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arXiv:2307.11200 · Advanced Quantum Technologies

Photon‐Assisted Landau Zener Transitions in a Tunable Driven Rabi Dimer Coupled to a Micromechanical Resonator

Daniel Melvin, Fulu Zheng, Kewei Sun, Zhengjie Tan, Yang Zhao

Published Sep 27, 2023• 0 citations
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Abstract

Abstract Employing the multiple Davydov D 2 Ansätze with the time‐dependent variational principle, photon‐assisted Landau–Zener (LZ) transitions and qubit manipulation in a hybrid quantum electrodynamics device have been investigated. Modeled as a Rabi dimer, the device comprises of two interacting transmission‐line resonators, each coupled to a qubit. The qubits, driven by independent harmonic fields, are further modulated by a micromechanical resonator mimicked by a phonon mode. The impacts of two independent driving fields on the qubit dynamics are carefully examined. The energy diagram of the system and the photon number mobilization on the resonators are analyzed to explain the behavior of the LZ transitions and qubit dynamics while taking into account the influence of the single phonon mode. Results show that low phonon frequencies can alter the qubit dynamics, particularly in the absence of the driving fields, and a strong phonon coupling strength can significantly perturb the qubit dynamics, thanks to a high influx of phonon energy. Notably, only the photon frequency affects the oscillation frequency of qubit polarization. This study unveils the imperative roles that photons and phonons play in the Rabi dimer model.

DOI
10.1002/qute.202300232

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Abstract Employing the multiple Davydov D 2 Ansätze with the time‐dependent variational principle, photon‐assisted Landau–Zener (LZ) transitions and qubit manipulation in a hybrid quantum electrodynamics device have been investigated. Modeled as a Rabi dimer, the device comprises of two interacting transmission‐line resonators, each coupled to a qubit. The qubits, driven by independent harmonic fields, are further modulated by a micromechanical resonator mimicked by a phonon mode. The impacts of two independent driving fields on the qubit dynamics are carefully examined. The energy diagram of the system and the photon number mobilization on the resonators are analyzed to explain the behavior of the LZ transitions and qubit dynamics while taking into account the influence of the single phonon mode. Results show that low phonon frequencies can alter the qubit dynamics, particularly in the absence of the driving fields, and a strong phonon coupling strength can significantly perturb the qubit dynamics, thanks to a high influx of phonon energy. Notably, only the photon frequency affects the oscillation frequency of qubit polarization. This study unveils the imperative roles that photons and phonons play in the Rabi dimer model.
We investigate multiple photon-assisted Landau–Zener (LZ) transitions in a hybrid circuit quantum electrodynamics device in which each of two interacting transmission-line resonators is coupled to a qubit, and the qubits are driven by periodic driving fields and also coupled to a common phonon mode. The quantum state of the entire composite system is modeled using the multi-D2 Ansatz in combination with the time-dependent Dirac–Frenkel variational principle. Applying a sinusoidal driving field to one of the qubits, this device is an ideal platform to study the photon-assisted LZ transitions by comparing the dynamics of the two qubits. A series of interfering photon-assisted LZ transitions takes place if the photon frequency is much smaller than the driving amplitude. Once the two energy scales are comparable, independent LZ transitions arise and a transition pathway is revealed using an energy diagram. It is found that both adiabatic and nonadiabatic transitions are involved in the dynamics. Used to model environmental effects on the LZ transitions, the common phonon mode coupled to the qubits allows for more available states to facilitate the LZ transitions. An analytical formula is obtained to estimate the short time phonon population and produces results in reasonable agreement with numerical calculations. Equipped with the knowledge of the photon-assisted LZ transitions in the system, we can precisely manipulate the qubit state and successfully generate the qubit dynamics with a square-wave pattern by applying driving fields to both qubits, opening up new venues to manipulate the states of qubits and photons in quantum information devices and quantum computers.
Recent progress on qubit manipulation allows application of periodic driving signals on qubits. In this study, a harmonic driving field is added to a Rabi dimer to engineer photon and qubit dynamics in a circuit quantum electrodynamics device. To model environmental effects, qubits in the Rabi dimer are coupled to a phonon bath with a sub-Ohmic spectral density. A nonperturbative treatment, the Dirac-Frenkel time-dependent variational principle together with the multiple Davydov D2 ansatz, is employed to explore the dynamical behavior of the tunable Rabi dimer. In the absence of the phonon bath, the amplitude damping of the photon number oscillation is greatly suppressed by the driving field, and photons can be created, thanks to the resonance between the periodic driving field and the photon frequency. In the presence of the phonon bath, one can still change the photon numbers in two resonators and indirectly alter the photon imbalance in the Rabi dimer by directly varying the driving signal in one qubit. It is shown that qubit states can be manipulated directly by the harmonic driving. The environment is found to strengthen the interqubit asymmetry induced by the external driving, opening up a new venue to engineer the qubit states.
Abstract A Rabi dimer is used to model a recently reported circuit quantum electrodynamics system composed of two coupled transmission‐line resonators with each being coupled to one qubit. In this study, a phonon bath is adopted to mimic the multimode micromechanical resonators and is coupled to the qubits in the Rabi dimer. The dynamical behavior of the composite system is studied by the Dirac–Frenkel time‐dependent variational principle combined with the multiple Davydov D2 ansätze. Initially, all the photons are pumped into the left resonator, and the two qubits are in the down state coupled with the phonon vacuum. In the strong qubit–photon coupling regime, the photon dynamics can be engineered by tuning the qubit–bath coupling strength α and photon delocalization is achieved by increasing α. In the absence of dissipation, photons are localized in the initial resonator. Nevertheless, with moderate qubit–bath coupling, photons are delocalized with quasiequilibration of the photon population in two resonators at long times. In this case, high‐frequency bath modes are activated by interacting with depolarized qubits. For strong dissipation, photon delocalization is achieved via frequent photon‐hopping within two resonators and the qubits are suppressed in their initial down state.
Abstract Recent developments in qubit engineering make circuit quantum electrodynamics devices promising candidates for the study of Bloch oscillations (BOs) and Landau–Zener (LZ) transitions. In this work, a hybrid circuit chain with alternating site energies under external electric fields is employed to study Bloch–Zener oscillations (BZOs), i.e. coherent superpositions of BOs and LZ transitions. We couple each of the tunable qubits in the chain to dispersionless optical phonons and build an extended Holstein polaron model with the purpose of investigating vibronic effects in the BZOs. We employ an extension of the Davydov ansatz in combination with the Dirac–Frenkel time-dependent variational principle to simulate the dynamics of the qubit chain under the influence of high-frequency quantum harmonic oscillators. Band gaps emerge due to energy differences in site energies at alternating qubit sites, and are shown to play key roles in tuning band structures and time periodic reconstructions of the wave patterns. In the absence of qubit–phonon interactions, the qubits undergo either standard BZOs or breathing modes, depending on whether the initial wave packet is formed by a broad or narrow Gaussian wave packet, respectively. The BZOs can get localized in space if the band gaps are sufficiently large. In the presence of qubit–phonon coupling, the periodic behavior of BZOs can be washed out and undergo dynamic localization. The influence of an ohmic bath on the dynamics of BZOs is investigated by means of a Markovian master equation approach. Finally, we calculate the von Neumann entropy as a measure of the entanglement between qubits and phonons.
In article number 1800351, Yang Zhao and co-workers adopt the Dirac–Frenkel time-dependent variational principle combined with multiple Davydov D2 ansätze to investigate the dynamical behavior of Rabi dimers with qubits coupled to a phonon bath. Photons can hop between two transmission-line resonators with a tunneling rate J. In each resonator, a qubit interacts with the photon mode with a coupling strength g. Two qubits are also coupled to a common phonon bath with a strength d, which can be used to engineer photon delocalization.
We investigate the many-body Landau-Zener (LZ) process in a two-site Bose-Hubbard model driven by a time-periodic field. We find that the driving field may induce sideband transitions in addition to the main LZ transitions. These photon-induced sideband transitions are a signature of the photon-assisted tunneling in our many-body LZ process. In the Rabi regime, where the system is dominated by the intermode coupling, the system can be looked as an ensemble of identical noninteracting single-particle LZ systems and the photon-induced sideband transitions are similar to the ones in single-particle LZ systems. In the Fock regime, where the system is dominated by the interparticle interaction, we develop an analytical theory for understanding the sideband transitions, which is confirmed by our numerical simulation. Furthermore, we discuss the quantization of the driving field. In the effective model of the quantized driving field, the sideband transitions can be understood as the LZ transitions between states of different ``photon'' numbers.