The phase sensitivity of a fully quantum three-mode nonlinear interferometer

Abstract

We study a nonlinear interferometer consisting of two consecutive parametric amplifiers, where all three optical fields (pump, signal and idler) are treated quantum mechanically, allowing for pump depletion and other quantum phenomena. The interaction of all three fields in the final amplifier leads to an interference pattern from which we extract the phase uncertainty. We find that the phase uncertainty oscillates around a saturation level that decreases as the mean number N of input pump photons increases. For optimal interaction strengths, we also find a phase uncertainty below the shot-noise level and obtain a Heisenberg scaling N 1 . This is in contrast to the conventional treatment within the parametric approximation, where the Heisenberg scaling is observed as a function of the number of down-converted photons inside the interferometer.

Squeezing metrology: a unified framework

“…The main result of this paper is a unified framework that describes all previous (and presumably future) metrology protocols that use squeezing in any quantum system and any observable, as it is based on the elegant general theory of squeezing for arbitrary systems [27]. As shown through various examples, the previously known results [1][2][3][4][5][6][7][8][9][10][11][12][13][14] can be recovered as specific instances of our theory. Squeezing the probe requires an amount of energy E = s|H|s , where |s is the squeezed state of the probe.…”

“…This is a very general setting that encompasses most estimations. While squeezing has been used in quantum metrology for specific systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14], there is no general theory of squeezing-based metrology that holds for arbitrary measurements and systems. In the general case, quantum metrology theory [15][16][17][18][19][20][21][22][23][24][25][26] focuses on entanglement: it analyzes the situation in which the estimation is repeated N times and shows that there is a quadratic improvement in resolution whenever the probes are entangled.…”

“…In this paper we focus on squeezing and consider the case in which a single probe is squeezed with respect to the observable A that is measured to estimate the parameter ϕ. We are not claiming to have discovered that squeezing is useful for quantum metrology (there is plenty of evidence for that in the literature [1][2][3][4][5][6][7][8][9][10][11][12][13][14]). The main result of this paper is a unified framework that describes all previous (and presumably future) metrology protocols that use squeezing in any quantum system and any observable, as it is based on the elegant general theory of squeezing for arbitrary systems [27].…”

Spectrally multimode integrated SU(1,1) interferometer

“…The phase sensitivity of this class of interferometers has been investigated for spectrally single-mode sources [12,13,14], including gainunbalanced [15,16] and fully quantum threemode [17] configurations, as well as configurations with different input states, such as coherent light [18], squeezed states [19], a mixture of coherent and squeezing states [20,21,22] and a mixture of thermal and squeezed states [23]. These studies have shown that it is generally possible to overcome the shot noise limit and even reach the Heisenberg limit.…”

Versatile Super-Sensitive Metrology Using Induced Coherence

“…ing the modes of the original nonlinear media with coherent light [10], which has been further theoretically investigated [11,12,13,14,15,16,17] and implemented experimentally [18,19,20,21,22,23,24] including several variations -accounting for loss and other experimental imperfections. Unlike the MZI the Yurke-type interferometers need not produce light modes of the same frequency.…”