Steady-state quantum chaos in open quantum systems

We introduce the notion of steady-state quantum chaos as a general phenomenon in open quantum many-body systems. Classifying an isolated or open quantum system as integrable or chaotic relies in general on the properties of the equations governing its time evolution. This however may fail in predicting the actual nature of the quantum dynamics, that can be either regular or chaotic depending on the initial state. Chaos and integrability in the steady state of an open quantum system are instead uniquely determined by the spectral structure of the time evolution generator. To characterize steady-state quantum chaos we introduce a spectral analysis based on the spectral statistics of quantum trajectories (SSQT). We test the generality and reliability of the SSQT criterion on several dissipative systems, further showing that an open system with chaotic structure can evolve towards either a chaotic or integrable steady state. We study steady-state chaos in the driven-dissipative Bose-Hubbard model, a paradigmatic example of out-of-equilibrium bosonic system without particle number conservation. This system is widely employed as a building block in state-of-the-art noisy intermediate-scale quantum devices, with applications in quantum computation and sensing. Finally, our analysis shows the existence of an emergent dissipative quantum chaos, where the classical and semi-classical limits display an integrable behaviour. This emergent dissipative quantum chaos arises from the quantum and classical fluctuations associated with the dissipation mechanism. Our work establishes a fundamental understanding of the integrable and chaotic dynamics of open quantum systems and paves the way for the investigation of dissipative quantum chaos and its consequences on quantum technologies.Comment: 23 pages, 12 figure

Strong Coupling Cavity QED with Gate-Defined Double Quantum Dots Enabled by a High Impedance Resonator

The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-detuned GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quantum interference devices (SQUIDs). In the resonant regime, we resolve the vacuum Rabi mode splitting of size $2g/2\pi = 238$ MHz at a resonator linewidth $\kappa/2\pi = 12$ MHz and a DQD charge qubit dephasing rate of $\gamma_2/2\pi = 80$ MHz extracted independently from microwave spectroscopy in the dispersive regime. Our measurements indicate a viable path towards using circuit based cavity QED for quantum information processing in semiconductor nano-structures

Fully tunable longitudinal spin-photon interactions in Si and Ge quantum dots

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 back-action on the qubit, that yield unavoidable residual qubit-qubit couplings and significantly affect 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 longitudinal interactions emerge naturally in state-of-the-art hole spin qubits. These interactions are fully tunable and can be parametrically modulated by external oscillating electric fields. We propose realistic protocols to measure these interactions and to implement fast and high-fidelity two-qubit entangling gates. These protocols work also at high temperatures, paving the way towards the implementation of large-scale quantum processors

Microwave photon-mediated interactions between semiconductor qubits

The realization of a coherent interface between distant charge or spin qubits in semiconductor quantum dots is an open challenge for quantum information processing. Here we demonstrate both resonant and non-resonant photon-mediated coherent interactions between double quantum dot charge qubits separated by several tens of micrometers. We present clear spectroscopic evidence of the collective enhancement of the resonant coupling of two qubits. With both qubits detuned from the resonator we observe exchange coupling between the qubits mediated by virtual photons. In both instances pronounced bright and dark states governed by the symmetry of the qubit-field interaction are found. Our observations are in excellent quantitative agreement with master-equation simulations. The extracted two-qubit coupling strengths significantly exceed the linewidths of the combined resonator-qubit system. This indicates that this approach is viable for creating photon-mediated two-qubit gates in quantum dot based systems.Comment: 14 pages, 10 figures and 6 table

Controlling Atom-Photon Bound States in an Array of Josephson-Junction Resonators

Engineering the electromagnetic environment of a quantum emitter gives rise to a plethora of exotic light -matter interactions. In particular, photonic lattices can seed long-lived atom-photon bound states inside photonic band gaps. Here, we report on the concept and implementation of a novel microwave architecture consisting of an array of compact superconducting resonators in which we have embedded two frequency -tunable artificial atoms. We study the atom-field interaction and access previously unexplored coupling regimes, in both the single-and double-excitation subspace. In addition, we demonstrate coherent interactions between two atom-photon bound states, in both resonant and dispersive regimes, that are suitable for the implementation of SWAP and CZ two-qubit gates. The presented architecture holds promise for quantum simulation with tunable-range interactions and photon transport experiments in the nonlinear regime

Controlling Atom-Photon Bound States in an Array of Josephson-Junction Resonators

Engineering the electromagnetic environment of a quantum emitter gives rise to a plethora of exotic light -matter interactions. In particular, photonic lattices can seed long-lived atom-photon bound states inside photonic band gaps. Here, we report on the concept and implementation of a novel microwave architecture consisting of an array of compact superconducting resonators in which we have embedded two frequency -tunable artificial atoms. We study the atom-field interaction and access previously unexplored coupling regimes, in both the single-and double-excitation subspace. In addition, we demonstrate coherent interactions between two atom-photon bound states, in both resonant and dispersive regimes, that are suitable for the implementation of SWAP and CZ two-qubit gates. The presented architecture holds promise for quantum simulation with tunable-range interactions and photon transport experiments in the nonlinear regime

Strong hole-photon coupling in planar Ge: probing the charge degree and Wigner molecule states

Semiconductor quantum dots (QDs) in planar germanium (Ge) heterostructures have emerged as frontrunners for future hole-based quantum processors. Notably, the large spin-orbit interaction of holes offers rapid, coherent electrical control of spin states, which can be further beneficial for interfacing hole spins to microwave photons in superconducting circuits via coherent charge-photon coupling. Here, we present strong coupling between a hole charge qubit, defined in a double quantum dot (DQD) in a planar Ge, and microwave photons in a high-impedance ($Z_\mathrm{r} = 1.3 ~ \mathrm{k}\Omega$) superconducting quantum interference device (SQUID) array resonator. Our investigation reveals vacuum-Rabi splittings with coupling strengths up to $g_{0}/2\pi = 260 ~ \mathrm{MHz}$, and a cooperativity of $C \sim 100$, dependent on DQD tuning, confirming the strong charge-photon coupling regime within planar Ge. Furthermore, utilizing the frequency tunability of our resonator, we explore the quenched energy splitting associated with strongly-correlated Wigner molecule (WM) states that emerge in Ge QDs. The observed enhanced coherence of the WM excited state signals the presence of distinct symmetries within related spin functions, serving as a precursor to the strong coupling between photons and spin-charge hybrid qubits in planar Ge. This work paves the way towards coherent quantum connections between remote hole qubits in planar Ge, required to scale up hole-based quantum processors.Comment: 22 pages, 12 figure

High-kinetic inductance NbN films for high-quality compact superconducting resonators

Niobium nitride (NbN) is a particularly promising material for quantum technology applications, as entails the degree of reproducibility necessary for large-scale of superconducting circuits. We demonstrate that resonators based on NbN thin films present a one-photon internal quality factor above 10$^5$ maintaining a high impedance (larger than 2k$\Omega$), with a footprint of approximately 50x100 $\mu$m$^2$ and a self-Kerr nonlinearity of few tenths of Hz. These quality factors, mostly limited by losses induced by the coupling to two-level systems, have been maintained for kinetic inductances ranging from tenths to hundreds of pH/square. We also demonstrate minimal variations in the performance of the resonators during multiple cooldowns over more than nine months. Our work proves the versatility of niobium nitride high-kinetic inductance resonators, opening perspectives towards the fabrication of compact, high-impedance and high-quality multimode circuits, with sizable interactions.Comment: 12 pages, 8 figure

Strong coupling between a microwave photon and a singlet-triplet qubit

Tremendous progress in few-qubit quantum processing has been achieved lately using superconducting resonators coupled to gate voltage defined quantum dots. While the strong coupling regime has been demonstrated recently for odd charge parity flopping mode spin qubits, first attempts towards coupling a resonator to even charge parity singlet-triplet spin qubits have resulted only in weak spin-photon coupling strengths. Here, we integrate a zincblende InAs nanowire double quantum dot with strong spin-orbit interaction in a magnetic-field resilient, high-quality resonator. In contrast to conventional strategies, the quantum confinement is achieved using deterministically grown wurtzite tunnel barriers without resorting to electrical gating. Our experiments on even charge parity states and at large magnetic fields, allow us to identify the relevant spin states and to measure the spin decoherence rates and spin-photon coupling strengths. Most importantly, at a specific magnetic field, we find an anti-crossing between the resonator mode in the single photon limit and a singlet-triplet qubit with an electron spin-photon coupling strength of $g = 114 \pm 9$ MHz, reaching the strong coupling regime in which the coherent coupling exceeds the combined qubit and resonator linewidth.Comment: 10 pages, 7 figure