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arXiv:1811.03878 · Annalen der Physik

Engineering Photon Delocalization in a Rabi Dimer with a Dissipative Bath

Fulu Zheng, Yuyu Zhang, Lu Wang, Yadong Wei, Yang Zhao

Published Nov 15, 2018• 7 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/andp.201800351

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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.
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.
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 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.
ABSTRACT We investigate the dynamics of two spins that are simultaneously coupled to a high‐Q cavity and an Ohmic phonon bath using the Dirac–Frenkel time‐dependent variational principle together with two types of the multiple Davydov ansatz. In our framework, the cavity mode can either be treated as part of the bath modes within the multi‐D 2 ansatz or regarded together with the spins as a dressed composite system within the multi‐D 1 ansatz. Although both approaches yield consistent results for the spin, cavity, and phonon observables, the multi‐D 1 ansatz proves to be numerically much more efficient than the multi‐D 2 ansatz. In the regime of relatively weak spin‐bath coupling, we find that the cavity induces intricate beat patterns in the spin population dynamics as well as multipeaked phonon spectra. These cavity‐related features can also be reproduced by a polaron‐like transformed Nakajima–Zwanzig master equation, where the multipeaked phonon spectra arise from transitions between dressed states. By contrast, under relatively strong spin‐bath coupling, both the beat patterns and the multipeaked phonon spectra become suppressed. Furthermore, even with strong spin‐cavity coupling, sufficiently strong spin‐bath interaction leads to spin localization, reminiscent of the single‐spin spin‐boson model. Overall, our results reveal how spin‐bath and spin‐cavity couplings compete to shape the dissipative dynamics.
The quantum Rabi model (QRM), composed of a qubit interacting with a quantized photonic field, is a cornerstone of quantum optics. The QRM with dominant unitary dynamics has been demonstrated in circuit quantum electrodynamics (QED) systems, but an open QRM with a strong photonic dissipation has not been experimentally explored. We here present the first experimental demonstration of such an open system in circuit QED, featuring a controlled competition between the coherent qubit-field interaction and the photonic dissipation. We map out the photon number distributions of the dissipative resonator for different coupling strengths in the steady state. We further observe the variation of the photon number during the system’s evolution toward the steady state with fixed control parameters. The results demonstrate that the system’s behavior is significantly modified by photonic dissipation.