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Lecture notes in physics

Electromagnetic Cavities and Cavity Quantum Electrodynamics

Alto Osada, Rekishu Yamazaki, Atsushi Noguchi

Published Jan 1, 2022• 0 citations
Publisher
DOI
10.1007/978-981-19-4641-7_8

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This chapter focuses on cavity quantum electrodynamics. It presents the modifications of the spontaneous radiation rate in a cavity and the shifts of energy levels. The chapter focuses on experimental work, with an outline of a theoretical framework in which the experiments may be understood. In the laboratory, the study of atoms in cavities is a relatively young field in which much of the effort is still aimed at elucidating the basic physical principles at work and demonstrating the elementary modifications of energies and the rates of an atom in a cavity. However, the ability to adjust the electromagnetic spectrum of the vacuum is leading into a remarkable new domain of quantum physics in which atoms can decay from the ground state to an excited state, radiative corrections can be far larger than fine structure, and electromagnetic fields can be prepared with an exact number of photons. This realm of physics is now known as “cavity quantum electrodynamics.”
Rapid advances in quantum technology have made possible the control of quantum states of elementary material quantum systems, such as atoms or molecules, and of the electromagnetic radiation field resulting from spontaneous photon emission of their unstable excited states to such a level of precision that subtle quantum electrodynamical phenomena have become observable experimentally. Recent developments in the area of quantum information processing demonstrate that characteristic quantum electrodynamical effects can even be exploited for practical purposes provided the relevant electromagnetic field modes are controlled by appropriate cavities. A central problem in this context is the realization of an ideal transfer of quantum information between a state of a material quantum system and a quantum state of the electromagnetic radiation field which contains a small number or even a single photon only. Despite much recent work in cavity quantum electrodynamics, which has explored this problem successfully in cases in which the number of accessible electromagnetic field modes is strongly restricted by a cavity, currently still much less is known about ideal quantum state transfer between matter and few-photon quantum states of the electromagnetic field in the extreme opposite case of free space. In this contribution we review recent work which explores characteristic quantum electrodynamical phenomena governing the interaction of a material quantum system with the electromagnetic field in extreme many-mode cases which are close to cavity-free situations. For this purpose the simplest possible quantum electrodynamical situation, namely the interaction of a single material two-level system with the wave packet of a single optical photon, is investigated in free space and in situations in which a large cavity modifies the mode structure of the electromagnetic field modes. It is demonstrated that perfect excitation of an atom by a properly shaped single-photon wave packet is possible even in free space. In particular, it is demonstrated that perfect excitation of an atom can be achieved by a single optical photon which is prepared initially in an appropriate superposition of plane-wave modes, provided this photon is focused subsequently onto the absorbing atom by a parabolic cavity.
Numerical analysis of few-atom cavity quantum electrodynamics (QED) is challenging due to the exponentially scaling size of the Hilbert space when multiple quantized electromagnetic modes are considered. To overcome this, we propose an approach based on coupling matrix transformations that allows adjustment of the coupling structures of QED Hamiltonians so that they are more compatible with tensor network algorithms such as matrix product states. We present the relevant Hamiltonians along with the coupling matrix transformation scheme and present few-atom cavity QED simulations in the time domain that is able to characterize the interactions between atoms efficiently.