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Physical Review A

Giant second-order cross nonlinearities via direct perturbation to the dark state in coherent population trapping

Guanghui Wang, Xiangming Hu, Qingping Hu, Liang Hu

Published Feb 12, 2020• 2 citations
Publisher

Abstract

We study the nonlinearities due to direct perturbation to the dark state in coherent population trapping (CPT). To extract the susceptibilities of the CPT atoms with respect to probe fields, we treat the CPT dressing fields as control parameters and redefine susceptibilities with respect to the probe fields alone. With such a redefinition, we reveal that a CPT-based system displays an ultralarge, resonantly enhanced second-order cross susceptibility ${\ensuremath{\chi}}^{(2)}$ together with vanishing linear absorption. Physically, this effect is based on the CPT dark-state shift, which is traced to the six-photon parametric processes for all involved fields (including the dressing and probe fields). Because of the lack of the direct perturbation, this effect is absent in the electromagnetically induced transparency (EIT)-based system, in which only resonantly enhanced third-order (Kerr) susceptibility ${\ensuremath{\chi}}^{(3)}$ is obtainable but much weaker than the second-order one. The second-order nonlinearity, because of its stronger effect, can be more sensitive for quantum nonlinear optics at low light levels than the third-order nonlinearity.

DOI
10.1103/physreva.101.023816

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We study the nonlinearities due to direct perturbation to the dark state in coherent population trapping (CPT). To extract the susceptibilities of the CPT atoms with respect to probe fields, we treat the CPT dressing fields as control parameters and redefine susceptibilities with respect to the probe fields alone. With such a redefinition, we reveal that a CPT-based system displays an ultralarge, resonantly enhanced second-order cross susceptibility \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) together with vanishing linear absorption. Physically, this effect is based on the CPT dark-state shift, which is traced to the six-photon parametric processes for all involved fields (including the dressing and probe fields). Because of the lack of the direct perturbation, this effect is absent in the electromagnetically induced transparency (EIT)-based system, in which only resonantly enhanced third-order (Kerr) susceptibility \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3) is obtainable but much weaker than the second-order one. The second-order nonlinearity, because of its stronger effect, can be more sensitive for quantum nonlinear optics at low light levels than the third-order nonlinearity.
A scheme for large enhancement of the third-order nonlinearity in a four-level system with double dark resonances is proposed. We obtain an analytical expression for the linear susceptibility and nonlinear susceptibility of a weak probe field and show that the properties of double electromagnetically induced transparency and the Kerr nonlinearity can be modified significantly by changing the ratio of the two coupling fields. A physical understanding of our numerical results using the dressed-state approach is presented. The obtained large nonlinearity with vanishing absorption can be used to generate optical solitons, polarization phase gates and optical Kerr shutters.
A theoretical investigation was carried out into the program for enhancing the Kerr nonlinearity by interacting double dark states resonances.Using density-matrix equations and perturbative iterative method,the dependence of the real part of the third-order susceptibility on the variation of the additional coherent driving field detuning was derived.It is found that the maximal Kerr nonlinearity induced by interacting dark resonances increases with increment of the detuning and enters gradually the electromagnetically induced transparency window,in which the corresponding linear absorption vanishes,moreover,by utilizing the dressed state theory,physical mechanisms for the results were presented.The realization of the giant Kerr nonlinearity with vanishing absorption is possible in a generic four-level system with double dark resonances.
A theoretical scheme for enhanced Kerr nonlinearity is proposed in a four-level ladder-type atomic system based on double dark resonances (DDRs). We solve the relevant density matrix equations in steady state and utilize the perturbation theory to obtain the analytical expressions for the third order susceptibility of the atomic system. The influence of system parameters on behavior of the first and third order susceptibilities is then discussed. In particular, it is found that an enhanced Kerr nonlinearity with reduced linear and nonlinear absorption is obtained around zero probe detuning under the slow light condition through proper adjusting the laser field intensity and frequency detuning of driving fields. The dressed state analysis is employed to explain the physical origin of the obtained result. The obtained results may be important for all-optical signal processing and quantum information technology.
We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg atoms under the condition of electromagnetically induced transparency (EIT). By using an approach beyond mean-field theory, we show that the system possesses not only enhanced third-order nonlinear optical susceptibility, but also giant fifth-order nonlinear optical susceptibility, which has a cubic dependence on atomic density. Our results demonstrate that both the third-order and the fifth-order nonlinear optical susceptibilities consist of two parts, contributed respectively by photon-atom interaction and Rydberg-Rydberg interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction plays a leading role at high atomic density. We find that the fifth-order nonlinear optical susceptibility in the Rydberg-EIT system may be five orders of magnitude larger than that obtained in traditional EIT systems. The results obtained may have promising applications in light and quantum information processing and transmission at weak-light level.
Electromagnetically induced transparency (EIT) is an optical phenomenon which allows a drastic modification of the optical properties of an atomic system by applying a control field. It has been largely studied in the last decades and nowadays we can find a huge number of experimental and theoretical related studies. Recently a similar phenomenon was also shown in quantum dot molecules (QDM), where the control field is replaced by the tunneling rate between quantum dots. Our results show that in the EIT regime, the optical properties of QDM and the atomic system are identical. However, here we show that in the strong probe field regime, i.e., "coherent population trapping" (CPT) regime, it appears a strong discrepancy on the optical properties of both systems. We show that the origin of such difference relies on the different decay rates of the excited state of the two systems, implying in a strong difference on their higher order nonlinear susceptibilities. Finally, we investigate the optical response of atom/QDM strongly coupled to a cavity mode. In particular, the QDM-cavity system has the advantage of allowing a better narrowing of the width of the dark state resonance in the CPT regime when compared with atom-cavity system.
Summary form only given. The field of quantum optics was greatly enriched with the discovery of dark states and electromagnetically induced transparency (EIT). Although these two processes give similar effects, they are distinctly different. Dark states (Gray et al, 1978) are quantum states created in a three-level lambda system that is decoupled from the excited state. Some of the main features are zero linear absorption, no population in the excited state and no spontaneous emission. One limiting factor of a dark state system is that self-phase modulation disappears together with absorption. EIT is a nonlinear effect that can provide transparency to a probe field in a variety of systems. Much work has been done on two-level, cascaded-three-level and even four-level systems. It has also been shown that a large third-order nonlinear susceptibility is present in the absence of absorption. However, spontaneous emission cannot be eliminated in such system, thereby limiting their applications, particularly, to squeezed light generation. Here, we combine the effects of both dark state and EIT to create a system that is suitable for squeezed light generation via self phase modulation.