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Oxford University Press eBooks

Schrödinger cat states in circuit QED

S. M. Girvin

Published May 16, 2019• 2 citations
Publisher

Abstract

Circuit quantum electrodynamics (‘circuit QED’) describes the quantum mechanics and quantum optics of superconducting electrical circuits operating in the microwave regime near absolute zero temperature. It is the analog of cavity QED in quantum optics with the role of the atoms being played by superconducting qubits. The present lecture notes present a brief overview of circuit QED and then focus on some of the novel quantum states that can be produced and measured (via photon number parity and the Wigner function) using the strong coupling between an artificial atom and one or more cavities. Of particular importance are Schrödinger cat states of photons. Despite long being considered exemplars of frail quantum superpositions that quickly decohere, such states have recently been used as the basis for quantum error correction codes which have reached the long-sought goal of enhancing the lifetime of quantum information through active quantum error correction.

DOI
10.1093/oso/9780198837190.003.0011

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Circuit quantum electrodynamics (‘circuit QED’) describes the quantum mechanics and quantum optics of superconducting electrical circuits operating in the microwave regime near absolute zero temperature. It is the analog of cavity QED in quantum optics with the role of the atoms being played by superconducting qubits. The present lecture notes present a brief overview of circuit QED and then focus on some of the novel quantum states that can be produced and measured (via photon number parity and the Wigner function) using the strong coupling between an artificial atom and one or more cavities. Of particular importance are Schrödinger cat states of photons. Despite long being considered exemplars of frail quantum superpositions that quickly decohere, such states have recently been used as the basis for quantum error correction codes which have reached the long-sought goal of enhancing the lifetime of quantum information through active quantum error correction.
Circuit quantum electrodynamics ('circuit QED') describes the quantum mechanics and quantum field theory of superconducting electrical circuits operating in the microwave regime near absolute zero temperature. It is the analog of cavity QED in quantum optics with the role of the atoms being played by superconducting qubits. The present lecture notes focus primarily on novel quantum states that can be produced and measured using the strong coupling between an artificial atom and one or more cavities. Of particular importance are Schrodinger cat states of photons. Despite long being considered exemplars of frail quantum superpositions that quickly decohere, such states have recently been used as the basis for quantum error correction codes which have reached the long-sought goal of enhancing the lifetime of quantum information through active quantum error correction.
A revolution is underway in the construction of ‘artificial atoms’ out of superconducting electrical circuits. ‘Circuit QED’ permits strong-coupling non-linear optics at the single-photon level and gives an architecture for novel quantum information processing. The dispersive coupling between a qubit and a microwave cavity can be orders of magnitude larger than the line widths of both qubit and cavity. This yields a new ‘quantum toolbox’ which permits arbitrary control of the entangled quantum state of the system. For example one can flip the state of the qubit conditioned on there being exactly n photons in the cavity or one can displace the cavity oscillation amplitude conditioned on the state of the qubit. Using these tools it is now possible to create large ‘Schrödinger cat’ states containing more than 100 photons. An introduction to circuit QED and a review of recent experimental results will be presented.
The last two decades have seen tremendous advances in our ability to generate and manipulate quantum coherence in mesoscopic superconducting circuits. These advances have opened up the study of quantum optics of microwave photons in superconducting circuits as well as providing important hardware for the manipulation of quantum information. Focusing primarily on charge-based qubits, we provide a brief overview of these developments and discuss the present state of the art. We also survey the remarkable progress that has been made in realizing circuit quantum electrodynamics (QED) in which superconducting artificial atoms are strongly coupled to individual microwave photons.
This review surveys the development over the last 15 years of circuit quantum electrodynamics, the nonlinear quantum optics of microwave electrical circuits. In analogy to cavity quantum electrodynamics, lasers are replaced by rf signal generators, optical cavities by superconducting resonators, and atoms by superconducting qubits. Circuit QED offers enhanced light-matter coupling in which strong quantum optical nonlinearities are observable at the level of individual photons. This new parameter regime leads to unique capabilities for fundamental studies in quantum optics, nearly ideal quantum-limited measurements, and quantum computation.
The founders of quantum physics used to analyse thought experiments, to discuss state superposition, complementarity and entanglement. They imagined manipulating single particles, such as electrons, atoms or photons; they would be surprised to see that experiments with isolated atoms, molecules or photons are now carried on in many laboratories throughout the world. In our Cavity Quantum Electrodynamics (CQED) studies, we stabilize and count photon number states in the cavity. We also prepare and reconstruct photonic superposition states suspended between different 'classical realities', generating a laboratory version of Schrodinger famous 'Cat', which he had imagined to be simultaneously dead and alive. We have also investigated the decoherence process, which explains the transition between the quantum and the classical worlds. CQED physics has recently been extended to artificial 'atoms' made from superconductors, in a new domain of mesoscopic physics called Circuit QED. This development opens the way to applications in quantum information science.
The new and rapidly growing field of circuit QED offers extremely exciting prospects for learning about and exercising intimate control over quantum systems, providing flexible, engineerable design and strong nonlinearities and interactions in systems consisting of microwave radiation fields and fixed artificial "atoms". These notes aim to provide a non-expert introduction to the field of circuit QED, to give a basic appreciation of the promise and challenges of the field, along with a number of key concepts that will hopefully be useful for the reader who is new to the field and beginning to explore the research literature. They were written as a pedagogical text designed to complement a course delivered to third-year undergraduate students. After a introductory section which discusses why studying circuit QED might be worthwhile and interesting, I introduce the basic theory tools from quantum optics and quantum information which are needed to understand the key elements of circuit QED. I also provide a brief overview of superconductivity, focussing on the concepts which are most relevant to operation in the regimes of interest in circuit QED. I then describe the three main types of superconducting qubits, and finally give a basic introduction to decoherence and mixture and how they relate to quantum behaviour in electronic circuits.