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Measurement Science and Technology

Measurement of the ‘single-photon’ velocity and classical group velocity in standard optical fibre

Jonathan D. Ingham, J.E. Carroll, Ian H. White, R. M. Thompson

Published Mar 27, 2007• 0 citations
Publisher

Abstract

When engineering secure optical communication networks, it may be important to know if the photon velocity may be altered in a dispersive fibre by selecting photonic states with different ranges of Schr?dinger frequencies, (N + 1/2)f where f is the modal frequency. This paper reports on a comparison between the velocity of approximate single-photon states (N ? 1) and the classical optical group velocity (N 1 with a range of N). The experiments use the same source and the same novel technique with a single temporal standard to measure the time of flight of both 'single photons' and classical optical energy over standard optical fibre. Within the experimental accuracy (approximately ?0.2 ns in 30?000 ns, or 6.3 km of fibre) there is no evidence for changes of velocity as the composition of the number states varies. This suggests that photons travel in a dispersive fibre with a velocity that is independent of the Schr?dinger frequencies. It is believed that this is the first such test on kilometre lengths of standard fibre.

DOI
10.1088/0957-0233/18/5/045

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When engineering secure optical communication networks, it may be important to know if the photon velocity may be altered in a dispersive fibre by selecting photonic states with different ranges of Schr?dinger frequencies, (N + 1/2)f where f is the modal frequency. This paper reports on a comparison between the velocity of approximate single-photon states (N ? 1) and the classical optical group velocity (N 1 with a range of N). The experiments use the same source and the same novel technique with a single temporal standard to measure the time of flight of both 'single photons' and classical optical energy over standard optical fibre. Within the experimental accuracy (approximately ?0.2 ns in 30?000 ns, or 6.3 km of fibre) there is no evidence for changes of velocity as the composition of the number states varies. This suggests that photons travel in a dispersive fibre with a velocity that is independent of the Schr?dinger frequencies. It is believed that this is the first such test on kilometre lengths of standard fibre.
Understanding the nature of single-photon propagation and any differences to the classical multi-photon regime is essential to better use the escalating number of single-photon technologies. Novel techniques and results are reported that demonstrate a consistent ability to measure the classical group velocity in an optical fiber to an accuracy in the time-offlight around ±0.2 ns in 30,000 ns. Identical techniques are then applied to single photons to determine their velocity and assess if there is any evidence that Schrödinger frequencies (N+1/2)ω alter the ω-k dispersion diagram. The evidence suggests that photons in a circular fiber show no additional dispersion but travel at the classical group velocity.
It is usually assumed that the energy dependent velocity of a photon moving in a dispersive medium is given by the group velocity at the frequency corresponding to the energy of the photon. This assumption corresponds to the notion that the velocity of a massive particle is determined by its momentum. However, a direct verification of this assumption for a single photon is impossible, since the velocity can only be obtained by measuring the position at two different times, and time-resolved measurements cannot also resolve photon energies. In previous work, I have shown how this limitation can be circumvented for position and momentum, demonstrating that quantum particles do not obey newton's first law in free space. Here, I apply a similar strategy to construct a quantum state in which a non-vanishing percentage of the photons travel a distance x in time t even though the probability of finding any photons with a group velocity of v = x/t is close to zero. Specifically, the suppression of frequencies with group velocities in the vicinity of v = x/t is achieved by destructive interference, while the probabilities of detecting the photons in the initial time window or in the final time window are simultaneously enhanced by constructive interferences between the mutually overlapping wavefunctions. Based on the statistical evidence obtained from separate measurements of single photon arrival times and frequencies, it is then possible to show that the group velocity does not represent the actual velocity at which individual photons propagate through the dispersive medium.
An experimental detection scheme is demonstrated for directly measuring the spectrum of a parametric down-conversion (PDC) source by the use of a highly dispersive fibre. A temporally narrow pulse envelope is spectrally stretched in time by chromatic group velocity dispersion. In order to maximise this effect the high group velocity dispersion of a commercially available dispersion compensating fibre is employed. If the pulse contains only a single photon on average, detection with a conventional APD yields precise information about the arrival time of the photon at the end of the fiber. When carefully calibrated one can accurately reconstruct the original spectral distribution from the measured temporal distribution. Harnessing a single mode fiber for this type of spectrometer brings the benefits of low loss due to efficient guidance, simplicity of alignment and the necessity of only a single detector to scan the spectrum. A fibre assisted single photon spectrograph is employed to measure the correlation spectrum of a bi-photonic state. State generation is achieved by a type-II parametric downconversion process at 1550 nm in a KTP waveguide structure.
Light, which is composed of discrete quanta, or photons, is one of the most fundamental concepts in physics. Being an elementary entity, the behaviour of photons is governed by the rules of quantum mechanics. The ability to create, manipulate and measure quantum states of light is not only useful in foundational tests of quantum theory, but also in a wide range of quantum technologies – which aim to utilize non-classical properties of quantum systems to perform tasks not possible with classical resources. Only recently has it been possible to control the properties of number states of light, which have a fixed photon-number. Two-photon states are central to testing fundamental physical theories (such as locality and reality) and the implementation of quantum information technologies. The versatility of photon-pair states is en- abled by the potential entanglement properties it can posses. Thus controlling the correlations between photons is crucial to both pure and applied physics. To produce a single photon, a photon-pair state can be used. Detection of one photon indicates its twin’s existence. Many applications, such as optical quantum computation, require pure indistinguishable single photons. Heralding single pho- tons from a photon-pair will, in general, produce single photons in a mixed quantum state due to correlations within the pair. A common approach to creating photon-pairs is through the nonlinear sponta- neous four-wave mixing interaction in optical fibres. This thesis presents a theoreti- cal and experimental implementation of a scheme to tailor the spectral correlations within the pairs. Emphasis is placed on engineering the two-photon state such that they are completely uncorrelated. Spatial entanglement is naturally avoided due to the discrete nature of the optical fibre modes. Spectral correlations are eliminated by careful choice of dispersion characteristics and conditions. The purity of the photons generated by this scheme is demonstrated by means of two-photon inter- ference from independent sources. We measure a purity of (85.9 ± 1.6)% with no spectral filtering, exhibiting the usefulness of this source for quantum technologies and applications.
In this presentation, we will introduce the quantum equivalent of white-light interferometry. However, instead of a classical light source with thermal or poissonian statistics, we use energy-time entangled photon pairs. This provides one with several important advantages, which are highly relevant for high-accuracy measurements of chromatic dispersion: 1.) The interferometer does not have to be balanced, which improves the set-up time, especially when comparing different fibres. 2.) Two data fitting parameters are cancelling out, which reduces systematic errors significantly. 3.) The wavelength at which dispersion is measured is not extracted from the data, but is rather inferred with arbitrary precision using a wavemeter or an atomic reference. 4.) Twice as many interference fringes are observed for the same spectral bandwidth, allowing to measure dispersion in standard telecom fibres down to about 3 cm with a 140 nm bandwidth source. After introducing the concept and highlighting the quantum advantages, we will demonstrate the performance of the quantum approach by comparing it to the best state-of-the-art approaches. Statistical analysis is performed by 2 times 100 measurements using either technique. In terms of precision, the quantum (classical) approach achieves a 1-sigmal precision of 21 fs/nm/km (51 fs/nm/km). In addition, the classical approach presents a systematic error of 12 fs/nm/km, which is unlikely to occur using the quantum approach, as the related fitting parameters cancel out automatically. In summary, we believe that combining fundamental and conceptual advantages enabled by quantum optics is a promising approach for the future development of applications requiring precise and accurate measurements.
Abstract The dynamical Casimir effect is the generation of pairs of real particles or photons from the vacuum as a result of a non-adiabatic change of a system parameter or boundary condition. As opposed to standard parametric amplification where the modulation occurs both in space and in time, this fundamental process requires a pure modulation in time, which makes its detection particularly challenging at optical frequencies. In this paper we experimentally demonstrate a realization of the analogue dynamical Casimir effect in the near-infrared optical regime in a dispersion-oscillating photonic crystal fibre. The experiments are based on the equivalence of the spatial modulation of the fibre core diameter to a pure temporal modulation when this is considered in the co-moving frame of the travelling pump pulse. We provide evidence of optical dynamical Casimir effect by measuring quantum correlations between the spectrally resolved photon pairs and prove their non-classical nature with photon anti-bunching.