Relativistic quantum field theory in the presence of an external electric potential in a general curved space-time geometry is considered. The Fermi coordinates adapted to the time-like geodesic are utilized to describe the low-energy physics in the
laboratory and to calculate the leading correction due to the curvature of the space-time geometry to the Schrodinger equation. The correction is employed to calculate the probability of excitation for a hydrogen atom that falls in or is scattered by a general Schwarzchild black hole. Since the excited states decay due to spontaneous photon emission, this study provides the theoretical base for detection of small isolated black holes by observing the decay of the excited states as neutral hydrogen atoms in the vacuum are devoured by the black hole.
The current race in quantum communication -- endeavouring to establish a global quantum network -- must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay, gravitational lens
ing, and frame dragging which all are due to how a mass distribution alters geodesics. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore, we investigate this distortion for anti-de Sitter and Schwarzschild geometries. For instance, the spacetime curvature causes a 0.10~radian phase-shift for communication between Earth and the International Space Station on a monochromatic laser beam and quadrupole astigmatism can cause a 12.2 % cross-talk between structured modes traversing through the solar system. Our finding shows that this gravitational distortion is significant, and it needs to be either pre- or post-corrected at the sender or receiver to retrieve the information.
Liquid crystals allow for the real-time control of the polarization of light. We describe and provide some experimental examples of the types of general polarization transformations, including universal polarization transformations, that can be accom
plished with liquid crystals in tandem with fixed waveplates. Implementing these transformations with an array of liquid crystals, e.g., a spatial light modulator, allows for the manipulation of the polarization across a beams transverse plane. We outline applications of such general spatial polarization transformations in the generation of exotic types of vector polarized beams, a polarization magnifier, and the correction of polarization aberrations in light fields.
In an effort to challenge the Copenhagen interpretation of quantum mechanics, Karl Popper proposed an experiment involving spatially separated entangled particles. In this experiment, one of the particles passes through a very narrow slit, and thereb
y its position becomes well-defined. This particle therefore diffracts into a large divergence angle; this effect can be understood as a consequence of the Heisenberg uncertainty principle. Popper further argued that its entangled partner would become comparably localized in position, and that, according to his understanding of the Copenhagen interpretation of quantum mechanics, the qo{mere knowledge} of the position of this particle would cause it also to diffract into a large divergence angle. Popper recognized that such behaviour could violate the principle of causality in that the slit could be removed and the partner particle would be expected to respond instantaneously. Popper thus concluded that it was most likely the case that in an actual experiment the partner photon would not undergo increased diffractive spreading and thus that the Copenhagen interpretation is incorrect. Here, we report and analyze the results of an implementation of Poppers proposal. We find that the partner beam does not undergo increased diffractive spreading. Our work resolves many of the open questions involving Poppers proposal, and it provides further insight into the nature of entanglement and its relation to the uncertainty principle of correlated particles.
We test experimentally the quantum ``paradox proposed by Lucien Hardy in 1993 [Phys. Rev. Lett. 71, 1665 (1993)] by using single photons instead of photon pairs. This is achieved by addressing two compatible degrees of freedom of the same particle, n
amely its spin angular momentum, determined by the photon polarization, and its orbital angular momentum, a property related to the optical transverse mode. Because our experiment involves a single particle, we cannot use locality to logically enforce non-contextuality, which must therefore be assumed based only on the observables compatibility. On the other hand, our single-particle experiment can be implemented more simply and allows larger detection efficiencies than typical two-particle ones, with a potential future advantage in terms of closing the detection loopholes.
Inspired by the classical phenomenon of random walk, the concept of quantum walk has emerged recently as a powerful platform for the dynamical simulation of complex quantum systems, entanglement production and universal quantum computation. Such a wi
de perspective motivates a renewing search for efficient, scalable and stable implementations of this quantum process. Photonic approaches have hitherto mainly focused on multi-path schemes, requiring interferometric stability and a number of optical elements that scales quadratically with the number of steps. Here we report the experimental realization of a quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous indistinguishable photons. The whole process develops in a single light beam, with no need of interferometers, and requires optical resources scaling linearly with the number of steps. Our demonstration introduces a novel versatile photonic platform for implementing quantum simulations, based on exploiting the transverse modes of a single light beam as quantum degrees of freedom.
In contrast to the case of quasi-monochromatic waves, a focused optical pulse in the few-cycle limit may exhibit two independent curved wavefronts, associated with phase and group retardations, respectively. Focusing optical elements will generally a
ffect these two wavefronts differently, thus leading to very different behavior of the pulse near focus. As limiting cases, we consider an ideal diffractive lens introducing only phase retardations and a perfect non-dispersive refractive lens (or a curved mirror) introducing equal phase and group retardations. We study the resulting diffraction effects on the pulse, finding both strong deformations of the pulse shape and shifts in the spectrum. We then show how important these effects can be in highly nonlinear optics, by studying their role in attosecond pulse generation. In particular, the focusing effects are found to affect substantially the generation of isolated attosecond pulses in gases from few-cycle fundamental optical fields.
In quantum information, complementarity of quantum mechanical observables plays a key role. If a system resides in an eigenstate of an observable, the probability distribution for the values of a complementary observable is flat. The eigenstates of t
hese two observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low as six, the identification of a maximal set of MUBs remains an open problem, although there is strong numerical evidence that no more than three simultaneous MUBs do exist. Here, by exploiting a newly developed holographic technique, we implement and test different sets of three MUBs for a single photon six-dimensional quantum state (a qusix), encoded either in a hybrid polarization-orbital angular momentum or a pure orbital angular momentum Hilbert space. A close agreement is observed between theory and experiments. Our results can find applications in state tomography, quantitative wave-particle duality, quantum key distribution and tests on complementarity and logical indeterminacy.
A proposal for an electron-beam device that can act as an efficient spin-polarization filter has been recently put forward [E. Karimi et al., Phys. Rev. Lett. 108, 044801 (2012)]. It is based on combining the recently developed diffraction technology
for imposing orbital angular momentum to the beam with a multipolar Wien filter inducing a sort of artificial non-relativistic spin-orbit coupling. Here we reconsider the proposed device with a fully quantum-mechanical simulation of the electron beam propagation, based on the well established multi-slice method, supplemented with a Pauli term for taking into account the spin degree of freedom. Using this upgraded numerical tool, we study the feasibility and practical limitations of the proposed method for spin-polarizing a free electron beam
We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge $q$ at its center ($q$-plate). The polarization topological structures for different $q$-plates and differ
ent input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned $q=1/2$-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.
