Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED (0812.2651v2)

Abstract: We present an ideal realization of the Tavis-Cummings model in the absence of atom number and coupling fluctuations by embedding a discrete number of fully controllable superconducting qubits at fixed positions into a transmission line resonator. Measuring the vacuum Rabi mode splitting with one, two and three qubits strongly coupled to the cavity field, we explore both bright and dark dressed collective multi-qubit states and observe the discrete square root of N scaling of the collective dipole coupling strength. Our experiments demonstrate a novel approach to explore collective states, such as the W-state, in a fully globally and locally controllable quantum system. Our scalable approach is interesting for solid-state quantum information processing and for fundamental multi-atom quantum optics experiments with fixed atom numbers.

• The paper confirms the discrete √N scaling of collective dipole coupling strength in a circuit QED setup.
• The study observes both bright and dark dressed states, revealing intricate qubit-cavity interaction dynamics.
• The results robustly verify Tavis-Cummings predictions, offering practical insights for quantum state engineering in multi-qubit systems.

Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED

The paper presents an experimental paper of the Tavis-Cummings model using superconducting qubits embedded in a transmission line resonator, establishing a novel pathway to explore collective quantum states in a controlled setup. By investigating systems with one, two, and three qubits resonantly coupled to a cavity field, this research demonstrates the discrete $\sqrt{N}$ scaling of the collective dipole coupling strength, a key prediction of the Tavis-Cummings model.

Experimental Setup and Methodology

The experiment utilized three transmon-type superconducting qubits positioned at the antinodes of a microwave resonator's electric field. This configuration ensured maximal and uniform coupling to the cavity mode, effectively minimizing fluctuations in atom number and coupling. The resonator, with a photon decay rate of $\kappa/2\pi=6.8$ MHz and a resonance frequency of $\omega_\textrm{r}/2\pi=6.729$ GHz, provided a platform to accurately measure the vacuum Rabi mode splitting. The qubit transition frequencies were independently controlled through magnetic flux, allowing the researchers to explore various coupling scenarios between the qubits and the cavity field.

Key Findings

1. Discrete $\sqrt{N}$ Scalability: The paper confirms the $\sqrt{N}$ scaling of the collective interaction strength, consistent with the Tavis-Cummings model. The strong coupling of the qubits to the cavity field enabled clear observation of this scaling, further validated by numerically accurate predictions without adjustable parameters.
2. Bright and Dark States: The resonant interaction leads to both bright and dark dressed collective states. The experimental setup allowed observation of these states in a spectroscopically clean manner, with bright states, such as the $W$-state, being easily excited and visible in the transmission spectrum. The presence of dark states illustrated the complex symmetries and interaction characteristics inherent in multi-qubit systems.
3. Verification of Theoretical Predictions: Through systematic measurements of one, two, and three qubits interacting with the cavity field, the research validated theoretical predictions by accurately matching measured coupling strengths to those forecasted by the model.

Implications and Future Directions

This research has notable implications for solid-state quantum information processing, particularly in exploring new quantum states that are not reliant on single-qubit operations. The ability to reliably create and manipulate collective qubit states, such as the $W$-state, opens avenues for quantum state engineering and possibly Heisenberg-limited spectroscopy using multi-qubit entangled states.

Future developments could include the controlled generation of Dicke states, exploiting flux tuning on nanosecond timescales. Furthermore, this scalable approach could lead to enhanced understanding and development of super- and sub-radiant states in artificial atoms, fostering advancements in collective quantum phenomena and quantum information theories.

Overall, this work enriches the field of circuit QED and provides a robust experimental framework for testing and understanding collective quantum interactions in a highly controlled environment.