Short-pulse cross-phase modulation in an electromagnetically-induced-transparency medium

Abstract

Electromagnetically-induced transparency (EIT) has been proposed as a way to greatly enhance cross-phase modulation, with the possibility of leading to few-photon-level optical nonlinearities. This enhancement grows as the transparency window width, ∆EIT , is narrowed. Decreasing ∆EIT , however, increases the response time of the effect, suggesting that for pulses of a given duration, there could be a fundamental limit to the strength of the nonlinearity. We show that in the regimes of most practical interest -narrow EIT windows perturbed by short signal pulses-the enhancement offered by EIT is not only in the magnitude of the nonlinear phase shift but in fact also in its increased duration. That is, for the case of signal pulses much shorter (temporally) than the inverse EIT bandwidth, the narrow window serves to prolong the effect of the passing signal pulse, leading to an integrated phase shift that grows linearly with 1/∆EIT even though the peak phase shift may saturate; the continued growth of the integrated phase shift improves the detectability of the phase shift, in principle without bound. For many purposes, it is this detectability which is of interest, more than the absolute magnitude of the peak phase shift. We present analytical expressions based on a linear time-invariant model that accounts for the temporal behavior of the cross-phase modulation for several parameter ranges of interest. We conclude that in order to optimize the detectability of the EIT-based cross-phase shift, one should use the narrowest possible EIT window, and a signal pulse that is as broadband as the excited state linewidth and detuned by half a linewidth.

Observation of a large, resonant, cross-Kerr nonlinearity in a cold Rydberg gas

“…The signal counter-propagates (see Figure 1) with the probe and reference with orthogonal polarizations and is also resonant with F=3 to F ′ =4. Setting the signal on resonance is particularly important in order to avoid the possibility of AC Stark shifts imparting an additional phase shift to the probe [38]. The typical resonant probe power was approximately 1 nW and the off-resonant "reference" probe was about 10 nW.…”

Digital communication with Rydberg atoms and amplitude-modulated microwave fields

“…This expected behavior has been seen in similar EIT-based cross-phase modulation systems where the EIT linewidth, which is inversely proportional to Ω c , sets the bandwidth of the modulation. 27,29 However, both the data and the numerical model show the opposite trend. This is due to a breakdown of the analytical model as the weak probe/strong EIT regime assumption becomes less valid.…”

“…resulting in greater probe transmission). 29 We show fitted rise times for the lowest and highest MW powers (green and maroon points, respectively) versus Ω EIT in units of the groundstate dephasing rate γ. In these units, Ω EIT 1 is considered to be in the strong EIT regime.…”

Observation of the Nonlinear Phase Shift Due to Single Post-Selected Photons

“…Moreover, by conditioning on detection of a photon in the signal pulse after it is transmitted, we have been able to detect the (quantized, in the ideal case) effect of a single additional photon on a probe beam, and measured this single-photon phase shift to be −18 ± 4 µrad. The theoretical prediction for the magnitude of the cross-phase shift, given the parameters of our experiment, is 13 µrad based on the model presented in [6]. This is a step towards the development of further "quantum nonlinear optics" techniques, including the potential for scalable quantum logic gates.…”