Research themes

State preparation is a key tool in quantum science. To obtain quantum-enhanced precision in metrology, one needs to, for example, prepare a GHZ state or a squeezed state.  To perform measurement-based quantum computation, one has to prepare a suitable resource state such as the cluster state. Quantum communication requires one to prepare entangled states, such as a Bell pair, and send one part to Alice and the other to Bob. The variational quantum eigensolver optimizes the energy given a variational class of states that can be prepared efficiently.

There are more examples, but the general underlying requirement for all states we consider is that they be efficiently preparable. For one-dimensional systems, one of the most important classes of states are matrix-product states (MPS). All MPS can be prepared with a sequential (staircase) quantum circuit (and thus a depth linear in system size) from a product state, and all sequential quantum circuits produce MPS. What about higher dimensions? Interestingly, there exist projected entangled-pair states (PEPS, the higher-dimensional generalization of MPS) that despite small bond dimension require exponential depth to prepare, so the answer is not as easy as in one dimension.

Together with Zhi-Yuan Wei and Ignacio Cirac, we introduced a natural generalization of sequentially prepared states to higher dimensions: the plaquette-PEPS [1]. These are states that can be prepared with a quantum circuit comprising a number of mutually overlapping plaquette unitaries that scales linearly in system size. We derive some of the properties of these states, and find that they can represent a wide variety of known states. The big advantage of defining states via quantum circuits is that this automatically provides an algorithm to prepare them on a quantum processors.

In a second part, we put forward a way to produce these states as flying photons in a circuit QED platform [2]. This will be useful to improve upon earlier experimental work of ours on preparing photonic MPS [3].

We are still working intensely on understanding state preparation more fully. Our most recent work demonstrates numerically that many tensor network states can be prepared very efficiently using specifically designed adiabatic paths [4].

Atomic arrays as a photonic medium

Photonic metamaterials are materials structured on the nanometre scale and can coax light into adopting properties it wouldn't otherwise have. For example, light can be slowed done by many orders of magnitude, made massive, or completely trapped. We can use this to produce tailored interactions between embedded atoms (or atoms brought in close proximity), with many exciting avenues for quantum simulation. 

Subwavelength atomic arrays levitated in free space are in some sense the most elementary metamaterial possible, in the simplest case consisting of only a simple cubic array of two-level systems with a dipole transition. 

My master student Katharina Brechtelsbauer and I have shown that three-dimensional versions of such arrays can host complete band gaps of light, which would mean that they completely reflect any incident light [1]. This implies that excited impurity atoms placed inside of these arrays no longer decay! This has never been observed in any other system, and we can show that it also enables long-range coherent interactions between the impurity atoms, and can therefore be used to realize the many proposals for quantum simulation with emitters coupled to nanophotonic structures.

Photon emission and absorption

Atoms (few-level systems / superconducting qubits) offer an exceptional level of control over their quantum states. While in free space they typically only interact weakly with each other, the light-matter interaction can be strongly enhanced with suitably confined light modes, such as cavities, waveguides, or subwavelength three-dimensional arrays.

With protocols how atomic states and photonic states can be exchanged or entangled, we can use the intrinsic nonlinearity of atoms to measure, control, and generate non-classical states of light.

Under this paradigm, we have shown that a one-dimensional array of atoms coupled to a waveguide (waveguide QED, see figure) makes a robust photon detector [3], and this also inspired us to define a new meterological task that exhibits a quantum advantage [4]. We have also shown that three-dimensional Rydberg arrays can be used to generate entangled photonic states in free space [5].

Looking more fundamentally at photon emission, we found an analytical solution to Dicke superradiance and proved rigorously that it converges in the limit of large atom numbers [6] and we explored the novel phenomenology that emerges when emitters are coupled to non-Hermitian baths [7, 8].

Superconducting circuits

The first generation of quantum computers has arrived, in the form of superconducting qubits. While the current devices are still far away from fault tolerance, to get here, experimentalists around the world have already devoted intense research on fabricating devices with extremely low noise and an incredible level of control.

I'm interested in alternative ways one can use a quantum computer (beyond "digital quantum computation"), motivated by the large amount of freedom one has when interrogating these devices. Rather than understanding them as "computers", one can ask questions about the properties and dynamics of the underlying system -- arrays of qubits with tunable coupling -- and use them for analogue quantum simulation. 

As a first step, Adam Smith and I did an experiment with continuous driving of a single superconducting qubit with two incommensurate frequencies. Confirming earlier predictions, this reveals a temporal topological band structure, which ultimately results in topological frequency conversion. The underlying physics is related to one of my other research interest: periodically modulated systems (below).

We extended this line of work to many qubits, where the hope is that we can very flexibly simulate a large class of time-dependent spin models [2]. We have shown experimentally that our approach works, but is currently still limited by too much frequency disorder. This is a technical rather than a fundamental issue, so we keep pursuing this direction.

Ultracold atoms

Atoms in optical lattices is an extremely successful platform for analogue quantum simulation. Most experiments with ultracold atoms in optical lattices have contact interactions, and therefore operate at high densities of around one atom per site to observe the effect of strong interactions. My research in this field is concerned with adding long-range interactions to this system. 

This is on the one hand a technological challenge. A direction I have explored previously is to use atomic arrays to mediate long-range XY interactions [1]. This is inspired by earlier proposals using nanophotonic structures [a]. This line of research is actively pursued experimentally by Jean-Baptiste Beguin at Copenhagen.

Strong ranged interactions can also be generated via Rydberg dressing, which opens the path to explore the physics of few interacting particles. Rather than the unit cells of a crystal, the sites of the optical lattice can now be interpreted as discretized space. This allows studying completely new types of problems in a familiar architecture. To explore this vision, Ignacio Cirac and I have investigated the possibility of realizing problems akin to those found in quantum chemistry, although with a different scaling law in the interactions. Through numerical simulation, we show that simple pseudo-atoms and -molecules could be prepared with high fidelity in state-of-the-art experiments. [2]

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 [4].

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 Φ can be tuned to obtain directional transport. Figure taken from Ref. [4].

Discrete time crystals

Time crystals are nonequilibrium phases of matter that spontaneously break time-translation symmetry. The classic example here is one of a spin chain with a pi-pulse applied every period. Two pi-pulses are equivalent to the identity, which means the systems recurs only after two periods [a].

In a generic closed system, one would expect the drive to heat up the system to a infinite temperature state, which is why it is understood that one needs to add MBL to stabilize the phase [a]. Yet, even in the absence of MBL gives a subharmonic response for time scales that are exponentially long in systems sizes, which would suggest time-crystalline order in the absence of MBL. In a numerical analysis, we have shown that a previously overlooked, subtle effect can explain why the apparent subharmonic response scaling is misleading, thus further clarifying the role of MBL in such systems [1].

In classical systems, it is less clear how time crystalline phases can arise, as also the "rules" are less clear. Previous work has suggested that in one-dimensional systems, short-range interactions are not sufficient [b], but long-range interactions may indeed stabilize DTC order [c]. In our work we take ask more questions about this classical setting, by studying the example of seasonal epidemic spreading on small-world graphs, and identify a setup where an arbitrarily small density of random (infinite-range) bonds is sufficient for a transition to a time-crystalline phase [2]. In contrast to previous models, our model includes non-Markovianity in the form of "immune sites" that are non-dynamical for a set period of time. This opens an interesting parallel between research on DTCs and models that have been in use for decades in epidemiology.

Information spreading in many-body systems

The spreading of entanglement has been a major research theme in the many-body physics community for several years now. Most recently, a lot of attention has been devoted to the entanglement phase transition that occurs in monitored quantum circuits. [d]

We were wondering how fundamentally "quantum" this phenomenology is. To our surprise, we found that one can define classical models that exihibt very similar behaviour [3].

Topological magnon amplification

This project concerns the amplification of magnons in chiral topological edge modes [4]. Such modes arise in certain (3D, but effectively 2D) magnetic insulators with Dzyaloshinskii-Moriya interaction, most notably with kagome [e] and honeycomb [f] 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.