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arXiv:2504.11361

Dynamical Casimir effect in superconducting cavities: from photon generation to universal quantum gates

Fernando C. Lombardo, Paula I. Villar

Published Apr 15, 2025• 0 citations
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Abstract

This chapter explores various aspects of the Dynamical Casimir Effect (DCE) and its implications in the context of circuit quantum electrodynamics (cQED). We begin by reviewing the origin and fundamental properties of the DCE, including three equivalent mathematical frameworks that offer complementary perspectives on the phenomenon. These formulations will serve as a foundation for the subsequent analyses. We then turn our attention to the practical realization of the DCE in cQED-based architectures, discussing how modern superconducting circuits can be engineered to exhibit this inherently quantum effect. Building on this, we examine how the presence of the DCE influences the performance of a quantum thermal machine operating with a quantum field, shedding light on the interplay between quantum fluctuations and thermodynamic processes. Further, we demonstrate how the DCE can be harnessed to implement a controlled-squeeze gate within a cQED platform, opening a path toward advanced quantum control and quantum information processing. The chapter concludes with a synthesis of the main results and a discussion of potential future directions.

DOI
10.48550/arxiv.2504.11361

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This chapter explores various aspects of the Dynamical Casimir Effect (DCE) and its implications in the context of circuit quantum electrodynamics (cQED). We begin by reviewing the origin and fundamental properties of the DCE, including three equivalent mathematical frameworks that offer complementary perspectives on the phenomenon. These formulations will serve as a foundation for the subsequent analyses. We then turn our attention to the practical realization of the DCE in cQED-based architectures, discussing how modern superconducting circuits can be engineered to exhibit this inherently quantum effect. Building on this, we examine how the presence of the DCE influences the performance of a quantum thermal machine operating with a quantum field, shedding light on the interplay between quantum fluctuations and thermodynamic processes. Further, we demonstrate how the DCE can be harnessed to implement a controlled-squeeze gate within a cQED platform, opening a path toward advanced quantum control and quantum information processing. The chapter concludes with a synthesis of the main results and a discussion of potential future directions.
We theoretically investigate the dynamical Casimir effect (DCE) in electrical circuits based on superconducting microfabricated waveguides with tunable boundary conditions. We propose implementing a rapid modulation of the boundary conditions by tuning the applied magnetic flux through superconducting quantum-interference devices that are embedded in the waveguide circuits. We consider two circuits: (i) An open waveguide circuit that corresponds to a single mirror in free space, and (ii) a resonator coupled to a microfabricated waveguide, which corresponds to a single-sided cavity in free space. We analyze the properties of the DCE in these two setups by calculating the generated photon-flux densities, output-field correlation functions, and the quadrature squeezing spectra. We show that these properties of the output field exhibit signatures unique to the radiation due to the DCE, and could, therefore, be used for distinguishing the DCE from other types of radiation in these circuits. We also discuss the similarities and differences between the DCE, in the resonator setup, and the down-conversion of pump photons in parametric oscillators.
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We investigate a quantum-circuit analog of the dynamical Casimir effect discussed in cavity quantum electrodynamics (QED). A double superconducting quantum interference device (SQUID), consisting of a superconducting loop interrupted by a dc-SQUID, is regarded as a harmonic oscillator with a time-dependent frequency imitating the nonadiabatic boundaries in a cavity QED. Squeezing occurs due to parametric processes inherent in the system. We reformulate squeezing based on the Bogoliubov transformation between eigenstates at different times and derive the analytic formula for quantum-state evolutions of the system. The squeezing parameter clearly reveals the relationship between squeezing and nonadiabatic nature of the system. Thus, the squeezing parameter serves as a measure for the dynamical Casimir effect. We demonstrate squeezing for two types of frequency modulation and propose a method for measuring squeezing by using a circuit QED technique under coherent oscillations between an artificial atom and an LC circuit in the presence of dissipation. These observations suggest that a quantum circuit with a Josephson junction is a promising candidate for detecting the dynamical Casimir effect.
As superconducting circuits emerge as a leading platform for scalable quantum information processing, building comprehensive bridges from the foundational principles of macroscopic quantum phenomena to the architecture of modern quantum devices is increasingly essential for introducing new researchers to the field. This tutorial provides a self-contained, pedagogical introduction to superconducting quantum circuits at the undergraduate level. Beginning with an overview of superconductivity and the Josephson effect, the tutorial systematically develops the quantization of microwave circuits into the framework of circuit quantum electrodynamics (cQED). The transmon qubit is then introduced as a state-of-the-art application, with a detailed derivation of its Hamiltonian and its interaction with control and readout circuitry. The theoretical formalism is consolidated through a numerical simulation of vacuum Rabi oscillations in a driven transmon-resonator system, a canonical experiment that demonstrates the coherent energy exchange characteristic of the strong coupling regime. This work serves as a foundational guide and first point of contact, equipping students and researchers with the conceptual and mathematical tools necessary to understand and engineer superconducting quantum hardware.
We demonstrate, in the regime of ultrastrong matter-field coupling, the strong connection between the dynamical Casimir effect (DCE) and the performance of quantum-information protocols. Our results are illustrated by means of a realistic quantum communication channel and show that the DCE is a fundamental limit for quantum computation and communication and that novel schemes are required to implement ultrafast and reliable quantum gates. Strategies to partially counteract the DCE are also discussed.
Nonadiabatic driving in ultrastrongly coupled light--matter systems is commonly regarded as a source of errors, as counter-rotating interactions convert vacuum fluctuations into real excitations through the dynamical Casimir effect (DCE). Here we show that, instead, the DCE can be harnessed as a resource for engineering nonclassical states of light. Considering a cavity mode ultrastrongly coupled to a frequency-tunable qubit, we employ optimal quantum control to design driving protocols that convert vacuum fluctuations into targeted states. Numerical optimization reveals a versatile and robust approach for the deterministic preparation of a broad class of nonclassical states, illustrated here through Fock states, squeezed states, and Schrödinger-cat-state superpositions.