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.

† authors with equal contribution to this work Superconducting qubits 1,2 behave as artificial two-level atoms and are used to investigate fundamental quantum phenomena. In this context, the study of multi-photon excitations 3,4,5,6,7 occupies a central role. Moreover, coupling superconducting qubits to on-chip microwave resonators has given rise to the field of circuit QED 8,9,10,11,12,13,14,15 . In contrast to quantum-optical cavity QED 16,17,18,19 , circuit QED offers the tunability inherent to solid-state circuits. In this work, we report on the observation of key signatures of a two-photon driven Jaynes-Cummings model, which unveils the upconversion dynamics of a superconducting flux qubit 20 coupled to an on-chip resonator. Our experiment and theoretical analysis show clear evidence for the coexistence of one-and two-photon driven level anticrossings of the qubit-resonator system. This results from the symmetry breaking of the system Hamiltonian, when parity becomes a not well-defined property 21 . Our study provides deep insight into the interplay of multiphoton processes and symmetries in a qubit-resonator system.In cavity QED, a two-level atom interacts with the quantized modes of an optical or microwave cavity. The information on the coupled system is encoded both in the atom and in the cavity states. The latter can be accessed spectroscopically by measuring the transmission properties of the cavity 16 , whereas the former can be read out by suitable detectors 18,19 . In circuit QED, the solid-state counterpart of cavity QED, the first category of experiments was implemented by measuring the microwave radiation emitted by a resonator (acting as a cavity) strongly coupled to a charge qubit 8 . In a dual experiment, the state of a flux qubit was detected with a DC superconducting quantum interference device (SQUID) and vacuum Rabi oscillations were observed 10 . More recently, both approaches have been exploited to extend the toolbox of quantum optics on a chip 11,12,13,14,15,22 . Whereas all these experiments employ one-photon driving of the coupled qubit-resonator system, multi-photon studies are available only for sideband transitions 15 or bare qubits 3,4,5,6,7 . The experiments discussed in this work explore, to our knowledge for the first time, the physics of the two-photon driven Jaynes-Cummings dynamics in circuit QED. In this context, we show that the dispersive interaction between the qubit and the two-photon driving enables real level transitions. The nature of our experiment can be understood as an upconversion mechanism, which transforms the two-photon coherent driving into single photons of the Jaynes-Cummings dynamics. This process requires energy conservation and a not well-defined parity 21 of the interaction Hamiltonian due to the symmetry breaking of the qubit potential. Our experimental findings reveal that such symmetry breaking can be obtained either by choosing a suitable qubit operation point or by the presence of additional spurious fluctuators 23 .The main elements of our setup, ...

In order to gain a better understanding of the origin of decoherence in superconducting flux qubits, we have measured the magnetic field dependence of the characteristic energy relaxation time (T(1)) and echo phase relaxation time (T(2)(echo)) near the optimal operating point of a flux qubit. We have measured T(2)(echo) by means of the phase cycling method. At the optimal point, we found the relation T(2)(echo) approximately 2T(1). This means that the echo decay time is limited by the energy relaxation (T(1) process). Moving away from the optimal point, we observe a linear increase of the phase relaxation rate (1/T(2)(echo)) with the applied external magnetic flux. This behavior can be well explained by the influence of magnetic flux noise with a 1/f spectrum on the qubit.

Macroscopic realism is the name for a class of modifications to quantum theory that allow macroscopic objects to be described in a measurement-independent manner, while largely preserving a fully quantum mechanical description of the microscopic world. Objective collapse theories are examples which aim to solve the quantum measurement problem through modified dynamical laws. Whether such theories describe nature, however, is not known. Here we describe and implement an experimental protocol capable of constraining theories of this class, that is more noise tolerant and conceptually transparent than the original Leggett–Garg test. We implement the protocol in a superconducting flux qubit, and rule out (by ∼84 s.d.) those theories which would deny coherent superpositions of 170 nA currents over a ∼10 ns timescale. Further, we address the ‘clumsiness loophole' by determining classical disturbance with control experiments. Our results constitute strong evidence for the superposition of states of nontrivial macroscopic distinctness.