# Quantum Noise

Definition: noise arising from quantum fluctuations

German: Quantenrauschen

Categories: quantum optics, fluctuations and noise

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Author: Dr. RĂ¼diger Paschotta

Whereas the noise performance of electronic systems is often limited by thermal noise, quantum-mechanical effects often set the limits for optical systems.
This is basically because owing to the high optical frequencies the photon energy in the optical domain is much higher than the thermal energy *k*_{B} *T* at room temperature.

According to quantum mechanics, the electric field of a light beam is described by quantum mechanical operators, and the outcome of optical measurements does not simply reflect the expectation values of these operators, but is also subject to quantum fluctuations.

Typical effects of this quantum noise are:

- some intensity noise (shot noise), phase noise, and a finite linewidth even in the output of a (hypothetical) single-frequency laser which is not subject to any technical noise such as mirror vibrations
- unavoidable excess noise in optical amplifiers (→
*amplifier noise*) - spontaneous emission of excited atoms or ions
- spontaneous Raman scattering
- parametric fluorescence
- partition noise occurring at beam splitters

Light with unusual quantum noise properties is called *nonclassical light* and occurs e.g. in the form of squeezed light.

Quantum noise is often a limiting factor for the performance of optoelectronic devices. However, it can occasionally be useful, e.g. in quantum cryptography.

For the description of quantum noise and for the calculation of quantum noise properties of devices such as lasers, some authors use a full quantum-theoretical treatment (with quantum operators), but it is often more convenient to use a semiclassical theory [2]. In the latter, the quantum fluctuations of the electromagnetic field are described in essentially the same way as classical fluctuations, so that the results are often fairly easy to interpret intuitively. However, certain rules must be observed. For example, the vacuum field is associated with white noise fluctuations of a certain magnitude. All kinds of fluctuations can be reduced by sending a field through an attenuator, but each attenuator introduces “fresh” quantum noise according to its degree of attenuation; in effect, strong attenuation leads back to the standard quantum noise.

Interesting effects occur e.g. in a laser, where vacuum fluctuations can get into the resonator e.g. through the output coupler mirror, but also at any other location where optical losses occur. Subsequently, this vacuum noise influences the noise of the circulating intracavity field, which is also influenced by, e.g., pump noise and spontaneous emission noise. The output field finally consists of two contributions: the part of the intracavity field leaking out of the resonator, and part of the vacuum field coming from outside the resonator and being reflected at the output coupler. These field contributions are partly correlated, and their combination depends on, e.g., the deviation from the resonance frequency, i.e. on the noise frequency. Far away from the resonance, the output field is dominated by reflected vacuum fluctuations, which lead to intensity noise at the shot noise level.

### Bibliography

[1] | C. M. Caves, “Quantum limits on noise in linear amplifiers”, Phys. Rev. D 26 (8), 1817 (1982) |

[2] | S. Reynaud and A. Heidmann, “A semiclassical linear input output transformation for quantum fluctuations”, Opt. Commun. 71 (3-4), 209 (1989) |

[3] | C. H. Henry and R. F. Kazarinov, “Quantum noise in photonics”, Rev. Mod. Phys. 68, 801 (1996) |

See also: shot noise, amplifier noise, laser noise, nonclassical light, vacuum noise

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