In the emerging field of quantum computation 1 and quantum information, superconducting devices are promising candidates for the implementation of solidstate quantum bits or qubits. Single-qubit operations 2−6 , direct coupling between two qubits 7−10 , and the realization of a quantum gate 11 have been reported. However, complex manipulation of entangled states − such as the coupling of a two-level system to a quantum harmonic oscillator, as demonstrated in ion/atom-trap experiments 12,13 or cavity quantum electrodynamics 14 − has yet to be achieved for superconducting devices. Here we demonstrate entanglement between a superconducting flux qubit (a two-level system) and a superconducting quantum interference device (SQUID). The latter provides the measurement system for detecting the quantum states; it is also an effective inductance that, in parallel with an external shunt capacitance, acts as a harmonic oscillator. We achieve generation and control of the entangled state by performing microwave spectroscopy and detecting the resultant Rabi oscillations of the coupled system.The device was realized by electron-beam lithography and metal evaporation. The qubit-SQUID geometry is shown in Fig. 1a: a large loop interrupted by two Josephson junctions (the SQUID) is merged with the smaller loop on the right-hand side comprising three in-line Josephson junctions (the flux qubit) 15 . By applying a perpendicular external magnetic field, the qubit is biased around Φ 0 /2, where Φ 0 = h/2e is the flux quantum. Previous spectroscopy 16 and coherent timedomain experiments 6 have shown that the flux qubit is a controllable two-level system with 'spin-up/spin-down' states corresponding to persistent currents flowing in 'clockwise/anticlockwise' directions and coupled by tunneling. Here we show that a stronger qubit−SQUID coupling allows us to investigate the coupled dynamics of a 'qubit−harmonic oscillator' system.The qubit Hamiltonian is defined by the charging and Josephson energy of the qubit outer junctions (E C = e 2 /2C and E J = hI C /4e where C and I C are their capacitance and critical current) 16 . In a two-level truncation, the Hamiltonian becomes H q /h = −ǫσ z /2−∆σ x /2 where σ z,x are the Pauli matrices in the spin-up/spin-down basis, ∆ is the tunnel splitting and ǫ ∼ = I p Φ 0 (γ q − π)/hπ (I p is the qubit maximum persistent current and γ q is the superconductor phase across the three junctions). The resulting energy level spacing represents the qubit Larmor frequency F L = √ ∆ 2 + ǫ 2 . The SQUID dynamics is characterized by the Josephson inductance of the junctions L J ≈ 80 pH, shunt capacitance C sh ≈ 12 pF (see Fig. 1a) and self-inductances L sl ≈ 170 pH of the SQUID and shunt-lines. In our experiments, the SQUID circuit behaves like a harmonic oscillator described by H sq = hν p (a † a + 1/2), where 2πν p = 1/ (L J + L sl )C sh is called the plasma frequency and a (a † ) is the plasmon annihilation (creation) operator. Henceforth |βn represents the state with the qubit in the ground(β = 0) or excited ...

We report the realization of a quantum circuit in which an ensemble of electronic spins is coupled to a frequency tunable superconducting resonator. The spins are nitrogen-vacancy centers in a diamond crystal. The achievement of strong coupling is manifested by the appearance of a vacuum Rabi splitting in the transmission spectrum of the resonator when its frequency is tuned through the nitrogen-vacancy center electron spin resonance.

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...

Following a recent proposal by S. B. Zheng and G. C. Guo [Phys. Rev. Lett. 85, 2392 (2000)], we report an experiment in which two Rydberg atoms crossing a nonresonant cavity are entangled by coherent energy exchange. The process, mediated by the virtual emission and absorption of a microwave photon, is characterized by a collision mixing angle 4 orders of magnitude larger than for atoms colliding in free space with the same impact parameter. The final entangled state is controlled by adjusting the atom-cavity detuning. This procedure, essentially insensitive to thermal fields and to photon decay, opens promising perspectives for complex entanglement manipulations.

The violation of J. Bell's inequality with two entangled and spatially separated quantum twolevel systems (TLS) is often considered as the most prominent demonstration that nature does not obey "local realism". Under different but related assumptions of "macrorealism", plausible for macroscopic systems, Leggett and Garg derived a similar inequality for a single degree of freedom undergoing coherent oscillations and being measured at successive times. Such a "Bell's inequality in time", which should be violated by a quantum TLS, is tested here. In this work, the TLS is a superconducting quantum circuit whose Rabi oscillations are continuously driven while it is continuously and weakly measured. The time correlations present at the detector output agree with quantum-mechanical predictions and violate the inequality by 5 standard deviations.

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...

We have studied the dephasing of a superconducting flux qubit coupled to a dc-SQUID based oscillator. By varying the bias conditions of both circuits we were able to tune their effective coupling strength. This allowed us to measure the effect of such a controllable and well-characterized environment on the qubit coherence. We can quantitatively account for our data with a simple model in which thermal fluctuations of the photon number in the oscillator are the limiting factor. In particular, we observe a strong reduction of the dephasing rate whenever the coupling is tuned to zero. At the optimal point we find a large spinecho decay time of 4 s. DOI: 10.1103/PhysRevLett.95.257002 PACS numbers: 74.50.+r, 03.67.Lx, 73.40.Gk Retaining quantum coherence is a central requirement in quantum information processing. Solid-state qubits, including superconducting ones [1][2][3], couple to environmental degrees of freedom that potentially lead to dephasing. This dephasing is commonly associated with lowfrequency noise [4]. However, resonant modes at higher frequencies are harmful as well. In resonance with the qubit transition they favor energy relaxation. Off resonance they may cause pure dephasing, due to fluctuations of the photon number stored in the oscillator. Experimentally we show that the quantum coherence of our superconducting flux qubit coupled to a dc-SQUID oscillator is limited by the oscillator thermal photon noise. By tuning the qubit and SQUID bias conditions we can suppress the influence of photon noise, and we measure a strong enhancement of the spin-echo decay time from about 100 ns to 4 s.In our experiment, a flux qubit of energy splitting h q is coupled to a harmonic oscillator of frequency p which consists of a dc SQUID and a shunt capacitor [5,6]. The oscillator is weakly damped with a rate and is detuned from the qubit frequency. In this dispersive regime, the presence of n photons in the oscillator induces a qubit frequency shift following q;n ÿ q;0 n 0 , where the shift per photon 0 depends on the effective oscillatorqubit coupling. Any fluctuation in n thus causes dephasing. Taking the oscillator to be thermally excited at a temperature T and assuming the pure dephasing time 1=, we find [7], after a reasoning similar to [8], n n 12 0 2with the average photon number stored in the oscillator n exph p =kT ÿ 1 ÿ1 . We note that a similar effect was observed in a recent experiment on a charge qubit coupled to a slightly detuned waveguide resonator [9]. When driving the oscillator to perform the readout, the authors observed a shift and a broadening of the qubit resonance due to the ac-Stark shift and to photon shot noise, well-known in atomic cavity quantum electrodynamics [10]. In our experiments, the oscillator is not driven but thermally excited. In addition, we are able to tune in situ the coupling constant and 0 and, therefore, to directly monitor the decohering effect of the circuit.Our flux qubit consists of a micron-size superconducting aluminum loop intersected by four Josephson junctio...

After quantum particles have interacted, they generally remain in an entangled state and are correlated at a distance by quantum-mechanical links that can be used to transmit and process information in nonclassical ways. This implies programmable sequences of operations to generate and analyze the entanglement of complex systems. We have demonstrated such a procedure for two atoms and a single-photon cavity mode, engineering and analyzing a three-particle entangled state by a succession of controlled steps that address the particles individually. This entangling procedure can, in principle, operate on larger numbers of particles, opening new perspectives for fundamental tests of quantum theory.