Quantum feedback control of levitating opto-mechanics

When confronted with the task of controlling a physical degree of freedom, observations and adjustments based on such observations are a most natural way to proceed. This is the basic idea behind the notion of feedback control, one of the standard paradigms of control engineering. If applied to systems subject to continuous noise, feedback control loops driven by continuous monitoring often allow one to cancel the effect of noise and to stabilise the system in a desirable configuration, up to a certain precision. Such powerful control routines are well established for macroscopic objects, obeying the laws of classical mechanics. However, it is becoming more and more desirable to extend the application of feedback control to microscopic degrees of freedom, governed by quantum mechanics. Due to the fundamentally probabilistic character of quantum mechanics, the observation of quantum objects typically results in a distribution of probabilistic outcomes, which manifests itself as additional noise (technically referred to as measurement back-action). This feature makes the theory of quantum feedback control, whereby quantum degrees of freedom are monitored and steered to desired states, rather more complex than its classical counterpart. Yet, the design and implementation of quantum feedback control schemes would be most timely and welcome, given the current struggle to achieve coherent manipulations for application in nano- and quantum technologies. The main obstacle standing in the way of exploitable quantum computation is still the problem of engineering multipartite microscopic systems where the interactions between the controlled subsystems are enhanced, while the unwanted interaction with their environment is suppressed. Feedback control schemes would offer an active way to suppress the effect of such environmental noise, with the possibility of stabilising the systems in quantum states useful as resources for quantum information processing.

Recent advances in cooling, trapping and manifacturing techniques are bringing more and more
degrees of freedom into the quantum regime. Among such degrees of freedom the family of cavity opto-mechanical systems, where resonating light is coupled to a micro- or nano-scopic mechanical oscillator, stand out for their interest in sensing, quantum information processing and as probes of the quantum to classical boundary (as they include massive oscillators of varying size). In particular, a new generation of such systems recently emerged where the mechanical oscillator is not clamped to a substrate but is instead a levitating bead, trapped by optical means. These set-ups are particularly promising because they are not influenced by the thermal fluctuations of a substratum. Still, because of their relatively low frequencies, which set much more stringent cooling requirements, they have not yet entered a fully quantum regime, where coherent, pure quantum states can be manipulated and observed. They would hence benefit greatly from the development of bespoke feedback control techniques.

Our research project is aimed at the design and implementation of feedback schemes for the cooling and quantum control of opto-mechanical systems, and in particular for the levitated bead set-ups at University College London and at the University of Vienna (project partner). We intend to achieve ground state cooling as well as squeezed states (states where the uncertainty on position is below the uncertainty of the ground state, of relevance to quantum metrology), as well as non-classical superpositions (Schroedinger cats) of the levitated beads.

The quantum control of opto-mechanical systems holds promise for application along at least three directions:
i) realisation of micro- and nano-scale position, mass and force sensors;
ii) realisation of quantum memories and `transducers' (devices that couple distinct quantum degrees of freedom);
iii) testing of wave-function reduction models, including gravitational collapse models.
By offering advanced tools for state control, and hence for the realisation of squeezed states with reduced uncertainties and non-classical superpositions, our project will directly contribute to i) and iii). Moreover, we shall also consider cases of operator control where, typically, we shall aim at optimising swap operations between impinging light and the mechanical oscillator, under realistic noisy conditions, by the use of real-time monitoring and feedback actions. We will thus also contribute to direction ii) with feedback driven operator control schemes.

The metrological deliverables i) will have direct economical implications thanks to their straightforward technological potential. Quantum memories and transducers, would also allow for the quantum information transfer between travelling degrees of freedom (light) and static degrees of freedom (the oscillators). As such, they would be exploitable for both quantum computation and quantum communication, a sector which is already commercially exploited.
The contribution to building the hardware of quantum computation might also have major societal and cultural implications, in that the switch to quantum computers could lead to another digital revolution within the next 50 years.
In regard to deliverable iii), it must be emphasised that discerning between different theories of quantum gravity is one of the main current challenges in fundamental theoretical physics. As such, it might rise wide interest amidst the general public, and hence have cultural and societal repercussions from which the research community would benefit (think of the public involvement and support which CERN was able to gather by reporting their recent findings concerning the Higgs boson).

Broadly, this project will contribute to keep the UK at the forefront of the field of quantum technologies, where UK research has always been leading, and where losing the prominence gained would be disastrous in view of the economic and cultural potential of such a field (as a somewhat loose, though relevant, analogy, think of the advantage in classical information technologies gained by the UK during World War II and then lost to the US).
More specifically, this project will focus on a subfield (cavity opto-mechanics) with, as outlined above, substantial strategic potential, and where further investment is needed to bring the UK on par with competing international research, mainly from the US, France, Germany and Austria.