Research

Nano-optomechanics with levitated nanocrystals



Our work in optomechanics is centered around an optical levitation apparatus, purpose built to maintain stable optical trapping of dielectric nanoparticles from atmospheric pressure down to high vacuum. The main apparatus consists of a low noise continuous-wave Nd:YAG laser which is focused to a diffraction limited focal spot by a high numerical aperture microscope objective inside a vacuum chamber. Unlike experiments which trap atoms or larger, micron-scale particles, we are able to trap our nanoparticles with a single beam. This photo shows a ~100 nm diamond being levitated by a 1064 nm laser and illuminated by a 532 nm laser (image credit to J. Adam Fenster, University of Rochester).


The geometry of the laser focus, and the interaction of the laser field with the dielectric particle, results in a 3-dimensional confining potential that is approximately harmonic. Under vacuum, the result is a multidimensional nanomechanical oscillator with a number of potential advantages over devices which rely on more conventional clamped or tethered oscillators. Most notably, the mechanical quality factors of our optically levitated oscillators are, in practice, limited only by the pressure of the ambient gas. This allows the quality of the oscillator to be tuned over a very large range (Q-factors can range from ~100 at low vacuum to ~1010 at ultra-high vacuum.


We measure the position of our nano-oscillator via a weak probe beam aligned confocally to the trapping beam. Scattered light from this probe beam interferes with unscattered light at balanced photodetectors downstream, resulting in voltage signals which are proportional to the particle displacement. All three components of linear motion are measured independently and simultaneously, and are used to modulate the intensity of the trapping laser (and hence the stiffness of the "optical spring constant") via an electro-optic modulator.


trapped


This active control mechanism allows us to optically excite or damp the oscillator motion via parametric resonance. Carefully preparing the phase of our feedback signal allows us to stabilize and "cool" the Center-Of-Mass (COM) motion of our levitated particles. The ultimate COM temperature our particles reach is determined by the depth of the modulation, and the rate of re-equilibration induced by collisions with residual gas particles. At lower vacuum pressures we can attain lower COM temperatures for the same levels of feedback gain.


trapped


The harmonic potential is created entirely by the interaction with the laser field. As a result, the mechanical resonance frequency (Ω0) is a function of the trapping power, and is thus tunable over a large range. The plot above shows the dependence of the resonance frequencies on trapping power for all tree axes of motion, in the absence of feedback (top left panel). In the bottom left panel, we see that the motional linewidth (Γ0) is essentially independent of trapping power. The plots in the right panel show the same parameters, except now the power is constant and the pressure is varied. In this case the frequency is constant, but the linewidth (or mechanical Q-factor) is tunable. The ability to independently tune both the center frequency and the quality factor is unique to levitated oscillators, and represents one of the chief advantages of these systems.


In the absence of parametric feedback, the thermal energy of the system is sufficient to drive the oscillator into the non-linear regime, resulting from the fact that the potential is actually Gaussian rather than quadratic (for more information check out this paper by our collaborators).


Below (left) is a plot of the radial displacement Power Spectral Density (PSD) of a 70 nm diameter silica nanosphere at 0.01 mbar. Plotted in red (or blue) is the PSD without (with) feedback cooling system active. Without feedback the resonance frequency fluctuates in time due to the thermal nonlinearity of the oscillator. However, with feedback stabilization the resonance frequency stabilizes. The right-hand panel below shows the that with the feedback system active, the COM temperature of the three components of particle motion decreases with decreasing pressure. This is a consequence of the increased mechanical Q-factor at lower pressures.


trapped


Our current research goals center around investigations into incorporating particles with extra degrees of freedom into this optomechanical scheme. In particular we are interested in coupling quantum degrees of freedom, for instance spins in nitrogen-vacancy defects in diamond, to the mechanical degrees of freedom. Such systems are fundamentally interesting, and may yield novel hybrid devices for potential applications in ultra-high-sensitivity force sensing and quantum information.


Publications:

  1. L.P. Neukirch, J. Gieseler, R. Quidant, L. Novotny and A.N. Vamivakas, Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond, Optics Letters 38, 2976-2979 (2013).
  2. L.P. Neukirch and A.N. Vamivakas, Nano-optomechanics with optically levitated nanoparticles, Contemporary Physics, (published online 2014).

Postdoctoral Research Scientist Position:

We currently have a post-doc position available for this research project. A description can be found here. Contact Nick if you are interested.


This project is funded by theOffice of Naval Research, award N000141410442.