Quantum holography with undetected light (2106.04904v3)

Abstract: Holography exploits the interference of light fields to obtain a systematic reconstruction of the light fields wavefronts. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. Extending holographic methods to the level of single photons has been proven challenging, since applying classical holography techniques to this regime pose technical problems. Recently the retrieval of the spatial structure of a single photon, using another photon under experimental control with a well-characterized spatial shape as reference, was demonstrated using the intrinsically non-classical Hong-Ou-Mandel interference on a beam splitter. Here we present a method for recording a hologram of single photons without detecting the photons themselves, and importantly, with no need to use a well-characterized companion reference photon. Our approach is based on quantum interference between two-photon probability amplitudes in a nonlinear interferometer. As in classical holography, the hologram of a single photon allows retrieving the complete information about the "shape" of the photon (amplitude and phase) despite the fact that the photon is never detected.

Quantum Holography with Undetected Light: A Technical Exposition

The pursuit of quantum imaging technologies has led to significant innovations, particularly in the field of quantum holography. "Quantum Holography with Undetected Light," a seminal paper authored by Sebastian Töpfer and collaborators, explores the use of quantum interference in nonlinear interferometers to achieve holography without directly detecting photons that interact with the object of interest. This paper presents a significant advancement in quantum imaging, pushing the boundaries of what's feasible with traditional detection-limited optical methods.

Core Contributions and Methodological Innovations

The paper introduces a novel approach to holography by leveraging phase-shifting techniques with nonclassical states of light. Through the implementation of quantum interference between two-photon probability amplitudes, a detailed reconstruction of the spatial shape of photons interacting with an object is made possible, even though these photons remain undetected. This is achieved without the necessity for a well-characterized reference beam, marking a departure from classical holography paradigms.

Key technical innovations include:

• Utilization of a SU(1,1) nonlinear interferometer, where the two-photon states generated by spontaneous parametric down conversion (SPDC) in nonlinear crystals serve as the basis for holography.
• Recording the interference pattern of coherent signal photons allows for the retrieval of amplitude and phase information of the undetected idler photons.
• The adaptation of phase-shifting holography techniques from the classical to the quantum domain, enabling the reconstruction of object information with high precision.

Numerical and Experimental Findings

The paper reports on the resolution and accuracy of the quantum holography setup, underscoring its potential for practical application. Experimental tests were performed on miniaturized resolution targets, demonstrating the retrieval of phase and amplitude information with a precision threshold at $0.1\pi$ and transmission accuracy within 6%. The work further outlines the spatial resolution capabilities, effectively resolving objects with features sizes as small as 79 micrometers.

The quantitative results suggest that increasing the number of image phases ($M$) and acquisition time enhances reconstruction accuracy, with optimal setups recommending at least four phase shift images and exposure times of 500 milliseconds. The measurements confirm that the transmission modulation follows theoretical predictions, validating the feasibility of the method for practical use.

Theoretical and Practical Implications

Theoretical implications of this research bridge the gap between classical holographic imaging and quantum technologies. By demonstrating that holography can operate independently of direct photon detection, this method heralds potential applications in spectral ranges where detector efficiency is currently a bottleneck, such as in the mid-infrared.

Practically, this research opens up new avenues in fields that demand non-invasive, low-light imaging, including biomedical imaging and materials assessment. The method's robustness against phase instability in an SU(1,1) interferometric setup points to its potential deployment in real-world settings outside controlled experimental environments.

Prospects for Future Research

The approach established in this paper provides a foundation for future exploration into three-dimensional quantum imaging and the expansion into broader spectral ranges via quantum optical coherence tomography. Further optimization of the system for industry-relevant spectral resolution, and the explicit extension into other quantum-enhanced technologies, such as quantum cryptography or sensing, presents an exciting frontier for both theoretical exploration and practical application in quantum optics.

In conclusion, this paper outlines a sophisticated technique in quantum holography that not only circumvents existing limitations of classical approaches but also extends the capabilities for imaging in novel spectral domains. This has broad implications for the development of next-generation quantum photonic devices, potentially revolutionizing fields contingent on detailed and accurate image acquisition.