Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System (0902.1827v1)

Abstract: The already very active field of cavity quantum electrodynamics (QED), traditionally studied in atomic systems, has recently gained additional momentum by the advent of experiments with semiconducting and superconducting systems. In these solid state implementations, novel quantum optics experiments are enabled by the possibility to engineer many of the characteristic parameters at will. In cavity QED, the observation of the vacuum Rabi mode splitting is a haLLMark experiment aimed at probing the nature of matter-light interaction on the level of a single quantum. However, this effect can, at least in principle, be explained classically as the normal mode splitting of two coupled linear oscillators. It has been suggested that an observation of the scaling of the resonant atom-photon coupling strength in the Jaynes-Cummings energy ladder with the square root of photon number n is sufficient to prove that the system is quantum mechanical in nature. Here we report a direct spectroscopic observation of this characteristic quantum nonlinearity. Measuring the photonic degree of freedom of the coupled system, our measurements provide unambiguous, long sought for spectroscopic evidence for the quantum nature of the resonant atom-field interaction in cavity QED. We explore atom-photon superposition states involving up to two photons, using a spectroscopic pump and probe technique. The experiments have been performed in a circuit QED setup, in which ultra strong coupling is realized by the large dipole coupling strength and the long coherence time of a superconducting qubit embedded in a high quality on-chip microwave cavity.

• The paper demonstrates the direct observation of √n nonlinearity using pump-probe spectroscopy in a circuit QED setup.
• It establishes strong coupling between a superconducting qubit and cavity photons, with vacuum Rabi splitting exceeding 100 linewidths.
• The study reveals the impact of higher qubit levels on spectral splitting, advancing prospects for quantum information and communication technologies.

Observations of Jaynes-Cummings Nonlinearity in a Cavity QED System

The paper "Climbing the Jaynes-Cummings Ladder and Observing its $\sqrt{n}$ Nonlinearity in a Cavity QED System" presents a significant advance in the paper of quantum mechanics through cavity quantum electrodynamics (QED). The research achieves a direct spectroscopic observation of the Jaynes-Cummings model's predicted nonlinearity, which scales with the square root of the photon number, $n$. This result is crucial as it provides clear evidence of the quantum nature of atom-photon interactions, distinguishing it from classical models.

Methodology

The experimental setup is grounded in a circuit QED architecture, involving a superconducting qubit embedded in a microwave cavity. The qubit, engineered as a transmon, achieves ultra-strong coupling with the photonic mode due to its large dipole moment and extended coherence time. This system's design addresses traditional challenges in cavity QED systems, such as the need for high coherence and strong coupling, which are essential for observing quantum phenomena at the single-photon level.

Main Results

1. Strong Coupling and Spectroscopy: The research demonstrates strong coupling between a superconducting qubit and cavity photons. Vacuum Rabi splitting was observed, with a mode splitting exceeding 100 linewidths, clearly demonstrating the strong coupling regime.
2. Observation of $\sqrt{n}$ Nonlinearity: Through a pump and probe technique, researchers selectively populated and probed transitions between Jaynes-Cummings ladder states. The $|1\pm\rangle$ and $|2\pm\rangle$ states exhibited characteristic splittings, aligning with the $\sqrt{2}$ scaling predicted by the Jaynes-Cummings model.
3. Higher Qubit Levels: The paper also considers the impact of higher qubit states on the observable splitting in the Jaynes-Cummings ladder, particularly the $|f,0\rangle$ state, which exerts subtle yet observable shifts in the spectral lines.

Implications and Future Directions

The implications of this work extend to several domains within quantum information science and quantum optics. By validating the distinct quantum mechanical nature of the atom-photon interaction via spectroscopic means, this research lays groundwork for more advanced quantum technologies:

• Quantum Information Processing: The strong nonlinear interaction at the single-photon level can be harnessed for quantum logic gates, photon-mediated entanglement, and other quantum computational operations.
• Quantum Communication: Circuit QED systems represent a robust interface between stationary and flying qubits, offering promising pathways for quantum networking and secure communication channels.
• Further Studies: The demonstrated methodology opens prospects for exploring multi-photon states and entangled states in complex quantum systems. Investigations can extend into time-resolved Rabi oscillation studies with photon number states and potential multi-photon quantum dynamics.

Overall, this paper contributes valuable insights into circuit QED systems, highlighting the potential for exploiting quantum nonlinearities in practical applications. This research stands as a pivotal example of how quantum mechanics continues to foster innovation across computing, communications, and fundamental physics.