Quantum Optics with Propagating Microwaves in Superconducting Circuits

We address recent advances in quantum optics with propagating microwaves in superconducting circuits. This research field exploits on the fact that the coupling between a superconducting artificial atom and propagating microwave photons in a one-dimensional (1D) open transmission line can be made strong enough to observe quantum effects, without using any cavity to confine the microwave photons. We embed an artificial atom, a superconducting transmon qubit, in a 1D open transmission line and investigate the scattering properties of coherent microwaves. When an input coherent state, with an average photon number much less than 1, is on resonance with the artificial atom, we observe extinction of up to 99% in the forward propagating field. We observe the strong nonlinearity of the artificial atom and under strong driving we observe the Mollow triplet. We also study the statistics of the reflected and transmitted beams, which are predicted to be nonclassical states. In particular, we demonstrate photon antibunching in the reflected beam by measuring the second-order correlation function. By applying a second control tone, we observe the Autler-Townes splitting and a giant cross-Kerr effect. Furthermore, we demonstrate fast operation of a single-photon router using the Autler-Townes splitting. This device provides important steps towards the realization of a quantum network. This thesis describes the motivation, theoretical background, design, implementation and measurement results

The Single-Photon Router

We have embedded an artificial atom, a superconducting "transmon" qubit, in an open transmission line and investigated the strong scattering of incident microwave photons ($\sim6$ GHz). When an input coherent state, with an average photon number $N\ll1$ is on resonance with the artificial atom, we observe extinction of up to 90% in the forward propagating field. We use two-tone spectroscopy to study scattering from excited states and we observe electromagnetically induced transparency (EIT). We then use EIT to make a single-photon router, where we can control to what output port an incoming signal is delivered. The maximum on-off ratio is around 90% with a rise and fall time on the order of nanoseconds, consistent with theoretical expectations. The router can easily be extended to have multiple output ports and it can be viewed as a rudimentary quantum node, an important step towards building quantum information networks.Comment: 5 pages, 3 figure

Ultimate quantum limit for amplification: A single atom in front of a mirror

We investigate three types of amplification processes for light fields coupling to an atom near the end of a one-dimensional (1D) semi-infinite waveguide. We consider two setups where a drive creates population inversion in the bare or dressed basis of a three-level atom and one setup where the amplification is due to higher-order processes in a driven two-level atom. In all cases, the end of the waveguide acts as a mirror for the light. We find that this enhances the amplification in two ways compared to the same setups in an open waveguide. Firstly, the mirror forces all output from the atom to travel in one direction instead of being split up into two output channels. Secondly, interference due to the mirror enables tuning of the ratio of relaxation rates for different transitions in the atom to increase population inversion. We quantify the enhancement in amplification due to these factors and show that it can be demonstrated for standard parameters in experiments with superconducting quantum circuits

Signal Amplification Assisted by Multiple Sideband Interference in 1D Waveguide QED Systems

This study theoretically investigates signal amplification resulting from multiple Rabi sideband coherence in a one-dimensional waveguide quantum electrodynamical system. Specifically, we explore the behavior of a transmon while strongly driven by a coherent microwave field through a semi-infinite waveguide. To understand the underlying mechanisms of amplification, we develop a theory that explicitly takes into account multiple dressed sidebands under a strong driving field, and analyze the reflection amplitude of the probe signal. Our findings show that amplification can be related to either population inversion or multiple sideband constructive interference in some cases without population inversion. We further examine the effect of qubit dephasing during the amplification process

Generation of nonclassical microwave states using an artificial atom in 1D open space

We have embedded an artificial atom, a superconducting transmon qubit, in a 1D open space and investigated the scattering properties of an incident microwave coherent state. By studying the statistics of the reflected and transmitted fields, we demonstrate that the scattered states can be nonclassical. In particular, by measuring the second-order correlation function, $g^{(2)}$, we show photon antibunching in the reflected field and superbunching in the transmitted field. We also compare the elastically and inelastically scattered fields using both phase-sensitive and phase-insensitive measurements.Comment: 5 pages, 3 figure

Giant Cross Kerr Effect for Propagating Microwaves Induced by an Artificial Atom

We have investigated the cross Kerr phase shift of propagating microwave fields strongly coupled to an artificial atom. The artificial atom is a superconducting transmon qubit in an open transmission line. We demonstrate average phase shifts of 11 degrees per photon between two coherent microwave fields both at the single-photon level. At high control power, we observe phase shifts up to 30 degrees. Our results provide an important step towards quantum gates with propagating photons in the microwave regime.Comment: 5 pages, 4 figure

Breakdown of the cross-kerr scheme for photon counting

We show, in the context of single-photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarizability model known as the cross-Kerr effect.We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single-photon applications. Our results are presented in the context of a transmon in a one-dimensional microwave waveguide, but the conclusions also apply to optical systems

Microwave amplification via interfering multi-photon processes in a half-waveguide quantum electrodynamics system

We investigate the amplification of a microwave probe signal by a superconducting artificial atom, a transmon, strongly coupled to the end of a one-dimensional semi-infinite transmission line. The end of the transmission line acts as a mirror for microwave fields. Due to the weak anharmonicity of the artificial atom, a strong pump field creates multi-photon excitations among the dressed states. Transitions between these dressed states, Rabi sidebands, give rise to either amplification or attenuation of the weak probe. We obtain a maximum amplitude amplification of about 18 %, higher than in any previous experiment with a single artificial atom, due to constructive interference between Rabi sidebands. We also characterize the noise properties of the system by measuring the spectrum of spontaneous emission

Strong Interaction Between a Single Artificial Atom and Propagating Microwave Photons

The realization of a quantum network composed of quantum nodes which process quantum fields and quantum channels to transfer quantum information has recently been proposed. In recent years, fundamental experiments produced by superconducting circuits suggest that they are promising candidates for realization of a quantum network. Superconducting circuit QED can act as quantum nodes, which can be linked by quantum channels, to transfer flying microwave photons (quantum information) from site to site on chip with high fidelity. Therefore, controlling the propagating microwave photons on chip is an essential step towards realization of a quantum network.In this thesis, we demonstrate a specific quantum node, namely the single photon router. The active element of the router is a single three-level artificial atom, a superconducting transmon type qubit, strongly coupled to a superconducting 1D transmission line. Strong coupling between the artificial atom and propagating microwave photons, revealed in high degree scattering of the resonance waves, has been observed. By exploiting the phenomenon of electromagnetically induced transparency (EIT), we can route a single photon signal from an input port to either of two output ports with an on-off ratio of approximately 90%. The switching time of the router is shown to be a few nanoseconds, consistent with theoretical expectations and the device parameters. Besides the router, we also observed some fundamental phenomenon of single atom, such as strong nonlinearity, anomalous dispersion and the Mollow Triplet.This thesis describes the motivation, theoretical background, design, implementation and the measurement results