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Towards Fast Light at the Single Photon Level

Paul Alstein

Published Jul 13, 2012• 0 citations
OpenAlex

Abstract

We study the propagation of single photons through an atomic vapour cell where group velocity exceeds the velocity of light in vacuum. The mechanism behind this phenomenon is a result of interference of Fourier components due to the dispersive properties of the medium. By considering the distinction between group velocity and information velocity and its implications for special relativity, we show that fast single photons do not violate the principle of relativistic causality. To produce fast single photons, we fine-tune the emission of a single GaAs quantum dot to the 87 Rb D2 atomic transition, where a spectrally narrow region of anomalous dispersion enables a group velocity of vg = 1.21c at room temperature. It is shown that our current configuration does not allow the detection of fast single photons by means of a time resolved measurement of the exciton lifetime. Instead, we propose an alternative detection scheme based on single photon interference, where the peak of the fringe visibility is shifted forward in time by t = -0.4167⌧c (where ⌧c denotes the coherence time of the photon).

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Optics and Photonics News•Dec 1, 2012•0 citations
We study the propagation of single photons through an atomic vapour cell where group velocity exceeds the velocity of light in vacuum. The mechanism behind this phenomenon is a result of interference of Fourier components due to the dispersive properties of the medium. By considering the distinction between group velocity and information velocity and its implications for special relativity, we show that fast single photons do not violate the principle of relativistic causality. To produce fast single photons, we fine-tune the emission of a single GaAs quantum dot to the 87 Rb D2 atomic transition, where a spectrally narrow region of anomalous dispersion enables a group velocity of vg = 1.21c at room temperature. It is shown that our current configuration does not allow the detection of fast single photons by means of a time resolved measurement of the exciton lifetime. Instead, we propose an alternative detection scheme based on single photon interference, where the peak of the fringe visibility is shifted forward in time by t = -0.4167⌧c (where ⌧c denotes the coherence time of the photon).
Summary form only given. Slow light has been explored for building quantum networks, with particular interest in slowing the group velocity of single photons [1], and more recently exploited to enhance the measurement of small phase shifts. Generally, slow-light effects have been characterized as the net effect of a pulse propagating through the slow-light medium, i.e., as a pulse delay time Δt measured with a fast photodiode at the output of the medium [2]. In this work, we use a single-photon imaging camera to observe slow light in situ, and thus provide a direct measurement of spatial pulse compression and temporal dispersion as the pulse travels through the slow light medium, in this case a hyperfine absorption doublet in hot Rb vapor. Our method combines light-in-flight imaging techniques with a camera comprised of an array of single-photon avalanche diodes (SPAD camera) [3] to image the photons scattered by the Rb vapor in the direction of the camera as shown in Fig. 1(a). In addition, the single photon nature of the SPAD detector allows us to obtain a measurement of the single photon group velocity. As shown in Fig. 1(c) and (d), we observe a significant delay, on the order of nanoseconds, in the detection of the photons scattered when the pulse first enters the slow-light medium. This lag in scattered-photon arrival time is a direct visualization of the slowing down of the single-photon group velocity. The pulses used here had a temporal full width at half maximum (FWHM) of τ ~1 ns, with measured group velocities as low as vg~ 0.006c. At these low group velocities we observe a full fractional pulse delay of up to F D = Δt/τ ~ 40 over 7 cm of propagation, and F D ~ 5 for the scattered single photons, which propagate through ~ 1 cm of Rb vapor prior to exiting the cell en-route to the camera.
Contemporary observational and theoretical studies on the temporal nature of microscopic measurements renewed the discussion about the fundamental constants, leading to the possibility of light speed variation and superluminal pulse propagation. Gain assisted experiments using anomalous dispersion near an absorption line in atomic gas, a "fast - light" medium, seem to lead to a wave group velocity vG exceeding c, the vacuum speed of light; moreover, definition of the information velocity vi sets the question of interpretation of the three speeds: one view is that vi = vG, but this violates Causality; another view is that vi = c in all situations, but this limits, a priori, the transport of information. Another view is that vi, vG and c are distinct. This contribution follows the last possibility. A draft discussion on space-time is given.
Experiments done with single photons in the early 1990's produced a surprising result: that single photons pass through a photonic tunnel barrier with a group velocity faster than the vacuum speed of light. This result has stimulated intense discussions related to causality, the speed of information transfer, the nature of barrier tunneling and the meaning of group velocity. The superluminality of tunneling photons is now textbook material, although the authors note that controversy still remains. Another paradoxical result, known as the Hartman effect, is that the tunneling time of the photons becomes independent of barrier length in the limit of opaque barriers. In this paper we examine the meaning of group velocity in the context of barrier tunneling. We ask whether a single tunneling photon can be described by a group velocity and whether the short group delays imply superluminal group velocity. We resolve the paradox of the Hartman effect and show that the predicted and measured group delays are not transit times but photon lifetimes.
Summary form only given. We use gain-assisted linear anomalous dispersion to demonstrate superluminal light pulse propagation with a negative group velocity through a transparent atomic medium. We place two Raman gain peaks closely to obtain an essentially lossless anomalous dispersion region that results in a superluminal group velocity. The group velocity of a pulse in this region exceeds c and can even become negative,while the shape of the pulse is preserved. We measured a negative group velocity index of n/sub g/=-315(/spl plusmn/5). Experimentally, a light pulse propagating through the spin-polarized atomic vapor cell exits from it earlier than propagating through the same distance in vacuum by a time difference that is 315 times of the vacuum light propagation time L/c=0.2 ns.
We present experimental results relative to superluminal propagation based on a single photon traversing an optical system, called 4f-system, which acts singularly on the photon's spectral component phases. A single photon is created by a CW laser light down{conversion process. The introduction of a linear spectral phase function will lead to the shift of the photon peak far beyond the coherence length of the photon itself (an apparent superluminal propagation of the photon). Superluminal group velocity detection is done by interferometric measurement of the temporal shifted photon with its correlated untouched reference. The observed superluminal photon propagation complies with causality. The operation of the optical system allows to enlighten the origin of the apparent superluminal photon velocity. The experiment foresees a superluminal effect with single photon wavepackets.
Manipulating the group velocity of light has resulted in many advances, including slowing light to a car’s pace, stopping light and even forcing pulses to propagate faster than the speed of light in a vacuum. While the group velocity is equal to or less than the speed of light in a vacuum (c) when propagating through a medium exhibiting normal dispersion, anomalous dispersion allows the group velocity to be greater than c, or even negative. Strangely, the peak of a pulse propagating with a negative group velocity through a medium appears to exit the medium before entering it. This is a result of interference from spectral components of a pulse propagating with different phase velocities in the medium.