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Physical review. B./Physical review. B

Absorption spectra of superconducting qubits driven by bichromatic microwave fields

Jiazheng Pan, Hossein Zolfghari Jooya, Guozhu Sun, Yun-Yi Fan, Peiheng Wu, Dmitry A. Telnov, Shih‐I Chu, Siyuan Han

Published Nov 27, 2017• 14 citations

Abstract

We report experimental observation of two distinct quantum interference patterns in the absorption spectra when a transmon superconducting qubit is subjected to a bichromatic microwave field with the same Rabi frequencies. Within the two-mode Floquet formalism with no dissipation processes, we propose a graph-theoretical representation to model the interaction Hamiltonian for each of these observations. This theoretical framework provides a clear visual representation of various underlying physical processes in a systematic way beyond rotating-wave approximation. The presented approach is valuable to gain insights into the behavior of multichromatic field driven quantum two-level systems, such as two-level atoms and superconducting qubits. Each of the observed interference patterns is represented by appropriate graph products on the proposed color-weighted graphs. The underlying mechanisms and the characteristic features of the observed fine structures are identified by the transitions between the graph vertices, which represent the doubly dressed states of the system. The good agreement between the numerical simulation and experimental data confirms the validity of the theoretical method. Such multiphoton interference may be used in manipulating the quantum states and/or generate nonclassical microwave photons.

DOI: 10.1103/physrevb.96.174518

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We report experimental observation of two distinct quantum interference patterns in the absorption spectra when a transmon superconducting qubit is subjected to a bichromatic microwave field with the same Rabi frequencies. Within the two-mode Floquet formalism with no dissipation processes, we propose a graph-theoretical representation to model the interaction Hamiltonian for each of these observations. This theoretical framework provides a clear visual representation of various underlying physical processes in a systematic way beyond rotating-wave approximation. The presented approach is valuable to gain insights into the behavior of multichromatic field driven quantum two-level systems, such as two-level atoms and superconducting qubits. Each of the observed interference patterns is represented by appropriate graph products on the proposed color-weighted graphs. The underlying mechanisms and the characteristic features of the observed fine structures are identified by the transitions between the graph vertices, which represent the doubly dressed states of the system. The good agreement between the numerical simulation and experimental data confirms the validity of the theoretical method. Such multiphoton interference may be used in manipulating the quantum states and/or generate nonclassical microwave photons.

Multiphoton up/down conversion in a transmon circuit, driven by a pair of microwaves tuned near and far off the qubit resonance, has been observed. The experimental realization of these high order non-linear processes is accomplished in the three-photon regime, when the transmon is coupled to weak bichromatic microwave fields with the same Rabi frequencies. A many-mode Floquet formalism, with longitudinal coupling, is used to simulate the quantum interferences in the absorption spectrum that manifest the multiphoton pumping processes in the transmon qubit. An intuitive graph theoretic approach is used to introduce effective Hamiltonians that elucidate main features of the Floquet results. The analytical solutions also illustrate how controllability is achievable for desired single- or multiphoton pumping processes in a wide frequency range.

We propose a graph-theoretical formalism to study generic circuit quantum electrodynamics systems consisting of a two level qubit coupled with a single-mode resonator in arbitrary coupling strength regimes beyond rotating-wave approximation. We define colored-weighted graphs, and introduce different products between them to investigate the dynamics of superconducting qubits in transverse, longitudinal, and bidirectional coupling schemes. The intuitive and predictive picture provided by this method, and the simplicity of the mathematical construction, are demonstrated with some numerical studies of the multiphoton resonance processes and quantum interference phenomena for the superconducting qubit systems driven by intense ac fields.

We experimentally investigate a strongly driven GaAs double quantum dot charge qubit weakly coupled to a superconducting microwave resonator. The Floquet states emerging from strong driving are probed by tracing the qubit-resonator resonance condition. In this way, we probe the resonance of a qubit that is driven in an adiabatic, a nonadiabatic, or an intermediate rate, showing distinct quantum features of multiphoton processes and a fringe pattern similar to Landau-Zener-Stückelberg interference. Our resonant detection scheme enables the investigation of novel features when the drive frequency is comparable to the resonator frequency. Models based on the adiabatic approximation, rotating wave approximation, and Floquet theory explain our experimental observations.

Abstract We propose a versatile scheme for multiphoton frequency up/down conversion in flux superconducting qubit circuits, driven by a pair of microwaves tuned near and far off the qubit resonance. Flux qubits can be engineered with strong anharmonicity such that the two lowest eigenstates are energetically well separated from the higher ones. We demonstrate the high order non-linear transitions between the two lowest levels in the three-photon regime, by coupling the qubit to bichromatic microwave fields with the same Rabi frequencies. Both up and down conversions are presented and accurately interpreted with many-mode Floquet formalism. An intuitive graph theoretic approach elucidates the physics of multiphoton pumping and population trapping. The analytical solutions also illustrate how controllability is achievable for desired single- or multiphoton pumping processes in a wide range of frequencies. The proposed design and theoretical approach are applicable in maintaining the inter-connectivity of future superconducting quantum machines.

We study theoretically dynamic properties of an interferometer-type Josephson charge qubit consisting of a single-Cooper-pair transistor (with capacitive gate) closed by a superconducting inductive loop. Analyzing the radio frequency response of the device to microwave fields within a two-band model, we present basic features of a method for observation of various Rabi oscillation modes. For this purpose, we apply the dressed-state approach in conjunction with the rotating-wave approximation to the strongly driven quantum bit. We demonstrate the existence of multiphoton excitations and Rabi frequency transitions between quantum levels connected with them. The resulting oscillations of the supercurrent in the interferometer modify the spectral loop susceptibility. This effect may be detected via the coil of a high-quality tank circuit inductively coupled to the qubit by measuring the tank-qubit impedance variations belonging to it.

In this work, I investigate how to implement and quantify \\emph{in-situ} tunable quantum interface between superconducting qubits and resonators using external transverse driving fields beyond the rotating wave approximation (RWA). When studying the system under the time-periodic driving field, we typically rely on RWA, a useful technique that significantly reduces the analytical difficulties in solving the dynamics with time-dependent Hamiltonian. Nonetheless, it does not correctly describe the systems' dynamics when the drive fields are excessively strong and far off-resonant. Especially in circuit QED platform, the RWA often breakdowns. Many studies before, however, mainly focus on the transition frequency shifts. How the RWA distorts the interaction rates between two systems has been rarely explored. I have performed quantitative studies over two different systems. One is the quantum Rabi model (QRM) where a two-level atom is dispersively coupled to a resonator mode. The other is dispersively coupled a transmon and resonator system, which is the same as the QRM except that the transmon replaces the two-level atom in QRM. In both cases, I have revealed that the RWA significantly mislead the sideband transition rates between two elements. In the latter case, I have performed the experiments, and the results nicely agree with the analytical and numerical calculations. In addition to these, I also have introduced a study where the tunable coupling between a transmon and resonator is used for non-invasive resonator probing.