Quantum Shot Noise

Fluctuations in the flow of electrons signal the transition

from particle to wave behavior. Published in

revised form in Physics Today, May 2003, page 37.

Carlo Beenakker & Christian Sch¨onenberger 

“The noise is the signal” was a saying of Rolf Landauer,

one of the founding fathers of mesoscopic physics. What

he meant is that fluctuations in time of a measurement

can be a source of information that is not present in the

time-averaged value. A physicist may delight in noise, in

a way reminiscent of figure 1.

Noise plays a uniquely informative role in connection

with the particle-wave duality. It was Albert Einstein

who first realized (in 1909) that electromagnetic fluctuations

are different if the energy is carried by waves or

by particles. The magnitude of energy fluctuations scales

linearly with the mean energy for classical waves, but it

scales with the square root of the mean energy for classical

particles. Since a photon is neither a classical wave

nor a classical particle, the linear and square-root contributions

coexist. Typically, the square-root (particle)

contribution dominates at optical frequencies, while the

linear (wave) contribution takes over at radio frequencies.

If Newton could have measured noise, he would

have been able to settle his dispute with Huygens on the

corpuscular nature of light — without actually needing

to observe an individual photon. Such is the power of

noise.

The diagnostic property of photon noise was further

developed in the 1960’s, when it was discovered that

fluctuations can tell the difference between the radiation

from a laser and from a black body: For a laser the wave

contribution to the fluctuations is entirely absent, while

it is merely small for a black body. Noise measurements

are now a routine technique in quantum optics and the

quantum mechanical theory of photon statistics (due to

Roy Glauber) is textbook material.

Since electrons share the particle-wave duality with

photons, one might expect fluctuations in the electrical

current to play a similar diagnostic role. Current fluctuations

due to the discreteness of the electrical charge are

known as “shot noise”. Although the first observations

of shot noise date from work in the 1920’s on vacuum

tubes, our quantum mechanical understanding of electronic

shot noise has progressed more slowly than for

photons. Much of the physical information it contains

has been appreciated only recently, from experiments on

nanoscale conductors.1