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ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)

Reducing the Free-Space Group Velocity of Single Photons by Transverse Structuring

Daniel Giovannini, Jacquiline Romero, Václav Potoček, Gergely Ferenczi, Fiona C. Speirits, Stephen Mark Barnett, Daniele Faccio, Miles J. Padgett

Published Jan 1, 2015• 0 citations
Publisher

Abstract

The group velocity of light in free space is decreased by controlling the transverse spatial structure of the beam. We present experimental results in the single-photon regime, supported by a simple geometric argument and a full theoretical treatment.
DOI
10.1364/cleo_qels.2015.ftu4a.4

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Comment on "Spatially structured photons that travel in free space slower than the speed of light"

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The speed of light is nominally given by c/n, where n is the refractive index of the medium in which the light is traveling. Since the refractive index of free space is 1, it is natural to expect that light travels at c in free space. We show that this is not the case if one considers real beams that have finite transverse extent. The modification of the wavevectors comprising the beam result in a change in the phase and group velocities. We study the group velocity of single photons, whose arrival times are unambiguously established by a click in a single-photon detector.We generate time-correlated photon pairs via spontaneous parametric down-conversion. One photon is sent through a fiber delay of a fixed length; the arrival time of this photon is the reference time to which we compare the arrival time of the other photon, which we can choose to be either unstructured or structured. The structuring is done by spatial light modulators that can be switched on and off, hence allowing photons to travel through exactly the same optical path, much like in a race. We consider photons in a Bessel mode and a focused Gaussian mode, and show that in both cases, the reduction in group velocity results in a delay of several micrometers over a propagation distance of 1 m or ~30 femtoseconds in terms of arrival time. The effect is well-understood from a geometric argument and from a rigorous calculation of the harmonic average of the group velocity, and hence, is not anomalous at all. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves.
That the speed of light in free space is constant is a cornerstone of modern physics. However, light beams have finite transverse size, which leads to a modification of their wave vectors resulting in a change to their phase and group velocities. We study the group velocity of single photons by measuring a change in their arrival time that results from changing the beam's transverse spatial structure. Using time-correlated photon pairs, we show a reduction in the group velocity of photons in both a Bessel beam and photons in a focused Gaussian beam. In both cases, the delay is several micrometers over a propagation distance of ~1 meter. Our work highlights that, even in free space, the invariance of the speed of light only applies to plane waves.
Optics We are taught that the speed of light in free space is one of the universal physical constants: c. Giovannini et al. now show that there are certain conditions under which such certainty can be broken (see the Perspective by Sambles). Adding spatial structure to an optical beam of single photons reduced the speed of light. The magnitude of the decrease depended on the complexity of the structure imprinted onto the photons. Science , this issue p. [857][1]; see also p. [828][2] [1]: /lookup/doi/10.1126/science.aaa3035 [2]: /lookup/doi/10.1126/science.aaa6931
Quantum mechanics, optics and indeed any wave theory exhibits the phenomenon of interference. In this thesis we present two problems investigating interference due to indistinguishable alternatives and a mostly unrelated investigation into the free space propagation speed of light pulses in particular spatial modes. In chapter 1 we introduce the basic properties of the electromagnetic field needed for the subsequent chapters. In chapter 2 we review the properties of interference using the beam splitter and the Mach-Zehnder interferometer. In particular we review what happens when one of the paths of the interferometer is marked in some way so that the particle having traversed it contains information as to which path it went down (to be followed up in chapter 3) and we review Hong-Ou-Mandel interference at a beam splitter (to be followed up in chapter 5). In chapter 3 we present the first of the interference problems. This consists of a nested Mach-Zehnder interferometer in which each of the free space propagation segments are weakly marked by mirrors vibrating at different frequencies [1]. The original experiment drew the conclusions that the photons followed disconnected paths. We partition the description of the light in the interferometer according to the number of paths it contains which-way information about and reinterpret the results reported in [1] in terms of the interference of paths spatially connected from source to detector. In chapter 4 we briefly review optical angular momentum, entanglement and spontaneous parametric down conversion. These concepts feed into chapter 5 in which we present the second of the interference problems namely Hong-Ou-Mandel interference with particles possessing two degrees of freedom. We analyse the problem in terms of exchange symmetry for both boson and fermion pairs and show that the particle statistics at a beam splitter can be controlled for suitably chosen states. We propose an experimental test of these ideas using orbital angular momentum entangled photons. In chapter 6 we look at the effect that the transverse spatial structure of the mode that a pulse of light is excited in has on its group velocity. We show that the resulting group velocity is slower than the speed of light in vacuum for plane waves and that this reduction in the group velocity is related to the spread in the wave vectors required to create the transverse spatial structure. We present experimental results of the measurement of this slowing down using Hong-Ou-Mandel interference.