[Paper Review] Perfectly capturing traveling single photons of arbitrary temporal wavepackets with a single tunable device

Hendra I. Nurdin, M. R. James+1 more|arXiv (Cornell University)|Sep 19, 2016

Quantum Information and Cryptography24 references3 citations

TL;DR

This paper derives the exact time-dependent coupling function for a tunable quantum system—realizable as a single qubit or resonator—that enables perfect absorption of traveling single photons with any arbitrary temporal wavepacket shape. Using quantum stochastic differential equations and the zero-dynamics principle, the authors show that perfect absorption is theoretically achievable, though the ideal coupling function exhibits a singularity at t=0, necessitating practical truncation and approximation in real devices.

ABSTRACT

We derive the explicit analytical form of the time-dependent coupling parameter to an external field for perfect absorption of traveling single photon fields with arbitrary temporal profiles by a tunable single input-output open quantum system, which can be realized as either a single qubit or single resonator system. However, the time-dependent coupling parameter for perfect absorption has a singularity at $t=0$ and constraints on real systems prohibit a faithful physical realization of the perfect absorber. A numerical example is included to illustrate the absorber's performance under practical limitations on the coupling strength.

Motivation & Objective

• To develop a tunable single-input, single-output quantum system capable of perfectly absorbing single photons with arbitrary temporal wavepacket shapes.
• To address the challenge of state transfer in quantum networks by enabling perfect absorption of arbitrary single-photon states into a matter qubit or resonator.
• To analytically determine the time-varying coupling parameter required for perfect absorption, overcoming limitations of prior mode-matching or symmetric-profile-only approaches.
• To investigate the feasibility of realizing the ideal absorber under physical constraints, particularly the singularity in the coupling function at t=0.
• To evaluate the performance of a truncated, physically realizable approximation of the ideal coupling function through numerical simulation.

Proposed method

• Formalize the system using quantum stochastic differential equations (QSDEs) to model the interaction between a single-photon field and a tunable quantum system.
• Apply the zero-dynamics principle—ensuring no output photons via destructive interference—to derive the necessary coupling function that leads to perfect absorption.
• Solve the QSDEs explicitly to obtain the analytical form of the time-dependent coupling parameter for perfect absorption.
• Re-derive the coupling function using the zero-dynamics principle from control theory, confirming consistency and providing a broader theoretical framework.
• Introduce a practical approximation of the ideal coupling function by truncating its singularity at t=0 and using a continuous, bounded function for numerical evaluation.
• Simulate the system's performance using a numerical example with an exponentially decaying wavepacket and varying truncation times T.

Experimental results

Research questions

• RQ1 What is the exact time-dependent coupling function that enables perfect absorption of a single photon with an arbitrary temporal wavepacket in a tunable quantum system?
• RQ2 Why does the ideal coupling function exhibit a singularity at t=0, and how does this prevent physical realization in real devices?
• RQ3 How does truncating the ideal coupling function affect the absorption fidelity in a practical implementation?
• RQ4 Can the zero-dynamics principle be systematically applied to derive the required coupling modulation for perfect absorption in open quantum systems?
• RQ5 What is the impact of finite truncation time T on the excitation probability of the absorber system in a realistic scenario?

Key findings

• The exact time-dependent coupling parameter for perfect absorption of an arbitrary single-photon wavepacket is analytically derived using QSDEs and the zero-dynamics principle.
• The ideal coupling function has a singularity at t=0, making it physically unrealizable in practice due to unbounded energy requirements.
• Numerical simulations show that truncating the coupling function at t=0 leads to reduced absorption fidelity, with steady-state excitation probabilities of approximately 0.9957, 0.9575, and 0.6037 for T = 0.001t₁, 0.01t₁, and 0.1t₁, respectively.
• The performance degrades with increasing truncation time T, as expected, due to incomplete absorption over the finite time window.
• The system can be realized as a single qubit or resonator with tunable coupling, such as in microwave superconducting circuits with variable inductance.
• The derived coupling function ensures that the output field contains no photons (zero output dynamics), confirming perfect absorption in the ideal case.