High cooperativity between a phosphorus donor spin ensemble and a microwave resonator

  1. Christoph W. Zollitsch,
  2. Kai Mueller,
  3. David P. Franke,
  4. Sebastian T. B. Goennenwein,
  5. Martin S. Brandt,
  6. Rudolf Gross,
  7. and Hans Huebl
We investigate the coupling of an ensemble of phosphorus donors in an isotopically purified 28Si host lattice interacting with a superconducting coplanar waveguide resonator. The microwave
transmission spectrum of the resonator shows a normal mode splitting characteristic for high cooperativity. The evaluated collective coupling strength geff is of the same order as the loss rate of the spin system γ, indicating the onset of strong coupling. We develop a statistical model to describe the influence of temperature on the coupling strength from 50mK to 3.5K and find a scaling of the coupling strength with the square root of the number of thermally polarized spins.

Quantum State Engineering with Circuit Electromechanical Three-Body Interactions

  1. Mehdi Abdi,
  2. Matthias Pernpeintner,
  3. Rudolf Gross,
  4. Hans Huebl,
  5. and Michael J. Hartmann
We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical
architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton–mechanical mode and a nonlinear transmon–mechanical mode interaction in the strong coupling regime. Together with the strong resonator–transmon interaction, these properties provide intriguing opportunities for manipulations of this hybrid quantum system. We show, in particular, the feasibility of cooling the mechanical motion down to its ground state and preparing various nonclassical states including mechanical Fock and cat states and hybrid tripartite entangled states.

Control of microwave signals using circuit nano-electromechanics

  1. Xiaoqing Zhou,
  2. Fredrik Hocke,
  3. Albert Schliesser,
  4. Achim Marx,
  5. Hans Huebl,
  6. Rudolf Gross,
  7. and Tobias J. Kippenberg
and circuit quantum electrodynamics (cQED) [2]. Coupled to artificial atoms in the form of superconducting"]qubits [3, 4], they now provide a technologically promising and scalable platform for quantum information processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots [13] or mechanical oscillators [14, 15] has been explored to realize hybrid systems with extended functionality. Here, we couple a superconducting coplanar waveguide resonator to a nano-coshmechanical oscillator, and demonstrate all-microwave field controlled slowing, advancing and switching of microwave signals. This is enabled by utilizing electromechanically induced transparency [16-18], an effect analogous to electromagnetically induced transparency (EIT) in atomic physics [19]. The exquisite temporal control gained over this phenomenon provides a route towards realizing advanced protocols for storage of both classical and quantum microwave signals [20-22], extending the toolbox of control techniques of the microwave field.