Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional point" occurs, around which many fascinating phenomena have recently been reported to arise [1][2][3][4][5][6] . Particularly intriguing behavior is predicted to appear when encircling an exceptional point sufficiently slowly 7,8 , like a state-flip or the accumulation of a geometric phase 9,10 . Experiments dedicated to this issue could already successfully explore the topological structure of exceptional points [11][12][13] , but a full dynamical encircling and the breakdown of adiabaticity inevitably associated with it 14-21 remained out of reach of any measurement so far. Here we

An extensively pursued current direction of research in physics aims at the development of practical technologies that exploit the effects of quantum mechanics. As part of this ongoing effort, devices for quantum information processing, secure communication, and high-precision sensing are being implemented with diverse systems, ranging from photons, atoms, and spins to mesoscopic superconducting and nanomechanical structures. Their physical properties make some of these systems better suited than others for specific tasks; thus, photons are well suited for transmitting quantum information, weakly interacting spins can serve as long-lived quantum memories, and superconducting elements can rapidly process information encoded in their quantum states. A central goal of the envisaged quantum technologies is to develop devices that can simultaneously perform several of these tasks, namely, reliably store, process, and transmit quantum information. Hybrid quantum systems composed of different physical components with complementary functionalities may provide precisely such multitasking capabilities. This article reviews some of the driving theoretical ideas and first experimental realizations of hybrid quantum systems and the opportunities and challenges they present and offers a glance at the near-and long-term perspectives of this fascinating and rapidly expanding field.hybrid quantum systems | quantum technologies | quantum information During the last several decades, quantum physics has evolved from being primarily the conceptual framework for the description of microscopic phenomena to providing inspiration for new technological applications. A range of ideas for quantum information processing (1) and secure communication (2, 3), quantum enhanced sensing (4-8), and the simulation of complex dynamics (9-14) has given rise to expectations that society may before long benefit from such quantum technologies. These developments are driven by our rapidly evolving abilities to experimentally manipulate and control quantum dynamics in diverse systems, ranging from single photons (2, 13), atoms and ions (11,12), and individual electron and nuclear spins (15-17), to mesoscopic superconducting (14, 18) and nanomechanical devices (19,20). As a rule, each of these systems can execute one or a few specific tasks, but no single system can be universally suitable for all envisioned applications. Thus, photons are best suited for transmitting quantum information, weakly interacting spins may serve as long-lived quantum memories, and the dynamics of electronic states of atoms or electric charges in semiconductors and superconducting elements may realize rapid processing of information encoded in their quantum states. The implementation of devices that can simultaneously perform several or all of these tasks, e.g., reliably store, process, and transmit quantum states, calls for a new paradigm: that of hybrid quantum systems (HQSs) (15, 21-24). HQSs attain their multitasking capabilities by combining different physical components wit...

Electric-field noise near surfaces is a common problem in diverse areas of physics, and a limiting factor for many precision measurements. There are multiple mechanisms by which such noise is generated, many of which are poorly understood. Laser-cooled, trapped ions provide one of the most sensitive systems to probe electric-field noise at MHz frequencies and over a distance range 30 − 3000 µm from the surface. Over recent years numerous experiments have reported spectral densities of electric-field noise inferred from ion heating-rate measurements and several different theoretical explanations for the observed noise characteristics have been proposed. This paper provides an extensive summary and critical review of electric-field noise measurements in ion traps, and compares these experimental findings with known and conjectured mechanisms for the origin of this noise. This reveals that the presence of multiple noise sources, as well as the different scalings added by geometrical considerations, complicate the interpretation of these results. It is thus the purpose of this review to assess which conclusions can be reasonably drawn from the existing data, and which important questions are still open. In so doing it provides a framework for future investigations of surface-noise processes.

We describe a technique that enables a strong, coherent coupling between a single electronic spin qubit associated with a nitrogen-vacancy impurity in diamond and the quantized motion of a magnetized nano-mechanical resonator tip. This coupling is achieved via careful preparation of dressed spin states which are highly sensitive to the motion of the resonator but insensitive to perturbations from the nuclear spin bath. In combination with optical pumping techniques, the coherent exchange between spin and motional excitations enables ground state cooling and the controlled generation of arbitrary quantum superpositions of resonator states. Optical spin readout techniques provide a general measurement toolbox for the resonator with quantum limited precision.PACS numbers: 07.10. Cm, 42.50.Pq, Techniques for cooling and quantum manipulation of motional states of nano-mechanical resonators are now actively explored. Work in this field is motivated by ideas from quantum information science [1,2], testing quantum mechanics for macroscopic objects [3,4] and potential applications in nano-scale sensing [5,6]. Approaches based on mechanical resonators coupled to optical cavities [7], superconducting devices [8,9] or cold atoms [10] are presently being investigated in experiments.In this paper we describe a technique that enables a coherent coupling between the quantized motion of a mechanical resonator and an isolated spin qubit. Specifically, we focus on the electronic spin associated with a nitrogen-vacancy (NV) impurity in diamond [11] which can be optically polarized and detected, and exhibits excellent coherence properties even at room temperature [12]. Since its precession frequency depends on external magnetic fields via the Zeeman effect, single spins can be used as magnetic sensors operating at nanometer scales [13,14].The essential idea of the present work can be understood by considering a prototype system shown in Fig. 1. Here a single spin is used to sense the motion of the magnetized resonator tip, that is separated from the spin by an average distance h and oscillates at frequency ω r . These oscillations produce a time-varying magnetic field that causes Zeeman shifts of the spin qubit. Specifically, the shift corresponding to a single quantum of motion is λ = g s µ B G m a 0 , where g s ≃ 2, µ B is the Bohr magneton, G m the magnetic field gradient and a 0 = /2mω r the amplitude of zero-point fluctuations for a resonator of mass m. For realistic conditions, h ≈ 25 nm, ω r /2π ≈ 5 MHz, a 0 ≈ 5 × 10 −13 m and G m ≈ 10 7 T/m we find that λ/2π can approach 100 kHz. Such a large shift can be easily measured within a fraction of a millisecond by detecting the electronic spin state [14]. More importantly, the coupling constant λ can considerably exceed both the electronic spin coherence time (T 2 ∼ 1 ms) and the intrinsic damping rate, κ = ω r /Q, of high-Q mechani- cal resonators. In this regime, the spin becomes strongly coupled to mechanical motion in direct analogy to strong coupling of cavity quantum electro...

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We analyze the photon statistics of a weakly driven optomechanical system and discuss the effect of photon blockade under single photon strong coupling conditions. We present an intuitive interpretation of this effect in terms of displaced oscillator states and derive analytic expressions for the cavity excitation spectrum and the two photon correlation function g (2) (0). Our results predict the appearance of non-classical photon correlations in the combined strong coupling and sideband resolved regime, and provide a first detailed understanding of photon-photon interactions in strong coupling optomechanics.PACS numbers: 42.50. Lc, 42.50.Wk, 07.10.Cm The implementation of strong optical non-linearities on a single photon level is one of the central goals in quantum optics with a significant practical relevance for applications ranging from optical computation [1] to quantum information processing [2] and photonic quantum simulation schemes [3]. The prototype system that has been widely studied in this context is cavity QED [4] where under strong coupling conditions effective photon non-linearities result from the hybridization between the optical field and a single atom. Recently, a fundamentally different type of light-matter interaction has attracted a lot of attention, which is the radiation pressure coupling between light and mechanical motion studied in optomechanical systems (OMS) [5]. In most experiments today radiation pressure forces are fairly weak and non-linear optical effects [6,7] occur in the classical, high photon number regime, where enhanced but linear photon-phonon interactions [8,9] are investigated for cooling [10] or the preparation of mechanical quantum states [11]. However, strong optomechanical interactions with single photons in analogy to cavity QED, are within reach of new generations of nano-fabricated OMS [12] or superconducting devices [8] and are already nowadays accessible in analogous cold atom experiments [13,14]. This could open up a new route towards non-linear quantum optics, which avoids single atom strong coupling and where instead photon-photon interactions are mediated by the motion of a macroscopic object.In this work we study OMS in the regime where the single photon coupling g 0 is comparable with the cavity decay rate κ. In contrast to previous studies [15][16][17][18][19] we here focus explicitly on the consequences of strong coupling for the quantum statistics of light, with the aim to identify the mechanism for photon-photon interactions in this system and the experimental conditions under which such effects could be observed in experiments. To do so we consider a weakly driven OMS as shown in Fig. 1 and evaluate the two photon correlation function g (2) (0). This quantity provides a direct experimental measure for non-classical anti-bunching effects, i.e. g (2) (0) < 1, and the limit g (2) (0) → 0 indicates a complete photon blockade [20][21][22], where strong photon-photon interactions prevent multiple photons from passing through the cavity at the same time...

Implementation of quantum information processing faces the contradicting requirements of combining excellent isolation to avoid decoherence with the ability to control coherent interactions in a many-body quantum system. For example, spin degrees of freedom of electrons and nuclei provide a good quantum memory due to their weak magnetic interactions with the environment. However, for the same reason it is difficult to achieve controlled entanglement of spins over distances larger than tens of nanometers. Here we propose a universal realization of a quantum data bus for electronic spin qubits where spins are coupled to the motion of magnetized mechanical resonators via magnetic field gradients. Provided that the mechanical system is charged, the magnetic moments associated with spin qubits can be effectively amplified to enable a coherent spin-spin coupling over long distances via Coulomb forces. Our approach is applicable to a wide class of electronic spin qubits which can be localized near the magnetized tips and can be used for the implementation of hybrid quantum computing architectures.

We describe a new scheme to interconvert stationary and photonic qubits which is based on indirect qubit-light interactions mediated by a mechanical resonator. This approach does not rely on the specific optical response of the qubit and thereby enables optical quantum interfaces for a wide range of solid state spin and charge based systems. We discuss the implementation of state transfer protocols between distant nodes of a quantum network and show that high transfer fidelities can be achieved under realistic experimental conditions.