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Optics Letters

High-speed properties of a phase-modulation scheme based on electromagnetically induced transparency

Holger Schmidt, Ataç İmamoğlu

Published Jul 1, 1998• 59 citations
Publisher

Abstract

Recently a cross-phase modulation scheme that yields giant Kerr nonlinearities by use of an electromagnetically induced transparency (EIT) was proposed [Schmidt and Imamoglu, Opt. Lett. 21, 1936 (1996)]. We analyze the high-speed properties of this scheme for short-pulse propagation. We discuss the relevant losses in this system and show that for short pulses one-photon losses are dominant. We demonstrate that over the entire bandwidth the attainable phase shift in an EIT scheme with a quasi-cw coupling field is orders of magnitude higher than in a conventional three-level scheme or in EIT schemes, in which matched pulses are used to create the transparency.

DOI
10.1364/ol.23.001007

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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.

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Towards Single Photon Nonlinearities using Cavity EIT

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In third order nonlinear mediums, the intensity of one optical field can modify the phase of another optical field. This is known as cross-phase modulation (XPM) and is important for Quantum Information Processing (QIP) as phase shifts of single-photons that exceed π rad can be used to implement two-qubit quantum logic gates. For a conventional XPM scheme, the Kerr nonlinearity responsible for XPM is too small for appreciable phase shifts to be achieved with low intensity optical fields. However, Electromagnetically Induced Transparency (EIT) can increase this nonlinearity by several orders of magnitude. This thesis discusses the experimental construction of a laser-atomic system capable of EIT modulated XPM. This includes construction of a rubidium magneto-optical trap (RbMOT), characterization of this RbMOT, demonstration of EIT in the RbMOT, and a system capable of detecting optical phase shifts produced by EIT. The talk will conclude with an outlook on further implementations to the experiment that will increase this nonlinearity such that phase shifts at the single-photon level are possible. | 76 pages

•Jan 1, 2014•0 citations
Recently a cross-phase modulation scheme that yields giant Kerr nonlinearities by use of an electromagnetically induced transparency (EIT) was proposed [Schmidt and Imamoglu, Opt. Lett. 21, 1936 (1996)]. We analyze the high-speed properties of this scheme for short-pulse propagation. We discuss the relevant losses in this system and show that for short pulses one-photon losses are dominant. We demonstrate that over the entire bandwidth the attainable phase shift in an EIT scheme with a quasi-cw coupling field is orders of magnitude higher than in a conventional three-level scheme or in EIT schemes, in which matched pulses are used to create the transparency.
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 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.
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.
In third order nonlinear mediums, the intensity of one optical field can modify the phase of another optical field. This is known as cross-phase modulation (XPM) and is important for Quantum Information Processing (QIP) as phase shifts of single-photons that exceed π rad can be used to implement two-qubit quantum logic gates. For a conventional XPM scheme, the Kerr nonlinearity responsible for XPM is too small for appreciable phase shifts to be achieved with low intensity optical fields. However, Electromagnetically Induced Transparency (EIT) can increase this nonlinearity by several orders of magnitude. This thesis discusses the experimental construction of a laser-atomic system capable of EIT modulated XPM. This includes construction of a rubidium magneto-optical trap (RbMOT), characterization of this RbMOT, demonstration of EIT in the RbMOT, and a system capable of detecting optical phase shifts produced by EIT. The talk will conclude with an outlook on further implementations to the experiment that will increase this nonlinearity such that phase shifts at the single-photon level are possible. | 76 pages