A Study On The Coupling Of Superconducting Coplanar-waveguide Resonator To Flux Qubit And Spin Ensemble

Cavity quantum electrodynamics(cavity QED)focuses on the strong coupling between atoms and photons in a cavity and has become an important field in atomic,molecular and opti-cal physics.As a circuit version,the circuit QED involves the strong and even ultrastrong cou-plings between a superconducting coplanar-waveguide resonator and a superconducting qubit or other solid-state quantum states.In particular,the ultrastrong coupling was never imple-mented in cavity QED based on atoms.Thus,its implementation in the circuit-QED system can provide a platform to demonstrate new physical phenomena.Moreover,the circuit QED has the advantage of tunability and can be extended to various hybrid quantum systems.This makes it useful in quantum technologies when harnessing the advantages of different subsys-tems constituting the hybrid quantum systems.In this PhD thesis,we study the circuit QED related to the ultrastrong coupling between a superconducting coplanar-waveguide resonator and a superconducting flux qubit,as well as the strong coupling between a superconducting coplanar-waveguide resonator and an ensemble of spins arising from the defects in diamond.We manage to reveal interest quantum effects and physical phenomena in these hybrid quantum systems.Our experimental study focuses on an ultrastrongly coupled circuit-QED system consisting of a four-junction superconducting flux qubit and a muti-mode coplanar-waveguide resonator.The transmission-spectrum measurement and numerical simulations show that the system is in the ultrastrong-coupling regime.By changing the photon number in the resonator,we ob-serve the frequency shift of the flux qubit via the spectroscopic measurement.This frequency shift contains the contributions from not only the rotating-coupling terms but also the counter-rotating terms,which is in a good agreement with the theory.Next,we report experimental observation of the critical behavior in the thermodynamic limit in a driven Tavis-Cummings model using an electron-spin ensemble coupled to a super-conducting microwave resonator.This behavior is demonstrated by measuring the Rabi splitting of the system due to its unique dependence on the collective spin excitations.We show that the quantum-state decoherence of the system plays an important role and the observed critical be-havior is in excellent agreement with our theoretical analysis.Moreover,we find that the critical exponents are close to those in the ideal case without driving and decoherence,evidencing the universality of the behavior.Finally,we study the dissipative quantum phase transition(QPT)in a biased Tavis-Cummings model consisting of an ensemble of two-level systems(TLSs)interacting with a cavity mode,where the TLSs are pumped by a drive field.In our proposal,we use a dissipative TLS ensemble and an active cavity with effective gain.In the weak drive-field limit,the QPT can occur under the combined actions of both loss and gain of the system.Owing to the active cavity,the QPT behavior can be much differentiated even for a finite strength of the drive field on the TLS en-semble.Also,we propose to implement our scheme based on the dissipative nitrogen-vacancy(NV)centers coupled to an active optical cavity made from the gain-medium-doped silica.Fur-thermore,we show that the QPT can be measured by probing the transmission spectrum of the cavity embedding the ensemble of the NV centers.