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arXiv:1601.05148 · Physical Review A

Polariton states in circuit QED for electromagnetically induced transparency

Xiu Quan Gu, Sainan Huai, Franco Nori, Yu-xi Liu

Published Jun 14, 2016• 35 citations
arXivHTMLPDF

Abstract

Electromagnetically induced transparency (EIT) has been extensively studied in various systems. However, it is not easy to observe in superconducting quantum circuits (SQCs) because the Rabi frequency of the strong-controlling field corresponding to EIT is limited by the decay rates of the SQCs. Here, we show that EIT can be achieved by engineering decay rates in a superconducting circuit QED system through a classical driving field on the qubit. Without such a driving field, the dressed states of the system, describing a superconducting qubit coupled to a cavity field, are approximately product states of the cavity and qubit states in the large-detuning regime. However, the driving field can strongly mix these dressed states. These doubly dressed states, here called polariton states, are formed by the driving field and dressed states, and are a mixture of light and matter. The weights of the qubit and cavity field in the polariton states can now be tuned by the driving field, and thus the decay rates of the polariton states can be changed. We choose the three lowest-energy polariton states with a $\mathrm{\ensuremath{\Lambda}}$-type transition in such a driven circuit QED system, and demonstrate how EIT and Autler-Townes splitting can be realized in this compound system. We believe that this study will be helpful for EIT experiments using SQCs.

DOI
10.1103/physreva.93.063827

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Electromagnetically induced transparency (EIT) has been extensively studied in various systems. However, it is not easy to observe in superconducting quantum circuits (SQCs) because the Rabi frequency of the strong-controlling field corresponding to EIT is limited by the decay rates of the SQCs. Here, we show that EIT can be achieved by engineering decay rates in a superconducting circuit QED system through a classical driving field on the qubit. Without such a driving field, the dressed states of the system, describing a superconducting qubit coupled to a cavity field, are approximately product states of the cavity and qubit states in the large-detuning regime. However, the driving field can strongly mix these dressed states. These doubly dressed states, here called polariton states, are formed by the driving field and dressed states, and are a mixture of light and matter. The weights of the qubit and cavity field in the polariton states can now be tuned by the driving field, and thus the decay rates of the polariton states can be changed. We choose the three lowest-energy polariton states with a \ensuremathΛ\mathrm{\ensuremath{\Lambda}}\ensuremathΛ-type transition in such a driven circuit QED system, and demonstrate how EIT and Autler-Townes splitting can be realized in this compound system. We believe that this study will be helpful for EIT experiments using SQCs.
We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in a driven three-level superconducting artificial system which is a dressed-state system resulting from the coupling of a superconducting charge qubit (an artificial atom) and a transmission line resonator. In the frame of the dressed-state approach and steady-state approximation, we study the linear absorption of the dressed artificial system to a weak probe signal in depth. In light of the spectrum-decomposition method and some other restrictions, we obtain the explicit conditions for the dressed-state realization of EIT and ATS and present a corresponding "phase diagram". In contrast to usual bare systems, these conditions given in the dressed system have an extra dependency on the qubit-resonator parameters. And by varying the qubit's Josephson coupling energy we demonstrate a transition from EIT to ATS.
Electromagnetically induced transparency (EIT) has been realized in atomic systems, but fulfilling the EIT conditions for artificial atoms made from superconducting circuits is a more difficult task. Here we report an experimental observation of the EIT in a tunable three-dimensional transmon by probing the cavity transmission. To fulfill the EIT conditions, we tune the transmon to adjust its damping rates by utilizing the effect of the cavity on the transmon states. From the experimental observations, we clearly identify the EIT and Autler-Townes splitting (ATS) regimes as well as the transition regime in between. Also, the experimental data demonstrate that the threshold ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{AIC}}$ determined by the Akaike information criterion can describe the EIT-ATS transition better than the threshold ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{EIT}}$ given by the EIT theory.
We study the microwave absorption of a driven three-level quantum system, which is realized by a superconducting flux quantum circuit (SFQC), with a magnetic driving field applied to the two upper levels. The interaction between the three-level system and its environment is studied within the Born-Markov approximation, and we take into account the effects of the driving field on the damping rates of the three-level system. We study the linear response of the driven three-level SFQC to a weak probe field. The linear magnetic susceptibility of the SFQC can be changed by both the driving field and the bias magnetic flux. When the bias magnetic flux is at the optimal point, the transition from the ground state to the second-excited state is forbidden and the three-level SFQC has a ladder-type transition. Thus, the SFQC responds to the probe field like natural atoms with ladder-type transitions. However, when the bias magnetic flux deviates from the optimal point, the three-level SFQC has a cyclic transition, thus it responds to the probe field like a combination of natural atoms with ladder-type transitions and natural atoms with $\ensuremath{\Lambda}$-type transitions. In particular, we provide detailed discussions on the conditions for realizing electromagnetically induced transparency and Autler-Townes splitting in three-level SFQCs.
We explore theoretically electromagnetically induced transparency (EIT) in a superconducting quantum circuit (SQC). The system is a persistent-current flux qubit biased in a $\ensuremath{\Lambda}$ configuration. Previously [Phys. Rev. Lett. 93, 087003 (2004)], we showed that an ideally prepared EIT system provides a sensitive means to probe decoherence. Here, we extend this work by exploring the effects of imperfect dark-state preparation and specific decoherence mechanisms (population loss via tunneling, pure dephasing, and incoherent population exchange). We find an initial, rapid population loss from the $\ensuremath{\Lambda}$ system for an imperfectly prepared dark state. This is followed by a slower population loss due to both the detuning of the microwave fields from the EIT resonance and the existing decoherence mechanisms. We find analytic expressions for the slow loss rate, with coefficients that depend on the particular decoherence mechanisms, thereby providing a means to probe, identify, and quantify various sources of decoherence with EIT. We go beyond the rotating wave approximation to consider how strong microwave fields can induce additional off-resonant transitions in the SQC, and we show how these effects can be mitigated by compensation of the resulting ac Stark shifts.
Electromagnetically induced transparency and absorption (EIT and EIA) are usually demonstrated using three-level atomic systems. In contrast to the usual case, we theoretically study the EIT and EIA in an equivalent three-level system: a superconducting two-level system (qubit) dressed by a single-mode cavity field. In this equivalent system, we find that both the EIT and the EIA can be tuned by controlling the level-spacing of the superconducting qubit and hence controlling the dressed system. This tunability is due to the dressed relaxation and dephasing rates which vary parametrically with the level-spacing of the original qubit and thus affect the transition properties of the dressed qubit and the susceptibility. These dressed relaxation and dephasing rates characterize the reaction of the dressed qubit to an incident probe field. Using recent experimental data on superconducting qubits (charge, phase, and flux qubits) to demonstrate our approach, we show the possibility of experimentally realizing this proposal.
A superconducting qubit coupled to a readout resonator is currently the building block of multiple quantum computing as well as quantum optics experiments. A typical qubit-resonator system is coupled in the dispersive regime, where the detuning between qubit and resonator is much greater than the coupling between them. In this work, we fabricated and measured a superconducting transmon-resonator system in the nondispersive regime. The dressed states formed by the mixing of the bare qubit and resonator states can be further mixed by applying a drive on the qubit, leading to the formation of polariton states. We report experimental studies of transitions between polariton states at varying driving powers and frequencies and show how the nondispersive coupling of the higher levels of the qubit-resonator system modifies the polariton eigenstates and the corresponding transition frequencies. We also report close agreement with numerical results obtained from a driven Jaynes-Cummings model beyond the dispersive regime.