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Physical Review A

Electromagnetically-induced-transparency-based cross-phase-modulation at attojoule levels

Hsiang-Yu Lo, Yen-Chun Chen, Po-Ching Su, Hao-Chung Chen, Jun-Xian Chen, Ying-Cheng Chen, Ite A. Yu, Yong‐Fan Chen

Published Apr 22, 2011• 68 citations
Publisher

Abstract

We report the experimental demonstration of electromagnetically-induced-transparency-based cross-phase-modulation at attojoule or, equivalently, few-hundred-photon levels. A phase shift of 0.005 rad of a probe pulse modulated by a signal pulse with an energy of $~100$ aJ, equivalent to $~400$ photons, was observed in a four-level system of cold $^{87}\mathrm{Rb}$ atoms.

DOI
10.1103/physreva.83.041804

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Journal of the Optical Society of America B•Jun 24, 2009•66 citations
We report the experimental demonstration of electromagnetically-induced-transparency-based cross-phase-modulation at attojoule or, equivalently, few-hundred-photon levels. A phase shift of 0.005 rad of a probe pulse modulated by a signal pulse with an energy of  100~100 100 aJ, equivalent to  400~400 400 photons, was observed in a four-level system of cold 87Rb^{87}\mathrm{Rb}87Rb atoms.
We report on the direct measurement of low-light-level cross-phase modulation (XPM) based on electromagnetically induced transparency (EIT) in the pulsed regime. A phase shift of 0.02 rad of a probe pulse modulated by a signal pulse with a peak intensity of 3 $\mathrm{\ensuremath{\mu}}\mathrm{W}/{\mathrm{cm}}^{2}$ was observed, which is the lowest intensity ever achieved for the N-type EIT-based XPM system. The experimental data make a quantitative prediction of the single-photon-level XPM phase shift arising from two interacting pulses with unequal group velocities that is consistent with the theoretical predictions proposed by Harris and Hau [Phys. Rev. Lett. 82, 4611 (1999)]. Furthermore, a proof-of-principle experiment demonstrating an enhancement of the nonlinear optical Kerr effect by shining the signal pulse twice is presented.
We present an experiment using a sample of laser-cooled Rb atoms to show that cross-phase modulation schemes continue to benefit from electromagnetically induced transparency (EIT) even as the transparency window is made narrower than the signal bandwidth (i.e., for signal pulses much shorter than the response time of the EIT system). Addressing concerns that narrow EIT windows might not prove useful for such applications, we show that while the peak phase shift saturates in this regime, it does not drop, and the time-integrated effect continues to scale inversely with EIT window width. This integrated phase shift is an important figure of merit for tasks such as the detection of single-photon-induced cross-phase shifts. Only when the window width approaches the system's dephasing rate γ does the peak phase shift begin to decrease, leading to an integrated phase shift that peaks when the window width is equal to 4γ.
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 [Schmidt and Imamoglu, Opt. Lett. 21, 1936 (1996)]. This enhancement grows as the transparency window width, ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$, is narrowed. Decreasing ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$, however, has been shown to increase the response time of the nonlinear medium. This suggests that, for a given pulse duration, the nonlinearity would diminish once the window width became narrower than this pulse bandwidth. We show that this is not the case: the peak phase shift saturates but does not decrease. 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 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 $1/{\mathrm{\ensuremath{\Delta}}}_{\mathrm{EIT}}$; this 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 more interest 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.
We investigate a four-level double-Λ atomic scheme interacting with four laser fields, a weak probe field, a weak signal field and two driven fields, in a closed-loop configuration. We study the Kerr nonlinearity associated with cross-phase modulation based on electromagnetically induced transparency. Our results show, in this closed-loop system, that the strength of cross-phase modulation and two-photon absorption are dependent critically on the relative phase between the excitation paths. By choosing the parameters appropriately, large cross-phase modulation can be achieved within a wide transparency window, while two-photon absorption is cancelled completely. The strength of cross-phase modulation can be enhanced much more by decreasing the intensities of two driven fields.
We investigate a four-level double-Lambda atomic scheme interacting with four laser fields, a weak probe field, a weak signal field and two driven fields, in a closed-loop configuration. We study the Kerr nonlinearity associated with cross-phase modulation based on electromagnetically induced transparency. Our results show, in this closed-loop system, that the strength of cross-phase modulation and two-photon absorption are dependent critically on the relative phase between the excitation paths. By choosing the parameters appropriately, large cross-phase modulation can be achieved within a wide transparency window, while two-photon absorption is cancelled completely. The strength of cross-phase modulation can be enhanced much more by decreasing the intensities of two driven fields.
We investigate, both theoretically and experimentally, the cross-Kerr nonlinearity generated in a four-level tripod system in the 87Rb D1 line. The system exhibits simultaneous electromagnetically induced transparency (EIT) windows for two weak (probe and trigger) fields and the enhanced cross-Kerr nonlinearity by EIT. The cross-Kerr nonlinear phase shifts for probe (trigger) field are measured at several different intensities of trigger (probe) field. The results show that large cross-phase modulation (XPM) coefficients can be achieved at low light intensities.