Rapid cooling of a strain-coupled oscillator by an optical phase-shift measurement

Abstract

We consider an optical probe that interacts with an ensemble of rare earth ions doping a material in the shape of a cantilever. By optical spectral hole burning, the inhomogeneously broadened transition in the ions is prepared to transmit the probe field within a narrow window, but bending of the cantilever causes strain in the material which shifts the ion resonances. The motion of the cantilever may thus be registered by the phase shift of the probe. By continuously measuring the optical field we induce a rapid reduction of the position and momentum uncertainty of the cantilever. Doing so, the probing extracts entropy and thus effectively cools the thermal state of motion towards a known, conditional oscillatory motion with strongly reduced thermal fluctuations. Moreover, as the optical probe provides a force on the resonator proportional to its intensity, it is possible to exploit the phase shift measurements in order to create an active feedback loop, which eliminates the thermal fluctuations of the resonator. We describe this system theoretically, and provide numerical simulations which demonstrate the rapid reduction in resonator position and momentum uncertainty, as well as the implementation of the active cooling protocol.

Position- and momentum-squeezed quantum states in micro-scale mechanical resonators

“…However, reducing the temperature to 0.7 mK, which is the lowest resonator temperature achievable with our active laser cooling described in previous work [4], and maintaining the coupling rate at 10 Hz, a modest level of squeezing is obtained (2σ=1.24 at 400 µs, with σ the lowest of σ(X m ) and σ(P m ). This is shown in figure 3.…”

“…We have previously proposed a quantum hybrid system consisting of a crystalline mechanical resonator which contains rare-earth ion dopants [3], and we have recently demonstrated how such resonator can be cooled significantly below the surrounding thermal bath temperature [4]. We will in the following summarize the main ideas of these schemes, as they constitute the starting point for the work presented here.…”

Mechanical Tunability of an Ultranarrow Spectral Feature of a Rare-Earth-Doped Crystal via Uniaxial Stress

“…Moreover, as the spectral properties of the individual ions are sensitive to the surrounding crystalline matrix, external stress applied to the crystal in the plastic regime will frequency displace a previously imprinted spectral hole, providing an interesting resource for tuning spectral holes reversibly, in addition to probing stress fields in a spatially resolved manner. Other applications of stress sensitivity can be found in the field of quantum optomechanics [13], where the vibrations of a mechanical resonator modulate the energy levels of quantum two-level system emitters embedded in the resonator material itself, as observed experimentally in resonators containing quantum dots [14] or Nitrogen-Vacancy centers [15][16][17], and proposed theoretically for rare-earth ions doped resonators [18,19].In this work, we concentrate on Eu 3+ ions in a Y 2 SiO 5 host matrix (Eu:YSO) at a temperature of 3.15 K, as this material exhibits one of the narrowest optical transitions among solid-state emitters. We exploit the 580 nm optical transition 7 F 0 → 5 D 0 which possesses near lifetime limited coherence times in the ms range [20,21].…”

“…[35]), can be designed, with the help of the presented measurements, to largely compensate the effect of acceleration-induced deformations due to residual vibrations. Finally, in the context of strain-coupled nano-optomechanics, the measured uniaxial strain sensitivity should be sufficiently large to provide a direct observation of quantum features of a mechanical resonator, such as the zero point motion [18,19].…”

Inhomogeneous response of an ion ensemble from mechanical stress

“…On the contrary, the electronic structure of trivalent lanthanide ions, in which the optical transitions inside the 4 f shell are protected by 5s and 5p fully populated shells, allows for record narrow transitions as well as the high strain sensitivity that is typical for an optical transition. Thus, when viewing the strain sensitivity as a resource, this kind of system represents the best of both worlds, as witnessed by proposals for creating strainengineered quantum hybrid systems based on this system [12,13]. On the other hand, depending on the application, this high sensitivity can also be a nuisance, of which the effect needs to be minimized.…”