The Tavis-Cummings model is intensively investigated in quantum optics and has important applications in generation of multi-atom entanglement. Here, we employ a superconducting circuit quantum electrodynamic system to study a modified Tavis-Cummings model with directly-coupled atoms. In our device, three superconducting artificial atoms are arranged in a chain with direct coupling through fixed capacitors and strongly coupled to a transmission line resonator. By performing transmission spectrum measurements, we observe different anticrossing structures when one or two qubits are resonantly coupled to the resonator. In the case of the two-qubit Tavis-Cummings model without qubit-qubit interaction, we observe two dips at the resonance point of the anticrossing. The splitting of these dips is determined by Δ λ =2 g 1 2 + g 3 2 , where g 1 and g 3 are the coupling strengths between Qubit 1 and the resonator, and Qubit 3 and the resonator, respectively. The direct coupling J 12 between the two qubits results in three dressed states in the two-qubit Tavis-Cummings model at the frequency resonance point, leading to three dips in the transmission spectrum. In this case, the distance between the two farthest and asymmetrical dips, arising from the energy level splitting, is larger than in the previous case. The frequency interval between these two dips is determined by the difference in eigenvalues (Δ λ = ε 1+ − ε 1− ), obtained through numerical calculations. What we believe as novel and intriguing experimental results may potentially advance quantum optics experiments, providing valuable insights for future research.
We present an ideal realization of the Tavis-Cummings model in the absence of atom number and coupling fluctuations by embedding a discrete number of fully controllable superconducting qubits at fixed positions into a transmission line resonator. Measuring the vacuum Rabi mode splitting with one, two, and three qubits strongly coupled to the cavity field, we explore both bright and dark dressed collective multiqubit states and observe the discrete square root N scaling of the collective dipole coupling strength. Our experiments demonstrate a novel approach to explore collective states, such as the W state, in a fully globally and locally controllable quantum system. Our scalable approach is interesting for solid-state quantum information processing and for fundamental multiatom quantum optics experiments with fixed atom numbers.
We report an experimental demonstration of resonance fluorescence in a two-level superconducting artificial atom under two driving fields coupled to a detuned cavity. One of the fields is classical and the other is varied from quantum (vacuum fluctuations) to classical by controlling the photon number inside the cavity. The device consists of a transmon qubit strongly coupled to a one-dimensional transmission line and a coplanar waveguide resonator. We observe a sideband anticrossing and asymmetry in the emission spectra of the system through a one-dimensional transmission line, which is fundamentally different from the weak-coupling case. By changing the photon number inside the cavity, the emission spectrum of our doubly driven system approaches the case when the atom is driven by two classical bichromatic fields. We also measure the dynamical evolution of the system through the transmission line and study the properties of the first-order correlation function, Rabi oscillations, and energy relaxation in the system. The study of resonance fluorescence from an atom driven by two fields promotes understanding decoherence in superconducting quantum circuits and may find applications in superconducting quantum computing and quantum networks. Published by the American Physical Society 2024
In this thesis, measurements on superconducting electrical circuits that exhibit quantum mechanical effects are presented. Nonlinear superconducting circuits can be regarded as artificial atoms with energy spectra that can be engineered. The artificial atoms can be used as quantum bits for quantum computation. By coupling the artificial atoms to the electromagnetic field inside a transmission line resonator, quantum optical effects can be studied in these electrical circuits.The possibility of using a frequency tunable transmission line resonators for coupling of superconducting quantum bits is investigated. Tunable superconducting resonators consisting of coplanar waveguide structures, terminated to ground in one end via a superconducting quantum interference device (SQUID), are characterized. By applying a magnetic field to the SQUID loop, the boundary condition of the resonator changes leading to a change in resonance frequency.A change of the resonance frequency by more than 250 linewidths is demonstrated. It is also demonstrated that the resonator can be tune by several hundred MHz on a time scale that is much shorter than the photon lifetime of the resonator.Circuits containing both one and two transmon qubits coupled to the resonator are characterized. Quantum mechanical interactions between the resonator and the qubits, in form of vacuum Rabi splitting, are observed. Coherent control of a single qubit coupled to the resonator is demonstrated by performing Rabi oscillations of the qubit. In the two qubit case, coherent interaction between the qubits is observed in terms of a nonlinear scaling of the coupling strength between the resonator and the collective two qubit system.Measurements on a strongly driven single Cooper-pair box, using a quantum capacitance readout, are also presented. A rich structure in the response is well explained in terms of longitudinal dressed states of the single-Cooper pair box.When measuring the response of a single-electron box, a gate dependent excess dissipation is observed. The dissipation is understood by considering the internal dynamics of the single electron box. The excess dissipation is modeled as an effective resistance named the Sisyphus resistance.
In the strong coupling regime of cavity QED where the characteristic damping rates are orders of magnitude below the coherent coupling, resolved multi-photon resonances can be observed for strong enough driving strength. In a certain frequency range, the external coherent drive field hits multi-photon resonances which correspond to very high order transitions that cannot be excited at the given power of the driving field. We found that in this range the cavity field evolves into a robust semiclassical solution which is the mixture of the vacuum and an excited quasi-classical state. The system is reminiscent of optical bistability, however, here a single atom produces a telegraph signal for the outgoing intensity by switching between two states with large photon number difference. We calculate this behavior also for the Tavis-Cummings model representing three qubits in an existing circuit QED experimental setting.
Artificially engineered atoms, built using superconducting electrical circuits, have had a broad impact on the field of quantum information and quantum computing. Based on the Josephson effect, superconducting qubits have provided a robust platform for engineering light-matter interactions at the single-photon level. The ability to precisely control and manipulate single photons using superconducting qubits and cavities, a field now popularly known as circuit quantum electrodynamics (circuit QED), has enabled new and novel regimes in quantum physics, which previously remained inaccessible. For instance, the coupling between individual photons and artificial atoms have been shown to reach the ultrastrong and deep-strong regimes, a feat which is difficult to achieve with natural atoms. The superconducting circuit platform is now a promising contender for building large-scale quantum processors, attracting large investments from academic, industry and government players. \n \nThis thesis uses superconducting circuits to engineer photon interactions in two separate studies. The first is aimed at studying the physics of ``giant" artificial-atoms. The second study explores the route towards building a quantum heat engine using two parametrically-coupled, superconducting microwave cavities. We review the theoretical ideas and concepts which motivate our work, along with discussions of the design methodology, simulations, fabrication, measurement setup and the experimental findings. \n \nIn the first study, we explore a giant artificial atom, formed from a transmon qubit, which is coupled to propagating microwaves at multiple points along an open transmission line. The multipoint coupling nature of the transmon allows its radiated field to interfere with itself leading to some striking ``giant" atom effects. For instance, we observe strong frequency dependent couplings of the transmon's transition levels to its electromagnetic environment, a feature which is not observed with ordinary artificial atoms. We measure large on/off ratios, as high as
380, for the coupling rate of the
ket0−ket1 transition. Furthermore, we show that we can enhance or suppress the coupling rate of the
ket1−ket2 transition relative to the
ket0−ket1 transition, by more than a factor of
200. The relative modulation of the coupling rates was exploited to engineer a metastable state in the giant transmon and demonstrate electromagnetically-induced transparency (EIT), a typical signature of a lambda system. Our results show that we can transform the ladder structure of an ordinary transmon into a more interesting lambda system using a giant transmon, thereby paving the way for exploring new possibilities to study three-level physics in a waveguide-QED setting. \n \nExtending giant atom physics to multiple giant atoms, we then explore a device with two giant artificial atoms connected in a braided configuration to a transmission line. The braided topology of the qubits, offers an interesting regime where the qubits can interact with each other in a decoherence-free environment, where the interaction is mediated by virtual photons in the transmission line. We probe the resonant behavior of the qubits at two different frequency bias points, where we observe qualitatively different scattering behavior. Furthermore, when probing for the Autler-Townes Splitting (ATS), multiple resonances are observed for both resonant and off-resonant cases instead of the familiar doublet in the ATS spectroscopy. This comes as a surprise as the frequency-level spacings in both qubits are nominally identical. We believe these features could be an indication of a novel resonant interaction between the qubits facilitated by the braided topology. An effort to understand this theoretically is underway. \n \nFor our second study, we explore a system with two parametrically-coupled superconducting resonators, which implements an optomechanical-like interaction in an all-electrical network. The nonlinear nature of this interaction is mediated by a superconducting quantum interference device (SQUID), where the current in one resonator couples to the photon number in the other resonator. We propose to use this system to build a ``photonic piston" engine in the quantum regime. We motivate the feasibility of the proposal by reviewing key theoretical results which demonstrate an Otto-cycle by appropriately driving the system with noise. Our experimental findings demonstrate the crucial nonlinear coupling that is required for the engine to work. We also show that we can increase the coupling strength between the resonators depending on the chosen flux operating point.
Superconducting quantum devices have drawn the attention of physicists greatly in recent years, not only because they are one of the most favorable candidates for developing a solid state quantum computer, but also because they can be employed as test systems for understanding quantum mechanics at nearly macro scale. Superconducting quantum devices can be divided into two groups: the superconducting resonators (linear devices), which have equally spaced discrete energy levels, and the artificial atoms (non-linear devices) consisting of Josephson junctions which have unequally spaced discrete energy levels. By combining these two kinds of devices together, a solid state counterpart of optical cavity quantum electrodynamics (QED) known as circuit QED emerges. Experiments of cavity QED and quantum optics can be reproduced in either circuit QED systems or in bare superconducting artificial atoms. As an example, we have observed the Autler-Townes effect in a three-level artificial atom called phase qutrit. \nMore than one decade has passed since the first experimental demonstration of superconducting two-level artificial atom (qubit). However, to build a practical quantum computer with thousands of superconducting qubits there is still a long way to go (we are at the stage of three qubits now). One of the main obstacles preventing us from scaling up a superconducting quantum computer, as well as some other kinds of quantum computers, has been decoherence, which is believed to be dominated by the low frequency noise due to the two-level system (TLS) fluctuators located inside the Josephson junction barrier. We have experimentally simulated the dynamics of a qubit longitudinally coupled to a randomly fluctuating TLS. A phenomenon known as motional averaging has been observed. \nIn this thesis, theoretical models for decoherence in both resonator and artificial atoms have been established and used for explaining phenomena observed in the experiments performed in our laboratory. The phenomenon of decoherence in coupled bipartite systems has been also studied, and besides the already known entanglement sudden death phenomenon, stable entanglement (robust under decoherence) generated from an arbitrary initial state has been found in these systems.