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 ...

The interaction between an atom and the electromagnetic field inside a cavity 1-6 has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies, including lasers and many quantum computing architectures. Superconducting qubits 7,8 have allowed the realization of strong 9,10 and ultrastrong 11-13 coupling between artificial atoms and cavities. If the coupling strength g becomes as large as the atomic and cavity frequencies (∆ and ω o , respectively), the energy eigenstates including the ground state are predicted to be highly entangled 14 . There has been an ongoing debate 15-17 over whether it is fundamentally possible to realize this regime in realistic physical systems. By inductively coupling a flux qubit and an LC oscillator via Josephson junctions, we have realized circuits with g/ω o ranging from 0.72 to 1.34 and g/∆ 1. Using spectroscopy measurements, we have observed unconventional transition spectra that are characteristic of this new regime. Our results provide a basis for ground-state-based entangled pair generation and open a new direction of research on strongly correlated light-matter states in circuit quantum electrodynamics.We begin by describing the Hamiltonian of each component in the qubit-oscillator circuit, which comprises a superconducting flux qubit and an LC oscillator inductively coupled to each other by sharing a tunable inductance L c , as shown in the circuit diagram in Fig. 1a.The Hamiltonian of the flux qubit can be written in the basis of two states with persistent currents flowing in opposite directions around the qubit loop 18 , |L q and |R q , as H q = − (∆σ x + εσ z )/2, where ∆ and ε = 2I p 0 (n φq − n φq0 ) are the tunnel splitting and the energy bias between |L q and |R q , I p is the maximum persistent current, and σ x, z are Pauli matrices. Here, n φq is the normalized flux bias through the qubit loop in units of the superconducting flux quantum, 0 = h/2e, and n φq0 = 0.5 + k q , where k q is the integer that minimizes |n φq − n φq0 |. The macroscopic nature of the persistent-current states enables strong coupling to other circuit elements. Another important feature of the flux qubit is its strong anharmonicity: the two lowest energy levels are well isolated from the higher levels.The Hamiltonian of the LC oscillator can be written asC is the resonance frequency, L 0 is the inductance of the superconducting lead, L qc ( L c ) is the inductance across the qubit and coupler (see Supplementary Section 2), C is the capacitance, andâ (â † ) is the oscillator's annihilation (creation) operator. Figure 1b shows a laser microscope image of the lumped-element LC oscillator, where L 0 is designed to be as small as possible to maximize the zeropoint fluctuations in the currentand hence achieve strong coupling to the flux qubit, while C is adjusted so as to achieve a desired value of ω o . The freedom of choosing L 0 for large I zpf is one of the advantages of lumped-element LC oscillators over coplanar-waveguide ...

During the past decade, research into superconducting quantum bits (qubits) based on Josephson junctions has made rapid progress. Many foundational experiments have been performed, and superconducting qubits are now considered one of the most promising systems for quantum information processing. However, the experimentally reported coherence times are likely to be insufficient for future large-scale quantum computation. A natural solution to this problem is a dedicated engineered quantum memory based on atomic and molecular systems. The question of whether coherent quantum coupling is possible between such natural systems and a single macroscopic artificial atom has attracted considerable attention since the first demonstration of macroscopic quantum coherence in Josephson junction circuits. Here we report evidence of coherent strong coupling between a single macroscopic superconducting artificial atom (a flux qubit) and an ensemble of electron spins in the form of nitrogen-vacancy colour centres in diamond. Furthermore, we have observed coherent exchange of a single quantum of energy between a flux qubit and a macroscopic ensemble consisting of about 3 × 10(7) such colour centres. This provides a foundation for future quantum memories and hybrid devices coupling microwave and optical systems.

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...