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.
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.
In this paper, we study the synchronization of qubits induced by the dynamical Casimir effect in an atom-cavity quantum electrodynamics system. Our investigation revolves around a pragmatic configuration of a quantum system, where two superconducting qubits are coupled to a shared coplanar waveguide resonator terminated at one end by a superconducting quantum interference device. The theoretical analyses of the system dynamics reveal sufficient conditions for ensuring synchronization which are anticipated to be accomplished by photon generation in the resonator. By numerically analyzing the time evolution of the system, we confirm that the conditions are satisfied by photon generation via the dynamical Casimir effect, resulting in qubit synchronization. Notably, we unveil a remarkable feature that is unique to synchronization induced by the dynamical Casimir effect: the differences in the initial states of qubits and the differences in the coupling strengths of qubits to an electromagnetic field affect the synchronization independently without overlap between these factors.
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 investigate theoretically how the dynamical Casimir effect can entangle quantum systems in different coupling regimes of circuit quantum electrodynamics, and show the robustness of such entanglement generation against dissipative effects, considering experimental parameters of current technology. We consider two qubit-resonator systems, which are coupled by a SQUID driven with an external magnetic field, and explore the entire range of coupling regimes between each qubit and its resonator. In this scheme, we derive a semianalytic explanation for the entanglement generation between both superconducting qubits when they are coupled to their resonators in the strong coupling regime. For the ultrastrong and deep strong coupling regimes, we design experimentally feasible theoretical protocols to generate maximally entangled polaritonic states.
Circuit quantum electrodynamics (cQED), exemplified by a coupled system of a superconducting qubit and a microwave cavity, is a powerful framework for the quantum control and measurement of macroscopic quantum states in solid-state circuits. Quantum circuits based on superconducting qubits have emerged as one of the leading platforms in the pursuit of fault-tolerant quantum computing. Despite significant progress in extending qubit lifetimes, refining experimental protocols, and scaling up quantum processors, errors arising from the control and measurement of superconducting qubits continue to hinder the realization of a universal quantum computer. To investigate the error mechanisms for state-of-the-art qubits, we realize long-lived superconducting transmon qubits that exhibit fluctuating lifetimes, with an average of 0.2 ms and a maximum exceeding 0.4 ms. We then investigate their dominant error mechanism. By introducing novel time-resolved error measurements that are synchronized with the operation of the pulse tube cooler in a dilution refrigerator, we find that mechanical vibrations from the pulse tube induce nonequilibrium dynamics in highly coherent qubits, leading to their correlated bit-flip errors. Our findings not only deepen our understanding of qubit error mechanisms but also provide valuable insights into potential error-mitigation strategies for achieving fault tolerance by decoupling superconducting qubits from their mechanical environments. We also present a novel scheme for operating a cQED system in a regime where the cavity is largely displaced. We find that a qubit drive at the bare cavity frequency can effectively displace the cavity field while minimizing the cavity-drive-induced dephasing and the ac Stark shift. Furthermore, we demonstrate that standard cQED protocols, such as qubit control, readout, and cavity single-photon generation, remain compatible with largely displaced cavity fields, even beyond the critical photon number. These findings open new pathways for exploring cQED dynamics in large-photon-number regimes, including the study of nonlinear phenomena in microwave cavities, the saturation of two-level system baths for extending the coherence of microwave quantum states, and the acceleration of the dispersive readout. Finally, mechanical resonators have emerged as integral components in quantum computing for storing and transducing quantum information. Low-frequency mechanical resonators, with extremely low energy dissipation rates, are particularly interesting for extending the lifetimes of stored quantum information. However, integrating low-frequency mechanical resonators with qubits is challenging because their small energy gaps make coherent energy exchange and ground-state preparation difficult. In this thesis, we report the first steps towards the characterization of a hybrid quantum device, consisting of a Transmon qubit and a circuit optomechanical system, both coupled to a 3D microwave cavity.
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.
In recent years, superconducting circuits have come to the forefront of certain areas of physics. They have shown to be particularly useful in research related to quantum computing and information, as well as fundamental physics. This is largely because they provide a very flexible way to implement complicated quantum systems that can be relatively easily manipulated and measured. In this thesis we look at three different applications where superconducting circuits play a central role, and explore their classical and quantum dynamics and behavior. \n \nThe first part consists of studying the Casimir [Proc. K. Ned. Akad. Wet (1948)] and Casimir-Polder like [Physical Review 73, 4 (1948)]effects. These effects have been discovered in 1948 and show that under certain conditions, vacuum field fluctuations can mediate forces between neutral objects. In our work, we analyze analogous behavior in a superconducting system which consists of a stripline cavity with a DC-SQUID on one of its boundaries, as well as, in a Casimir-Polder case, a charge qubit coupled to the field of the cavity. Instead of a force, in the system considered here, we show that the Casimir and Casimir-Polder like effects are mediated through a circulating current around the loop of the boundary DC-SQUID. Using detailed analysis, we examine how the values of these currents change as we vary different physical circuit parameters. We show that for the set of physical parameters that can be easily obtained experimentally, the Casimir and Casimir-Polder currents can be of the order of 10^(-8) A and 10^(-13) A respectively. \n \nIn the second part, we theoretically model an experiment which was performed by Britton Plourde's group at Syracuse University, and which studied the transient dynamics of a nonlinear superconducting oscillator, based on a capacitively shunted DC-SQUID. Such DC-SQUID oscillators are used in many areas of physics and engineering, for example, as building blocks of amplifiers or qubits, qubit couplers, or as sensitive magnetic field detectors. In many of these situations, their steady state behavior is often considered, while in the experiment performed at Syracuse, of specific interest, was the response of a DC-SQUID oscillator to a short radiation that only briefly excited the system. In this thesis, we simulate this response at the experimental temperature, by numerically solving a set of classical stochastic differential equations that mimic the behavior of the circuit. This is done for different settings of the flux that is threaded through the DC-SQUID as well as different input pulse amplitudes. Furthermore, we briefly outline just how these kinds of brief excitations could be useful when applied in flux measurement protocols. We find that our simulations show good agreement with the experimentally obtained data. \n \nThe final part considered in this thesis, looks at the dynamics of a qubit coupled to a measuring probe, which is modeled as a harmonic oscillator. An example superconducting circuit, that could be used to implement such a setup, consists of a flux qubit inductively coupled to a DC-SQUID. This measurement scenario has already been explored in [Phys. Rev. B 78, 5 (2008)], but there, the authors only consider very short interaction times between the DC-SQUID and the qubit. Here, in contrast, we concentrate our efforts on studying the evolution of qubit as the measurement takes place, by solving the corresponding Lindblad master equation, but over longer measurement times. This is done by calculating the measurement induced dephasing rate of the qubit, as well as, discussing its sometimes present effective relaxation, in regimes where the measurement is considered to not be quantum non-demolition (QND). Finally, we briefly explore how well a potentially complicated evolution of the qubit can be approximated as a very simple Kraus map.