1. Introduction

All-optical switch is an important component in high-speed optical communication networks and has potential applications in quantum information systems. In the past decade, all-optical ultrafast switching has been a subject of numerous studies and many interesting proposals toward its realization have been carried out. Several promising proposals, e.g. based on quantum interference, are demonstrated with differentmechanisms, such as electromagnetically induced transparency (EIT) [1, 2, 3, 4, 5], transverse optical pattern [6, 7], stimulated raman adiabatic passage (STIRAP) [8, 9], electromagnetically induced absorption grating (EIG) [10], Fano interference [11], and stored light pulses [12, 13], etc. Quantum interference based all-optical switching exhibits such favorable advantages as high response speed and low switching power comparedwith electro-optical switching and the ones of using silicon waveguides or fiber-based systems.

In our knowledge, all-optical switch is usually implemented by turning on or off one light beam with another light beam (defined here as one-way switch). Compared with one-way switch, it is obvious that multi-way switch, where two or more light beams are controlled synchronously or asynchronously by a single light beam, is more advantageous in improving the communication capacity [14]. In this letter, we report an experimental observation of dual-channel all-optical switching based on four-wavemixing (FWM) in a four-level atomic system. Of interest to this letter is that two light signals with different wavelengths can be switched on or off respectively by a single pump field. The key point is that ⁸⁷ Rb and ⁸⁵ Rb isotopes are simultaneously driven by the applied coupling and pump fields, which then result in the generation of two FWM signals with different wavelengths as the probe fields are sent into the atomic sample. We show in particular that, in this dual-channel optical switch, intensities of the two FWM signals can be well controlled by modulating the pump frequency.

2. Energy Structure and Theoretical Basis

The atom-light interaction scheme for the proposed all-optical switching is depicted in Fig. 1. For ⁸⁷ Rb atoms, a standard three-level Λ-type EIT configuration is formed when a strong coupling field Ω₁ with the detuning of δ ₁ and a weak probe field Ω_p with the detuning of δ_p are applied on the medium to drive respectively transitions |2〉↔|3〉 and |1〉↔|3〉. A strong pump field Ω₂ with the detuning of δ₂ drives transition |2〉↔|4i to facilitate the generation of a FWM signal Ω_f with the detuning of δf on transition |1〉↔|4〉. Here the detuned probe and coupling fields are kept in two-photon resonance δ_p=δ ₁, thus another two-photon resonant condition δ_f=δ ₂ is also satisfied due to the energy-conservation and phase-matching requirements. On the other hand, for ⁸⁵ Rb atoms, the coupling field Ω₁ drives transition |2′〉↔|3′〉 with the detuning of δ′₁=δ ₁-913MHz and the pump field Ω₂ drives transition |2′〉↔|4′〉 with the detuning of δ′₂=δ ₂-1218 MHz. When the probe field Ω′_p is applied on transition |1′〉↔|3′〉 with the detuning of δ′_p and the two-photon resonance δ′_p=δ′₁ is satisfied, the second generated FWM signal Ω′_f with the detuning of δ′_f=δ′₂ may be observed due to the energy-conservation phase-matching requirements. The frequency detunings for the respective transitions are defined as δ ₁=ω ₁-ω ₂₃, δ ₂=ω ₂-ω ₂₄, δ_p=ω_p-ω ₁₃, δ_f=ω_f-ω ₁₄, δ′₁=ω _1-ω2′3′, δ′2=ω ₂-ω _2′4′, δ′p=ω′_p-ω _1′3′, δ′_f=ω′_f-ω _1′4′[ω_i(i=1,2, p, p′, f, f′) is the angular frequency of the corresponding laser field].

 

Fig. 1. (Color online) Diagrams of the four-level double-L system of ⁸⁵ Rb and ⁸⁷ Rb atom for strong nonlinear interactions. The two laser fields Ω₁ and Ω₂ drive the transitions in ⁸⁵ Rb and ⁸⁷ Rb atom as shown. When the probe field Ω_p (or Ω′_p) is applied to the transition in ⁸⁷ Rb (or ⁸⁵ Rb) atom and two-photon resonance is formed in lower-L configuration, a FWM signal Ω_f (or Ω′_f) is observed at the end of the vapor cell.

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It is well known that, within an EIT window, the linear susceptibility χ ⁽¹⁾ can be substantially reduced as a result of destructive quantum coherence while the nonlinear coefficient χ ⁽³⁾ associated with the nonlinear-optical generation process may be greatly enhanced [15]. But when a pump field sharing the same lower-level with the coupling field is resonantly applied on an auxiliary transition as shown in Fig. 1, the depth of the EIT window will be remarkably reduced due to the two-photon absorption [16]. This then leads to a reduction of the nonlinear coefficient χ ⁽³⁾ as well as an attenuation of the generated FWM signal. Fortunately, this attenuation can be compensated with a large pump detuning [17] leading to the improved the nonlinear coefficient χ ⁽³⁾ in off-resonance regions, which means that the FWM signal intensity can be well controlled by modulating the pump detuning. We should note that, however, the pump detuning corresponding to the signal peak generated in ⁸⁷ Rb atoms is quite different from that in ⁸⁵ Rb atoms because of the isotope shifts between ⁸⁵ Rb and ⁸⁷ Rb atoms. That is, we can separately enhance or reduce intensities of the two FWM signals by simply adjusting the pump frequency. Thus our scheme may also be used as a wavelength-conversion [18, 19, 20] quantum switch, where the pump field turns on or off the FWM signals at different frequencies. Moreover, during the process of switching, informations carried by the probe field will be reserved and converted into the generated FWM field with a different wavelength [17]. This is true, for instance, if informations are loaded onto the probe field by amplitude modulation, because the intensity of the output FWM field depends linearly on the intensity of the input probe field.

3. Experimental Setup

The experiment is done with hot ⁸⁵ Rb (natural abundance ~72.17%) and ⁸⁷ _Rb (~27.83%) atoms in a 7.5-cm-long temperature-stabilized vapor cell filled with 0.4Torr Ne buffer gas. The temperature of the cell is set to ~62°C (atomic density of ~2.2×10¹¹cm^-3) and the optical depth NσL is ~311 for the incident probe field and ~300 for the generated FWM field. An experimental setup is depicted in Fig. 2 where a Ti:sapphire ring laser (Coherent 899 ring laser system) with a power of ~24mW, acting as the coupling field Ω₁, simultaneously drives transition |2〉↔|3〉 of ⁸⁷ Rb atoms and |2′〉↔|3′〉 of ⁸⁵ Rb atoms. An external cavity diode laser (ECDL1, DL100) with a power of ~0.5mW, acting as the probe field Ω_p (Ω′ _p), is scanned across the D ₁ line of ⁸⁵ Rb and ⁸⁷ Rb atoms. Another external cavity diode laser (ECDL2, DL100) with a power of ~10mW, acting as the pump field Ω₂, simultaneously drives transition |2〉↔|4〉 of ⁸⁷ Rb atom and |2′〉↔|4′〉 of ⁸⁵ Rb atoms. All laser beams are linearly polarized and collinearly propagate inside the vapor cell with the help of a half-wave plate and a polarization beam splitter (PBS1). The collinear laser beams are also focused inside the vapor cell by a lens to allow the probe beam to be completely contained in the coupling and pump beams so that all probed atoms are coherently prepared. After leaving the vapor cell, most of the coupling field Ω₁ and the generated FWM signal Ω_f(Ω′_f) will be reflected by a polarization beam splitter (PBS2), while the pump field Ω₂ and the probe field Ω_p (Ω′_p) will pass through PBS2 due to their perpendicular polarizations relative to the coupling field and the FWM signal. A grating with a groove density of 1200 lines/mm is used to spatially separate the pump field Ω₂ at 780nm and the probe field Ω_p (Ω′_p) at 795nm. Photodiode D1 monitors the transmission spectrum of the probe beam Ω_p (Ω′_p) or the pump beam Ω₂ when it is scanned in frequency. Another grating, same as the first one, is used to spatially separate the coupling field Ω₁ and the FWM signal Ω_f (Ω′_f). Photodiode D2 is used to detect the generated FWM signal.

 

Fig. 2. (Color online) Simplified diagram of the experimental setup. Ti:sapphire: Ti:sapphire ring laser; ECDL: external cavity diode laser; BS: beam splitter; λ/2: half-wave plate; PBS: polarization beam splitter; D1&D2: photodiode.

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4. Experimental Results and Discussions

The measured FWM signals as a function of the pump detuning are shown in Fig. 3. For these measurements, the coupling field Ω₁ is always resonant with transition |2〉↔|3〉 of ⁸⁷ Rb atoms (δ ₁=0) while the probe frequency ω_p is fixed to form the two-photon resonance δ ₁=δ_p or δ′₁=δ′_p, separately. For the FWM signal generated in ⁸⁷ Rb atoms (red square), a peak is found in this curve due to the improved nonlinear coefficient χ ⁽³⁾ and the reduced resonant interaction between the pump field and transition |2〉↔|4〉. The pump detuning corresponding to the FWM signal peak is ~-1.127GHz (relative to transition |2〉↔|4〉 of ⁸⁷ Rb atoms). The profile of the FWM signal generated in ⁸⁵ Rb atoms (black circle) is similar to that in ⁸⁷ Rb atom. But the pump detuning corresponding to the FWM signal peak is ~-96MHz, which is quite different from that in ⁸⁷ Rb atoms. The difference in pump frequency opens a way to implement a dual-channel optical switching. Let’s pay more attention to the tick points A, B, C, and D in Fig. 3. With the gradual departure from the pump resonance, four different output statuses are shown in turn. With a small pump detuning, a maximal FWM signal of ⁸⁵ Rb atoms is shown at point A while the FWMsignal of ⁸⁷ Rb is small enough to be negligible. With increased pump detunings, the FWM signal intensity of ⁸⁵ Rb atoms decreases while that of ⁸⁷ Rb atoms increases instead. This leads to the same FWM signal intensities for both ⁸⁵ Rb and ⁸⁷ Rb atoms at point B, as well as the phenomena of the maximum FWM signal for ⁸⁷ Rb atoms and the negligible FWM signal for ⁸⁵ Rb atoms at point C. As the pump detuning is larger enough, both FWM signals become even hard to be seen at point D.

 

Fig. 3. (Color online) The output FWM signal spectra of ⁸⁷ Rb atom (red square) and ⁸⁵ Rb atom (black circle) versus the pump detuning δ ₂. The red and black solid curves are the guideline for the measured data. The points A, B, C, and D demonstrate the four statuses of this proposed optical switching, which are marked by the dash lines at different pump detuning.

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For a clear sight on this dual-channel optical switching, we present now the experimental results as viewed from the channel statuses. A series of measured FWM signals as a function of the probe detuning are plotted in Fig. 4. For these measurements, the pump detuning is fixed sequentially at the tick points A, B, C, and D as shown in Fig. 3. The channel I (the FWM signal of ⁸⁵ Rb atoms depicted as the left part in Fig. 4) is switched on (Fig. 4A) and off (Fig. 4D) when the pump detuning is set as -96MHz (point A) and -1.826GHz (point D) in turn, with frequency conversion efficiencies η=I_f(z=L)/I_p(z=0) respectively to be ~65% and ~2%. During the process of switching on and off channel I, the output of channel II (the FWM signal of ⁸⁷ Rb atoms depicted as the right part in Fig. 4) is always small (η≤2%). On the other hand, the channel II is switched on (Fig. 4C) and off (Fig. 4D) when the pump detuning is set as -1.127GHz (point C) and -1.826GHz (point D) in turn, with frequency conversion efficiencies h respectively to be ~72% and ~2%. During this switching process, the output of channel I is also very small (η≤5%). For the case where channel II is on, the absorption coefficient for the probe field is estimated to be 0.26cm^-1. This estimation is based on the fact that the transmissivity is ~14.38% at the EIT window center and the output probe field has an intensity ~0.115mW corresponding to the total light losses ~5%. Furthermore, both channel I and channel II are switched on (Fig. 4B, η≃30%) when the pump detuning is set as -838MHz (point B), and are switched off (Fig. 4D) when the pump detuning is set as -1.826GHz (point D). It is convinced that the output of the dual-channel optical switch is the combination of two FWM signals Ω_f and Ω′ _f with different frequencies because the applied laser beams can interact with either ⁸⁷ Rb atoms or ⁸⁵ Rb atoms when the probe detuning is continuously scanned. As discussed above, this dual-channel optical switch has four distinct statuses: only channel I open, only channel II open, both channels open, and both channels closed, which are mainly determined by the pump detuning. Finally, we note that the FWM signal intensity depends critically on the buffer gas pressure. In the presence of buffer atoms, the spectral line broadening occurs and the atom-light resonant interaction is enhanced, which have led in fact to the broadened spectra of the FWM signals. Additionally, this will further result in the unclosed channel I at the pump detuning -1.127GHz if the buffer gas pressure is much higher than 0.4Torr. It is expected that intensities of the two FWM signals will be negligibly small at the pump detuning -838MHz if the buffer gas pressure is very low compared with the present one.

 

Fig. 4. (Color Online) The output FWM signal spectra of ⁸⁵ Rb atom and ⁸⁷ Rb atom versus the probe detuning ∞ ₁. These FWMsignals (from upper to lower) denote the four switching statuses corresponding to the marked point A, B, C, and D in Fig. 3.

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5. Conclusion

In conclusion, we have demonstrated in experiment a dual-channel all-optical wavelength-conversion switching scheme utilizing the four-wave mixing process in a hot vapor cell containing both ⁸⁵ Rb and ⁸⁷ Rb isotopes. We find that two channels of this all-optical switching at different probe frequencies can be separately switched on or off by simply modulating the the pump frequency.