Protecting a Spin Ensemble against Decoherence in the Strong-Coupling Regime of Cavity QED

Hybrid quantum systems based on spin ensembles coupled to superconducting microwave cavities are promising candidates for robust experiments in cavity quantum electrodynamics (QED) and for future technologies employing quantum mechanical effects. Currently the main source of decoherence in these systems is inho- mogeneous spin broadening, which limits their performance for the coherent transfer and storage of quantum information. Here we study the dynamics of a superconducting cavity strongly coupled to an ensemble of nitrogen-vacancy centers in diamond. We experimentally observe for the first time, how decoherence induced by a non-Lorentzian spin distribution can be suppressed in the strong-coupling regime - a phenomenon known as "cavity protection". To demonstrate the potential of this effect for coherent control schemes, we show how appropriately chosen microwave pulses can increase the amplitude of coherent oscillations between cavity and spin ensemble by two orders of magnitude.Comment: 16 pages, 4 figure

Engineering Long-Lived Collective Dark States in Spin Ensembles

Ensembles of electron spins in hybrid microwave systems are powerful and versatile components for future quantum technologies. Quantum memories with high storage capacities are one such example which require long-lived states that can be addressed and manipulated coherently within the inhomogeneously broadened ensemble. This broadening is essential for true multimode memories, but induces a considerable spin dephasing and together with dissipation from a cavity interface poses a constraint on the memory's storage time. In this work we show how to overcome both of these limitations through the engineering of long-lived dark states in an ensemble of electron spins hosted by nitrogen-vacancy centres in diamond. By burning narrow spectral holes into a spin ensemble strongly coupled to a superconducting microwave cavity, we observe long-lived Rabi oscillations with high visibility and a decay rate that is a factor of forty smaller than the spin ensemble linewidth and thereby a factor of more than three below the pure cavity dissipation rate. This significant reduction lives up to the promise of hybrid devices to perform better than their individual subcomponents. To demonstrate the potential of our approach we realise the first step towards a solid-state microwave spin multiplexer by engineering multiple long-lived dark states. Our results show that we can fully access the "decoherence free" subspace in our experiment and selectively prepare protected states by spectral hole burning. This technique opens up the way for truly long-lived quantum memories, solid-state microwave frequency combs, optical to microwave quantum transducers and spin squeezed states. Our approach also paves the way for a new class of cavity QED experiments with dense spin ensembles, where dipole spin-spin interactions become important and many-body phenomena will be directly accessible on a chip.Comment: 9 pages, 7 figure

Non-Markovian dynamics of a single-mode cavity strongly coupled to an inhomogeneously broadened spin ensemble

We study the dynamics of a spin ensemble strongly coupled to a single-mode resonator driven by external pulses. When the mean frequency of the spin ensemble is in resonance with the cavity mode, damped Rabi oscillations are found between the spin ensemble and the cavity mode which we describe very accurately, including the dephasing effect of the inhomogeneous spin broadening. We demonstrate that a precise knowledge of this broadening is crucial both for a qualitative and a quantitative understanding of the temporal spin-cavity dynamics. On this basis we show that coherent oscillations between the spin ensemble and the cavity can be enhanced by a few orders of magnitude, when driving the system with pulses that match special resonance conditions. Our theoretical approach is tested successfully with an experiment based on an ensemble of negatively charged nitrogen-vacancy (NV) centers in diamond strongly coupled to a superconducting coplanar single-mode waveguide resonator.Comment: 15 pages, 13 figure

Implementation of the Dicke lattice model in hybrid quantum system arrays

Generalized Dicke models can be implemented in hybrid quantum systems built from ensembles of nitrogen-vacancy (NV) centers in diamond coupled to superconducting microwave cavities. By engineering cavity assisted Raman transitions between two spin states of the NV defect, a fully tunable model for collective light-matter interactions in the ultra-strong coupling limit can be obtained. Our analysis of the resulting non-equilibrium phases for a single cavity and for coupled cavity arrays shows that different superradiant phase transitions can be observed using existing experimental technologies, even in the presence of large inhomogeneous broadening of the spin ensemble. The phase diagram of the Dicke lattice model displays distinct features induced by dissipation, which can serve as a genuine experimental signature for phase transitions in driven open quantum systems.Comment: 4+1 pages, 3 figures and supplementary materia

Magnetic conveyor belt transport of ultracold atoms to a superconducting atomchip

We report the realization of a robust magnetic transport scheme to bring 3x10^8 ultracold 87Rb atoms into a cryostat. The sequence starts with standard laser cooling and trapping of 87Rb atoms, transporting first horizontally and then vertically through the radiation shields into a cryostat by a series of normal- and superconducting magnetic coils. Loading the atoms in a superconducting microtrap paves the way for studying the interaction of ultracold atoms with superconducting surfaces and quantum devices requiring cryogenic temperatures.Comment: 4 pages, 4 figure

Smooth optimal quantum control for robust solid state spin magnetometry

Nitrogen-vacancy centers in diamond show great potential as magnetic, electric and thermal sensors which are naturally packaged in a bio-compatible material. In particular, NV-based magnetometers combine small sensor volumes with high sensitivities under ambient conditions. The practical operation of such sensors, however, requires advanced quantum control techniques that are robust with respect to experimental and material imperfections, control errors, and noise. Here, we present a novel approach that uses Floquet theory to efficiently generate smooth and simple quantum control pulses with tailored robustness properties. We verify their performance by applying them to a single NV center and by characterising the resulting quantum gate using quantum process tomography. We show how the sensitivity of NV-ensemble magnetometry schemes can be improved by up to two orders of magnitude by compensating for inhomogeneities in both the control field and the spin transition frequency. Our approach is ideally suited for a wide variety of quantum technologies requiring high-fidelity, robust control under tight bandwidth requirements, such as spin-ensemble based memories involving high-Q cavities.Comment: 12 pages, 5 figure

Collective Strong Coupling with Homogeneous Rabi Frequencies using a 3D Lumped Element Microwave Resonator

We design and implement 3D lumped element microwave cavities for the coherent and uniform coupling to electron spins hosted by nitrogen vacancy centers in diamond. Our design spatially focuses the magnetic field to a small mode volume. We achieve large homogeneous single spin coupling rates, with an enhancement of the single spin Rabi frequency of more than one order of magnitude compared to standard 3D cavities with a fundamental resonance at \SI{3}{GHz}. Finite element simulations confirm that the magnetic field component is homogeneous throughout the entire sample volume, with a RMS deviation of 1.54\%. With a sample containing $10^{17}$ nitrogen vacancy electron spins we achieve a collective coupling strength of \Omega=\SI{12}{MHz}, a cooperativity factor $C=27$ and clearly enter the strong coupling regime. This allows to interface a macroscopic spin ensemble with microwave circuits, and the homogeneous Rabi frequency paves the way to manipulate the full ensemble population in a coherent way.Comment: 3 figure

Cavity QED with magnetically coupled collective spin states

We report strong coupling between an ensemble of nitrogen-vacancy center electron spins in diamond and a superconducting microwave coplanar waveguide resonator. The characteristic scaling of the collective coupling strength with the square root of the number of emitters is observed directly. Additionally, we measure hyperfine coupling to 13C nuclear spins, which is a first step towards a nuclear ensemble quantum memory. Using the dispersive shift of the cavity resonance frequency, we measure the relaxation time T1 of the NV center at millikelvin temperatures in a non-destructive way.Comment: 5 pages, 4 figure

Dynamical Exploration of Amplitude Bistability in Engineered Quantum Systems

Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena which have profoundly changed our technological landscape over the last 50 years. Recently the ability to engineer quantum metamaterials through hybridisation has allowed to explore these nonlinear effects in systems with no natural analogue. Here we investigate amplitude bistability, which is one of the most fundamental nonlinear phenomena, in a hybrid system composed of a superconducting resonator inductively coupled to an ensemble of nitrogen-vacancy centres. One of the exciting properties of this spin system is its extremely long spin life-time, more than ten orders of magnitude longer than other relevant timescales of the hybrid system. This allows us to dynamically explore this nonlinear regime of cavity quantum electrodynamics (cQED) and demonstrate a critical slowing down of the cavity population on the order of several tens of thousands of seconds - a timescale much longer than observed so far for this effect. Our results provide the foundation for future quantum technologies based on nonlinear phenomena

Creation of ensembles of nitrogen-vacancy centers in diamond by neutron and electron irradiation

We created dense ensembles of negatively charged nitrogen-vacancy (NV-) centers in diamond by neutron and electron irradiation for applications in hybrid quantum systems and magnetometry. We characterize fluorescence intensity, optical and coherence properties of the resulting defects by confocal microscopy, UV/Vis and FTIR spectroscopy, optically detected magnetic resonance and small angle X-ray scattering. We find the highest densities of NV- at neutron fluences on the order of 10^17 cm^-2 and electron doses of 10^18 cm^-2, with spin resonance linewidths of 6 MHz. Lower electron energies increase the ratio of centers in the desired negative charge state to those in the neutral one. Annealing at 900 {\deg}C during the irradiation reduces the spin resonance linewidth. Electron irradiation furthermore results in substantially higher optical transparency compared to neutron irradiation.Comment: 12 pages, 9 figures, 1 tabl