[Paper Review] Strong coupling between a single-photon and a two-photon Fock state

Shuai-Peng Wang, Alberto Mercurio+10 more|arXiv (Cornell University)|Jan 5, 2024

Mechanical and Optical Resonators4 citations

TL;DR

This paper demonstrates strong coupling between a single photon and a two-photon Fock state in an ultrastrongly-coupled circuit-QED system using a detuned flux qubit as a nonlinear coupler. The experiment resolves quantum Rabi-like avoided crossings and observes second harmonic generation at mean photon numbers below one, enabling deterministic, coherent photon-photon interactions without external driving fields.

ABSTRACT

The realization of strong nonlinear coupling between single photons has been a long-standing goal in quantum optics and quantum information science, promising wide impact applications, such as all-optical deterministic quantum logic and single-photon frequency conversion. Here, we report an experimental observation of the strong coupling between a single-photon and a two-photon Fock state in an ultrastrongly-coupled circuit-QED system. This strong nonlinear interaction is realized by introducing a detuned flux qubit working as an effective coupler between two modes of a superconducting coplanar waveguide resonator. The ultrastrong light--matter interaction breaks the excitation number conservation, and an external flux bias breaks the parity conservation. The combined effect of the two enables the strong one--two-photon coupling. Quantum Rabi-like avoided crossing is resolved when tuning the two-photon resonance frequency of the first mode across the single-photon resonance frequency of the second mode. Within this new photonic regime, we observe the thresholdless second harmonic generation for a mean photon number below one. Our results represent a key step towards a new regime of quantum nonlinear optics, where individual photons can deterministically and coherently interact with each other in the absence of any stimulating fields.

Motivation & Objective

• To achieve strong nonlinear coupling between single-photon and two-photon Fock states in a superconducting circuit-QED platform.
• To overcome the challenge of negligible photon-photon interactions at the single-photon level in conventional optical media.
• To realize deterministic, coherent interactions between individual photons without external stimulating fields or atomic excitation.
• To explore a new regime of quantum nonlinear optics where individual photons can coherently interact via ultrastrong light-matter coupling.
• To demonstrate second harmonic generation at mean photon numbers below one, indicating strong effective photon-photon interaction.

Proposed method

• Employed a superconducting coplanar waveguide resonator with two distinct modes (n=1 and n=2) coupled via a detuned flux qubit acting as an effective nonlinear coupler.
• Utilized a three-junction flux qubit with optimized Josephson energy and charging energy to enable ultrastrong coupling and break excitation number conservation.
• Applied an external flux bias to break parity symmetry, enabling transitions between even- and odd-number photon states.
• Engineered the system to achieve comparable transition matrix elements between bare states |2,0,g⟩ and |0,1,g⟩ at the anticrossing point, enabling strong effective coupling.
• Used generalized master equations and eigenstate-based input-output relations to model the time evolution and field dynamics in the ultrastrong coupling regime.
• Performed microwave spectroscopy to resolve avoided level crossings between single-photon and two-photon resonances, confirming strong coupling.

Figure 1: $|$ Setup. a, Schematic of the device. A flux qubit embedded in a ${\lambda}/{2}$ coplanar waveguide resonator, working as a nonlinear coupler between two modes of the resonator. The dashed cyan lines represent the vacuum current distribution of the $n=1$ ( ${\lambda}/{2}$ ) and $n=2$ ( $\

Experimental results

Research questions

• RQ1 Can strong coupling be experimentally realized between a single-photon Fock state and a two-photon Fock state in a circuit-QED system?
• RQ2 What role does ultrastrong light-matter coupling and parity breaking play in enabling effective photon-photon interactions at the single-photon level?
• RQ3 Can second harmonic generation be observed at mean photon numbers below one, indicating deterministic photon fusion?
• RQ4 How does the effective coupling strength compare to losses, and what is the potential for near-unity efficiency in single-photon to photon-pair conversion?
• RQ5 To what extent can the generalized quantum Rabi Hamiltonian describe the observed dynamics in the ultrastrong coupling regime?

Key findings

• The experiment observed a resolved quantum Rabi-like avoided crossing between the single-photon resonance of the second mode and the two-photon resonance of the first mode, confirming strong coupling.
• Second harmonic generation was observed with a mean photon number below one, indicating deterministic, coherent fusion of a single photon into a photon pair.
• The effective coupling strength $ g_{\rm eff} $ was large enough to enable Rabi oscillations with a period $ T_R = 2\pi / g_{\rm eff} $, suggesting potential for near-100% conversion efficiency.
• The system exhibited simultaneous mixing of even- and odd-number photon states due to ultrastrong coupling and broken parity, a hallmark of the generalized quantum Rabi model.
• The transition matrix elements between the key states |2,0,g⟩ and |0,1,g⟩ were comparable in magnitude (~1), enabling strong effective coupling despite large detuning.
• The results demonstrate a new regime of quantum nonlinear optics where individual photons interact coherently without external driving or atomic excitation, enabling deterministic quantum optics operations.

Figure 2: $|$ Quantum Rabi-like splitting. Quantum Rabi-like splitting between a single photon and a photon pair. The left part in each panel (negative flux offset) reports the measured spectra. The corresponding calculated spectra are reported for positive flux offset (right), using the parity symm