes. Though the amplitudes of these motions are small, both types of motion can be classical and involve many energy quanta. But how does one detect the single-quantum flip of a single spin? (In conventional magnetic resonance experiments, EPR and NMR, the sample is macroscopic and contains many spins.) To solve this problem, Dehmelt developed what he called the “continuous Stern-Gerlach (CSG) effect.” If the magnetic field is deliberately made nonuniform—usually with a quadratic variation—the extra force, from the interaction of the magnetic moment with the magnetic field gradient, changes the frequency of the axial motion by a small amount, and this frequency shift depends on the direction of the electron spin. Hence a spin flip can be detected, elegantly and nondestructively, by detecting the small change in the axial frequency. The problem with extending this CSG technique from an electron to a proton is that the magnetic moment of the proton is times smaller than that of the electron. The tiny shift in axial frequency due to a proton spin flip is thus very hard to detect.

Introduction to electrodynamics-Griffits DJ Solution manual E book

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Introduction to electrodynamics

Introduction to electrodynamics

An Introduction to Electrodynamics

An Introduction to Electrodynamics

Introduction to electrodynamics