Historical research guide · 0697 · 2015
Spin-dependent two-color Kapitza-Dirac effects
S. McGregor · W. C.-W. Huang · B. A. Shadwick · H. Batelaan
In one minute
Light can push electrons around: fire two counter-propagating laser beams at an electron beam and the electrons diffract off the standing wave of light, which is the Kapitza–Dirac effect. Sean McGregor, Wayne Cheng-Wei Huang, Bradley Shadwick and Herman Batelaan at Nebraska ask whether light can also flip an electron’s spin, using ordinary visible or near-infrared lasers and electrons moving far below the speed of light. Their answer is a designed experiment. Cross the electron beam at right angles with two lasers an octave apart, one at a frequency and one at twice it, with the polarization set perpendicular to the electron’s motion. That geometry silences the two stronger, spin-blind scattering channels and leaves one process standing: the electron absorbs one high-frequency photon, emits two low-frequency ones, takes four photon recoils and flips its spin in the same event. The team backs the perturbation calculation with a numerical solution of the Pauli equation and a relativistic classical check that the electrons stay slow.
Connection
Chapter 10 is about controlling matter through the electromagnetic potential rather than through brute force, and this is the cleanest textbook case of it: the spin flip comes out of the magnetic-moment term of the interaction Hamiltonian while the two much stronger vector-potential terms are switched off by geometry. It is also a working lesson in chapter 2’s photon bookkeeping — a three-photon exchange with the field, counted vertex by vertex.
From the source
The proposed spin-Kapitza–Dirac effect is a three-photon process: the electron absorbs one photon of frequency two omega, emits two photons of frequency omega, receives four photon recoils along the laser axis and flips its spin in the same event, driven by the magnetic-moment term of the interaction Hamiltonian in combination with the vector-potential-squared term.Section 1, paragraph 4; Section 2, Eq. 1 and Eq. 12; Figure 2a
The geometry is what makes the weak effect dominant. Choosing the two laser frequencies an octave apart removes the ordinary Kapitza–Dirac effect, and choosing the laser polarization perpendicular to the electron velocity removes the two-color Kapitza–Dirac effect, which lives in the momentum-dot-vector-potential term.Section 1, paragraph 4; Section 3, paragraphs 4 and 5
At a laser intensity of 10 to the 18 watts per square metre, a wavelength of 1064 nanometres, an electron velocity of 10 million metres per second and an interaction time of 100 picoseconds, the calculated probability of the spin-flip-with-recoil process is 0.00128, against 0.00576 for the spin flip that merely depolarizes and 7.4 times 10 to the minus 4 for the two-color Kapitza–Dirac effect.Section 2, Table 1
A numerical integration of the Pauli equation, which includes every order the Hamiltonian allows, agrees with the perturbation result and puts the spin-Kapitza–Dirac probability at about 0.01 at 10 to the 19 watts per square metre. On the intensity plot the spin process and the two-color Kapitza–Dirac effect rise with slope three, marking them as three-photon processes, while the depolarizer and the ordinary Kapitza–Dirac effect rise with slope two.Section 4, Figure 3 and the paragraph following it
The authors name the tolerances an experiment has to hold. The up-converted beam must be optically separated from its parent to about one part in a million in intensity, and the angle between the electron velocity and the laser polarization must be held to better than 0.01 milliradians from perpendicular, because the competing effect scales with the cosine of that angle and is about 100,000 times stronger.Section 6, paragraphs 3 to 5
A classical calculation of the same configuration with the Bargmann–Michel–Telegdi equations gives a vanishing spin flip, so the authors read this as an effect with no classical counterpart — a way around Pauli’s argument that spin cannot be fully analysed by a device built on classical trajectories. The measurement that would settle it is the experiment itself, and its payoff would be an ultrafast spin-polarized electron source and the analyser that non-relativistic femtosecond pulses currently lack.Section 6, paragraphs 1 and 2; Section 7
The way in
https://doi.org/10.1103/PhysRevA.92.023834How to cite it
S. McGregor, W. C.-W. Huang, B. A. Shadwick, H. Batelaan (2015) Spin-dependent two-color Kapitza-Dirac effects doi:10.1103/PhysRevA.92.023834