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Physical Review Letters

Optical Precursor of a Single Photon

Shanchao Zhang, J. F. Chen, Chang Liu, M. M. T. Loy, George K. Wong, Shengwang Du

Published Jun 16, 2011• 77 citations
Publisher

Abstract

We report the direct observation of optical precursors of heralded single photons with step- and square-modulated wave packets passing through cold atoms. Using electromagnetically induced transparency and the slow-light effect, we separate the single-photon precursor, which always travels at the speed of light in vacuum, from its delayed main wave packet. In the two-level superluminal medium, our result suggests that the causality holds for a single photon.

DOI
10.1103/physrevlett.106.243602

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We report the direct observation of optical precursors of heralded single photons with step- and square-modulated wave packets passing through cold atoms. Using electromagnetically induced transparency and the slow-light effect, we separate the single-photon precursor, which always travels at the speed of light in vacuum, from its delayed main wave packet. In the two-level superluminal medium, our result suggests that the causality holds for a single photon.
We report the observation of Sommerfeld-Brillouin optical precursors generated from a long square-modulated laser pulse propagating through a cold atomic ensemble with electromagnetically induced transparency. The optical depth (alpha(0)L) of the medium can be varied from 0 up to 50. We demonstrated that the step-on rising and step-off falling edges propagate with the speed of light in vacuum without a slow light effect. At high alpha(0)L, the precursor is separated from the delayed main pulse at the rising edge, while at the falling edge, we observe damped oscillatory structures resulting from the interference between the precursor and main field.
We report results of both theoretical and experimental studies of optical precursors generated from a square-modulated probe laser pulse having a finite rise and fall time and propagating through a cold atomic ensemble, under the conditions of either a two-level Lorentz absorber system or a three-level system with electromagnetically induced transparency (EIT). Because of the finiteness of the rise (and fall) time, the precursor signal is observed to decrease with increasing optical depth (α 0 L ). We find that the precursor can experience little absorption even at high optical depth if the rise (and fall) time is sufficiently short. At an optical depth of α 0 L = 42, the normalized precursor peak intensity is observed to increase from 9% to 27% when the rise (and fall) time is shortened from 7 to 3 ns. Meanwhile, we reaffirm that there is no violation of Einstein's causality principle in light propagation through both slow and fast light media. In the EIT system with high optical depth, the main field propagates with a subluminal group velocity and it is separated from the precursor. In the two-level system, the effect of negative group velocity in the anomalous dispersion regime is observed, but we detect no advancement in the rising edge of the precursors. In both cases, the leading edges of the precursors show no detectable delay to that through vacuum.
When a broadband signal propagates through a dispersive medium, some frequency components move faster than the center of the pulse. This leads to the appearance of precursors, transient signals that emerge from the medium earlier than the main part of the pulse and seem to propagate superluminally. Here, we investigate the microscopic origin of precursors in a minimal setup: an array of qubits coupled to a waveguide. The linear transmission function only converges to that of a continuous medium for large qubit numbers. Nevertheless, the dispersion produced by only two qubits is enough to produce oscillatory transients. Precursors are best observed under conditions of electromagnetically induced transparency, as the center of the pulse is significantly delayed. Under these conditions, just a single qutrit is enough to generate a precursor. Our results pave the way towards dispersion engineering of light with just a few qubits and can be realized with superconducting qubits coupled to transmission lines or atoms coupled to optical waveguides.
Optical precursors were first studied by Sommerfield and Brillouin in 1914 to resolve the apparent contradictions between fast light propagation and the theory of relativity. They showed theoretically that the front edge of a step-modulated pulse does not interact with the medium and always travels at c because the dispersive material has a finite response time to the optical pulse. The past experimental studies of precursors in classical pulse propagation were always focused on an opaque medium with single or multiple Lorentz absorption lines. In these cases, the precursor signal cannot be separated from the main pulse or otherwise the main field is absorbed. However, the electromagnetically induced transparency (EIT) technique was successfully used to separate precursors from the main pulse due to the slow-light effect in cold atoms. The EIT refers to the absorption suppression or elimination of a probe field through atomic coherence in a certain medium dressed by a strong coupling field. In this paper, a four-level double-lambda atomic system with two upper states coupled to the excited state is explored to separate optical precursors from a square-modulated laser pulse with the effect of spontaneously generated coherence (SGC). The SGC effect occurs in the process of spontaneous emission, in which the atom decays from closely placed upper levels to a single ground level. The quantum interference between the decay channels takes place, which leads to decay induced transparency, thus enhancing the Kerr nonlinearity and amplification without inversion. With the assistance of spontaneously generated coherence, an EIT window appears with steep normal dispersion when the trigger field is far from resonance. Then we can obtain the optical precursors which are separated from the main pulse due to the slow-light effects in the EIT window. In the absence of SGC, the main pulse is absorbed by an opaque medium with Lorentz absorptive lines, so the slow-light effect could not take place. In addition, we obtain the stacked optical precursors with the input probe field amplitude or phase modulated by designing a series of square pulses. For the amplitude modulation case, the peak power reaches about 4.5 times that of the input pulse. With the phase modulation we obtain a transient pulse with a peak power of 14 times that of the input, as a result of constructive interference between the stacked precursors and main field. We expect these findings to be instructive in devising optical devices for optical communication, detection and medical imaging among other applications.