Nat. Photonics quantum entanglement of photons captured in real time!

Researchers at the University of Ottawa, in collaboration with Danilo Zia and Fabio Sciarrino from the University of Rome, have demonstrated a new technique to visualize in real time the wave function of two entangled photons, the elementary particles that make up light.

The results are published in Nature Photonics under the title "Interferometric imaging of amplitude and phase of spatial biphoton states".

Using the analogy of a pair of shoes, the concept of entanglement can be compared to choosing a shoe at random. The moment you recognize one shoe, the nature of the other (whether it's the left or right shoe) is immediately discerned, regardless of its place in the universe. What is intriguing, however, is the inherent uncertainty associated with the recognition process prior to the exact moment of observation.

The wave function is a central principle of quantum mechanics that provides a comprehensive understanding of the quantum state of a particle. For example, in the case of a shoe, the shoe's "wave function" can carry information about left and right, size, color, and so on.

More precisely, the wave function allows quantum scientists to predict the possible outcomes of various measurements of quantum entities, such as position, velocity, etc. This ability is invaluable, especially as it allows quantum scientists to make predictions about the position of a particle.

This predictive ability is invaluable, especially in the rapidly advancing field of quantum technology, where knowledge of the quantum states generated by or input to a quantum computer allows testing of the computer itself. In addition, the quantum states used in quantum computing are extremely complex, involving many entities that may exhibit strong nonlocality (entanglement).

Understanding the wave function of such a quantum system is an extremely challenging task - this is also known as quantum state lamination or simply quantum lamination. Comprehensive tomography using standard methods (based on so-called projective transformationsprojective operations) requires a large number of measurements, the number of which increases rapidly with the complexity (dimensionality) of the system.

On this occasion, previous experiments conducted by this research group using this method have shown that characterizing or measuring the high-dimensional quantum state of two entangled photons can take hours or even days. Moreover, the quality of the results is very sensitive to noise, and the quality of these results also depends on the complexity of the experimental setup.

The projective measurement method of quantum tomography can be understood as observing the shadows of high-dimensional objects projected onto different walls from independent directions. All the researcher can see are these shadows, and from these shadows they can infer the shape (state) of the whole object. In CT scanning (computed tomography), for example, information about a three-dimensional object can be reconstructed from a set of two-dimensional images.

However, in classical optics, there is another method of reconstructing three-dimensional objects. This method, known as digital holography (digital holography), is based on recording a single image - known as an interferogram - that is obtained by interfering light scattered by an object with a reference light.

A research group led by Ebrahim Karimi, Canada Research Chair in Structural Quantum Waves, co-director of the Joint Institute for Quantum Technologies (NexQT) in Ottawa, and an associate professor in the Faculty of Science, has extended this concept to the two-photon case.

Reconstructing a two-photon state involves superimposing it on a hypothetical, well-known quantum state, and then analyzing the spatial distribution of the locations where the two photons arrive simultaneously. Imaging two photons that arrive at the same time is known as ghost imaging (coincidence image). These photons may come from a reference source or from an unknown source. Quantum mechanics states that the source of the photons cannot be determined.

This gives rise to an interference pattern that can be used to reconstruct the unknown wave function. Advanced cameras that record events at each pixel with nanosecond resolution make this experiment possible.

Holographic reconstruction of two-photon states

Image reconstruction. a) Interferometric overlap image between the reference SPDC state and the state obtained by pumping the beam in the shape of the yin and yang symbols (shown in the inset). b) Interferometric overlap image between the reference SPDC state and the state obtained by pumping the beam. The scale in the inset is the same as in the main image. b) Reconstructed amplitude and phase structure of the image imprinted on the unknown pump.

Dr. Alessio D'Errico, one of the co-authors of the paper and a post-doctoral fellow at the University of Ottawa, emphasizes the great advantages of this innovative approach: "This method is several times faster than previous techniques, taking only minutes or seconds instead of days. Importantly, the detection time is independent of system complexity - this solves the long-standing scalability challenge in projection tomography."

The impact of this research is not limited to academia. It has the potential to accelerate advances in quantum technology, such as improved quantum state characterization, quantum communications and the development of new quantum imaging techniques.

Reference links:

[1]https://phys.org/news/2023-08-visualizing-mysterious-quantum-entanglement-photons.html

[2]https://www.nature.com/articles/s41566-023-01272-3