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arXiv:1905.04044 · Physical Review A

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

Signe Louise Seidelin, Yann Le Coq, Klaus Mølmer

Published Jul 16, 2019• 16 citations
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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.

DOI
10.1103/physreva.100.013828

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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.
By spectrally hole burning an inhomogeneously broadened ensemble of ions while applying a controlled perturbation, one can obtain spectral holes that are functionalized for maximum sensitivity to different perturbations. We propose to use such hole-burned structures for the dispersive optical interaction with rare-earth-ion dopants whose frequencies are sensitive to crystal strain due to the bending motion of a crystal cantilever. A quantitative analysis shows that good optical sensitivity to the bending motion is obtained if a magnetic-field gradient is applied across the crystal during hole burning and that the resulting optomechanical coupling strength is sufficient for observing quantum features such as zero-point vibrations.
Material strain has recently received growing attention as a complementary resource to control the energy levels of quantum emitters embedded inside a solid-state environment.Some rare-earth ion dopants provide an optical transition which simultaneously has a narrow linewidth and is highly sensitive to strain.In such systems, the technique of spectral hole burning, in which a transparent window is burned within the large inhomogeneous profile, allows one to benefit from the narrow features, which are also sensitive to strain, while working with large ensembles of ions.However, working with ensembles may give rise to inhomogeneous responses among different ions.We investigate experimentally how the shape of a narrow spectral hole is modified due to external mechanical strain, in particular, the hole broadening as a function of the geometry of the crystal sites and the crystalline axis along which the stress is applied.Studying these effects is essential in order to optimize the existing applications of rare-earth-doped crystals in fields which already profit from the more-well-established coherence properties of these dopants, such as frequency metrology and quantum information processing, or even suggest alternative applications of these materials, for example, as robust devices for force-sensing or highly sensitive accelerometers.
Material strain has recently received growing attention as a complementary resource to control the energy levels of quantum emitters embedded inside a solid-state environment. Some rare-earth ion dopants provide an optical transition which simultaneously has a narrow linewidth and is highly sensitive to strain. In such systems, the technique of spectral hole burning, in which a transparent window is burned within the large inhomogeneous profile, allows one to benefit from the narrow features, which are also sensitive to strain, while working with large ensembles of ions. However, working with ensembles may give rise to inhomogeneous responses among different ions. We investigate experimentally how the shape of a narrow spectral hole is modified due to external mechanical strain, in particular, the hole broadening as a function of the geometry of the crystal sites and the crystalline axis along which the stress is applied. Studying these effects is essential in order to optimize the existing applications of rare-earth-doped crystals in fields which already profit from the more-well-established coherence properties of these dopants, such as frequency metrology and quantum information processing, or even suggest alternative applications of these materials, for example, as robust devices for force-sensing or highly sensitive accelerometers.Received 24 December 2019Accepted 20 February 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.013306Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDopantsFine & hyperfine structureOptics & lasersStressPhysical SystemsRare-earth doped crystalsGeneral Physics
Thermal decoherence is a major obstacle to the realization of quantum coherence for massive mechanical oscillators. Although optical trapping has been used to reduce the thermal decoherence rate for such oscillators, it also increases the rate by subjecting the oscillator to stochastic forces resulting from the frequency fluctuations of the optical field, thereby setting a fundamental limit on the reduction. This is analogous to the noise penalty in an active feedback system. Here, we directly measure the rethermalization process for an initially cooled and optically trapped suspended mirror, and identify the current limiting decoherence rate as due to the optical trap. Our experimental study of the trap-induced decoherence rate will enable future advances in the probing of fundamental quantum mechanics in the bad-cavity regime, such as testing of deformed commutators.
A challenge of modern physics is to investigate the quantum behavior of a bulk material object, for instance a mechanical oscillator. We have earlier demonstrated that by coupling a mechanical oscillator to the energy levels of embedded rare-earth ion dopants, it is possible to prepare such a resonator in a low phonon number state. Here, we describe how to extend this protocol in order to prepare momentum- and position-squeezed states, and we analyze how the obtainable degree of squeezing depends on the initial conditions and on the coupling of the oscillator to its thermal environment.
Laser cooling is a fundamental technique used in primary atomic frequency standards, quantum computers, quantum condensed matter physics and tests of fundamental physics, among other areas. It has been known since the early 1990s that laser cooling can, in principle, be improved by using squeezed light as an electromagnetic reservoir; while quantum feedback control using a squeezed light probe is also predicted to allow improved cooling. Here we show the implementation of quantum feedback control of a micro-mechanical oscillator using squeezed probe light. This allows quantum-enhanced feedback cooling with a measurement rate greater than it is possible with classical light, and a consequent reduction in the final oscillator temperature. Our results have significance for future applications in areas ranging from quantum information networks, to quantum-enhanced force and displacement measurements and fundamental tests of macroscopic quantum mechanics.