Across various areas in the optical world, there has been a growing interest in exploiting the properties of non-separable optical fields. A class of non-separable fields, known as vector modes, exhibit a coupling between the spatial and polarisation degrees of freedom that is akin of entanglement in quantum mechanics. These vector modes, however, are typically characterized using qualitative measurements which are inadequate in determining to what extent an optical field is non-separable. Here, we present tools to characterize the degree of non-separability of an arbitrary optical field, exploiting the similarities between vector modes and quantum entangled states. As an example, we use vector modes carrying orbital angular momentum to demonstrate the effectiveness of our scheme, and note that the approach can be generalized to vector modes as a whole.
We study the realization of quantum algorithms using classical optical elements and a coherent laser source. The encoded qubits are present in form of path qubits, polarization and orbital angular momentum. In particular, we propose an implementation for the Deutsch Algorithm in a Sagnac interferometer and the Deutsch-Jozsa Algorithm in a ring cavity.
Vector beams are spatial modes of light with spatially variant polarization states in the transverse profile. Over the years, vector beams have found their way into plenty of applications ranging from material processing and lithography to electron acceleration and particle trapping. Though qualitative measurements are routinely used to analyse vector beams, there is currently no quantitative measure for vector beam purity. Here, we introduce a new measure, the vector quality factor (VQF), that maps the purity of vector beams to a scale ranging from 0 to 1. We demonstrate a simple optical setup to generate and detect vector beams using a birefringent phase plate known as a q-plate. Tomographic measurements are performed by decomposing the vector beam into its circular basis states, and measuring the expectation values of the Pauli matrices as intensity measurements which, are used to evaluate the VQF of vector beams.
Vector beams are defined by spatially inhomogeneous states of polarization, that is, the spatial distribution and polarization state of the beam are non-separable. These beams have found interest in a variety of optical fields such as microscopy, interferometry and optical tweezing. It is therefore important to determine the degree to which these beams are non-separable or to determine the vectorness of such beams. We show that the nonseparability of vector beams is analogous to that of entangled quantum states and as such, we use traditionally quantum techniques such as a Bell inequality, to determine the vectorness of our generated vector vortex beams.
Considering the quantum state produced in type I spontaneous parametric down-conversion with collinear, degenerate signal and idler beams, and a Gaussian pump, we show that the azimuthal Schmidt number in the Laguerre-Gaussian (LG) basis increases when the radial indices of the LG modes detected in the signal and idler beams are different. These observations are confirmed by the good agreement between theoretical and experimental results. The theoretical results are obtained by deriving expressions for the probability amplitude to detect LG modes with any combination of azimuthal and radial indices in a down-converted photonic quantum state.
Bessel-Gaussian (BG) modes possess unique characteristics that have been exploited in the classical world and which may also offer advantages over other modes in the quantum regime. The easily adjustable radial scale of BG modes provides a more favourable basis of orbital angular momentum (OAM) entanglement over Laguerre- Gaussian (LG) modes, where the radial dependence is often ignored. We demonstrate high-dimensional entanglement with the BG modes and show a higher fidelity than the LG modes. We use the reconstruction property of BG modes to recover the degree of entanglement of our quantum state after encountering an obstruction. By moving the obstruction along the path of propagation of the entangled photon pairs, we quantitatively show a increase in the degree of entanglement as the obstruction was moved beyond that minimum distance.
We present a simple way of simulating Spontaneous parametric down-conversion (SPDC) by modulating a classical laser beam with two spatial light modulators (SLM) through a back projection setup. This system has the advantage of having very high photon count rates, it can simulate a large range of pump beam profiles simply by modifying the hologram on the SLM, and it can be easily converted to a SPDC setup by simply changing only two of its components without the need to perform realignment. This setup can be used to give an indication whether a SPDC experiment will be feasible in a very short amount of time.
Quantum ghost imaging using entangled photon pairs has become an interesting field of investigation as it illustrates the quantum correlation between the photon pairs. We introduce a new technique using spatial light modulators encoded with appropriate digital holograms to recover not only the amplitude, but also the phase of the digital object. Down-converted photon pairs are entangled in the orbital angular momentum basis, which are typically measured using a spiral phase hologram. Thus by encoding a spiral annular slit hologram into the idler arm, and varying it radially we can simultaneously recover the phase and amplitude of the field in question. We show that there is a good correlation between the encoded field function and the reconstructed images.
We propose a 2-dimensional method for Bessel Gaussian beam azimuthal and radial decomposition using digital holograms. We illustrate the reconstruction of a Bessel Gaussian beam after encountering an obstruction. From the measured decomposition we show the reconstruction of the amplitude, phase and azimuthal index of the field with high degree of accuracy.
We encode mutually unbiased bases (MUBs) using the higher-dimensional orbital angular momentum (OAM) degree of freedom and illustrate how these states are encoded on a phase-only spatial light modulator (SLM). We perform (d - 1)- mutual unbiased measurements in both a classical prepare and measure scheme and on entangled photon pairs for dimensions ranging from d = 2 to 5. The calculated average error rate, mutual information and secret key rate show an increase in information capacity as well as higher generation rates as the dimension increases.
The use of Higher-dimensional entangled systems have been proved to signi cantly improve many quantum in- formation tasks. For instance, it has been shown that the use of higher-dimensional entangled systems provides a higher information capacity and an increased security in quantum cryptography. The orbital angular momentum (OAM) state of light is a potential candidate for the implementation of higher-dimensional entangled systems and has thus been considered for free-space quantum communication. However, atmospheric turbulence severely affects the OAM state of photons. In this work, we study the evolution of the OAM entanglement between two qutrits (three-dimensional quantum systems) in atmospheric turbulence both numerically and experimentally. The qutrits are photons entangled in their orbital angular momentum (OAM) states generated by spontaneous parametric down conversion. We propagate one of the photons through turbulence while leaving the other undis- turbed. To compare our results with previous work, we simulate the turbulent atmosphere with a single phase screen based on the Kolmogorov theory of turbulence and we use the tangle to quantify the amount of entangle- ment between the two qutrits. We compare our results with the evolution of OAM entanglement between two qubits.
Bessel-Gaussian (BG) modes possess unique characteristics that have been exploited in the classical world and which may also o er advantages over other modes in the quantum regime. We use the reconstruction property of BG modes to recover the degree of entanglement of our quantum state after encountering an obstruction. For BG modes, there exists a minimum distance behind an obstruction before reconstruction of the mode occurs. By moving the obstruction along the path of propagation of the entangled photon pairs, we quantitatively show a increase in the degree of entanglement as the obstruction moved beyond that minimum distance.
The OAM or spiral bandwidth indicates the dimensionality of an entangled state that is produced by the spontaneous parametric down-conversion process. Normally this bandwidth is determined by modulating the signal and idler beams with helical phase functions with opposite azimuthal indices on the spatial light modulators in the signal and idler beams, respectively. We added an additional binary Bessel function to the helical phase, thereby specifying the radial dependence of the mode to be Bessel-Gaussian (BG) modes. This comes down to a post selection process, which is known to have the ability to increase entanglement. The result is a modification to the shape of the OAM spectrum, which leads to a higher dimensionality for the quantum states. We perform analytical calculations to show that the bandwidths obtained by measuring in the BG modal basis are larger than those for the LG modes. These theoretical predictions are confirmed by experimental measurements of the bandwidths for LG modes and for BG modes with different transverse scales.
The investigation into Bessel beams has been a topic of immense research during the past 20 years, due to the
interesting properties they display. Bessel beams not only exhibit diffraction free propagation, but also reconstruction of
the amplitude and phase of the beam after encountering an obstruction. Although this self reconstruction property has
been previously modelled by numerous groups, the techniques involve rigorous, time-consuming computations. In this
work we present an efficient method to accurately calculate the reconstruction of a Bessel beam after an arbitrary
obstruction. Our method considers the well-known conical wave features of Bessel beams and looks at the projection of
the obstruction in space as a result of the travelling conical waves that produce the Bessel beams.