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arXiv:quant-ph/0301157 · Physical Review A

Experimental investigation of delayed self-interference for single photons

Nicklas Ohlsson, Mattias Nilsson, Stefan Kröll

Published Dec 12, 2003• 24 citations
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Abstract

A photon echo experiment has been performed using accumulated highly attenuated laser pulses. We show experimentally that the photon echo process can be performed with, on the average, less than one photon in each pair of excitation pulses. The results support an interpretation where this nonlinear process can be performed with, on the average, less than one photon shared between two of the optical fields involved in the degenerate four-wave-mixing process. Further, we argue that the experiment can be interpreted as a form of delayed self-interference for photon wave packets that do not overlap in both space and time.

DOI
10.1103/physreva.68.063812

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Physical Review A•Jan 30, 2017•0 citations
A photon echo experiment has been performed using accumulated highly attenuated laser pulses. We show experimentally that the photon echo process can be performed with, on the average, less than one photon in each pair of excitation pulses. The results support an interpretation where this nonlinear process can be performed with, on the average, less than one photon shared between two of the optical fields involved in the degenerate four-wave-mixing process. Further, we argue that the experiment can be interpreted as a form of delayed self-interference for photon wave packets that do not overlap in both space and time.
Summary form only given. Consider an experiment where a single photon is split into two wave-packets by a beam splitter and where the two wave packets are made to overlap in a specific region in space. If the two wave-packets arrive at the same time, an interference pattern can be recorded by a classical detector such as a photographic plate. If however, the difference in arrival time between the two wave-packets is made to be larger than the coherence time of the wave packets, the interference pattern, as recorded by the detector, will disappear. It has been argued that if the classical detector is replaced by a material that can remember the phase of the electromagnetic field, i.e. a material with a long homogeneous dephasing time, it would be possible to record the interference between the two wave-packets even if the time difference between them is much larger than the coherence time. We denote this single-photon self-interference. The interference pattern would take the form of a frequency dependent population grating in the material and could be detected by diffracting a light pulse on this grating. The delayed single-photon self-interference experiment has several unique features. It is a four-wave mixing experiment where the two first pulses share a total of only one photon. Thus interaction between these two pulses and the material, normally considered as a nonlinear multiphoton process, is here carried out by a single photon. We have performed experiments with multiphoton excitation pulses and extrapolated the data to the single photon level. These experiments support the conclusion from the theoretical calculations that delayed single-photon self-interference could be observed.
The three-pulse stimulated photon echo has been considered as one of the most fundamental transient four wave mixing processes1, where each of the three excitation pulses induces a single elementary interaction process between a laser field and an inhomogeneously broadened two-level system., resulting in a burst of the fourth wave, i.e., echo. Now if four or more optical pulses are applied to a medium, a number of photon echoes should be expected, in general. At low excitation intensities where the perturbation theory is applicable, however, the dominant nonlinear process is still the three-pulse stimulated echo and consequently each echo signal is generated only by three of the preceding pulses. It is rather a remarkable result that the echo intensity is unaffected by the presence of all the rest of the pulses other than its three generators. With this in mind, it is theoretically and experimentally shown that by applying a single optical pulse (#1) propagating along k1 followed by N pairs of counter-propagating pulses (#2j (k2j) and #3j− (k3j = −k2j); j=1,…N) in various directions, it is possible to obtain N photon echoes along the direction -k1 opposite to the first pulse #1. We will call this degenerate photon echoes, degenerate in. the sense that the echoes are spatially overlapping and temporally simultaneous. When N=l, this scheme is reduced to the ordinary backward photon echo2,3. The doubly degenerate case (N=2) is illustrated in Fig. 1. The j-th echo will be generated by the set of pulses (#1, #2j, #3j) and appear at t = t3j + t2j − t1 where t1, i2j and t3j are the arrival times of the pulses #1, #2j and #3j, respectively.
We describe and discuss an experiment in peaks in the autocorrelation. The spacing which two temporally stretched femtosecond between the peaks in the autocorrelation pulses interact in a Kerr-like nonlinear medium increases as the delay ΔT at the input increases, to generate new pulses of comparable duration. In contrast to photon-echo experiments, both advanced and retarded pulses are observed. The results can be explained by drawing an analogy between four-wave mixing in real space and diffraction in the time domain.
We report on the dynamics of two-pulse photon echoes in a two-level system. We consider two different types of excitation pulse pairs: pulses with the same carrier envelope phases (CEP pulse pairs) and pulse pairs cut from the same carrier wave train (labeled as normal pulse pairs). We show that for CEP pulse pairs when the pulses overlap somewhat the photon-echo emission time is strongly sensitive to the relative phase (i.e., delay time) between the two pulses. We also show how the photon-echo emission time for such CEP pulse pairs depends on the dephasing time of the polarization (T2{T}_{2}T2​) and the pulse width of the applied pulses. This phase sensitivity can be utilized to control the emission time of the photon echo which may prove useful in storing and retrieving light signals from an atomic ensemble. Our results also inform the interpretation of photon-echo signals at short delay time when used to measure fast coherence decay rates.