Coherent control of multi-qubit dark states in waveguide quantum electrodynamics

Quantum physics has transitioned with great success from research on fundamental effects to harvesting technological applications that influence our everyday life. Stimulated emission in atoms allowed the development of laser systems, quantum mechanical descriptions explain tunneling effects in transistors and other semiconducting devices, and the utilization of the atomic spin enabled the development of novel medical devices via magnetic resonance imaging (MRI). New technologies are trying to improve classical systems with the help of quantum phenomena such as quantum entanglement, quantum superposition or quantum tunneling. These technologies include quantum communication, quantum sensing and quantum computing. In order to realize these new applications it is necessary to achieve coherent control over individual quantum states. This demands the ability to prepare, manipulate and read out the state of the encoded quantum information. Many platforms are trying to realize the interaction between matter and light by interfacing various emitters and electromagnetic environments. These include trapped ions, ultracold atoms or molecules, single spins in silicon, quantum dots, nitrogen-vacancy centers in diamond, photons, and superconducting quantum circuits. Quantum electrodynamics (QED) is the theoretical description of the interaction between matter and light at the level of single excitations and thus the basis for all applications using light-matter interfaces. For a long time it has been proven difficult to observe QED phenomena in fundamental research. The main problem is the weak interaction between the atomic emitter and the three dimensional mode environment of open space. Cavity QED confines light inside a closed volume, which can be used to enhance the interaction between the atom and the light field and enabled the exploration of many QED effects. Circuit QED adapted this approach by using superconducting qubits, serving as artificial atoms and microwave resonators, replacing optical cavities. One of the key ingredients for new quantum technological applications, like quantum computing and quantum information processing is strong light-matter interaction. Hence, most state of the art superconducting quantum information systems use qubits that are embedded in a resonator or cavity to enhance the interaction. Commonly, the strong-coupling limit is defined as the limit where the desired qubit coupling to a specific channel exceeds the coupling to all dissipative channels. Superconducting qubit-cavity systems protect the quantum information by designing the circuit such that the frequencies of the qubit and cavity are far detuned from each other. In this so-called dispersive regime, the cavity acts as a filter for noise around the qubit frequency that travels through the coaxial lines. At the same time the strong-coupling between the cavity and qubit allows for a quantum non-demolition readout of the qubit state due to the dispersive cavity shift that depends on the state of the qubit. The qubit remains accessible for coherent manipulation by applying pulses through weakly coupled control lines. The combination of these fundamental requirements led to the rapid development of circuit QED as one of the leading platforms for realizing a quantum computer. Waveguide QED combines open space and enhanced interaction by allowing photon propagation in one dimension and confining the other two dimensions. This allows studying quantum effects in an environment that is closer to the original QED description in free space. Waveguide quantum electrodynamics has become a popular platform to study light-matter interactions by coupling localized quantum emitters to one dimensional photonic channels. There are various platforms, that can be assessed by the ability to deterministically and efficiently couple individual quantum emitters to the waveguide. Due to their small dipole moment, natural atoms can only be coupled very weakly to propagating photons, at best achieving that 50% of the emitted radiation is coupled into the waveguide. Artificial atoms, like quantum dots can be coupled very efficiently, such that over 99% of the emission is guided into the waveguide modes. They have high engineering potential but suffer from inhomogeneous broadening which makes it very difficult to have more than two resonant emitters. Superconducting qubits are usually realized by integrating a nonlinear Josephson junction into an electrical circuit to obtain an anharmonic oscillator that plays the role of an artificial multilevel atom. Superconducting qubits and microwave waveguides can achieve coupling efficiencies of 99.9%, the qubits can be reliably fabricated as arrays, and they can be designed so that their resonance frequency can be controlled locally by magnetic flux. The engineering capabilities of superconducting qubits led to the observation of a broad range of quantum optical phenomena such as the Mollow triplet, ultra strong coupling, generation of non-classical photonic states, qubit-photon bound states, topological physics as well as collective effects. Despite the success of superconducting waveguide quantum electrodynamics, one of many crucial questions remains unanswered: How valid is the two-level approximation, especially for describing collective states beyond the single excitation manifold? Collective states appear in waveguide QED as a result of waveguide-mediated interactions and interference effects in an ensemble of emitters. The relative phase between individual emitters determines whether the collective state obtains a sub- or superradiant decay rate, i.e. whether it becomes a dark or a bright state. Collective bright states have been measured in various waveguide QED systems, whereas dark states have only been observed spectroscopically in superconducting waveguide QED. More recently a multi-qubit dark state has been used to build a microwave cavity, but full coherent control of the dark state has not been achieved. The difficulty arises from the main property of the dark state - it decouples from the electromagnetic environment of the waveguide. Full control over the dark state provides the possibility to realize a quantum computation and simulation platform using decoherence-free subspaces. For quantum computation purposes the multi-level nature of collective systems requires accurate knowledge of the energy and decay characteristics beyond the single excitation states to avoid detrimental leakage errors out from the computational subspace. Coherent control over the dark states enables the usage as a qubit in waveguide QED. Moreover, the long-lived nature offers a starting point for an accurate characterization of the spectrum and the decay properties of such collective systems, especially for the higher excitation manifolds. In the scope of this thesis, we investigated the interaction between four superconducting transmon qubits that are coupled to a common waveguide mode environment. The hybridization of the transmon yields collective states that strongly depend on the coupling parameters and transmon anharmonicities. The pairwise arrangement gives rise to a direct coupling that is caused by the capacitance between the metallic transmon pads. Each pair obtains a local dark state in the first excitation manifold, that is long-lived and can serve as a resource for coherence in an open quantum system, such as the waveguide environment. The waveguide-mediated interaction depends on the effective separation and causes coherent exchange coupling or collective dissipation. In this setting we focus on the collective behavior, thus tune the qubits to a frequency that corresponds to a distance of half a wavelength. The emerging dark state is non-local and shared between the distant qubits. Then, the phase of a collective drive must match the phase of the hybridized transitions in order to drive them. We show that two local ports at the qubit pairs can be used to match the drive phase to the symmetry of the bright and dark states, and show that the dark state serves as a starting point for studying the multi-level spectrum of the coupled transmons. The doctoral thesis is organized as follows: The introductory chapter contains the basic concepts of circuit QED and a description of cavity and waveguide QED. The second chapter summarizes the waveguide QED theory, which is necessary to understand the experimental results. Many results can already be reproduced by QuTiP simulations. But an accurate prediction of the energy spectrum, the decay rates of the states, and the symmetries with respect to a given mode environment are obtained by numerical simulations of the pairwise transmon setup. In the third chapter, a practical approach to the design and development of a waveguide QED setup is presented and the measurement procedure is briefly discussed. In the fourth chapter, the results of the conducted experiments are presented and discussed, while in the conclusion, the significance of the results in a broader sense is explained to conclude the thesis. (author)