Cavity lab
joint lab with the group of Markus Aspelmeyer at the University of Vienna
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In this experiment, we study cavity quantum electrodynamics with optically trapped silica nanoparticles. We explore every facet of the optomechanical interaction and apply it to engineer nonclassical states of motion of single and multiple optically trapped nanoparticles.
We specialize in building stable Fabry-Pérot optical cavity designs of various geometries. Read below about our latest cavity and the accompanying experimental setup.
TEAM
TEAM
Postdocs
Postdocs
PhD students
PhD students
Master's students
Master's students
Maximilian Raderer
Alumni
Alumni
Kahan Dare
Dr. Aisling Johnson
THE APPARATUS
THE APPARATUS
We've been steadily working on upgrading our cavity optomechanics experiment since 2021. We decided to switch from operating the experiment at a wavelength of 1064 nm to 1550 nm, as all components and parameters, such as the photon recoil heating rate, are better for a larger wavelength.
We've learned a lot from our previous experiments that we implemented into a new state-of-the-art experiment. The major improvements are:
We made a near-concentric optical cavity with a smaller waist and a significantly larger cooperativity. You can read more about it in the section The optical cavity below.
We implemented clean and deterministic loading of nanoparticles through a hollow-core optical fiber. You can read more about it in the part Trapping a particle array below.
We made the whole vacuum system UHV compatible down to 10-11 mbar.
We implemented 2D tweezer arrays created by acousto-optical deflectors.
The tweezer lens and the hollow-core fiber are mounted on nanopositioner stages, which allows for the alignment of all parts to the fixed optical cavity.
Figure 1: Our experimental assembly combines programmable optical tweezer arrays, loading of particles through a hollow-core fiber, and a high-finesse optical cavity inside an ultra-high vacuum chamber.
THE OPTICAL CAVITY
THE OPTICAL CAVITY
With over a decade of experience building and using optical cavities, our Fabry-Pérot cavity design also underwent a significant upgrade. We aimed to decrease the cavity mode volume to reach ultrastrong and deep-strong coupling. At the same time, we wanted to boost the Purcell factor η and the optomechanical cooperativity C=5η/4 to create quantum states with high purity. Increasing the cavity finesse and decreasing the cavity waist while using the laser wavelength of 1550 nm results in a maximized Purcell factor:
A near-concentric cavity (Figure 2), with its length approaching the stability limit of twice the mirror radius of curvature (Rc = 10 mm), satisfies all design criteria. Furthermore, to optimize the detection of the cavity photons, we chose a single-sided design where one mirror has a significantly larger transmission than the other. In Figure 3, we show how the cavity waist, cavity mode volume, and cooperativity change as a function of the cavity length. Beyond 19 mm, all parameters vary significantly with the length, and the cavity mode volume drops below its value for the confocal cavity. After assembling the cavity, we reached a length of 19.8 mm and a cooperativity of about 500, more than an order of magnitude larger than existing cavities in levitated optomechanics. The cavity waist is about 22 µm, more than two times smaller than the waist of a confocal cavity.
Designing the cavity holder as stable as possible for such extreme cavity lengths is essential. We built it as a monolithic rectangular piece of low thermal expansion material, Invar. Due to its shape, we avoided significant propagation of any vibration modes within the holder and suppressed pitchfork modes of the mirror holders.
Figure 2: Our near-concentric cavity is built from two mirrors with different reflectivities and negligible losses. Its length is 19.8 mm, just 200 µm short of a concentric cavity.
Figure 3: Design considerations for our cavity involved (i) decreasing the cavity waist (red, dashed), (ii) decreasing the cavity mode volume (red, solid), and (iii) boosting the cooperativity or Purcell factor (blue solid line) by a significant factor in comparison to a confocal design. All three are satisfied for a cavity length roughly above 19 mm (green region).
TRAPPING A PARTICLE ARRAY
TRAPPING A PARTICLE ARRAY
Maintaining an ultra-high vacuum in the vacuum chamber when loading particles is challenging. Standard techniques, such as nebulization, laser-induced acoustic desorption (LIAD), or piezo shaking, release particles with high velocities and at various angles. If particles stick to the mirror surface, this can decrease cavity finesse.
In our experiment, we apply the recently developed loading technique through a photonic crystal hollow-core fiber (HCF) [1] to deterministically populate large arrays of optical tweezers. This fiber is installed through a feedthrough flange and connects the main chamber to the loading chamber. There, the particles are launched using any other method and trapped in the optical standing wave in front of the HCF. When we detune the laser from one side of the HCF, the particles can "surf" on top of the moving standing wave, the so-called "optical conveyor belt". Once the particle is transported into the main chamber, the HCF tip is aligned to any optical tweezer, and the tweezer takes over the particle trapping by ramping up its power. The procedure is then repeated to form an arbitrary particle array (Figure 4). Read about the method to create tweezer arrays on the page Binding lab.
[1] Lindner et al., Appl. Phys. Lett. 124, 143501 (2024)
Figure 4: Hollow-core fiber loading in combination with programmable tweezer arrays enables arbitrary arrangement of particles in 1D and 2D geometries. Top: Four particles on the diagonal. Bottom: 3x3 array
CAVITY OPTOMECHANICS VIA COHERENT COUPLING
CAVITY OPTOMECHANICS VIA COHERENT COUPLING
If a dielectric object is placed in an optical cavity, it shifts the cavity resonance frequency as it changes the optical path length of light inside the cavity (Figure 5a). The magnitude of the dispersive shift depends on the object's position, which maximally influences the resonance at the maximum intensity. This results in an optomechanical interaction between the object's motion and the light. Conversely, the cavity light can be used to read out the object's motion. At the same time, the interaction forms a feedback loop where the light can change the object's motion through the optical damping and spring effects.
A trapped nanoparticle is an induced dipole that coherently scatters light like a dipole antenna into free space. Therefore, if the particle is illuminated transversely to the cavity axis, it will scatter light into the cavity mode (Figure 5b). Similar to dispersive optomechanics, the cavity will act back on the particle's motion, which can be used to control its temperature [2,3]. This interaction is called cavity cooling by coherent scattering or coherent coupling. If the optical tweezer is used as a transverse drive, then the optomechanical cooperativity becomes a function of just the cavity parameters, such as the cavity finesse F, wavelength, and the cavity waist, and is almost the same as the Purcell factor.
This interaction is advantageous compared to dispersive coupling for several reasons, but most notably, it is resilient to classical laser intensity and phase noises.
[2] Delić et al., Phys. Rev. Lett. 122, 123602 (2019)
[3] Delić et al., Science, 367, 892 (2020)
Figure 5: Difference between the dispersive and coherent coupling. a. A particle trapped in an optical tweezer is placed inside an optical cavity driven through the input mirror. The particle dispersively shifts the cavity resonance. b. The cavity is effectively driven through the coherently scattered tweezer light off the nanoparticle.
ULTRASTRONG COUPLING
ULTRASTRONG COUPLING
The coherent coupling g can be simultaneously larger than the mechanical frequency Ω and the cavity decay rate κ, which is rarely available in other optomechanical systems. In our system, we are operating in the sideband resolved regime where Ω > κ. As we increase the coupling rate, we first overcome the limit of strong coupling g > κ/2, when the particle motion exhibits splitting into two peaks (Figure 6). The splitting is symmetric around the intrinsic mechanical frequency if the coupling rate is small compared to the frequency. However, as g/Ω = 0.35 in our system, the splitting becomes asymmetric, moving both peaks to slightly lower frequencies. This is one signature of ultrastrong coupling [4]. The coupling is inherently linear, so the system becomes unstable when the ratio g/Ω becomes greater than 50 %. This effect could create squeezed states of mechanical motion (see this work for more details).
[4] Dare et al., Phys. Rev. Research 6, L042025 (2024)
Figure 6: Strong hybridization of optical and mechanical modes due to strong optomechanical coupling is observed through the splitting of the peak into two broad peaks. The figure is taken from Dare et al., Phys. Rev. Research 6, L042025 (2024).
FINISHED PROJECTS
FINISHED PROJECTS
Dispersively coupled particle as a cavity probe
Dispersively coupled particle as a cavity probe
In our experiment, we continuously monitor the particle's motion through a homodyne measurement of the cavity transmission. If we move the optical trap along the cavity standing wave, we observe how the linear and quadratic optomechanical coupling rates are maximized at the slope of the intensity profile and the intensity maxima and minima, respectively (Figure 7) [5]. Furthermore, the cavity standing wave contributes weakly to the total trapping potential, thus decreasing (increasing) the mechanical frequency at the intensity minimum (maximum). Such measurements allow us to use the cavity standing wave as an etalon to calibrate the trap position along the cavity standing wave and the nanopositioner step size. Using this calibration, we can then measure the cavity mode waists by moving the optical trap transversely to the cavity axis.
[5] Delić et al., Quantum Sci. Technol. 5, 025006 (2020)
Figure 7: The mechanical frequency (above) and the linear and quadratic optomechanical coupling rates g0 and gq (below), respectively, as a function of the particle position along the cavity standing wave, can be used to deduce the positions of intensity maxima and minima. Figure adapted from Quantum Sci. Technol. 5, 025006.
3D cavity cooling by coherent scattering
3D cavity cooling by coherent scattering
As predicted by our theory, the maximum coupling of the x- and y-motion (radial modes in the optical tweezer) is realized at the cavity node (intensity minimum). At the same time, the z-motion is maximized at the cavity antinode (intensity maximum). The coupling rates gx and gy can be further varied by changing the polarization of the optical tweezer, which modifies their orientation and projection onto the cavity axis. We show three different cases in Figure 8: (a) tweezer light is polarized along the cavity axis, such that optomechanical effects are negligible; (b) tweezer light is polarized under 45 degrees to the cavity axis, and the particle is positioned halfway between a maximum and a minimum, such that all three modes are coupled to the cavity mode and cooled; (c) tweezer light is polarized orthogonal to the cavity axis, such that only the x- and z-motion are coupled to the cavity and cooled. In conclusion, cavity cooling by coherent scattering indeed allows for simultaneous cooling of all three center-of-mass degrees of freedom of a trapped nanoparticle.
Note that the x- and y-motions are coupled at the same time, which might lead to their strong hybridization due to the proximity of mechanical frequencies. Our theoretical study [6] provides a detailed analysis of the conditions under which one reaches two-dimensional ground-state cooling.
[2] Delić et al., Phys. Rev. Lett. 122, 123602 (2019)
[6] Toroš et al., Phys. Rev. Research 3, 023071 (2021)
Figure 8: Three-dimensional cavity cooling. a. If the tweezer light is polarized along the cavity, light scattering is minimized such that almost no optomechanical effect is observed. b. If the polarization is turned by 45 degrees and the particle is placed between an intensity maximum and a minimum, all three modes are cooled by the cavity. c. For the tweezer polarization orthogonal to the cavity axis, the x- and the z-motion are cooled. In contrast, the y-motion (along the polarization axis) is coupled only quadratically and weakly to the cavity mode.
Position-dependent cooling
Position-dependent cooling
We can change between strong cooling of the x- and z-motion by moving the particle along the cavity standing wave. We monitor the optical power P leaving the cavity, from which we can reconstruct the correct particle position (Figure 9a). At the same time, homodyne detection of the light scattered in the forward direction of the tweezer is used to detect the particle motion directly. We recover the damping rates (Figure 9b) and effective temperatures (Figure 9c) of the x- (light red: cooled, dark red: uncooled) and z-motion (light blue: cooled, dark blue: uncooled) from fits to the power spectral densities. As expected, the largest cooling of the x(z)-motion is recovered for the particle positioned at the intensity minimum (maximum), where the optical power P is 0 (maximum).
[2] Delić et al., Phys. Rev. Lett. 122, 123602 (2019)
Figure 9: Cavity cooling performance as a function of the particle position along the cavity standing wave. a. Output optical power. b. Damping rate of uncooled (dark) and cooled (light) x-(red) and z-motion (blue). c. The effective temperature of the x-(red) and z-motion (blue).
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