# Research themes

This is a brief overview of my main research themes (complete list of Publications).

## Number-resolving photon detector in waveguide QED

Number-resolving single-photon detectors represent a key technology for a host of quantum optics protocols, comprising quantum state preparation, quantum metrology, entanglement distribution, and quantum computing. Despite significant advances over the last few decades, state-of-the-art technology can distinguish only very low photon numbers with high fidelity. We show that (artificial) atoms coupled to photonic waveguides constitute an ideal platform to entirely absorb incident photonic wavepackets, even in the presence of disorder and finite Purcell factors, with a fidelity increasing with the number of atoms. Absorption is achieved through engineering a decay channel to a metastable state, such that readout of the atomic state after absorption yields a number-resolving measurement of photon number.

(Artificial) atoms coupled to semi-infinite **(a)** or infinite **(b) **waveguides in addition to engineered dissipation **(c)** are the ingredients for number-resolving photon detection that is robust against disorder and experimental imperfections.

## Topological Magnon Amplification

This project concerns the amplification of magnons in chiral topological edge modes [10]. Such modes arise in certain (3D, but effectively 2D) magnetic insulators with Dzyaloshinskii-Moriya interaction, most notably with kagome [a] and honeycomb [b] lattices. We show that driving such systems with light can lead to edge mode instabilities and nonequilibrium steady states with large edge magnon population and further show that driving with a gradient leads to some sort of driven magnon Hall effect, two aspects that will aid their direct experimental detection. Beyond the characterisation these materials, our magnon amplification mechanism can be used to build a coherent magnon source (a magnon laser) and a travelling-wave magnon amplifier, two devices with great potential in the realm of magnon spintronics.

This work is in collaboration with Andreas Nunnenkamp and Johannes Knolle.

[10] Topological magnon amplification;

*DM, Johannes Knolle, Andreas Nunnenkamp,*Nature Communications,

**10**, 3937 (2019), arXiv:1901.02282.

A kagome topological magnon insulator driven with a field gradient will exhibit a *driven Hall effect, *due to selective amplification of edge modes, as we show in our article [10].

## Nonreciprocal systems

There is an ongoing significant interest in nonreciprocal optomechanical devices for photons (and phonons). The motivation for this work comes from the shortcomings of current implementations of directional devices, such as isolators, circulators and directional amplifiers. Such devices are of crucial importance in measurement and communication systems. Conventionally, nonreciprocal devices rely on magneto-optic effects and strong magnetic fields. They are bulky, lossy, and cannot be integrated on a superconducting chip, which makes it difficult to combine them with modern quantum architecture. Moreover, stray magnetic fields due to these devices lead to additional decoherence, which exacerbates the problem.

In collaboration with Tobias Kippenberg's lab in Lausanne, we have demonstrated an **magnetic-field-free optomechanical isolator** for photons [3]. The experiment is an *optomechanical plaquette*, which is a circuit where two cavity modes interact with two mechanical resonator modes (schematically shown on the right). There are two paths from one cavity to the other, and destructive interference can lead to isolation. Due to the dissipation in the intermediate mechanical modes, photons can still travel in the reverse direction, i.e., the device is non-reciprocal.

This work led on to a proposal for **directional, quantum-limited, optomechanical amplifiers**, both phase-preserving and phase-sensitive (shown on the right) [4], which have recently been realized in experiment [a].

[13] Nonreciprocal transport based on cavity Floquet modes in optomechanics, arXiv:1912.10541.[6] Current rectification in double quantum dot through fermionic reservoir engineering; Phys. Rev. B 97, 165308 (2018).[4] Quantum-limited directional amplifiers with optomechanics, Phys. Rev. Lett. 120, 023601 (2018).[3] Nonreciprocal reconfigurable microwave optomechanical circuit, Nature Communications 8, 604 (2017).

A sketch of the *optomechanical plaquette*. The mechanical modes are represented by circles, the cavity modes by squares. Figure taken from Ref. [4].

Inspired by the results in optomechanics, which pertain to bosonic excitations, we have shown that in a similar way, directional transport of fermions can be achieved. Specifically, we proposed to use this mechanism to obtain current **rectification in a double quantum dot** [6].

The model we consider to achieve fermionic directional transport is shown on the right. The two green sites are two energy levels of a double quantum dot, the grey areas represent leads. An applied magnetic field Î¦ can be tuned to obtain directional transport. Figure taken from Ref. [6].

## Periodically modulated optomechanical systems

Another common theme in my research are periodically modulated optomechanical systems. The quadratures of a mechanical resonator rotate in phase space with the mechanical frequency, which is why protocols to measure, amplify, or control single quadratures of the mechanical resonator, such as backaction-evading/quantum nondemolition measurements (experiments in Tobias Kippenberg's lab: [8,9]), phase-sensitive amplification, or entanglement schemes commonly employ periodically modulated drives. In the rotating-wave approximation there is often a frame in which the Hamiltonian becomes time-independent, but occasionally the off-resonant terms are important, too.

We have rigorously developed a framework to calculate noise spectra in such a situation [1], and used it to find a closed, exact solution to an optomechanical backaction-evading measurement outside the rotating-wave approximation [2]. Together with Tania Monteiro's group at UCL we have checked our framework against related ones and developed it further [5].

Employing a backaction-evading measurement it is possible to produce a *conditionally-squeezed mechanical state* -- essentially, acquiring a lot of information about a quadrature X reduces its uncertainty, thus squeezing it. Together with Matteo Brunelli and Andreas Nunnenkamp, we describe this and obtain analytical and numerical results for this case in a recent article [11].

In fact, our work on nonreciprocal optomechanical system also involves cavities with a modulated drive and some of the techniques developed in Refs [1,2] have been useful in analysing the effect of non-resonant terms in the optomechanical plaquette [3,4].

The theoretical framework to describe a periodically driven optomechanical system involves several copies of the system, which can conveniently be drawn as a lattice of modes. The figure has been taken from Ref. [7].

*;*Phys. Rev. Lett.

**123**, 093602 (2019).[9] Two-Tone Optomechanical Instability and Its Fundamental Implications for Backaction-Evading Measurements; Phys. Rev. X

**9**, 041022 (2019).[8] Optical Backaction-Evading Measurement of a Mechanical Oscillator;

*Nature Communications*

**10**, 2086 (2019).[7] Floquet dynamics in quantum measurement of mechanical motion;

*Phys. Rev. A 100, 053852 (2019).[5] Quantum noise spectra for periodically-driven cavity optomechanics, Phys. Rev. A 96, 063836 (2017).[2] Optomechanical dual-beam backaction-evading measurement beyond the rotating-wave approximation, Phys. Rev. A 94, 053820 (2016).[1] Floquet approach to bichromatically driven cavity optomechanical systems,Phys. Rev. A 94, 023803 (2016).*