Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2407.14351 · Physical Review A

Superconducting quantum circuit to simulate the dynamical Casimir effect in a double cavity

Jean Paul Louys Sansó, Nicolás F. Del Grosso, Fernando C. Lombardo, Paula I. Villar

Published Jan 22, 2025• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.111.013714

Related papers

Photon generation and entanglement in a double superconducting cavity

Cruz I. Velasco, Nicolás F. Del Grosso, Fernando C. Lombardo +2 more

We study the dynamical Casimir effect in a double superconducting cavity in a circuit quantum electrodynamics architecture. Parameters in the quantum circuit are chosen in such a way the superconducting cavity can mimic a double cavity, formed by two perfectly conducting outer walls and a dielectric wall, with arbitrary permittivity separating both halves. We undertake a spectral analysis of the cavity, showing that the spectrum varies significantly depending on the values of the susceptibility of the dielectric mirror and the relative lengths of both cavities. We study the creation of photons when the walls oscillate harmonically with a small amplitude. Furthermore, we explore the possibility of entangling two uncoupled cavities, starting from a symmetric double cavity and having both of its halves become uncoupled at a later given instant. We consider both cases: (i) when the field is initially in a vacuum state and (ii) the situation in which photon creation via the dynamical Casimir effect has already taken place. We show that the cavities become entangled in both cases but, in the latter, the quantum correlation between individual modes can be greatly increased at the cost of diminishing the entanglement between most pairs of modes.

arXiv:2207.08747•Physical Review A•Oct 3, 2022•6 citations

Dynamical Casimir effect in superconducting microwave circuits

J. R. Johansson, Göran Johansson, Christopher M. Wilson +1 more

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.

arXiv:1007.1058•Physical Review A•Nov 11, 2010•194 citations

Photon generation in a doubly tunable resonator

Ida-Maria Svensson

In November 2011 the first experimental observation of the dynamical Casimir effect was published [1]. Superconducting circuits were used to show that a single mirror moving in vacuum could generate photons, by parametric amplification of vacuum uctuations. This project is a side track of this research where a second mirror is introduced to investigate photon generation in-between the mirrors. The work includes both theory studies and experimental practice. Resonators have been fabricated on chip in a cleanroom and measured in a dilution refrigerator. The focus has been on how the different boundary conditions of the resonator field affect the photon generation. A superconducting circuit has been used including a = 2/2 resonator with two SQUIDs inducing tunability of the resonance frequency via on-chip ux tuning lines. The two SQUIDs are placed in each end of the cavity in order to simulate moving mirrors. The mirrors are used to modulate the boundary conditions of the cavity. This is done by changing the SQUID inductance which is achieved by applying a magnetic ux to the SQUID loop. Depending on if the mirrors move in or out of phase, a breathing or translational mode can be created in the cavity. Theory predicts photon generation in different modes depending on if the pump frequency is two or three times the resonance frequency [2]. Measurements have been done at a temperature of around 50mK, which is low enough to have a negligible amount of thermal photons and quasi-particles in the cavity. The static tuning of the resonator have been probed by sweeping the uxes applied to the two SQUIDs and at each point the resonance frequency has been extracted. Good results have been achieved and two dimensional tuning is shown. A high frequency, ux modulation have been applied to the SQUIDs both one at a time and simultaneously to generate photons. In the two mirror modulation case qualitative agreement with theory has been observed for driving in the breathing and translational mode respectively. Generation occurs first for the breathing mode at 2*omega (twice the resonance frequency) and for the translational mode at 3*omega.

•Jan 1, 2012•3 citations

Photon Generation from Quantum Vacuum using a Josephson Metamaterial

Pasi Lähteenmäki, Gheorghe Sorin Paraoanu, Juha Hassel +1 more

When one of the parameters in the Euler-Lagrange equations of motion of a system is modulated, particles can be generated out of the quantum vacuum. This phenomenon is known as the dynamical Casimir effect, and it was recently realized experimentally in systems of superconducting circuits, for example by using modulated resonators made of coplanar waveguides, or arrays of superconducting quantum intereference devices (SQUIDs) forming a Josephson metamaterial. In this paper, we consider a simple electrical circuit model for dynamical Casimir effects, consisting of an LC resonator, with the inductor modulated externally at 10.8 GHz and with the resonant frequency tunable over a range of $\pm$ 400 MHz around 5.4 GHz. The circuit is analyzed classically using a circuit simulator (APLAC). We demonstrate that if an additional source of classical noise couples to the resonator (on top of the quantum vacuum), for example via dissipative "internal modes", then the resulting spectrum of the photons in the cavity will present two strongly asymmetric branches. However, according to the theory of the dynamical Casimir effect, these branches should be symmetric, a prediction which is confirmed by our experimental data. The simulation presented here therefore shows that the origin of the photons generated in our experiment with Josephson metamaterials is the quantum vacuum, and not a spurious classical noise source.

arXiv:1401.7875•Jan 30, 2014•1 citation

Microscopic toy model for the cavity dynamical Casimir effect

I M de Sousa, Alexandre V. Dodonov

We develop a microscopic toy model for cavity dynamical Casimir effect (DCE), namely, the photon generation from vacuum due to a nonstationary dielectric slab in a fixed single-mode cavity. We represent the slab by N ≫ 1 noninteracting two-level atoms coupled to the field via the standard dipole interaction. We show that the DCE is contained implicitly in the light–matter interaction Hamiltonian when its parameters are assumed externally prescribed functions of time. We also predict several new phenomena, such as saturation of the photon growth due to effective Kerr nonlinearity, generation of pairs of atomic excitations instead of photons (‘inverse DCE’) and coherent annihilation of pair of system excitations due to the atomic modulation (‘anti-DCE’). These results are extended to the circuit QED architecture where similar effects can be implemented with a single qubit, providing an alternative way to generate novel cavity and atom–field entangled states.

arXiv:1504.02413•Journal of Physics A Mathematical and Theoretical•May 27, 2015•30 citations

Robustness of Dynamical Casimir Effect-Induced Quantum Synchronization

Sebastián Francisquez, Fernando C. Lombardo, Paula I. Villar

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.

quant-pharXiv:2609.05659•Sep 8, 2026•0 citations
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.
We study the dynamical Casimir effect in a double superconducting cavity in a circuit quantum electrodynamics architecture. Parameters in the quantum circuit are chosen in such a way the superconducting cavity can mimic a double cavity, formed by two perfectly conducting outer walls and a dielectric wall, with arbitrary permittivity separating both halves. We undertake a spectral analysis of the cavity, showing that the spectrum varies significantly depending on the values of the susceptibility of the dielectric mirror and the relative lengths of both cavities. We study the creation of photons when the walls oscillate harmonically with a small amplitude. Furthermore, we explore the possibility of entangling two uncoupled cavities, starting from a symmetric double cavity and having both of its halves become uncoupled at a later given instant. We consider both cases: (i) when the field is initially in a vacuum state and (ii) the situation in which photon creation via the dynamical Casimir effect has already taken place. We show that the cavities become entangled in both cases but, in the latter, the quantum correlation between individual modes can be greatly increased at the cost of diminishing the entanglement between most pairs of modes.
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 November 2011 the first experimental observation of the dynamical Casimir effect was published [1]. Superconducting circuits were used to show that a single mirror moving in vacuum could generate photons, by parametric amplification of vacuum uctuations. This project is a side track of this research where a second mirror is introduced to investigate photon generation in-between the mirrors. The work includes both theory studies and experimental practice. Resonators have been fabricated on chip in a cleanroom and measured in a dilution refrigerator. The focus has been on how the different boundary conditions of the resonator field affect the photon generation. A superconducting circuit has been used including a = 2/2 resonator with two SQUIDs inducing tunability of the resonance frequency via on-chip ux tuning lines. The two SQUIDs are placed in each end of the cavity in order to simulate moving mirrors. The mirrors are used to modulate the boundary conditions of the cavity. This is done by changing the SQUID inductance which is achieved by applying a magnetic ux to the SQUID loop. Depending on if the mirrors move in or out of phase, a breathing or translational mode can be created in the cavity. Theory predicts photon generation in different modes depending on if the pump frequency is two or three times the resonance frequency [2]. Measurements have been done at a temperature of around 50mK, which is low enough to have a negligible amount of thermal photons and quasi-particles in the cavity. The static tuning of the resonator have been probed by sweeping the uxes applied to the two SQUIDs and at each point the resonance frequency has been extracted. Good results have been achieved and two dimensional tuning is shown. A high frequency, ux modulation have been applied to the SQUIDs both one at a time and simultaneously to generate photons. In the two mirror modulation case qualitative agreement with theory has been observed for driving in the breathing and translational mode respectively. Generation occurs first for the breathing mode at 2*omega (twice the resonance frequency) and for the translational mode at 3*omega.
When one of the parameters in the Euler-Lagrange equations of motion of a system is modulated, particles can be generated out of the quantum vacuum. This phenomenon is known as the dynamical Casimir effect, and it was recently realized experimentally in systems of superconducting circuits, for example by using modulated resonators made of coplanar waveguides, or arrays of superconducting quantum intereference devices (SQUIDs) forming a Josephson metamaterial. In this paper, we consider a simple electrical circuit model for dynamical Casimir effects, consisting of an LC resonator, with the inductor modulated externally at 10.8 GHz and with the resonant frequency tunable over a range of ±\pm± 400 MHz around 5.4 GHz. The circuit is analyzed classically using a circuit simulator (APLAC). We demonstrate that if an additional source of classical noise couples to the resonator (on top of the quantum vacuum), for example via dissipative "internal modes", then the resulting spectrum of the photons in the cavity will present two strongly asymmetric branches. However, according to the theory of the dynamical Casimir effect, these branches should be symmetric, a prediction which is confirmed by our experimental data. The simulation presented here therefore shows that the origin of the photons generated in our experiment with Josephson metamaterials is the quantum vacuum, and not a spurious classical noise source.
We develop a microscopic toy model for cavity dynamical Casimir effect (DCE), namely, the photon generation from vacuum due to a nonstationary dielectric slab in a fixed single-mode cavity. We represent the slab by N ≫ 1 noninteracting two-level atoms coupled to the field via the standard dipole interaction. We show that the DCE is contained implicitly in the light–matter interaction Hamiltonian when its parameters are assumed externally prescribed functions of time. We also predict several new phenomena, such as saturation of the photon growth due to effective Kerr nonlinearity, generation of pairs of atomic excitations instead of photons (‘inverse DCE’) and coherent annihilation of pair of system excitations due to the atomic modulation (‘anti-DCE’). These results are extended to the circuit QED architecture where similar effects can be implemented with a single qubit, providing an alternative way to generate novel cavity and atom–field entangled states.
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.