### Description

Quantum entanglement is the invisible non-classical link that can exist between objects separated from each other. Although disputed by Einstein, entanglement is now accepted as a fundamental property of the universe. Light sources exist where photons are emitted as entangled pairs, each photon is ill-defined in direction and energy, but measurement of either gives knowledge of both. If one of the beams of photons is used to illuminate an object, then the image is imprinted onto the other / enabling detection by a remote camera. This is called Quantum or Ghost Imaging, an object placed in one location and be imaged at another! This is all thanks to the coherence of quantum mechanics. Making Ghost Imaging work is a technological challenge, one needs to detect the position of individual photons and distinguish these from any and all sources of noise. To date this has only been possible by raster-scanning single detectors backwards and forwards over the image plane / meaning any Ghost image takes a long time to record. In this work we will develop a real-time Ghost Camera giving live Ghost Images. The system will allow us to explore still disputed questions in the interpretation of Quantum Mechanics including the correct angular form of Heisenberg's uncertainty principle; the pioneering of ghost spectroscopy and explore potential applications in covert imaging, surveillance and sensing. To succeed we will develop a new way of using state of the art photon detectors, computer controlled holograms and short pulse laser sources, while verifying the quantum aspects of our work will require a careful theoretical analysis.

### Key findings

This project was a collaboration between the Strathclyde group and the groups of Profs. Padgett and Buller. This was very much a joint experimental and theoretical project to which we contribued the theoretical work. This summary emphasises these theoretical contributions.

Our principal objective was to address the controversial question of whether or not ghost imaging is a quantum phenomenon or has a classical explanation. It is now clear that ghost imaging, although it does possess a classical analogue, is indeed a quantum phenomenon or, to be more precise, it is a phenomenon in which quantum effects can be manifest. To demonstrate this we designed ghost imaging experiments in which non-local phenomena were evident. This included, in particular, an experiment in which we were able to demonstrate quantum non-locality through the violation of a Bell inequality [Jack et al, Phys. Rev. Lett. 103, 08083602 (2009)].

In order to pursue our objective of gaining insight into the nature of quantum imaging we carried out an in-depth investigation of the entanglement properties of our down-converted photons. This included, in particular, using angular position/orbital angular momentum entanglement to study two-photon interference by passing our photons through apertures in the form of double angular slits [Jha et al, Phys. Rev. Lett. 104, 010501 (2010).]. In this way we were able to investigate and quantify the entanglement of effective qubits. As a demonstration of our ability to manipulate the quantum state we performed the first realisation of optical entanglement localized in three spatial dimensions [Romero et al, Phys. Rev. Lett. 106, 100407 (2011)].

For us, the highlight of our collaboration was the theoretical formulation and experimental confirmation of an Einstein-Podolsky-Rosen paradox for angle and angular momentum [Leach et al, Science 329, 662 (2010)]. This included deriving testable inequalities based on measured uncertainties and on information entropy, the violation of which constitutes the EPR paradox. The resulting correlations were found to violate the effective uncertainty principle by an order of magnitude, making our experiment the strongest realization on record.

As we enhance the precision of our experiments, the long-standing issue of how to separate the spin and orbital components of the total angular momentum becomes even more pressing. A major step in this direction was the realization that there exists a natural helicity in conventional electromagnetic theory [Barnett et al, Phys. Rev. A 86, 013845 (2012)]. This quantity is the analogue of the helicities appearing in particle physics, in plasmas and in fluid mechanics.

In total the project led to 23 journal papers. Including the ones mentioned above, there were 1 paper in Science and 5 in Physical Review Letters. These 23 included further theoretical and experimental studies of entanglement and a review article on orbital angular momentum [Yao and Padgett, Adv. Opt. Photonics 3, 161 (2011)].

Finally, I should mention the paper "Resolution of the Abraham-Minkowski Dilemma" Barnett; Phys. Rev. Lett. 104, 070401 (2010). In this paper I resolve the century-long dilemma of the correct form of optical momentum in a medium. This work, although not listed in the original objectives, was the completion of work initiated under an earlier EPSRC-funded proposal.

Our principal objective was to address the controversial question of whether or not ghost imaging is a quantum phenomenon or has a classical explanation. It is now clear that ghost imaging, although it does possess a classical analogue, is indeed a quantum phenomenon or, to be more precise, it is a phenomenon in which quantum effects can be manifest. To demonstrate this we designed ghost imaging experiments in which non-local phenomena were evident. This included, in particular, an experiment in which we were able to demonstrate quantum non-locality through the violation of a Bell inequality [Jack et al, Phys. Rev. Lett. 103, 08083602 (2009)].

In order to pursue our objective of gaining insight into the nature of quantum imaging we carried out an in-depth investigation of the entanglement properties of our down-converted photons. This included, in particular, using angular position/orbital angular momentum entanglement to study two-photon interference by passing our photons through apertures in the form of double angular slits [Jha et al, Phys. Rev. Lett. 104, 010501 (2010).]. In this way we were able to investigate and quantify the entanglement of effective qubits. As a demonstration of our ability to manipulate the quantum state we performed the first realisation of optical entanglement localized in three spatial dimensions [Romero et al, Phys. Rev. Lett. 106, 100407 (2011)].

For us, the highlight of our collaboration was the theoretical formulation and experimental confirmation of an Einstein-Podolsky-Rosen paradox for angle and angular momentum [Leach et al, Science 329, 662 (2010)]. This included deriving testable inequalities based on measured uncertainties and on information entropy, the violation of which constitutes the EPR paradox. The resulting correlations were found to violate the effective uncertainty principle by an order of magnitude, making our experiment the strongest realization on record.

As we enhance the precision of our experiments, the long-standing issue of how to separate the spin and orbital components of the total angular momentum becomes even more pressing. A major step in this direction was the realization that there exists a natural helicity in conventional electromagnetic theory [Barnett et al, Phys. Rev. A 86, 013845 (2012)]. This quantity is the analogue of the helicities appearing in particle physics, in plasmas and in fluid mechanics.

In total the project led to 23 journal papers. Including the ones mentioned above, there were 1 paper in Science and 5 in Physical Review Letters. These 23 included further theoretical and experimental studies of entanglement and a review article on orbital angular momentum [Yao and Padgett, Adv. Opt. Photonics 3, 161 (2011)].

Finally, I should mention the paper "Resolution of the Abraham-Minkowski Dilemma" Barnett; Phys. Rev. Lett. 104, 070401 (2010). In this paper I resolve the century-long dilemma of the correct form of optical momentum in a medium. This work, although not listed in the original objectives, was the completion of work initiated under an earlier EPSRC-funded proposal.

Status | Finished |
---|---|

Effective start/end date | 1/04/08 → 31/05/12 |

### Funding

- EPSRC (Engineering and Physical Sciences Research Council): £400,397.00

### Fingerprint

ghosts

photons

angular momentum

paradoxes

orbitals

quantum mechanics

cameras

raster scanning

analogs

momentum

fluid mechanics

detectors

pressing

surveillance

bells

slits

proposals

light sources

universe

apertures