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arXiv:1405.3720 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

New signatures of the dynamical Casimir effect in a superconducting circuit

Andreson L. C. Rego, Hector O. Silva, Danilo T. Alves, Carlos Farina

Published Jul 1, 2014• 18 citations
arXivHTMLPDF

Abstract

We found new signatures of the dynamical Casimir effect (DCE) in the context of superconducting circuits. We show that if the recent experiment made by Wilson et al., which brought the DCE into reality for the first time, is repeated with slight modifications (for instance, different values for the capacitance of the superconducting quantum interference device), three remarkable results will show up, namely, (i) a quite different spectral distribution for the created particles, deviating from the typical parabolic shape, (ii) an enhancement by a factor of approximately $5\ifmmode\times\else\texttimes\fi{}1{0}^{3}$ in the number of created particles with half driving frequency of the effective moving mirror, and (iii) an enhancement by a factor of $3\ifmmode\times\else\texttimes\fi{}1{0}^{2}$ in the particle creation rate. These results may guide the experimentalists in their search for alternative routes to observe the DCE in future experiments.

DOI
10.1103/physrevd.90.025003

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We found new signatures of the dynamical Casimir effect (DCE) in the context of superconducting circuits. We show that if the recent experiment made by Wilson et al., which brought the DCE into reality for the first time, is repeated with slight modifications (for instance, different values for the capacitance of the superconducting quantum interference device), three remarkable results will show up, namely, (i) a quite different spectral distribution for the created particles, deviating from the typical parabolic shape, (ii) an enhancement by a factor of approximately 5\ifmmode×\else\texttimes\fi1035\ifmmode\times\else\texttimes\fi{}1{0}^{3}5\ifmmode×\else\texttimes\fi103 in the number of created particles with half driving frequency of the effective moving mirror, and (iii) an enhancement by a factor of 3\ifmmode×\else\texttimes\fi1023\ifmmode\times\else\texttimes\fi{}1{0}^{2}3\ifmmode×\else\texttimes\fi102 in the particle creation rate. These results may guide the experimentalists in their search for alternative routes to observe the DCE in future experiments.
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.
In this work we study simulations of photon generation due to the dynamical Casimir effect (DCE) in a one-dimensional ( 1 + 1 ) double superconducting cavity. To achieve this, we propose the use of a superconducting quantum circuit so as to be able to experimentally perform quantum simulations of the DCE. The simulated cavity consists of two perfectly conducting mirrors and a dielectric membrane of infinitesimal depth that effectively couples two cavities. The total length of the double cavity L , the difference in length between the two cavities Δ L , and the electric susceptibility χ and conductivity v of the dielectric membrane are tunable parameters. All four parameters are treated as independent and are allowed to be tuned at the same time, even with different frequencies. We analyze the cavity's energy spectra under different conditions, finding a transition between two distinct regimes that is accurately described by k c = v / χ . In particular, a lowest-energy mode is forbidden in one of the regimes while it is allowed in the other. We compare analytical approximations obtained through the multiple-scale analysis method with exact numerical solutions, obtaining the typical results when χ is not being tuned. However, when the susceptibility χ is tuned, different behaviors (such as oscillations in the number of photons of a cavity prepared in a vacuum state) can arise if the frequencies and amplitudes of all parameters are adequate. These oscillations might be considered as adiabatic shortcuts where all generated photons are eventually destroyed.
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.
The robustness of quantum synchronization induced by the dynamical Casimir effect (DCE) is analyzed within a circuit quantum electrodynamics (cQED) architecture consisting of two superconducting qubits coupled to a shared, parametrically driven cavity. Using a Lindblad master equation approach, this study evaluates the impact of various decoherence channels (including photon loss, relaxation, thermal excitation, and pure dephasing) on the resulting synchronization dynamics. The results demonstrate that DCE-induced synchronization persists under dissipation rates achievable in state-of-the-art superconducting platforms, confirming its experimental feasibility. Among the studied mechanisms, pure dephasing is identified as the dominant factor limiting the fidelity of the synchronized state. Furthermore, it is shown that in strongly dissipative regimes, the Pearson correlation coefficient may overestimate the degree of quantum synchronization, as environmental relaxation can generate classical correlations that mimic synchronized behavior. These findings establish the parameter regimes necessary for observing genuine DCE-induced quantum synchronization and provide practical guidelines for future cQED experiments.
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.
Abstract Real photon pairs can be created in a dynamic cavity with an oscillating boundary or temporally modulated refractive index of the constituent medium. This effect is called dynamic Casimir effect (DCE), which represents one of the most amazing predictions of quantum field theory. The DCE has been experimentally observed in Josephson metamaterials embedded in a microwave cavity. However, the efficiency of the observed DCE is extremely weak, entailing a complex external signal enhancement process to detect the signal. Here, it is shown that the DCE can be drastically enhanced in a dynamic 1D cavity consisting of a superconducting quantum interference device (SQUID)‐based Josephson transmission line with both temporal and spatial modulation on the effective inductance profile through flux‐biasing. Such a system can resonantly generate photons at driving frequencies equal to even or odd integer times of that of the fundamental cavity mode governed by the symmetry of the spatial modulation. Interesting spectral and scaling behaviors for photons excited at the band edge are further observed. The discovery introduces a new degree of freedom—spatial modulation—to enhance the efficiency of DCE.