Optically measuring force near the standard quantum limit

Abstract

The Heisenberg uncertainty principle sets a lower bound on the noise in a force measurement based on continuously detecting a mechanical oscillator's position. This bound, the standard quantum limit, can be reached when the oscillator subjected to the force is unperturbed by its environment and when measurement imprecision from photon shot noise is balanced against disturbance from measurement back-action. We applied an external force to the center-of-mass motion of an ultracold atom cloud in a high-finesse optical cavity and measured the resulting motion optically. When the driving force is resonant with the cloud's oscillation frequency, we achieve a sensitivity that is a factor of 4 above the standard quantum limit and consistent with theoretical predictions given the atoms' residual thermal disturbance and the photodetection quantum efficiency.

Cavity-mediated coupling of mechanical oscillators limited by quantum back-action

“…where S SN is the total spectral density of the shot noise power and ≈ 0.05 is half the quantum efficiency (use of heterodyne rather than homodyne detection) 19 . The single-photon/single-phonon coupling strength g i for each oscillator is then determined by C i = 4ng 2 i /(κ i ), with the mean intracavity photon numbern.…”

“…We scale the real and imaginary parts of the filter output to each harmonic oscillators' units by multiplying with 19 1/ √ S SN C i i . This takes variations in i and C i between oscillators into account and allows identification of filter coefficients with dimensionless harmonic oscillator displacements Z i .…”

“…We observe the quantum back-action noise imparted by the optical coupling resulting in correlated mechanical fluctuations of the two oscillators. Our results illustrate challenges and opportunities of coupling quantum objects with light for applications of quantum cavity optomechanics [8][9][10][11][12][13][14] .Cavity optomechanical systems comprised of a single mechanical oscillator interacting with a single electromagnetic cavity mode 15 serve useful quantum-mechanical functions, such as generating squeezed light [16][17][18] , detecting forces with quantum-limited sensitivity 19 or through back-action-evading measurement 20 , and both entangling and amplifying mechanical and optical modes 21 . Systems containing several mechanical elements offer additional capabilities.…”

“…Cavity optomechanical systems comprised of a single mechanical oscillator interacting with a single electromagnetic cavity mode 15 serve useful quantum-mechanical functions, such as generating squeezed light [16][17][18] , detecting forces with quantum-limited sensitivity 19 or through back-action-evading measurement 20 , and both entangling and amplifying mechanical and optical modes 21 . Systems containing several mechanical elements offer additional capabilities.…”

“…The transmission of this pump/probe light through the cavity is detected by a heterodyne optical receiver. At a typical average cavity photon numbern = 2, C 1,2 2, allowing single-shot detection of the motion of each oscillator near the standard quantum limit 19 . Probing at this intensity reveals the resonance frequencies ({ω 1 , ω 2 } ≈ 2π × {116.4, 110} kHz) and linewidths ( 1,2 ≈ 2π × 1.5 kHz) of the centre-of-mass oscillations of the two ensembles.…”