Direct Measurement of Superluminal Group Velocity and Signal Velocity in an Optical Fiber

Abstract

We present an easy way of observing superluminal group velocities using a birefringent optical fiber and other standard devices. In the theoretical analysis, we show that the optical properties of the setup can be described using the notion of "weak value". The experiment shows that the group velocity can indeed exceed c in the fiber; and we report the first direct observation of the so-called "signal velocity", the speed at which information propagates and that cannot exceed c.The physics of light propagation is a very timely topic because of its relevance for both classical [1] and quantum [2] communication. Two kind of velocities are usually introduced to describe the propagation of a wave in a medium with dispersion ω(k): the phase velocity v ph = ω k and the group velocity v g = ∂ω ∂k . Both of these velocities can exceed the speed of light in vacuum c in suitable cases [3]; hence, neither can describe the speed at which the information carried by a pulse propagates in the medium. Indeed, since the seminal work of Sommerfeld, extended and completed by Brillouin [4], it is known that information travels at the signal velocity, defined as the speed of the front of a square pulse. This velocity cannot exceed c [5]. The fact that no modification of the group velocity can increase the speed at which information is transmitted has been directly demonstrated in a recent experiment [6]. Superluminal (or even negative) and, on the other extreme, exceedingly small group velocities, have been observed in several media [7]. In this letter we report observation of both superluminal and delayed pulse propagation in a tabletop experiment that involves only a highly birefringent optical fiber and other standard telecom devices.Before describing our setup, it is useful to understand in some more detail the mechanism through which anomalous group velocities can be obtained. For a light pulse sharply peaked in frequency, the speed of the center-of-mass is the group velocity v g of the medium for the central frequency [3]. In the absence of anomalous light propagation, the local refractive index of the medium is n f , supposed independent on frequency for the region of interest. The free propagation simply yields v g = L/t f where L is the length of the medium and t f = n f L/c is the free propagation time. One way to allow fast-and slow-light amounts to modify the properties of the medium in such a way that it becomes opaque for all but the fastest (slowest) frequency components. The center-of-mass of the outgoing pulse appears then at a time t = t f + t , with t the mean time of arrival once the free propagation has been subtracted; obviously t < 0 for fast-light, t > 0 for slow-light. If the deformation of the pulse is weak, the group velocity is still the speed of the center-of-mass, now given by( 1) This can become either very large and even negative ( t → −∞) or very small ( t → ∞) -although in these limiting situations the pulse is usually strongly distorted, so that our reasoning breaks down.We can now move to our setu...

Quantum averages of weak values

“…The usefulness of this description has been demonstrated, both theoretically and experimentally, in a number of applications in which novel aspects of quantum processes have been uncovered when analyzed in terms of * Electronic address: abotero@uniandes.edu.co weak values. These include photon polarization interference [7,8,9,10,11], barrier tunnelling times [12,13,14], photon arrival times [15,16], anomalous pulse propagation [17,18,19], correlations in cavity QED experiments [20], complementarity in "which-way" experiments [21,22], non-classical aspects of light [23,24], communication protocols [25] and retrodiction "paradoxes" of quantum entanglement [26,27,28].…”

Pre- and postselected quantum states: Density matrices, tomography, and Kraus operators

“…The concept was also explored experimentally [6] and shown to be useful in a wide range of contexts, ranging from superluminal light propagations [7,8] to cavity QED [9]. More recently, weak measurements on post-selected states have found surprising applications in metrology, with the development of novel amplification techniques for precision measurements [10][11][12][13].…”

Об Эффекте Хартмана И Скорости Распространения Электромагнитной Волны В Процессе Туннелирования

“…Несмотря на необычность этого результата с точки зрения специальной теории относительности (СТО), в классической электродинамике эффект Хартмана получил в настоящее время статус экспериментально наблюдае-мого эффекта (см., например, [3][4][5][6][7]), который нужно лишь примирить с принципами СТО. Впрочем, и в этом вопросе, за исключением отдельных авторов (см., например, [3]), имеется практически полное единодушие при-нято считать, что возникновение сверхсветовых групповых скоростей в задаче туннелирования не противоречит СТО.…”