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Publication# Fully Tunable Longitudinal Spin-Photon Interactions in Si and Ge Quantum Dots

Résumé

Spin qubits in silicon and germanium quantum dots are promising platforms for quantum computing, but entangling spin qubits over micrometer distances remains a critical challenge. Current prototypical architectures maximize transversal interactions between qubits and microwave resonators, where the spin state is flipped by nearly resonant photons. However, these interactions cause backaction on the qubit that yields unavoidable residual qubit-qubit couplings and significantly affects the gate fidelity. Strikingly, residual couplings vanish when spin-photon interactions are longitudinal and photons couple to the phase of the qubit. We show that large and tunable spin-photon interactions emerge naturally in state-of-the-art hole spin qubits and that they change from transversal to longitudinal depending on the magnetic field direction. We propose ways to electrically control and measure these interactions, as well as realistic protocols to implement fast high-fidelity two-qubit entangling gates. These protocols work also at high temperatures, paving the way toward the implementation of large-scale quantum processors.

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A primary challenge in quantum science and technology is to isolate the fragile quantum states from their environment in order to prevent the irreversible leakage of energy and information which causes decoherence. In the late 1990s, however, a new paradigm emerged, in which
the environment itself, as well as the coupling to this environment of the quantum state, are engineered in ways which, counterintuitively, facilitate the creation and stabilization of desired quantum properties. This paradigm, coined reservoir engineering, has been pursued experimentally in various implementations, in which the states of trapped ions, atomic clouds or artificial atoms based on superconducting circuits were driven into a desired target state using a dissipative reservoir. In all these cases, the cold electromagnetic environment served as the engineered reservoir, capitalizing on the tremendous progress in the ability to shape the modes of the electromagnetic field using masers and lasers.
In optomechanics, which is the study of the coupling between light and mechanical motion, a similar scenario has been prevalent. Light is used to read out and control the mechanical motion, and in the past few years, various optomechanical architectures both in the optical and microwave domain have enabled to push mechanical systems into the quantum regime. These results can be interpreted in the context of reservoir engineering: cooling and many other optomechanical phenomena exploit the cold, dissipative nature of light.
This thesis reports on the development of a multimode superconducting circuit with a mechanically compliant element - fitting into the field of circuit cavity electromechanics -, with which we pursue two themes. In the first set of experiments, reversing the roles of dissipation described above, we engineer the mechanical oscillator into a cold, dissipative environment for microwave light. The mechanical element is the fundamental mode of a free-standing top electrode of a capacitor, 100 nm thick and 32 micron in diameter made of aluminum with an effective mass of around 170 pg, vibrating at a resonance frequency of 5.5 MHz. The dissipative mechanical reservoir is prepared using an auxiliary microwave mode with engineered parameters.We utilize it to control the properties - in particular, the susceptibility - of the electromagnetic field and to perform low-noise amplification close to the quantum limit. The noise analysis reveals that the reservoir is close to its quantum ground state with a mean thermal occupation number well below 1, demonstrating its utility as a resource in the quantum regime. We also show that the system can be driven to the parametric instability threshold, above which self-sustained oscillations of the microwave field (masing) is observed. Finally, we demonstrate injection locking of the maser using an external seed pump.
In a second set of experiments, a similar electromechanical circuit is used to implement a microwave isolator based on optomechanical interactions. The overarching theme is that dissipation of the mechanical oscillator, albeit intrinsic and not engineered via an auxiliary mode s a key ingredient for the device to function as a nonreciprocal frequency converter and isolator. In these experiments, an additional mechanical mode is used, such that a 4-mode optomechanical plaquette is realized.

The enormous advancements in the ability to detect and manipulate single quantum states have lead to the emerging field of quantum technologies. Among these, quantum computation is the most far-reaching and challenging, aiming to solve problems that the classic computers could never address because of the exponential scaling, while quantum sensing exploits the ability to address single quantum states to realize ultra-sensitive and precise detectors. Defect centers in semiconductors play a primary role in these fields. The possibility to store information in the spin of their ground state, manipulate it through microwaves, and read it optically allows to use them as qubits. In addition, the very sharp dependence of their properties on temperature, strain and magnetic fields makes them very promising quantum sensors. In this Thesis we aim at contributing to the progress of quantum technologies both at the hardware and software level. From a hardware point of view, we study a key property of defect centers in semiconductors, the phonon-assisted luminescence, which can be measured to perform the readout of the information stored in a quantum bit, or to detect temperature variations. We predict the luminescence and study the exciton-phonon couplings within a rigorous many-body perturbation theory framework,an analysis that has never been performed for defect centers.In particular, we study the optical emission of the negatively-charged boron vacancy in 2D hexagonal boron nitride, which currently stands out among defect centers in 2D materials thanks to its promise for applications in quantum information and quantum sensing. We show that phonons are responsible for the observed luminescence, which otherwise would be dark due to symmetry. We also show that the symmetry breaking induced by the static Jahn-Teller effect is not able to describe the presence of the experimentally observed peak at 1.5 eV.The knowledge of the coupling between electrons and phonons is fundamental for the accurate prediction of all the features of the photoluminescence spectrum. However, the large number of atoms in a defect supercell hinders the possibility use density functional perturbation theory to study this coupling. In this work we present a finite-differences technique to calculate the electron-phonon matrix elements, which exploits the symmetries of the defect in such a way to use the very same set of displacement needed for the calculation of phonons. The computation of electron-phonon coupling thus becomes a simple post-processing of the finite-differences phonons calculation. On the quantum software side, we propose an improved quantum algorithm to calculate the Green's function through real-time propagation, and use it to compute the retarded Green's function for the 2-, 3- and 4-site Hubbard models. This novel protocol significantly reduces the number of controlled operations when compared to those previously suggested in literature. Such reduction is quite remarkable when considering the 2-site Hubbard model, for which we show that it is possible to obtain the exact time propagation of the $\ket{N\pm 1}$ states by exponentiating one single Pauli component of the Hamiltonian, allowing us to perform the calculations on an actual superconducting quantum processor.

Jean-Philippe Brantut, Victor Youri Helson, Hideki Konishi, Kevin Etienne Robert Roux

Strong quantum correlations in matter are responsible for some of the most extraordinary properties of material, from magnetism to high-temperature superconductivity, but their integration in quantum devices requires a strong, coherent coupling with photons, which still represents a formidable technical challenge in solid state systems. In cavity quantum electrodynamics, quantum gases such as Bose-Einstein condensates or lattice gases have been strongly coupled with light. However, neither Fermionic quantum matter, comparable to electrons in solids, nor atomic systems with controlled interactions, have thus far been strongly coupled with photons. Here we report on the strong coupling of a quantum-degenerate unitary Fermi gas with light in a high finesse cavity. We map out the spectrum of the coupled system and observe well resolved dressed states, resulting from the strong coupling of cavity photons with each spin component of the gas. We investigate spin-balanced and spin-polarized gases and find quantitative agreement with ab-initio calculation describing light-matter interaction. Our system offers complete and simultaneous control of atom-atom and atom-photon interactions in the quantum degenerate regime, opening a wide range of perspectives for quantum simulation.

2019