Perspective on witnessing entanglement in hybrid quantum systems

  1. Yingqiu Mao,
  2. Ming Gong,
  3. Kae Nemoto,
  4. William J. Munro,
  5. and Johannes Majer
Hybrid quantum systems aim at combining the advantages of different physical systems and to produce novel quantum devices. In particular, the hybrid combination of superconducting circuits
and spins in solid-state crystals is a versatile platform to explore many quantum electrodynamics problems. Recently, the remote coupling of nitrogen-vacancy center spins in diamond via a superconducting bus was demonstrated. However, a rigorous experimental test of the quantum nature of this hybrid system and in particular entanglement is still missing. We review the theoretical ideas to generate and detect entanglement, and present our own scheme to achieve this.

Coupling spin ‚clock states‘ to superconducting circuits

  1. Ignacio Gimeno,
  2. David Zueco,
  3. Yan Duan,
  4. Carlos Sánchez-Azqueta,
  5. Thomas Astner,
  6. Alejandro Gaita-Ariño,
  7. Stephen Hill,
  8. Johannes Majer,
  9. Eugenio Coronado,
  10. and Fernando Luis
A central goal in quantum technologies is to maximize GT2, where G stands for the rate at which each qubit can be coherently driven and T2 is the qubit’s phase coherence time.
This is challenging, as increasing G (e.g. by coupling the qubit more strongly to external stimuli) often leads to deleterious effects on T2. Here, we study a physical situation in which both G and T2 can be simultaneously optimized. We measure the coupling to microwave superconducting coplanar waveguides of pure (i.e. non magnetically diluted) crystals of HoW10 magnetic clusters, which show level anticrossings, or spin clock transitions, at equidistant magnetic fields. The absorption lines give a complete picture of the magnetic energy level scheme and, in particular, confirm the existence of such clock transitions. The quantitative analysis of the microwave transmission allows monitoring the overlap between spin wave functions and gives information about their coupling to the environment and to the propagating photons. The formation of quantum superpositions of spin-up and spin-down states at the clock transitions allows simultaneously maximizing the spin-photon coupling and minimizing environmental spin perturbations. Using the same experimental device, we also explore the coupling of these qubits to a 11.7 GHz cavity mode, arising from a nonperfect microwave propagation at the chip boundaries and find a collective spin to single photon coupling GN = 100 MHz. The engineering of spin states in molecular systems offers a promising strategy to combine sizeable photon-mediated interactions, thus scalability, with a sufficient isolation from unwanted magnetic noise sources.

Dynamical Exploration of Amplitude Bistability in Engineered Quantum Systems

  1. Andreas Angerer,
  2. Stefan Putz,
  3. Dmitry O. Krimer,
  4. Thomas Astner,
  5. Matthias Zens,
  6. Ralph Glattauer,
  7. Kirill Streltsov,
  8. William J. Munro,
  9. Kae Nemoto,
  10. Stefan Rotter,
  11. Jörg Schmiedmayer,
  12. and Johannes Majer
Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena which have profoundly changed our
technological landscape over the last 50 years. Recently the ability to engineer quantum metamaterials through hybridisation has allowed to explore these nonlinear effects in systems with no natural analogue. Here we investigate amplitude bistability, which is one of the most fundamental nonlinear phenomena, in a hybrid system composed of a superconducting resonator inductively coupled to an ensemble of nitrogen-vacancy centres. One of the exciting properties of this spin system is its extremely long spin life-time, more than ten orders of magnitude longer than other relevant timescales of the hybrid system. This allows us to dynamically explore this nonlinear regime of cavity quantum electrodynamics (cQED) and demonstrate a critical slowing down of the cavity population on the order of several tens of thousands of seconds – a timescale much longer than observed so far for this effect. Our results provide the foundation for future quantum technologies based on nonlinear phenomena.

Engineering Long-Lived Collective Dark States in Spin Ensembles

  1. Stefan Putz,
  2. Andreas Angerer,
  3. Dmitry O. Krimer,
  4. Ralph Glattauer,
  5. William J. Munro,
  6. Stefan Rotter,
  7. Jörg Schmiedmayer,
  8. and Johannes Majer
Ensembles of electron spins in hybrid microwave systems are powerful and versatile components for future quantum technologies. Quantum memories with high storage capacities are one
such example which require long-lived states that can be addressed and manipulated coherently within the inhomogeneously broadened ensemble. This broadening is essential for true multimode memories, but induces a considerable spin dephasing and together with dissipation from a cavity interface poses a constraint on the memory’s storage time. In this work we show how to overcome both of these limitations through the engineering of long-lived dark states in an ensemble of electron spins hosted by nitrogen-vacancy centres in diamond. By burning narrow spectral holes into a spin ensemble strongly coupled to a superconducting microwave cavity, we observe long-lived Rabi oscillations with high visibility and a decay rate that is a factor of forty smaller than the spin ensemble linewidth and thereby a factor of more than three below the pure cavity dissipation rate. This significant reduction lives up to the promise of hybrid devices to perform better than their individual subcomponents. To demonstrate the potential of our approach we realise the first step towards a solid-state microwave spin multiplexer by engineering multiple long-lived dark states. Our results show that we can fully access the „decoherence free“ subspace in our experiment and selectively prepare protected states by spectral hole burning. This technique opens up the way for truly long-lived quantum memories, solid-state microwave frequency combs, optical to microwave quantum transducers and spin squeezed states. Our approach also paves the way for a new class of cavity QED experiments with dense spin ensembles, where dipole spin-spin interactions become important and many-body phenomena will be directly accessible on a chip.

Nanometric constrictions in superconducting coplanar waveguide resonators

  1. Mark David Jenkins,
  2. Uta Naether,
  3. Miguel Ciria,
  4. Javier Sesé,
  5. James Atkinson,
  6. Carlos Sánchez-Azqueta,
  7. Enrique del Barco,
  8. Johannes Majer,
  9. David Zueco,
  10. and Fernando Luis
We report on the design, fabrication and characterization of superconducting coplanar waveguide resonators with nanometric constrictions. By reducing the size of the center line down
to 50 nm, the RF currents are concentrated into a small cross section and the magnetic field in its vicinity is increased. The device characteristics are only slightly modified by the constrictions, with changes in resonance frequency lower than 1% and changes in transmission and Q-factor lower than 20%. These devices could enable the achievement of higher couplings to small magnetic samples or even to single molecular spins and have applications in circuit quantum electrodynamics, quantum computing and electron paramagnetic resonance.