My work, Physics

Nanoparticle motion entering the quantum regime

A child on a swing can keep the swing in motion by repeatedly standing up and squatting down. This movement changes the frequency of the swings and amplifies them. This simple concept—known as parametric amplification—finds use also in modern quantum physics.

Parametric amplification—although simple—is a powerful tool that can change noise all the way down to the quantum level. We can use it to create squeezed states, in which the noise in position and momentum is unequal. Parametric amplificaion can generate squeezed light quite easily. But the producing mechanical squeezing this way is difficult.

The process works by modifying the frequency of the harmonic oscillator that it aims to amplify. For manipulating light, this means sending several light beams through an optical crystal. The effect is weak, but light is not very noisy and we can get strong squeezing in this way.

Mechanical oscillators suffer from much stronger noise owing to their low frequencies. The parametric squeezing still remains weak as we cannot change the strength with which they are clamped to their substrate. Instead, we have to shine light onto the oscillator, creating a weak additional spring that confines the motion. But this force is much weaker than the clamping and its squeezing effect is small.


Optically levitated particle (using the red tweezer) coupled to an optical cavity to control its motion. Right: depiction of the squeezing process in phase space.

The situation changes when we use a levitated particle as our mechanical resonator. Here, the force that keeps the particle in place comes from a laser beam and not any solid clamp. The strength of this force (and thus the frequency with which the particle oscillates around its equilibrium) depends on the intensity of the laser. If we now modulate the intensity of this laser, we’ll achieve the same effect but it will be much stronger.

The reduction of noise by squeezing can be useful when we are trying to measure weak forces. Levitated particles are good force sensors since they are small and easy to push by a variety of forces. The sensitivity of such a measurement—the weakest force we can reliably measure—depends on the noise we see alongside the force. If we push the noise down (for example by squeezing), we will be able to measure weaker forces.

Since the particle can move in three directions, we can also use the laser to squeee the noise in two (or even all three) directions at once. We can thus create quantum correlations between the directions in a process called two-mode squeezing. One might even think about trying to reduce noise in all three directions at once but that is not so simple. For squeezing of one mechanical mode, the laser intensity must be modulated with frequency that is twice the frequency of the motion. For two-mode squeezing, the modulation is at the sum of the two frequencies. Since there are always two frequencies involnved, it is difficult to see how to squeeze three modes at once.

But squeezing two (or all three) mechanical modes could be useful too. One-mode squeezing can achieve better measurements of the size of a force. Squeezing of more modes would allow us to measure the direction of a force with better precision. Only using all three mechanical modes can give us all possible information about a force’s direction. But already the measurement of two mechanical modes can give us some useful information.

The appeal of interesting quantum states of levitated particles goes beyond practical applications. An optically levitated particle is—by the standards of quantum mechanic—large. It is interesting to see what kinds of states we can prepare and what tools we can use for that. Working with the particle motion in all three dimensions allows us to create complex quantum states. And observing how these states lose their quantum features and become classical might teach us an important lesson about the border between the quantum world of small objects and the classical world of our everyday experience.

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