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Floquet formulation for the investigation of multiphoton quantum interference in a superconducting qubit driven by a strong field

Son Son, Sang-Kil

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

We present a Floquet investigation of multiphoton quantum interference in a strongly driven superconducting qubit. The procedure involves a transformation of a time-dependent problem into an equivalent time-independent infinitedimensional Floquet matrix eigenvalue problem. The results of a two-level qubit system show quantum interference fringes around multiphoton resonance positions in agreement with the experimental results1). We further explore the interference patterns in terms of quasienergies and the resonance position shifts as the tunneling strength increased. The Floquet formulation promises a new and accurate approach for the investigation of quantum interference phenomenon in the qubits.

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We present a Floquet investigation of multiphoton quantum interference in a strongly driven superconducting qubit. The procedure involves a transformation of a time-dependent problem into an equivalent time-independent infinitedimensional Floquet matrix eigenvalue problem. The results of a two-level qubit system show quantum interference fringes around multiphoton resonance positions in agreement with the experimental results1). We further explore the interference patterns in terms of quasienergies and the resonance position shifts as the tunneling strength increased. The Floquet formulation promises a new and accurate approach for the investigation of quantum interference phenomenon in the qubits.
We present a Floquet treatment of multiphoton quantum interference in a strongly driven superconducting flux qubit. The periodically time-dependent Schr\"odinger equation can be reduced to an equivalent time-independent infinite-dimensional Floquet matrix eigenvalue problem. For resonant or nearly resonant multiphoton transitions, we extend the generalized Van Vleck (GVV) nearly degenerate high-order perturbation theory for the treatment of the Floquet Hamiltonian, allowing the reduction of the infinite-dimensional Floquet matrix to an $N\ifmmode\times\else\texttimes\fi{}N$ effective Hamiltonian, where NNN is the number of eigenstates under consideration. The GVV approach allows accurate treatment of ac Stark shift, power broadening, time-dependent and time-averaged transition probability, etc., well beyond the rotating wave approximation. We extend the Floquet and GVV approaches for numerical and analytical studies of the multiphoton resonance processes and quantum interference phenomena for the superconducting flux qubit system (N=2)(N=2)(N=2) 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.
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.
We present experiments on the driven dynamics of a two-level superconducting artificial atom. The driving strength reaches 4.78 GHz, significantly exceeding the transition frequency of 2.288 GHz. The observed dynamics is described in terms of quasienergies and quasienergy states, in agreement with Floquet theory. In addition, we observe the role of pulse shaping in the dynamics, as determined by nonadiabatic transitions between Floquet states, and we implement subnanosecond single-qubit operations. These results pave the way to quantum control using strong driving with applications in quantum technologies.
We perform Floquet spectroscopy in a GaAs double quantum dot system coupled to a high-impedance superconducting resonator. By applying microwave-induced consecutive passages under a double-resonance condition, we observe Landau-Zener-St\"uckelberg-Majorana interference patterns that stem from a cavity-assisted interference pattern modified by the depletion of the ground state. Our experimental results reveal the stationary state behavior of a strongly driven two-level system and are consistent with the simulations based on our theoretical model. This study provides an excellent platform for investigating the dynamics of Floquet states in the presence of strong driving.
We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the case of large driving amplitudes. If the pulse amplitude changes very fast, the evolution is nonadiabatic, with transitions taking place between the Floquet states. We quantify and analyze the nonadiabatic transitions during the pulse by employing adiabatic perturbation theory and exact numerical simulations. We find that, for certain combinations of pulse rise and fall times and maximum driving amplitude, a destructive interference effect leads to a remarkably strong suppression of transitions between the Floquet states. This effect provides the basis of a quantum control protocol, which we name Floquet interference efficient suppression of transitions in the adiabatic basis (FIESTA), that can be used to design ultrafast high-fidelity single-qubit quantum gates.