A rotation in light's electric-field vector can alter the light's frequency. This rotational equivalent of the Doppler effect has proved surprisingly elusive, but has now been spotted in the laboratory.
When an observer moves towards or away from a light source, the measured frequency of the light shifts in proportion to the source and observer's relative velocity. Perhaps the best-known example of this Doppler shift is the 'redshift' — a displacement towards lower frequencies — of light emitted by receding galaxies. The Doppler shift also applies to sound waves, causing the characteristic rise and fall in the pitch of a passing police siren. As they report in Physical Review Letters1, Barreiro and colleagues have now measured the broadening of a spectral line caused by an effect analogous to the conventional Doppler effect. In this case, however, the shift in frequency arises not from linear motion, but from rotation — the rarely encountered rotational Doppler effect.
Place a watch at the centre of a rotating turntable, and, viewed from above, its hands will seem to rotate more quickly (Fig. 1). This classical effect applies to all rotating vectors, for example to the spatial pattern of the electric field of any light beam carrying angular momentum. The electric-field vector rotates at the frequency of the light, but an additional rotation of the beam about its axis of propagation will speed up or slow down the field rotation, resulting in a frequency shift proportional to the rate of rotation of the beam.
Importantly, the rotational Doppler effect is seen by looking at a rotating body along or parallel to its axis of rotation. It is therefore distinct from the linear Doppler shift that arises from viewing the edges of an extended body — a galaxy, say — in a direction perpendicular to its rotation axis. The effect was originally observed and analysed in terms of Jones polarization matrices, which describe the effect of a medium on the orientation of the electric-field vector2. The effect has also been cited as an example of a geometric, or Berry, phase shift that occurs in a system whose parameters are progressively changed before it is brought back to its initial state3.
At a more subtle level, the angular momentum of light can be divided into spin and orbital components4. The spin angular momentum is associated with the rotation of the electric-field vector. This corresponds to circular polarization, meaning that the tip of the vector traces a circular pattern in space as it rotates. The orbital angular momentum, on the other hand, is associated with a rotation of the light wave's phase. Whereas the spin angular momentum can take only two independent states (clockwise or anticlockwise, according to the sense of the field vector's rotation), the orbital angular momentum can take any number of states with different values of angular momentum. In all cases, for a given field rotation speed, the Doppler frequency shift is proportional to the total angular momentum. This shift has been directly quantified for the rotation of electromagnetic beams at millimetre wavelengths5.
Barreiro et al.1 examined the spectrum of transitions between energy levels in rubidium gas, using as probes two light beams carrying different values of orbital angular momentum. The rotational Doppler effect is easily masked by larger frequency shifts, such as the normal linear Doppler shift. The authors used a geometry in which all these unwanted frequency shifts balanced to zero, and chose an intricate rubidium transition that needs two photons and a magnetic field to be activated. The transition had an initial linewidth of 52 kilohertz, but when orbital angular momentum was introduced to the light beams, this broadened to 300 kHz — a clear signal of the rotational Doppler effect.
Although such phenomena are based purely on the equations of nineteenth-century physics, it has only been realized in the past two decades that a light beam generated in the laboratory can carry a distinct orbital angular momentum, in addition to its spin. Many resulting phenomena have been reported6 in both the classical and quantum regimes: optical spanners, for instance, in which light's angular momentum causes microscopic objects to both spin and orbit; nonlinear effects whereby the conservation of orbital angular momentum causes the light beam's phase to change; and Heisenberg-type uncertainty relationships, where measurement of angular position sets the orbital angular momentum of light.
The rotational Doppler effect is particularly interesting because here the spin and orbital components of the angular momentum are indistinguishable; instead it is the total angular momentum of the light beam that is crucial. Astoundingly, more than 100 years after its formulation, classical electromagnetism still has surprises in store.