Engineering Photon Delocalization in a Rabi Dimer with a Dissipative Bath

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 D 2 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.circuit QED architectures have been designed and fabricated as research platforms in quantum computation [2,[6][7][8][9][10][11][12] and quantum information. [13][14][15][16] Due to high flexibility and tunability, circuit QED devices offer the possibility to simulate light-matter interactions in quantum systems with an integrated circuit. [1,10,12,17,18] Experiments focus on engineering the coupling between a single resonator and a qubit for controllable single-resonator systems. [19][20][21] A key challenge is to carry out quantum simulations of strongly correlated photons of coupled-resonator systems by controlling the inter-resonator photon coupling and device-environment interactions. [22,23] It gives rise to an interesting phenomenon of photon self-trapping due to the competition between the qubit-photon coupling and the inter-resonator photon hopping, which has been realized in experiment using transmon qubits and two coupled transmission-line resonators. [24] Another QED system composed of two coupled nonlinear resonators has been fabricated for quantum amplification. [25] Described as a Bose-Hubbard dimer, this device can also be used for photon generation. [26][27][28][29][30] Recent theoretical studies model the tunnel-coupled resonators each containing a qubit as a Jaynes-Cumming (JC) dimer, which is the smallest possible coupled-resonator system. [3,4,24,31,32] The JC Hamiltonian describes a QED system with weak qubit-photon coupling, which omits the counterrotating-wave (CRW) interactions between the qubit and the photon mode. [33] Experimental progress has made it possible to achieve ultra-strong coupling, [1,[34][35][36][37] where the qubit-photon coupling strength is comparable to the resonator frequency. In this regime, the JC...

Photon-assisted Landau-Zener transitions in a periodically driven Rabi dimer coupled to a dissipative mode

“…Both the left and right qubits are initially prepared in their down states with A n (t = 0) = B n (t = 0) = C n (t = 0) = D n =1 (t = 0) = 0 and D 1 (t = 0) = 1. The convergence of our method has been proved in our previous work [37]. Balancing between accuracy and computational cost, we choose multiplicity M = 6.…”

“…In contrast to the constant energy spacings of the two qubits in Ref. [37], here we make them tunable by imposing a periodic harmonic driving field F i cos(Ω i t+Φ i ) independently on each of the two qubits. In the ith (i = L, R) Rabi system, a photon mode with frequency ω i is coupled to a qubit with an interaction strength g i .…”

“…In a bare resonant Rabi dimer given by Hamiltonian (2), where each of the two coupled photon modes interacts with a qubit individually and the photon frequency is the same as the qubit bias, the dynamics of the photons and the qubits are governed by the competitive effects of the qubit-photon coupling g and the inter-resonator photon hopping rate J [36,37]. Hwang et al constructed a phase diagram of the time-averaged photon imbalance Z(t) with respect to g and J for this system, and discovered localized and delocalized photonic phases [36].…”

“…It is known that the photon-assisted LZ transition probability is dependent on the average photon number in the resonator [64] and a fast change of the average photon number during the transition time may lead to a large deviation from the standard LZ transition phenomena. To better understand the LZ transition in the Rabi dimer with periodic driving, we adopt a small photon tunneling rate J = 0.01 ω 0 and a relatively strong qubit-photon coupling strength g = 0.3 ω 0 , leading to a photon localization in the bare resonant Rabi dimer system [36,37].…”

“…By cal-culating time-averaged photon imbalance under different qubit-photon coupling strengths and photon tunneling rates, they discovered three photonic phases [36]. Recently the effects of a phonon environment and an external driving field on the dynamics of qubits and photons in the Rabi dimer have been elucidated in various parameter regimes using the time-dependent variational principle with the multiple Davydov D 2 Ansatz [37,38]. However, the LZ transitions and their susceptibility to environmental effects in this Rabi dimer system have not been well investigated, in contrast to systematically studied LZ transitions in single-qubit QED devices.…”