[Paper Review] Quantum catalysis in cavity quantum electrodynamics

A. de Oliveira, Martí Perarnau-Llobet+2 more|arXiv (Cornell University)|May 30, 2023

Quantum Information and Cryptography66 references4 citations

TL;DR

This paper demonstrates deterministic quantum catalysis in the Jaynes-Cummings model, where a two-level atom acts as a catalyst to generate non-classical light in a cavity without being consumed. By engineering the atomic state and interaction time, the cavity evolves into a non-classical state—evidenced by sub-Poissonian statistics or Wigner negativity—while the atom is returned to its initial state exactly, enabling reuse.

ABSTRACT

Catalysis plays a key role in many scientific areas, most notably in chemistry and biology. Here we present a catalytic process in a paradigmatic quantum optics setup, namely the Jaynes-Cummings model, where an atom interacts with an optical cavity. The atom plays the role of the catalyst, and allows for the deterministic generation of non-classical light in the cavity. Considering a cavity prepared in a ``classical'' coherent state, and choosing appropriately the atomic state and the interaction time, we obtain an evolution with the following properties. First, the state of the cavity has been modified, and now features non-classicality, as witnessed by sub-Poissonian statistics or Wigner negativity. Second, the process is catalytic, in the sense that the atom is deterministically returned to its initial state exactly, and can be re-used multiple times. What is more, we also show that our findings are robust under dissipation and can be applied to scenarios featuring cavity loss and atomic decay. Finally, we investigate the mechanism of this catalytic process, in particular highlighting the key role of correlations and quantum coherence.

Motivation & Objective

• To demonstrate that quantum catalysis, previously studied in abstract resource theories, can be realized in a realistic quantum optics platform.
• To investigate whether a two-level atom can act as a catalyst to generate non-classical states in a cavity without being permanently altered.
• To identify the quantum resources—specifically correlations and quantum coherence—enabling this catalytic process.
• To explore the conditions under which catalytic non-classicality generation is possible, including dependence on initial cavity and atomic states.
• To assess the potential for experimental implementation in cavity QED or trapped ion systems.

Proposed method

• Utilizes the Jaynes-Cummings Hamiltonian to model the interaction between a two-level atom and a single-mode optical cavity.
• Imposes a unitary evolution $ U = \exp(-iH_{\text{SC}}\tau) $ over a carefully chosen interaction time $ \tau $, ensuring the atom returns to its initial state.
• Analyzes the final state of the cavity to detect non-classicality via $ g^{(2)} < 1 $ (sub-Poissonian statistics) or Wigner negativity.
• Employs quantum state tomography and correlation analysis to verify the catalytic nature and quantify non-classicality.
• Investigates the role of quantum coherence in the catalyst by analyzing superpositions in the atomic energy basis.
• Performs numerical simulations with bounds on interaction strength ($ g\tau \leq 100 $) to explore the catalytic parameter space.

Figure 1: Quantum catalysis in the Jaynes-Cummings model. (a) An atom (the catalyst C ) interacts with a single-mode optical cavity (the system S ), initially prepared in a “classical” coherent state. (b) We consider the evolution $U$ over a well-chosen time interval (from $t=0$ to $t=\tau$ ) such t

Experimental results

Research questions

• RQ1 Can a two-level atom act as a deterministic catalyst to generate non-classical light in a cavity QED system?
• RQ2 What are the necessary quantum resources—correlations or coherence—for such catalytic non-classicality generation?
• RQ3 How does the initial atomic state influence the ability to catalytically generate non-classicality in the cavity?
• RQ4 Is the catalytic process robust across different initial cavity states, including coherent and Fock states?
• RQ5 Can the catalytic protocol be generalized to boost existing non-classicality in the cavity?

Key findings

• The cavity state achieves sub-Poissonian statistics ($ g^{(2)} < 1 $) for all $ \alpha \in (0,2] $, confirming non-classicality generation.
• The atom is returned to its initial state exactly after the interaction, satisfying the condition for deterministic catalysis.
• Non-classicality generation is generic in the regime $ g\tau \leq 100 $, with $ g^{(2)} $ approaching zero for low-energy coherent states.
• Pure atomic states cannot catalytically generate non-classicality due to the absence of system-catalyst correlations.
• The catalytic set of atomic states includes nearly pure states, indicating a strong dependence on the initial cavity state.
• Catalysis can enhance existing non-classicality in the cavity when starting from states with moderate non-classicality, but cannot increase it beyond the Fock state limit.

Figure 2: First illustrative example. Catalytic process for generating non-classicality in the cavity, as captured by the second-order auto-correlation function. Its time evolution, $g^{(2)}(t):=g^{(2)}(\sigma_{\textsf{S}}(t))$ , is shown in the top panel, while the bottom panel shows the modificati