Quantum noise

Quantum noise is uncertainty of some physical quantity due to its quantum origin.

In the case of number of particles (photons or electrons), the quantum noise is also called shot noise. Most optical communications use amplitude modulation. In this case, the quantum noise appears as shot noise only.

In the case of uncertainty of electric field in some lasers, the quantum noise is not just shot noise; uncertainties of both amplitude and phase contribute to the quantum noise. This issue becomes important in the case of noise of a quantum amplifier, which preserves the phase. The phase noise becomes important at the frequency modulation or phase modulation of waves with energy of quantum comparable to the energy of a signal (which is believed to be more robust with respect to additive noise than an amplitude modulaiton).

Origin of quantum noise

Quantum noise may appear in any system while conventional sources of noise (industrial noise, vibration, fluctuations of voltage in the electric power supply, thermal noise due to Brownian motion, etc.) are somehow suppressed. Generally, quantum noise can be considered as error of description of any physical system within classical (not quantum) theory. In an electric circuit, the random fluctuations of a signal due to discrete character of electrons can be called quantum noise C. W. Gardiner and Peter Zoller, "Quantum Noise", Springer-Verlag (1991, 2000, 2004)] .The random error of interferometric measurement of position due to discrete character of photons registered can be attributed to quantum noise. Even uncertainty of position of a probe in the probe microscopy may cause the quantum noise although this is not dominant mechanism that determines the resolution of such a device. In most cases, quantum noise refers to the fluctuations of signal in extremely accurate optical systems with stabilized lasers and efficient detectors.

Coherent states and noise of a quantum amplifier

Although the coherent states can be realized in wide variety of physical systems, they refer mainly to the state of optical light. In the most of cases, the light of a laser can be interpreted as a classical wave. Within quantum mechanics, such a wave can be approximated with a coherent state. At total amount of photons of order of 10¹⁰ (which still corresponds to very moderate energy), the relative error of measurement of intensity due the the quantum noise is only of order of 10^-5 which is good precision for most of applications. Quantum noise becomes important at the amplification of a small signal. Roughly, the quantum uncertainty of the quadrature components of the field is amplified as well as the signal; and the resulting uncertainty appears as noise. This determines the lower limit of noise of a quantum amplifier.

In general, amplifier is a device which may increase the mean value of some parameter at its output dependently on its input. Amplifiers reproduce some parameters of the input signal. For example, the electric circuit which replaces the poor and weak sound of a pop-artist with a strong sound of previously recorded singer is not amplifier. A powerful laser on the way of an optical beam which replaces the beam with stronger one also is not an amplifier. But an acoustical system which makes the song of a singer hearable over a large stadium, or an active medium which produces photons in about roughly proportional to its input should be considered as amplifiers.

Quantum amplifier is am amplifier which operates close to the quantum limit of its performance. In this sense, the acousto-electrical circuit which converts the small electric signal from a microphone to the powerful sound wave (which may cause revergeration of glasses in windows and extasis of fanats of heavy rock music) is not a quantum amplifier. The minimal noise of q quantum amplifier depends on the property of the input signal, which is reproduced at the output. In narrow sense, the optical quantum amplifier reproduces both, amplitude and phase of the input wave. Usually, the amplifier amplifies many modes of the optical field (and special efforts are required to reduce the number of these modes). In the idealized case, one may consider just one mode of the electromagnetic field, which corresponds of a pulse with definite polarization, definite transversal structure and deginite arrival time, duration and frequency, with uncertainties limited with the Heisenberg uncertainty principle. The input mode may carry some information in its amplitude and phase; the output signal carries the same phase but larger amplitude, roughly proportional to the amplitude of the input pulse. Such an amplifier is called phase-invariant amplifier cite journal
title= Quantum limit of noise of a phase-invariant amplifier
author=D. Kouznetsov
coauthors=D. Rohrlich, R.Ortega
journal=PRA
volume=52
issue=2
pages=1665–1569
year=1995
url=http://prola.aps.org/abstract/PRA/v52/i2/p1665_1
doi= 10.1103/PhysRevA.52.1665] . Mathematically, quantum amplification can be represented with an unitary operator, which entangles the state of the optical filed with internal degrees of freedom of the amplifier. This entanglement appears as quantum noise; the uncertainty of the field at the output is larger than that of the coherent state with the same amplitude and phase. The lower bound for this noise follows from the fundamental properties of the operator of creation and annihilation.

ee also

*Shot noise
*Quantum amplifier
*coherent state
*Quantum optics

References