In this work we keep exploiting the implementation of the Rabi Hamiltonian in superconducting technologies, and propose a biperiodic driving of the qubit gap Ĥd(t) = Σ2j=1ħΩjηjcos(Ωjt)σ̂z, with Ωjand ηjreal and positive, to dissipatively drive the cavity field into a squeezed state, or an entangled state if more than one cavity mode is considered. Such a driving term is easily implementable in superconducting qubits, whose gap can be modified at real time via external fields.
In this work we keep exploiting the implementation of the Rabi Hamiltonian in superconducting technologies, and propose a biperiodic driving of the qubit gap Ĥd(t) = Σ2j=1ħΩjηjcos(Ωjt)σ̂z, with Ωjand ηjreal and positive, to dissipatively drive the cavity field into a squeezed state, or an entangled state if more than one cavity mode is considered. Such a driving term is easily implementable in superconducting qubits, whose gap can be modified at real time via external fields.
We show how a pair of superconducting qubits coupled to a microwave cavity mode can be used to engineer a single-atom laser that emits light into a nonclassical state. Our scheme relies on the dressing of the qubit-field coupling by periodic modulations of the qubit energy. In the dressed basis, the radiative decay of the first qubit becomes an effective incoherent pumping mechanism that injects energy into the system, hence turning dissipation to our advantage. A second, auxiliary qubit is used to shape the decay within the cavity, in such a way that lasing occurs in a squeezed basis of the cavity mode. We characterize the system both by mean-field theory and exact calculations. Our work may find applications in the generation of squeezing and entanglement in circuit QED, as well as in the study of dissipative few- and many-body phase transitions.
Superconducting circuits provide an architecture upon which cavity quantum electrodynamics (QED) can be implemented at microwave frequencies in a highly tunable environment. Known as circuit QED, these systems can achieve larger nonlinearities, stronger coupling and greater controllability than can be achieved in cavity QED, all in a customisable, solid state device, making this technology an exciting test bed for both quantum optics and quantum information processing. These new parameter regimes open up new avenues for quantum technology, while also allowing older quantum optics results to finally be tested. In particular is is now possible to experimentally produce nonclassical states, such as squeezed and Schr\\"odinger cat states, relatively simply in these devices. Using open quantum systems methods, in this thesis we investigate four problems which involve the use of nonclassical states in circuit QED. First we investigate the effects of a Kerr nonlinearity on the ability to preserve transported squeezed states in a superconducting cavity, and whether this setup permits us to generate, and perform tomography, of a highly squeezed field using a qubit, with possible applications in the characterisation of sources of squeezed microwaves. Second, we present a novel scheme for the amplification of cat states using a coupled qubit and external microwave drives, inspired by the stimulated Raman adiabatic passage. This scheme differs from similar techniques in circuit QED in that it is deterministic and therefore compatible with a protocol for stabilising cat states without the need for complex dissipation engineering. Next we use solutions of Fokker-Planck equations to study the exact steady-state response of two nonlinear systems: a transmon qubit coupled to a readout resonator, where we find good agreement with experiments and see simultaneous bistability of the cavity and transmon; and a parametrically driven nonlinear resonator, where we compare the classical and quantum phases of the system and discuss applications in the generation of squeezed states and stabilisation of cat states. Finally, we investigate the use of two different types of superconducting qubits in a single experiment, seeing that this enables engineering of the self- and cross-Kerr effects in a line of cavities. This could provide a valuable means of entangling cavity states, in addition to a resource for quantum simulation.
We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and non-classical driving. In this scenario, we show that an effective Hartree-type decoupling yields a good approximation to the dynamics of the system. We find that the stationary states are squeezed vacuum states of the non-interacting system which are enhanced by the Q-factor of the cavity. We show that this effective interaction could be realised with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. The qubit non-linearity, therefore, does not significantly influence the highly squeezed intracavity microwave field but, for a range of parameters, enables quantum state tomography of the cavity.
We propose a new scheme for generating the superposition and entanglement of the coherent states and squeezed states by considering N superconducting charge qubits (or artificial two-level atoms) interacting with photons in a high finesse cavity on a chip, assisted by a strong driving field. By virtue of the parameters of this system, we can generate novel quantum states, for example, multiparty entangled states and Schro¨dinger cat states among the superconducting qubits, coherent states and squeezed states of the cavity. These states, whose amplitudes are about two orders greater than those from the atomic quantum electrodynamics in classical cavity, are important for understanding the boundary between quantum and classical behavior and can be utilized in experimental studies on decoherence. This device may be an architecture for future solid-state quantum computation and communication.
We study the dynamics of a general quartic interaction Hamiltonian under the influence of dissipation and nonclassical driving. We show that this scenario could be realized with a cascaded superconducting cavity-qubit system in the strong dispersive regime in a setup similar to recent experiments. In the presence of dissipation, we find that an effective Hartree-type decoupling with a Fokker-Planck equation yields a good approximation. We find that the stationary state is approximately a squeezed vacuum, which is enhanced by the Q factor of the cavity but conserved by the interaction. The qubit nonlinearity, therefore, does not significantly influence the highly squeezed intracavity microwave field but, for a range of realistic parameters, enables characterization of itinerant squeezed fields.
Superconducting quantum bits are one of the leading frontrunners in the race to build a solid-state quantum computer. In circuit quantum electrodynamics (cQED), electronic quantum circuits, playing the role of quantum bits, qubits, are placed into superconducting cavities with incredibly weak dissipation. The resulting system exhibits both photon and qubit characteristics, and it is possible to perform complex operations by driving the system with microwaves. Progress has been rapid, with vast improvements in cavities, qubits, and in controlling the interaction between the two. As a result, the first simple quantum algorithms to utilize this architecture have recently been implemented. \nAt the same time, there have been significant developments in improving our understanding of the heat flow in nanoelectronics. In particular the development of tunnel junctions has reached such a level, that it is now possible to control and measure the temperature of small metal islands with high precision. Such techniques have enabled the first observations of quantum-limited heat conduction through the photonic modes of a circuit. \nThis thesis introduces some of the benefits that come with the unification of these two fields. Theoretical models for experiments in a superconducting cavity are presented, with heat conduction due to individual cavity photons discussed in detail, along with a novel method to vary the lifetime of a qubit over many orders of magnitude. The realisation of these experiments would be the first steps on the road to integrating normal-metal components with cQED.