Squeezing Light

Laser light can be described in many ways. If one considers just the amplitude and the phase of one ray in a laser beam, there will always be shot noise that is, random variations caused by virtual particle interactions in the vacuum with the beam. Yet we’ve heard that there may be techniques to reduce the shot noise in the amplitude, for example. Then what happens to the shot noise in the phase?

Answer

Classically, a ray of light is an electromagnetic wave having an amplitude and a phase, both being expressed in terms of the electric field components E_x and E_y. Quantum mechanically, the normal modes of the electromagnetic field are quantized and treated as an ensemble of harmonic oscillators, one harmonic oscillator per normal mode. The number of photons in each harmonic oscillator is the energy in the corresponding oscillator. An harmonic oscillator obeys the Heisenberg uncertainty principle, so one expects the electromagnetic field to behave likewise.

As the electric field in a light ray is reduced, even a ray from a laser source, the fixed amount of intrinsic quantum noise in the light intensity becomes more obvious. This quantum noise in an electrical field is ever present. If you shine any light on a photodectector such as a photodiode, there will be fluctuations in the diode current corresponding to the individual photons being detected. One sees that the photons are not spread out evenly in time nor in spatial extent. Heisenberg’s uncertainty relation dictates this behavior. The QM operators of phase- and amplitude-quadrature (i.e., for the perpendicular components of the E field) of the electromagnetic field do not commute, similar to position and momentum of a particle. The product of phase- and amplitudeuncertainty has a fixed lower limit. The more precisely the phase of a light wave is measured, the less determined becomes its amplitude and vice versa. States of the light with the smallest possible amount of overall quantum noise are minimum uncertainty states.

The reduction in quantum noise in one observable of the light (e.g., the phase) at the expense of enhancing it in the complementary observable (i.e., the amplitude) can be done by parametric amplification procedures. The resulting states of the light are called squeezed states, since the quantum noise got squeezed at a particular phase angle. Their wave packets oscillate in time and get wider and narrower that is, they breathe.

Alternately, the uncertainty in the amplitude of a laser beam can be reduced to a level below that normally allowed by the Heisenberg uncertainty principle, a level known as the zero point quantum noise level. However, this increased knowledge comes at the expense of greater uncertainty in the frequency of the light. Essentially, one is using an uncertainty relation of the form ΔE_xΔE_y ≥ V, where V is a constant. Reducing the uncertainty in E_x to gE_x means that the uncertainty in E_y becomes E_y /g to keep their product the same.

Experiments with squeezed light promise to enhance our understandings of quantum mechanics at the individual atom and photon levels. Recently, a new type of ultraprecise laser pointer made by “squeezing” a beam in two directions was able to position the beam with a precision of 1.6 A, about 1.5 times better than the theoretical limit for a conventional laser.