Generation of Fock states in a superconducting quantum circuit.

Spin systems and harmonic oscillators comprise two archetypes in quantum mechanics 1 . The spin-1/2 system, with two quantum energy levels, is essentially the most nonlinear system found in nature, while the harmonic oscillator represents the most linear, with an infinite number of evenlyspaced quantum levels. A significant difference between these systems is that a two-level spin can be prepared in an arbitrary quantum state using classical excitations, whereas classical excitations applied to an oscillator generate a coherent state, nearly indistinguishable from a classical state 2 . Quantum behaviour in an oscillator is most obvious in Fock states, states with specific numbers of energy quanta, but such states are hard to create 3-7 . Here we demonstrate the first controlled generation of multi-photon Fock states in a solid-state system. We use a superconducting phase qubit 8 , a close approximation to a two-level spin system, coupled to a microwave resonator, acting as a harmonic oscillator, to prepare and analyse pure Fock states with up to 6 photons. We contrast the Fock states with coherent states generated using classical pulses applied directly to the resonator. The difficulty of generating quantum number states in a linear resonator has been overcome by interposing a nonlinear quantum system, such as an ion, between a classical radiation source and the resonator. A classical pulse applied to the nonlinear system creates a quantum state that can subsequently be transferred to the resonator. Repeating this process multiple times results in a quantum number state in the resonator. Such a method was used to deterministically generate Fock number states for the mechanical motion of ions in a harmonic ion trap 3 . The analogous deterministic creation of Fock states in electrodynamic resonators has only been demonstrated for states with one or two photons 5,6 , although Fock states with larger photon numbers have been recorded using projective measurements 7,9 . The deterministic creation of pure Fock states in a solid-state system, as described here, represents a significant step forward. Solid-state systems permit highly complex, integrated circuitry to employ such bosonic states in, for example, quantum computational architectures. The integration of microwave resonators with solid state qubits has recently attracted significant interest 10-16 , but to date such implementations have only used zero or one photons in the resonator, a regime where the bosonic nature of the linear resonator is not apparent. The method we use here to generate multi-photon Fock states is scalable to arbitrary photon numbers 3,17 , limited only by decoherence times and the speed at which photons can be transferred into the resonator. We generate the Fock states using the qubit as an intermediary between a classical microwave source and the resonator, and following generation, measure the resulting states using the qubit. The Fock states are compared to coherent states, generated by driving the resonator directly with a classical radiation pulse. The complexity of the pulse sequences used to create and analyse the resonator states, and the high fidelity of the resulting measurements, demonstrate a significant advance in the control of superconducting quantum circuits. Our experimental system (see When the qubit and resonator are tuned off-resonance, so that |ν r − ν q | ≫ Ω/2π, no photons are exchange