[Paper Review] Probing non-classical light fields with energetic witnesses in Waveguide Quantum Electro-Dynamics

Maria Maffei, Patrice A. Camati+1 more|arXiv (Cornell University)|Jan 1, 2021

Quantum Information and CryptographyComputer Science56 references25 citations

TL;DR

This paper proposes an operational framework to characterize energy exchanges between a qubit and a waveguide light field using energetic witnesses in waveguide quantum electrodynamics. By defining work as energy transfer via unitary interactions and showing that non-classical light pulses violate the classical ergotropy bound, the study establishes a quantitative, energy-based witness for quantum non-classicality in light fields.

ABSTRACT

We analyze energy exchanges between a qubit and a resonant field propagating in a waveguide. The joint dynamics is analytically solved within a repeated interaction model. The work received by the qubit is defined as the unitary component of the field-induced energy change. Using the same definition for the field, we show that both work flows compensate each other. Focusing on the charging of a qubit battery by a pulse of light, we evidence that the work provided by a coherent field is an upper bound for the qubit ergotropy, while this bound can be violated by non-classical fields, e.g. a coherent superposition of zero- and single-photon states. Our results provide operational, energy-based witnesses to probe the non-classical nature of a light field.

Motivation & Objective

• To develop an operational, energy-based framework for characterizing work and correlation energy flows in coupled quantum systems.
• To establish a quantitative link between energy extraction efficiency and quantum non-classicality in light fields.
• To demonstrate that quantum light pulses violate classical bounds on extractable work, enabling detection of non-classicality.
• To provide a symmetric, unified treatment of work providers and receivers in quantum energy exchange protocols.
• To validate the framework in the analytically solvable waveguide QED platform, where light-matter interactions are fully coherent and isolated.

Proposed method

• Defines work as the component of energy flow stemming from effective unitary interactions between two isolated quantum systems (qubit and light field).
• Introduces a scenario where energy is locally injected to prepare a product state, then exchanged during unitary interaction, followed by local work extraction.
• Uses the von Neumann-Liouville equation in the interaction picture to derive reduced dynamics for each subsystem, separating unitary (work) and non-unitary (correlation energy) contributions.
• Applies the condition of local energy conservation ([Hq + Hf, V] = 0) and orthogonality of coupling to free Hamiltonians to ensure consistent energy definitions.
• Derives the work flow equation ˙Wk(t) = −i/ℏ Trk{[Hk, Hk(t)]ρk(t)} and correlation energy flow ˙Qk(t) = −i/ℏ Tr{Hk[V(t), χ(t)]} for each system.
• Demonstrates that ˙Wq(t) + ˙Wf(t) = 0 under local energy conservation, confirming a quantum action-reaction principle.

Experimental results

Research questions

• RQ1 Can work and correlation energy flows be operationally distinguished in a bipartite quantum system?
• RQ2 What is the bound on extractable work from a qubit driven by a coherent light pulse, and does it depend on the statistics of the light field?
• RQ3 Can violations of this bound serve as a witness for non-classical light?
• RQ4 How does entanglement between the qubit and light field prevent full local energy recovery?
• RQ5 What is the role of self-reaction work in spontaneous emission within this energetic framework?

Key findings

• The classical ergotropy bound—where work performed on a qubit by a coherent pulse exceeds the extractable work (ergotropy)—is violated when a single-photon pulse drives the qubit.
• This violation provides a direct, operational witness for non-classicality in the light field, as coherent states obey the bound while single-photon states do not.
• The work flows ˙Wq and ˙Wf exactly compensate each other, confirming a quantum version of the action-reaction principle.
• The framework identifies the self-reaction work responsible for spontaneous emission as a distinct component of the total energy exchange.
• In the waveguide QED setup, the total energy exchange is fully unitary and isolated, enabling exact analytical treatment of work and correlation energy flows.
• The results establish that non-classical light fields can be probed via energetic witnesses based on work extraction inefficiency.