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Chinese Physics Letters

Measurement of Berry Phase Associated with Higher Dimensional Orbital Angular Momentum of Light by Interference Method

Yuan Xu, Yuan-Yuan Huang, Ling Hu, Pei Zhang, Dong Wei, Hongrong Li, Hong Lin Gao, Fuli Li

Published Oct 1, 2013• 3 citations
Publisher

Abstract

Berry phase of higher-dimensional orbital angular momentum of light is studied. When an N th order orbital state, described by a vector in (N + 1)-dimensional space, evolves through a closed path in space of orbital states, there will exist a higher order orbital Berry phase. We calculate this phase by using the matrix transformation theory. A direct measurement of the higher-order orbital Berry phase is also carried out by the interference method. The experimental results are in good agreement with the theoretical description, which shows that the Berry phase is proportional to the orbital angular momentum of light.

DOI
10.1088/0256-307x/30/10/100304

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Berry phase of higher-dimensional orbital angular momentum of light is studied. When an N th order orbital state, described by a vector in (N + 1)-dimensional space, evolves through a closed path in space of orbital states, there will exist a higher order orbital Berry phase. We calculate this phase by using the matrix transformation theory. A direct measurement of the higher-order orbital Berry phase is also carried out by the interference method. The experimental results are in good agreement with the theoretical description, which shows that the Berry phase is proportional to the orbital angular momentum of light.
The beam with orbital angular momentum is a present domestic and foreign research key direction. Its application and development will bring the profound influence in the optical communications field. At the same time, light's orbital angular momentum promises potential applications in both classical and quantum optical communication. The research progress of the beam with orbital angular momentum and encoding information as light's OAM for free-space optical communication were reviewed in this article, the existing design method, mechanism and description methods of encoding information as light's OAM were discussed. In quantum communication, qudits can be encoded in photons using their OAM for creating high-dimensional entanglement based on entangled photon pairs from SPDC. In this paper, light's OAM is used as information carrier for classical and quantum communication, which is promising to ensures the security of atmospheric laser communication, improves the density and precision of information transmission. It is apparent that an efficient way to measure the orbital angular momentum of individual photons and light beams with good efficiency would be of potentially great importance for optical communications and quantum information. In view of the above, the measurements of orbital angular momentum of individual photons and light beams are analyzed and discussed in detail.
The orbital angular momentum of light (OAM) is a fundamental property of light. Beams with OAM have a helical wave front that carries quantized orbital angular momentum L hbar per photon, where L is any integer. This unbounded Hilbert space can increase information capacity of both classical and quantum communications and also improve and extend qubit and qudit quantum algorithms. Additionally, the use of the OAM modes allows for novel imaging techniques to directly observe and measure various topological properties of objects ranging from defects in semiconductors to rotating black holes and extrasolar planets. However, measuring such higher dimensional OAM states is fundamentally important, albeit challenging, in order to use this rich degree of freedom. In the work that follows, I present two novel OAM to time mapping schemes and an application using the higher dimensionality of OAM to non-destructively probe quantum states. These are the first OAM measuring schemes to use the temporal degree of freedom to measure OAM. The use of the novel loop nature allows for high fidelity and high speed measurements of a large number of OAM states without significant increase in experimental resources. The first scheme experimentally demonstrates a compact and practical device to measure the OAM spectrum. I report a fidelity of -21.3 dB for 5 different OAM states. The second scheme extends the first, but uses non-demolition measurements to iteratively test for specific OAM values. While this increases experimental complexity, it allows for the detection of an arbitrarily large OAM value from a single photon. I also discuss details of each technique investigate the affects of misalignment on the OAM spectrum. In the remaining part, I discuss my novel generalized quantum Zeno interrogation. The original quantum Zeno interrogation is limited to the two-dimensional state of a single object; while the generalized version has the ability to non-destructively probe the quantum state a set of objects, and deterministically imprint that information onto a single photon using the OAM degree of freedom.
Introduction Although the orbital angular momentum (OAM) of light is often quantified in terms of ℓℏ per photon, one should recognise that this result can be derived directly from Maxwell's equations and is most certainly not an exclusively quantum property. Following the recognition of optical OAM in 1992 [1], the immediate thrust of experimental work was to observe OAM transfer to microscopic objects. These exciting experiments by Rubinsztein- Dunlop [2, 3] and others established that the predicted angular momentum was truly mechanical, but did not provide insight on OAM at the level of single photons. Laguerre- Gaussian modes were identified as being a natural basis set for describing beams with OAM, where their phase terms describe the helical phasefronts corresponding to an OAM of ℓℏ per photon. The polarisation of light has played an important historical role in the experimental investigation of quantum entanglement, quantum gate operations and quantum cryptography. A potential advantage of OAM is that it resides in a higher-dimensional state space which, as follows from the theory, is infinite-dimensional. One of the experimental challenges is to access a large number of these dimensions. In quantum communication, the most obvious advantage of high n -dimensional systems is the increased bandwidth [4], but qunits also lead to stronger security [5, 6]. An increase in the number of entangled quantum modes has also been shown to improve measures of nonlocality [7], to allow quantum computation with better fault tolerance [8] and to simplify quantum logic structures [9].
It is well established now that light carries both spin and orbital angular momentum which are associated with circular polarisation and helical phase fronts. Orbital angular momentum degrees of freedom recently have been used frequently in quantum information processing as their states are described by vectors in a higher-dimensional Hilbert space which enhances the possibility of realising superior quantum information protocols. On the other hand, quantum coherence, which arises from the superposition principle, is a distinct feature of quantum mechanics that cannot be satisfactorily described by classical physics. Coherence is also identified as essential ingredient for applications of quantum information, computation, and quantum thermodynamics. Three research projects, with their related background information, are presented in this thesis. In the first one, we design a linear optical system to transform the maximally entangled state of a down-converted photon pair into a genuine entangled χ-type state, as this class of genuine entangled states has been showed to have many interesting entanglement properties and can be employed in several quantum information protocols. In the second project, we study the mechanism of angular momentum transfer from light to a dielectric medium when it undergoes total internal reflection. The result shows that the torque associated with angular momentum transfer appears shortly, when the light pulse hits the interface. Finally, we study quantum coherence transfer from a coherence resource initialised in a coherence state to an atomic state by the Jaynes-Cummings model, and we compare it to the coherent operation that uses a resource prepared in a ladder state described by Åberg’s model. We found that a resource in a coherent state is more robust against failures.
The nondiffracting higher-order Bessel beams carry the orbital angular momentum(OAM). During free propagation,their transverse intensity profile remains nearly invariant in a range.The beam comprises the topological charge l helical phasefronts and carries an orbital angular momentum of lh per photon.The angular momentum number carried by the photon in each eigenmode is represented by l, and the eigenstates |l〉can generate multidimensional quantum entangled states.A method of optical communication is presented that encodes information in two orthogonal orbital angular momentum states based on higher-order Bessel beams.Each photon carries OAM states of information,which can increase the key generation rate of the protocol,and offer a quantum solution for increase of the optical communication distance.