Mirrorless Oscillation Based on Resonantly Enhanced 4-Wave Mixing: All-Order Analytic Solutions

Fleischhauer, Michael

doi:10.1007/978-3-662-07313-1_7

Cited by 2 publications

(4 citation statements)

References 13 publications

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“…This is due to the fact that in the fourlevel system the finite detuning ∆ is associated with an AC Stark effect, which leads to intensity dependent dynamical phase shifts of the fields. These phase shifts are of minor consequence in the case where the fields are counter-propagating [19], but for co-propagating fields have a detrimental influence leading to impaired phase matching and inefficient frequency conversion. As shown in [20] these phase shifts are eliminated in the five-level scheme when the relative sign of the dipole moments of the |4 → |2 , |1 transitions is opposite to that of the |3 → |2 , |1 transitions.…”

Section: System and Effective Field Equationsmentioning

confidence: 99%

Nonperturbative quantum solutions to resonant four-wave mixing of two single-photon wave packets

Johnsson

Fleischhauer

2003

Phys. Rev. A

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We analyze both analytically and numerically the resonant four-wave mixing of two co-propagating single-photon wave packets. We present analytic expressions for the two-photon wave function and show that soliton-type quantum solutions exist which display a shape-preserving oscillatory exchange of excitations between the modes. Potential applications including quantum information processing are discussed.

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Section: System and Effective Field Equationsmentioning

confidence: 99%

Nonperturbative quantum solutions to resonant four-wave mixing of two single-photon wave packets

Johnsson

Fleischhauer

2003

Phys. Rev. A

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“…These phase shifts are of minor consequence in the case where the fields are counterpropagating [13]. They do have a detrimental influence, however, for co-propagation.…”

mentioning

confidence: 98%

“…Phase matching will thus favor two-photon resonance and we assume that this condition is fulfilled. Resonant four-wave mixing has been analyzed both theoretically and experimentally with co-propagating as well as counter-propagating fields [6,7,8,9,10,11,12,13].…”

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confidence: 99%

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Eliminating nonlinear phase mismatch in resonantly enhanced four-wave mixing

Johnsson¹,

Korsunsky²,

Fleischhauer³

2002

Optics Communications

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Resonantly enhanced four wave mixing in double-Λ systems is limited by ac-Stark induced nonlinear phase shifts. With counter-propagating pump fields the intensity-phase coupling has minimal impact on the dynamics, but it is of critical importance for co-propagation. The nonlinear phase terms lead to an increase of the conversion length linearly proportional to the inverse seed intensity, while without nonlinear phase-mismatch the scaling is only logarithmic. We here show that the ac-Stark contributions can be eliminated while retaining the four-wave mixing contribution by choosing a suitable five level system with appropriate detunings.PACS numbers: 42.50. Gy, 32.80.Qk, 42.50.Hz Ever since the cancellation of resonant linear absorption and refraction via electromagnetically induced transparency (EIT) [1] was first demonstrated, quantum and nonlinear optics have successfully been exploring the consequences. Many interesting effects have been proposed and investigated [2]. One important application of EIT is optical frequency mixing close to atomic resonances where it allows making use of the resonantly enhanced nonlinear interaction without suffering from linear absorption and refraction. It has been predicted that EIT could even lead to a new regime of nonlinear optics on the level of few light quanta [3,4,5].In this paper we consider one particular EIT-based scheme, namely resonantly enhanced four wave mixing in a double lambda system as shown in Fig. 1. The two fields with (complex) Rabi frequencies Ω 1 and Ω 2 are initially excited and form the pump fields, while the other fields with (complex) Rabi frequencies E 1 and E 2 are generated during the interaction process. Ω 1 and E 1 are taken to be exactly on resonance while the other two are assumed to be detuned by an amount ∆. A finite detuning ∆, large compared to the Rabi frequencies, Doppler broadening and decay rates from the excited states, is necessary to maximize the ratio of nonlinear gain to linear absorption. Decay from the two lower levels is considered to be negligible. Because of energy conservation all fields are in four-photon resonance. It can be shown furthermore that the contributions of the resonant transitions to the linear refractive index vanish if the fields are pairwise in two-photon resonance. Phase matching will thus favor two-photon resonance and we assume that this condition is fulfilled. Resonant four-wave mixing has been analyzed both theoretically and experimentally with co-propagating as well as counter-propagating fields [6,7,8,9,10,11,12,13].Associated with the finite detuning ∆ are ac-Stark shifts which lead to intensity dependent dynamical phase shifts of the fields. These phase shifts are of minor consequence in the case where the fields are counterpropagating [13]. They do have a detrimental influence, however, for co-propagation. In the following we will concentrate on the latter situation and show how to eliminate these terms leading to a considerable improvement of nonlinear frequency conversion.The standard method ...

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Mirrorless Oscillation Based on Resonantly Enhanced 4-Wave Mixing: All-Order Analytic Solutions

Cited by 2 publications

References 13 publications

Nonperturbative quantum solutions to resonant four-wave mixing of two single-photon wave packets

Nonperturbative quantum solutions to resonant four-wave mixing of two single-photon wave packets

Eliminating nonlinear phase mismatch in resonantly enhanced four-wave mixing

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