Quantum electrodynamics in superconducting circuits

From Institute for Theoretical Physics II / University of Erlangen-Nuremberg

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Circuit QED

Recent progress in the design of ultrasmall superconducting circuits has reached a point where the coherent dynamics of superconducting "qubits" has been observed by several experimental groups worldwide. A particularly interesting new development over the past few years merges concepts from the field of quantum optics with those of superconducting circuits. In 2004, the Schoelkopf lab at Yale succeeded to combine a superconducting microwave transmission line resonator with a "Cooper-pair box".

In effect, this system provides a very well controllable analogy to cavity quantum electrodynamics experiments from the field of atomic optics, where the role of the atom is now played by the qubit. The initial experiments were able to demonstrate a dispersive quantum non-demolition measurement scheme to read out the state of the qubit, do spectroscopy, induce coherent Rabi oscillations and measure the decoherence time using Ramsey oscillations, among other achievements. These experiments have opened up what may be called a new field of "superconducting circuit cavity quantum electrodynamics", or, for short, "circuit QED".

In the most recent experimental developments, groups at Yale, Santa Barbara, Zürich and other places have been able to couple several qubits, create and read out arbitrary quantum states of the photon field inside the microwave resonator, and couple strongly to a nanomechanical resonator.

Our theoretical work

Our theoretical work is inspired by the rapidly evolving experimental capabilities. In the following, we discuss a few examples from our recent research.

The cavity grid, allowing operations between 3 qubits not directly linked by cavities
  • Cavity grid - In 2007, we proposed the first 2D quantum computing architecture for circuit QED. The idea is to have a 2D grid of vertical and horizontal microwave resonators, with qubits at the intersection points. A carefully chosen arrangement of frequencies avoids unwanted cross-talk, and the 2D design here offers strong advantages over 1D geometries. Future experimental progress towards larger numbers of qubits will enable experimental groups to implement this proposal (first, crucial aspects like "coupling around the corner", and later, in more fully functional devices). See: Cavity grid for scalable quantum computation with superconducting circuits, F. Helmer et al., EPL 85, 50007 (2009) Journal PDF Cite. See also: A recent application of Optimal Control Theory to obtain faster gates in such a cavity grid design: Fisher et al., Phys. Rev. B 81, 085328 (2010) Journal PDF Cite
  • Single-photon detection - It is an outstanding challenge to detect propagating single microwave photons in circuit QED. In our work, we proposed a detector where the presence of a photon is measured via a QND, dispersive interaction with another resonator mode. Interestingly, for reasons connected fundamentally to the quantum measurement process, the Quantum Zeno effect sets a limit on the efficieny of such a detector (still much higher than anything achieved up to now). See: Quantum nondemolition photon detection in circuit QED and the quantum Zeno effect, F. Helmer et al., Phys. Rev. A 79, 052115 (2009) Journal PDF Cite
  • Entanglement by measurement - When doing a suitable QND measurement on a collection of qubits inside a resonator, one may entangle them. The condition for this to work is that the measurement cannot distinguish between different collective qubit states, which can be fulfilled in careful experiments. We presented a stochastic master equation simulation of the gradual collapse towards an entangled state, for two qubits (where this had been done before), but also for three qubits (GHZ, W states). See: Measurement-based Synthesis of multi-qubit Entangled States in Superconducting Cavity QED, F. Helmer and F. Marquardt, Phys. Rev. A 79, 052328 (2009) Journal PDF Cite
  • Entangled photon pairs - In quantum optics, parametric down conversion is the fundamental process where one photon splits into a pair of photons, whose properties are often entangled. We have proposed a very efficient on-chip source of (energy-time) entangled photon pairs. The idea is to use a properly chosen three-level artificial atom (e.g. a "transmon"-type device). The prerequisite for carrying out this experiment is to be able to characterize the state of the emitted field carefully, something which is now being explored by several groups. See: Efficient on-chip source of microwave photon pairs in superconducting circuit QED, F. Marquardt, Phys. Rev. B 76, 205416 (2007)