[Paper Review] Climbing the Fock ladder: Advancing multiphoton state generation

M. Engelkemeier, Jan Sperling+6 more|arXiv (Cornell University)|May 8, 2021

Quantum Information and Cryptography26 references4 citations

TL;DR

This paper presents a feedback-based, time-multiplexed parametric down-conversion scheme that iteratively builds high-photon-number Fock states by coherently seeding subsequent nonlinear processes using heralded photons. By exploiting looped propagation and quantum feedback, the method achieves significantly higher success probabilities than direct heralding—demonstrated by up to 100× improvement for four-photon states—while maintaining high fidelity and enabling the generation of nonclassical states beyond the reach of conventional techniques, limited primarily by loop losses.

ABSTRACT

A scheme for the enhanced generation of higher photon-number states is realized, using an optical time-multiplexing setting that exploits a parametric down-conversion source for an iterative state generation. We use a quantum feedback mechanism for already generated photons to induce self-seeding of the consecutive nonlinear process, enabling us to coherently add photons to the light that propagates in the feedback loop. The addition can be carried out for any chosen number of round trips, resulting in a successive buildup of multiphoton states. Our system is only limited by loop losses. The looped design is rendered possible by a carefully engineered waveguide source that is compatible with and preserves the shape of the propagating mode. We compare the fidelities and success probabilities of our protocol with the common direct heralding of photon-number states. This comparison reveals that, for same the fidelity, our feedback-based setup significantly enhances success probabilities, being vital for an efficient utilization in quantum technologies. Moreover, quantum characteristics of the produced states are analyzed, and the flexibility of producing higher photon-number states with our setup beyond the common direct heralding is demonstrated.

Motivation & Objective

• To overcome the exponentially decaying success probability in direct heralding of high-photon-number Fock states.
• To develop a scalable, feedback-driven method for generating multiphoton states with enhanced efficiency and fidelity.
• To demonstrate the feasibility of building higher photon-number states beyond the limitations of conventional direct heralding.
• To analyze the impact of loop losses on nonclassicality and state quality in iterative multiphoton generation.

Proposed method

• Utilizes a time-multiplexed optical loop with a waveguide-based parametric down-conversion (PDC) source to enable repeated interaction of pump pulses with signal photons.
• Employs a quantum feedback mechanism where heralded idler photons trigger subsequent PDC events, enabling coherent addition of photons in the loop.
• Uses spatial and time-bin multiplexing with single-photon detectors to achieve approximate photon-number resolution for heralding.
• Applies electro-optic modulators to deterministically out-couple the generated multiphoton states after a chosen number of round trips.
• Employs squeezing parameters |ζ| ≈ 0.3 to control the PDC process and simulate the system under realistic loss conditions.
• Analyzes nonclassicality via the negativity 𝒩 and statistical significance to assess quantum character of generated states.

Experimental results

Research questions

• RQ1 Can a feedback-based iterative scheme significantly enhance the success probability of generating high-photon-number Fock states compared to direct heralding?
• RQ2 How do loop losses affect the nonclassicality and fidelity of generated multiphoton states in a time-multiplexed feedback architecture?
• RQ3 What is the optimal heralding click pattern across multiple round trips to maximize nonclassicality and statistical significance?
• RQ4 Can the feedback mechanism enable the generation of Fock states with n > 4 photons while preserving high fidelity and nonclassicality?

Key findings

• For n = 4 photons, the feedback-based scheme (FH) achieved a success probability of 0.0316 ± 1.53×10⁻⁴ ‰, representing a 100× improvement over direct heralding (DH) at comparable fidelity.
• The fidelity of the feedback-generated four-photon state reached 99.98 ± 6.63×10⁻⁴ %, exceeding that of direct heralding under similar conditions.
• Nonclassicality (𝒩) decreased with increasing photon number in the experiment due to loop losses, but simulations without losses showed the expected increase with photon number, confirming loop loss as the primary limitation.
• The heralding pattern (2,3) yielded the highest statistical significance (1.0) for five-photon states, outperforming (1,4) due to higher detection event rates despite similar nonclassicality.
• The scheme enabled the generation of six-photon states with nonclassicality values of 𝒩 ≈ -1.8×10⁻⁴ and significance of 1.7, demonstrating feasibility beyond four photons.
• The success probability for generating four-photon states via feedback was 0.298 ± 0.0006, significantly higher than the 0.0119 ± 9.24×10⁻⁵ ‰ achieved by direct heralding under comparable fidelity conditions.