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arXiv:1710.03179

Schrodinger Cat States in Circuit QED

S. M. Girvin

Published Oct 9, 2017• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1710.03179

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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.
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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.
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 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.
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.
In the last 25 years a new understanding has evolved of the role of information in quantum mechanics. At the same time there has been tremendous progress in atomic/optical physics and condensed matter physics, and particularly at the interface between these two formerly distinct fields, in developing experimental systems whose quantum states are long-lived and which can be engineered to perform quantum information processing tasks. These lecture notes will present a brief introduction to the basic theoretical concepts behind this `second quantum revolution.' These notes will also provide an introduction to `circuit QED.' In addition to being a novel test bed for non-linear quantum optics of microwave electrical circuits which use superconducting qubits as artificial atoms, circuit QED offers an architecture for constructing quantum information processors.