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Chinese Physics B

A low noise, high fidelity cross phase modulation in multi-level atomic medium*

Liangwei Wang, Jia Guan, Chengjie Zhu, Runbing Li, Jing Shi

Published Jun 3, 2021• 2 citations
Publisher

Abstract

We develop a hybrid scheme of cross phase modulation based on electromagnetically induced transparency (EIT) and active Raman gain (ARG) in a multi-level atomic medium. The cross phase modulation, with low loss and without noise, is demonstrated in a room-temperature 85Rb vapor. We show that a π radian nonlinear Kerr phase shift of the signal light relative to a reference light is observed when the signal light is modulated by the phase control field with the low light intensity. We also show that the linear and the third-order absorption can be eliminated via the Raman gain, and the phase noise of the signal light can be ignored when the phase control light is applied in this hybrid scheme.

DOI
10.1088/1674-1056/ac078d

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•Jan 1, 2007•0 citations
We develop a hybrid scheme of cross phase modulation based on electromagnetically induced transparency (EIT) and active Raman gain (ARG) in a multi-level atomic medium. The cross phase modulation, with low loss and without noise, is demonstrated in a room-temperature 85Rb vapor. We show that a π radian nonlinear Kerr phase shift of the signal light relative to a reference light is observed when the signal light is modulated by the phase control field with the low light intensity. We also show that the linear and the third-order absorption can be eliminated via the Raman gain, and the phase noise of the signal light can be ignored when the phase control light is applied in this hybrid scheme.
We propose a multifunction phase-shifting manipulator with low noise at a single-photon level,by using a threelevel atomic scheme.This three-level system interacts with a strong pumping field and a weak probe field with a large detuning.Due to this large detuning,two lower states can be coherently prepared prior to the injection of the pump and probe fields.In our configuration,the duration of the pumping field is much longer than that of the probe field. By solving the Heisenberg-Langevin equations of our system under the steady state approximation,we calculate the linear susceptibility of the system and examine the quantum noise properties of the probe field in detail.We show that this scheme,which rests on the process of two-wave mixing with initial atomic coherence,exhibits many interesting properties that neither typical electromagnetically induced transparency (EIT) schemes nor active Raman gain (ARG) schemes possess.Although both EIT-and ARG-based schemes have been widely investigated in atomic medium,the direct generalizations of these schemes to the single/few photon limit prove to be more problematic.The low fidelity due to the significant probe-field attenuation in EIT medium and the large quantum noise due to the amplification of the probe field in an active Raman gain medium are the main obstacles that prohibit a high-fidelity,low-noise phase shifter from being realized in the single/few photon limit.Physically,this scheme can be viewed as a hybrid scheme in which two processes of different physical principles are allowed to interfere with each other to achieve many desired functionalities. For instance,it can be used as a lossless two-photon-broadband phase-shifter with suitable system parameters.It can also be used as an attenuator/amplifier and a total transparency with a zero phase shift.In particular,we show that by locking the pump field intensity and the two-photon detuning simultaneously a flat constant π-phase shift can be realized with unit probe fidelity in a broad probe field frequency range.Applying the quantum regression theorem,we calculate the noise spectrum of the outgoing probe field as a large phase shift is achieved,and show that this two-photon-insensitive π-phase shift may significantly reduce the quantum noise fluctuations associated with a Raman gain process,and have a lot of potential applications for quantum information processing and optical telecommunication.The realization of this broadband π-phase-shift with significantly reduced quantum noise fluctuations makes this scheme attractive for the realization of low-noise phase-gate/polarization-gate at single-photon level.
We experimentally demonstrate a low-light-level cross-phase-modulation (XPM) scheme based on the light-storage technique in laser-cooled 87Rb atoms. The proposed scheme can achieve a similar phase shift and has the same figure of merit as one using static electromagnetically induced transparency under the constant coupling field. Nevertheless, the phase shift and the energy loss of a probe pulse induced by a signal pulse are neither influenced by the coupling intensity nor by the atomic optical density in the light-storage XPM scheme. This scheme enhances the flexibility of the experiment and makes possible conditional phase shifts on the order of pi with single photons.
We consider an active-Raman-gain scheme for realizing giant Kerr nonlinearity and superluminal optical solitons in a four-state atomic system with a gain doublet. We show that this scheme, which is fundamentally different from those based on electromagnetically induced transparency (EIT), is capable of working at room temperature and eliminating nearly all attenuation and distortion.We demonstrate that, due to the appearance of a gain spectrum hole induced by the quantum interference effect induced by a signal field, a significant enhancement of Kerr nonlinearity of probe field can be realized effectively, which can be more than ten times larger than that arrived by the EIT-based scheme with the same energy-level configuration. Based on these important features, we obtain a giant cross-phase modulation effect and hence a stable long-distance propagation of optical solitons, which have superluminal propagating velocity and very low generating power.
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 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.