The interaction of an object with its surrounding bath can lead to a coupling between the object's internal degrees of freedom and its center-of-mass motion. This coupling is especially important for nanomechanical oscillators, which are among the most promising systems for preparing macroscopic objects in quantum mechanical states. Here we exploit this coupling to derive the internal temperature of a levitated nanoparticle from measurements of its center-of-mass dynamics. For a laser-trapped silica particle in high vacuum, we find an internal temperature of $1000(60)\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The measurement and control of the internal temperature of nanomechanical oscillators is of fundamental importance because black-body emission sets limits to the coherence of macroscopic quantum states.
The interaction of an object with its surrounding bath can lead to a coupling between the object's internal degrees of freedom and its center-of-mass motion. This coupling is especially important for nanomechanical oscillators, which are among the most promising systems for preparing macroscopic objects in quantum mechanical states. Here we exploit this coupling to derive the internal temperature of a levitated nanoparticle from measurements of its center-of-mass dynamics. For a laser-trapped silica particle in high vacuum, we find an internal temperature of 1000(60)K. The measurement and control of the internal temperature of nanomechanical oscillators is of fundamental importance because black-body emission sets limits to the coherence of macroscopic quantum states.
Abstract Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence [1-4]. Quantum control of mechanical motion has been achieved by engineering the radiation pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator [5-8]. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states [9]. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects [10,11], since their trapping potential is fully controllable. In this work, we optically levitate a femto-gram dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its center-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 43%. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales [12,13].
Levitodynamics is a fast growing field that studies the levitation and manipulation of micro- and nanoobjects, fuelled by both fundamental physics questions and technological applications. Due to the isolated nature of trapped particles, levitated systems are highly decoupled from the environment, and offer experimental possibilities that are absent in clamped nanomechanical oscillators. In particular, a central question in quantum physics is how the transition between the classical and quantum world materializes, and levitated objects represent a promising avenue to study this intermediate regime. In the last years, most levitation experiments have been restricted to optically trapped silica nanoparticles in vacuum, controlling the particle's position with intensity modulated laser beams. However, the use of optical traps severely constrains the experiments that can be performed, because few particle materials can withstand the optical absorption and resulting heating in vacuum. This completely prevents the use of objects with internal degrees of freedom, which---coupled to mechanical variables---offer a clear path towards the study of quantum phenomena at the macroscale. In this thesis, we address these issues by considering other types of trap and feedback schemes, achieving excellent control on the dynamics of optically active nanoparticles. With stochastic calculus, simulations and experiments, we study the dynamics of trapped particles in different regimes, considering also a hybrid quadrupole-optical trapping scheme. Then, using a Paul trap of our own design, we demonstrate the trapping, interrogation and feedback cooling of a nanodiamond hosting a single NV center in vacuum, a clear candidate to perform quantum physics experiments at the single spin level. Finally, we discuss and implement an optimal controller to cool the center of mass motion of an optically levitated nanoparticle. The feedback is realized by exerting a Coulomb force on a charged particle with a pair of electrodes, and thus requires no optics. La levitodinàmica és un camp de la física en ràpida expansió que estudia la levitació i manipulació de micro- i nano-objectes, empesa per la possibilitat de solucionar trencaclosques de física fonamental i de desenvolupar noves aplicacions tecnològiques. Gràcies al gran aïllament de les partícules en levitació, l’evolució dels sistemes levitodinàmics està molt desacoplada del seu entorn. Per consegüent, permeten fer experiments que no serien possibles en nanooscil·ladors mecànics sobre substrat. En particular, una qüestió central en física consisteix en entendre com es produeix la transició entre els mons clàssic i quàntic; els objectes en levitació permeten estudiar aquest règim intermedi de manera innovadora. En els últims anys, la majoria d’experiments de levitodinàmica s’han limitat a atrapar òpticament partícules de sílice en el buit, tot controlant la posició de la partícula amb feixos làser modulats. Tot i així, l’ús de trampes òptiques suposa un obstacle a l’hora d’exportar aquests experiments a règims més diversos perquè, a baixes pressions, pocs materials són capaços de suportar les altes temperatures resultants de l’absorció de llum làser. Això impedeix l’ús d’objectes amb graus de llibertat interns, que –acoplats a variables mecàniques– suposen un full de ruta clar per estudiar fenòmens quàntics a escala macroscòpica En aquesta tesi, adrecem aquestes qüestions tot considerant altres tipus de trampa i tècniques de feedback, i assolim un control excel·lent de la dinàmica de nanopartícules òpticament actives en levitació. Mitjançant càlcul estocàstic, simulacions i experiments, estudiem la dinàmica de les partícules en règims diversos, àdhuc considerant un esquema híbrid de trampa de Paul-òptica. A continuació, utilitzant una trampa de Paul, demostrem experimentalment l’atrapament, interrogació i feedback-cooling en el buit d’un nanodiamant que conté un únic NV− center, un clar candidat per a la realització d’experiments de física quàntica amb un únic spin. Finalment, estudiem i implementem un controlador òptim per a refredar el centre de massa d’una partícula òpticament levitada. El feedback es realitza exercint una força de Coulomb sobre una partícula carregada positivament mitjançant un parell d’elèctrodes, i per tant no requereix elements òptics
Abstract Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence1–3. Quantum control of mechanical motion has been achieved by engineering the radiation–pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator4–7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states8. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects9, 10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10−15 grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales11.
Cooling the center-of-mass motion of levitated nanoparticles provides a route to quantum experiments at mesoscopic scales. Here we demonstrate three-dimensional sympathetic cooling and detection of the center-of-mass motion of a levitated silica nanoparticle. The nanoparticle is electrostatically coupled to a feedback-cooled particle while both particles are trapped in the same Paul trap. We identify two regimes, based on the strength of the cooling: in the first regime, the sympathetically cooled particle thermalizes with the directly cooled one, while in the second regime, the sympathetically cooled particle reaches a minimum temperature. This result provides a route to efficiently cool and detect particles that cannot be illuminated with strong laser light, such as absorptive particles, and paves the way for controlling the motion of arrays of several trapped nanoparticles.
Levitated nanoparticles in vacuum are prime candidates for generating macroscopic quantum superposition states of massive objects. Most protocols for preparing these states necessitate coherent expansion beyond the scale of the zero-point motion to produce sufficiently delocalized and pure phase-space distributions. Here, we spatially expand and subsequently recontract the thermal state of a levitated nanoparticle by modifying the stiffness of the trap holding the particle. We achieve state-expansion factors of 25 in standard deviation for a particle initially feedback-cooled to a center-of-mass thermal state of \SI{155}{\milli\kelvin}. Our method relies on a hybrid scheme combining an optical trap, for cooling and measuring the particle's motion, with a Paul trap for expanding its state. Consequently, state expansion occurs devoid of measurement backaction from photon recoil, making this approach suitable for coherent wavefunction expansion in future experiments.
Manipulating the motion of macroscopic objects near their quantum mechanical uncertainties has been desired in diverse fields, including fundamental physics, sensing, and transducers. Despite progress in ground-state cooling of a levitated solid particle, realizing its nonclassical states has been elusive. Here, we demonstrate quantum squeezing of the motion of a single nanoparticle by rapidly varying its oscillation frequency. We reveal appreciable narrowing of the velocity variance to -4.9 ± 0.1 decibels of that of the ground state using free-expansion measurements. Our work shows that a levitated nanoparticle offers an ideal platform for studying nonclassical states of its motion and provides a route to developing applications in quantum sensing and exploring quantum mechanics at a macroscopic scale.