Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory

Pack, Michael V.; Camacho, Ryan M.; Howell, John C.

doi:10.1103/physreva.74.013812

Cited by 27 publications

(14 citation statements)

References 36 publications

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“…The slow dynamics reported for step-responses [22][23][24] windows perturbed by short, intense signal pulses. While the peak phase shift saturates when τ s ≤ 1/∆ EIT , it does not decrease as ∆ EIT → 0, and the narrow EIT bandwidth serves to prolong the effect of the short signal pulse.…”

mentioning

confidence: 94%

“…This suggests that a fundamental limitation may exist for EITenhanced XPM schemes; once the inverse EIT bandwidth, 1/∆ EIT , exceeds the temporal width of the signal pulse, τ s (i.e.once the signal pulse is shorter in time than the response time of the medium), it appears as though the EIT medium could not respond quickly enough to provide a practical benefit. Theoretical [22,23] and experimental [24] investigations of step-function signal fields have, indeed, found that narrower windows, while providing a larger steady state phase shift, require more time to reach this steady state. The authors went on to conclude that such a slow response time may be a limitation in the case of pulsed signal fields.…”

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confidence: 99%

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Experimental Demonstration of the Effectiveness of Electromagnetically Induced Transparency for Enhancing Cross-Phase Modulation in the Short-Pulse Regime

et al. 2016

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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.The interaction between individual photons is notoriously weak. This is an obstacle, for instance, to optical quantum computing; while the lack of interactions is helpful for coherent communications, it leaves the construction of deterministic logic gates between photonic qubits a difficult challenge.Non-linear optical properties of matter have been used to mediate an effective interaction between two optical fields. For example, an intensity-dependent refractive index provided by an atomic medium can lead to a conditional phase shift written on one optical 'probe' field in the presence of a second 'signal' field. This effective interaction serves as the basis for a two-photon gate proposal, which requires a π rad phase shift to be acquired by the probe field [1]. The difficulty of achieving such a large phase shift has prompted the proposal of a new approach that relies merely on the single-shot detectability of any observable cross-phase shift, not necessarily π rad [2]. However, even the non-linearities required for this 'weak non-linearity' scheme are many orders of magnitude larger than those achievable in typical situations.A number of approaches have been proposed for greatly enhancing the strength of cross-phase modulation (XPM), including cavity QED [3], unconventional media such as photonic crystal fibers [4] and hollow-core fibers filled with alkali gas [5], and finally, novel physical effects such as electromagnetically induced transparency (EIT) [6,7]; this Letter addresses the latter.The original 'N-scheme' proposed by Schmidt anḋ Imamoglu [8] made use of a single EIT window, while later works investigated double-Lambda systems [9,10] to overcome limitations arising from the group-velocity mismatch between signal and probe pulses. Many variations on these multi-level schemes have been introduced [11][12][13][14][15][16] and the ability to store light using EIT has even led to cross-phase modulation between stored pulses of light [17]. In the past 3 years, remarkably high nonlinearities have been observed relying on Rydberg blockade in the presence of EIT [18][19][20][21], presaging potentially huge cross-phase shifts.The enhancement provided by EIT schemes arises from the spectral narrowness of the transparency window, which results in a steep refractive index profile for the probe ...

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confidence: 94%

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confidence: 99%

Experimental Demonstration of the Effectiveness of Electromagnetically Induced Transparency for Enhancing Cross-Phase Modulation in the Short-Pulse Regime

et al. 2016

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“…dephasing rate according to ∆ EIT = 2(R + γ) [24]. The presence of the signal field inside the medium completes the 'N-scheme', serving to perturb the ground-state coherence created by the Lambda system in two ways: first, the scattering of the signal photons from the excited state |e s dephases the ground-state coherence at the rate of Ω 2 s Γ/4∆ 2 s ; second, the Stark shift caused by the signal pulse, ∆ AC = Ω 2 s /4∆ s , detunes the system out of twophoton resonance and causes the probe field to experience a different refractive index, thereby acquiring a cross-phase shift.…”

Section: Modelmentioning

confidence: 99%

“…The equations of motion, eq. 2, can be solved using approximate analytical methods [24] or numerical techniques. We take the latter route, using a first-order difference method to discretize the spatial coordinate and then the 4th-order Runge-Kutta method to take the time integral, which yields the solution to the density matrix of the combined light-matter system for different sets of parameter choice.…”

Section: A Maxwell-bloch Modelmentioning

confidence: 99%

“…In addition, the transient properties of the associated nonlinearities, both absorptive (photon switching) [19,20] and dispersive (cross-Kerr effect) [21][22][23][24][25] have since been investigated. In particular, it was found that the rise time of the cross-phase modulation, that is, the time required for the phase of the probe field to reach its new steady state value in response to a step-function signal field, is inversely proportional to the EIT window width, ∆ EIT .…”

Section: Introductionmentioning

confidence: 99%

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

2016

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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. 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.

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Enhancement of the Goos–Hänchen shift by electromagnetically induced transparency with amplification

Deng

2012

Optics Communications

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Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory

Cited by 27 publications

References 36 publications

Experimental Demonstration of the Effectiveness of Electromagnetically Induced Transparency for Enhancing Cross-Phase Modulation in the Short-Pulse Regime

Experimental Demonstration of the Effectiveness of Electromagnetically Induced Transparency for Enhancing Cross-Phase Modulation in the Short-Pulse Regime

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

Enhancement of the Goos–Hänchen shift by electromagnetically induced transparency with amplification

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