Introduction to quantum noise, measurement, and amplification

TLDR: In this paper, a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification is given, and the basics of weak continuous measurements are described.

Abstract: The topic of quantum noise has become extremely timely due to the rise of quantum information physics and the resulting interchange of ideas between the condensed matter and atomic, molecular, optical--quantum optics communities. This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. After introducing quantum noise spectra and methods for their detection, the basics of weak continuous measurements are described. Particular attention is given to the treatment of the standard quantum limit on linear amplifiers and position detectors within a general linear-response framework. This approach is shown how it relates to the standard Haus-Caves quantum limit for a bosonic amplifier known in quantum optics and its application to the case of electrical circuits is illustrated, including mesoscopic detectors and resonant cavity detectors.

Figures

TABLE II. Contents of online appendix material. Page numbers refer to the supplementary material.

FIG. 13. Schematic of a minimal two-port amplifier which reaches the quantum limit in the scattering mode of operation, but misses the quantum limit when used as a weakly coupled op-amp. See text for further description.

TABLE IV. Two different amplifier modes of operation.

FIG. 9. Color online Schematic of a two-port bosonic amplifier. Both the inputs and outputs of the amplifier are attached to transmission lines. The incoming and outgoing wave amplitudes in the input output transmission line are labeled âin , âout b̂in , b̂out , respectively. The voltages at the end of the two lines V̂a , V̂b are linear combinations of incoming and outgoing wave amplitudes.

FIG. 1. Quantum noise spectral density of voltage fluctuations across a resistor resistance R as a function of frequency at zero temperature dashed line and finite temperature solid line .

FIG. 11. Color online Schematic of a generic linear-response position detector, where an auxiliary oscillator y is driven by the detector output.

Frequently asked questions

Q1. What are the contributions in "Introduction to quantum noise, measurement, and amplification" ?

This review gives a pedagogical introduction to the physics of quantum noise and its connections to quantum measurement and quantum amplification. 

Q2. What future works have the authors mentioned in the paper "Introduction to quantum noise, measurement, and amplification" ?

Among the most significant is the possibility of quantum feedback control Wiseman and Milburn, 1993, 1994, where one uses the continuously obtained measurement output to tailor the state of the mechanical resonator. Other important directions in nanomechanics include the possibility of detecting quantum jumps in the state of a mechanical resonator via QND measurement of its energy Santamore, Doherty, and Cross, 2004 ; Santamore, Goan, et al., 2004 ; Jayich et al., 2008 ; Thompson et al., 2008, as well as the possibility of making back-action-evading measurements cf. Sec. V. H. Fully understanding the potential of these techniques, as well as differences that occur in condensed matter versus atomic physics contexts, remains an active area of research. A promising method for superconducting qubit readout currently employed is a so-called latching measurement, where the hysteretic behavior of a strongly driven anharmonic system e. g., a Josephson junction is exploited to toggle between two states depending on the qubit state Siddiqi et al., 2004 ; Lupaşcu et al., 2006. 

Q3. What is the key concept to introduce in discussing “real” quantum measurements?

In discussing “real” quantum measurements, another key notion to introduce is that of weak continuous measurements Braginsky and Khalili, 1992 . 

Q4. What does it mean to have significant in-phase correlations between current and voltage noise?

It also follows that to reach the quantum limit while having a large power gain, an amplifier cannot have significant in-phase correlations between its current and voltage noise. 

Q5. What is the damping of a cavity?

The damping is parametrized by rate , which tells us how quickly energy leaks out of the cavity; the authors consider the case of a high-quality factor cavity, where Qc c / 1. 

Q6. What is the obvious case where the quantum noise constraint vanishes?

The most obvious case where the quantum noise constraint vanishes is for a detector which has equal forward and reverse gains, FI= IF* . 

Q7. Does the back-action noise feed back into the input of the amplifier?

Physically speaking, by matching the signal source to the input line the back-action noise de-scribed by F̂a= ûin does not feed back into the input of the amplifier. 

Q8. What is the way to make the noise constraint of Eq. 4.11 vanish?

At finite frequencies, there is a second way to make the RHS of the quantum noise constraint of Eq. 4.11 vanish: one needs the quantity S̄IF / ̃IF to be purelyimaginary, and larger in magnitude than /2. 

Q9. How do the authors measure the power gain of a mechanical nanoresonator?

These nanoresonators are typically studied by coupling them either to electrical often superconducting circuits or to optical cavities.