Parametric feedback cooling and squeezing of optically levitated particles

Abstract

Free space gradient force traps are hugely versatile experimental systems. Their realisation opens up new avenues for the exploration of various areas of fundamental physics, including both quantum physics and thermodynamics. Their high levels of sensitivity also have attractive implications for force sensing. In this thesis a novel experimental setup will be presented, along with experimental protocols, as a framework upon which such studies can be built.
Using a paraboloidal mirror to create a diffraction limited, gradient force optical trap, the motion of nanoparticles ranging from 18 nm to 312 nm in diameter was detected via a single photodiode. Several properties of the levitated particles were measured, including: the mass, radius, oscillation amplitude (via the use of a volts to metre conversion factor) and the damping experienced at various pressures. This was done via two methods. The first, widely established, method required fitting a power spectral density, derived using the kinetic theory of gases, to the motion of the particle. The second, novel method, involved scanning the wavelength of the trapping laser. Using this method, it was possible to determine the mass of a levitated particle without assuming the kinetic model and material density. From the wavelength scan, the sensitivity of the experimental system was measured to be 200 fm/√Hz. Within this optical setup, the ability to control the trap frequencies of all three motional degrees of freedom, through varying the power of the trapping laser, was demonstrated. The ability to independently control and separate the transverse trapping frequencies from one another, as well as from the z axis, was also shown to be possible, using elliptically polarized light. The effect of changing the pressure inside the chamber in which a levitated nanoparticle is trapped is also explored. Trapping of nanoparticles at pressures as low as 10^-5 mbar, without any active feedback, was achieved.
A method for measuring the internal temperature of levitated particles was then demonstrated. This was done through measuring and fitting the Planck equation to the emitted thermal spectrum of a levitated silica nanoparticle. It was then shown that the temperature of levitated particles can be controlled via the intensity of the laser light as well as the pressure within the chamber. Over a pressure range of 1000 mbar to 0.04 mbar, an increase of temperature from 388 K to 480 K was measured. In the range of trapping laser intensities between 0.21 TW/m² and 0.4 TW/m², the resulting change of a particle's temperature, from 367 K to 463 K, was observed.
To control the centre of mass motion of levitated particles within the optical trap, parametric feedback cooling was implemented via modulation of the trap depth. Using this technique, the effect different feedback parameters have on particle motion was explored. The combination of optimizing the feedback parameters, alongside reducing the pressure, resulted in temperatures of T_z = 14 ±1 mK, T_x = 5 ±1 mK and T_y = 7 ±1 = mK. The observed Q factors on the order of 10⁷ with predicted Q factors on the order of 10¹² hold great promise for the realisation of ultrasensitive force detection. The system presented here has a force sensitivity on the order of 10^-20 N pHz. Theoretical considerations show that, with some improvements to the experimental system, it would be possible to achieve centre of mass temperatures, and thus low phonon numbers, close to the quantum ground state.
The second method to control the centre of mass motion of a levitated nanoparticle used squeezing pulses to classically squeeze its mechanical motion. This quadrature squeezing was achieved via non-adiabatic shifts of the nanoparticle's trap frequency and was carried out on a number of particles. The squeezing pulses implemented consisted of a rapid reduction in the trap frequency, followed by a brief period in time where the system was allowed to evolve, before the trapping frequency was rapidly returned to its original value. The effect of using single and multiple pulses to control this was explored and the optimal duration for a squeezing pulse characterized. For a single pulse, the maximum amount of squeezing was found to be λ = 3.2 ± 0.2 dB.
To further increase the amount of squeezing applied to the levitated nanoparticle, a multiple pulse scheme was implemented. The effect of varying the time between pulses was investigated and the optimal time was found. The maximum amount of squeezing achieved in the system, occurred after 5 pulses, giving a squeezing factor of λ 9.4 ± 0.1 dB. The multiple pulse scheme was then applied to parametrically feedback cooled nanoparticles. The effect on the phase space, including its decay to a thermal state, after the application of squeezing pulses was characterized. The squeezing on parametricaly cooled particles. after the application of 5 pulses, was measured and the squeezing factor found to be λ = 8.4 ± 0.1 dB.

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Identifiers

ORCID for Jamie Alexander Vovrosh: orcid.org/0000-0002-4097-872X

ORCID for Hendrik Ulbricht: orcid.org/0000-0003-0356-0065

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