Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions1,2. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter3-6. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases7, which spontaneously break the discrete time-translation symmetry of the underlying drive8-11. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered †

Measuring local temperature with a spatial resolution on the order of a few nanometers has a wide range of applications from semiconductor industry over material to life sciences [1]. When combined with precision temperature measurement it promises to give excess to small temperature changes caused e.g. by chemical reactions or biochemical processes [2]. However, nanoscale temperature measurements and precision have excluded each other so far owing to the physical processes used for temperature measurement of limited stability of nanoscale probes [3]. Here we experimentally demonstrate a novel nanoscale temperature sensing technique based on single atomic defects in diamonds. Sensor sizes range from millimeter down to a few tens of nanometers. Utilizing the sensitivity of the optically accessible electron spin level structure to temperature changes [4] we achieve a temperature noise floor of 5 mK/ √ Hz for single defects in bulk sensors. Using doped nanodiamonds as sensors yields temperature measurement with 130 mK/ √ Hz noise floor and accuracies down to 1 mK at length scales of a few ten nanometers. The high sensitivity to temperature changes together with excellent spatial resolution combined with outstanding sensor stability allows for nanoscale precision temperature determination enough to measure chemical processes of few or single molecules by their reaction heat even in heterogeneous environments like cells.Several kinds of nanoscale temperature sensing techniques have been developed in the recent past [1]. These are scanning thermal microscopes (SThM) [5], dispersed or scanned individual nanoprobes [3,6], direct methods like micro-Raman spectroscopy [7] or near-field optical temperature measurements [8]. SThMs have temperature sensitive elements at a scanning tip (e.g. thermocouple), the nanoprobes have temperature dependent properties (e.g. fluorescence spectrum) which can be accessed without direct contact.In this study utilize a single quantum system in a solid state matrix as a temperature nanoprobe, namely the negatively charged nitrogen-vacancy (NV) center in diamond, which allows probe sizes down to ∼ 5 nm [9]. High fidelity control of its ground state electronic and nuclear spins has been demonstrated for various quantum information test experiments [10-15] as well as for nanometer scale metrology purposes [16][17][18][19] e.g. measuring small magnetic and electric fields. Here we show that it also allows tracking temperature with high precision. Temperature nanoprobes can be either dispersed in the specimen to be investigated or used in scanning probe geometry (see fig. 1a).The NV center is a molecular impurity in diamond comprising a substitutional nitrogen impurity and an adjacent carbon vacancy. Optical excitation in a wavelength range from 460 nm to 580 nm yields intense fluorescence emission [20]. Excitation also leads to a high degree of ground state electron spin polarization (S = 1, the actual sensor level) into its m S = 0 (|0 ) sublevel [21]. Furthermore the fluorescence decreases upo...

NV defect centres in diamond are promising solid-state magnetometers. Single centres allow for high spatial resolution field imaging but are limited in their magnetic field sensitivity to around 𝟏𝟎 𝐧𝐓/√𝐇𝐳 at room temperature. Using defect centre ensembles sensitivity can be scaled as √𝑵 when 𝑵 is the number of defects. In the present work, we use an ensemble of 10 11 defect centres for sensing. By carefully eliminating all noise sources like laser intensity fluctuations, microwave amplitude and phase noise we achieve a photon shot noise limited field sensitivity of 𝟎. 𝟗 𝐩𝐓/√𝐇𝐳 at room-temperature with an effective sensor volume of 𝟖. 𝟓𝐞-𝟒 𝐦𝐦 𝟑 . The smallest field we measured with our device is 𝟏𝟎𝟎 𝐟𝐓. While this denotes the best diamond magnetometer sensitivity so far, further improvements using decoupling sequences and material optimization could lead to 𝐟𝐓/√𝐇𝐳 sensitivity.

Nuclear magnetic resonance (NMR) spectroscopy is a key analytical technique in chemistry, biology, and medicine. However, conventional NMR spectroscopy requires an at least nanoliter-sized sample volume to achieve sufficient signal. We combined the use of a quantum memory and high magnetic fields with a dedicated quantum sensor based on nitrogen vacancy centers in diamond to achieve chemical shift resolution in H andF NMR spectroscopy of 20-zeptoliter sample volumes. We demonstrate the application of NMR pulse sequences to achieve homonuclear decoupling and spin diffusion measurements. The best measured NMR linewidth of a liquid sample was ~1 part per million, mainly limited by molecular diffusion. To mitigate the influence of diffusion, we performed high-resolution solid-state NMR by applying homonuclear decoupling and achieved a 20-fold narrowing of the NMR linewidth.

Present-day implementations of quantum information processing rely on two widely different types of quantum bits (qubits). On the one hand, microscopic systems such as atoms or spins are naturally well decoupled from their environment and as such can reach extremely long coherence times [1,2]; on the other hand, more macroscopic objects such as superconducting circuits are strongly coupled to electromagnetic fields, making them easy to entangle [3,4] although with shorter coherence times [5,6]. It thus seems appealing to combine the two types of systems in hybrid structures that could possibly take the best of both worlds. Here we report the first experimental realization of a hybrid quantum circuit in which a superconducting qubit of the transmon type [5,7] is coherently coupled to a spin ensemble consisting of nitrogen-vacancy (NV) centers in a diamond crystal [8] via a frequency-tunable superconducting resonator [9] acting as a quantum bus. Using this circuit, we prepare arbitrary superpositions of the qubit states that we store into collective excitations of the spin ensemble and retrieve back later on into the qubit. We demonstrate that this process preserves quantum coherence by performing quantum state tomography of the qubit. These results constitute a first proof of concept of spin-ensemble based quantum memory for superconducting qubits [10][11][12]. As a landmark of the successful marriage between a superconducting qubit and electronic spins, we detect with the qubit the hyperfine structure of the NV center.Superconducting qubits have been successfully coupled to electromagnetic [13] as well as mechanical [14] resonators; but coupling them to microscopic systems in a controlled way has up to now remained an elusive perspective -even though qubits sometimes turn out to be coupled to unknown and uncontrolled microscopic degrees of freedom with relatively short coherence times [15]. Whereas the coupling constant g of one individual microscopic system to a superconducting circuit is usually too weak for quantum information applications, ensembles of N such systems are coupled with a constant g √ N enhanced by collective effects.This makes possible to reach a regime of strong coupling between one collective variable of the ensemble and the circuit. This collective variable, which behaves in the low excitation limit as a harmonic oscillator, has been proposed [10-12] as a quantum memory for storing the state of superconducting qubits. Experimentally, the strong coupling between an ensemble of electronic spins and a superconducting resonator has been demonstrated 2 spectroscopically [16][17][18], and the storage of a microwave field into collective excitations of a spin ensemble has been observed very recently [19,20]. These experiments were however carried out in a classical regime since the resonator and spin ensemble behaved as two coupled harmonic oscillators driven by large microwave fields. In the perspective of building a quantum memory, it is instead necessary to perform experiments at the level of a...