Researchers have been working on how to realize the nonlinear photon–atom interaction at low power, a topic of great importance in both nonlinear optics^[1] and quantum optics.^[2,3] To enhance the nonlinear effects, the nonlinear optical polarization of matter can be enhanced by quantum interference. A famous example is electromagnetically induced transparency (EIT).^[4] On the other hand, an efficient way to enhance the nonlinear effect of low light is to reduce the mode volume. Approaches toward this direction including confining light in waveguides and cavities, where photonic band-gap fiber, integrated waveguide or optical nanofiber (ONF) can achieve this characteristic very well.^[5–12] There are also researches that combines the two methods, so as to explore quantum interference-enhanced nonlinear effects with confined light field.^[13,14] In this work, we use nanofiber to study the EIT effect at ultralow power, which belongs to this category as well. Compared with other structures, the nanofiber can confine the light field more tightly in the surface of fiber, forming the tightly-confined evanescent optical mode interacting with surrounding atoms at long distance.^[11,15] This property of ONF provides a new platform for studying nonlinear effects at ultralow power.

The electromagnetically induced transparency is a special nonlinear effect exhibited by the interaction between light and matter. The absorption of the weak probe field at the resonant frequency is reduced when a strong control field is used.^[4,16–18] The EIT effect can be widely used in four-wave mixing,^[19–21] all-optical switching,^[22,23] slow light, and optical storage.^[24,25] Recently, researchers have demonstrated EIT phenomenon in cold atoms ONF-based systems at ultralow power, and achieved the optical storage at the single photon level by the Λ-type EIT.^[26,27]

In this paper, we use an ONF-based system with hot cesium (Cs) atomic vapor to study the three-level ladder-type EIT phenomenon at ultralow power. This system is simpler than the cold atom system, and we can still observe obvious EIT phenomenon with a few microwatts of the control laser. The probe laser field couples the transition of 6S_1/2 → 6P_3/2, and the control laser field couples the 6P_3/2 → 8S_1/2. The EIT spectrum with Doppler-broadened background is obtained by scanning the frequency of the probe laser and fixing the frequency of the control laser when both lasers propagating in opposite directions. The transmission and linewidth of the EIT window as a function of the control laser power are also investigated. To systematically study the EIT effect, we numerically simulate the EIT spectrum by solving the steady-state density-matrix equations and integrating over the atomic velocity distribution. The simulation results show a good agreement with the experimental measurements.

We use the “flame-brush” technique with a hydrogen–oxygen flame to produce ONFs from standard fiber (Fiber Core SM800 5.6/125).^[28,29] The nanofiber for the experiment is composed of three parts: the input and output sections composed of a standard fiber, the 5-mm nanofiber regime with 500-nm diamter, and two tapered fiber regimes that smoothly connect the two parts. The simple structure of ONF is shown in Fig. 1(a). The guided optical mode of the ONF exhibits single mode guiding, tight radial confinement, as well as substantial evanescent field.^[15] Compared with free space experiments that typically requires milliwatt laser power for the nonlinear experiment, in the ONF experiments, the small evanescent mode and long interaction length of nanofibers allow us to observe the nonlinear effects with a few picowatts powers.^[26]

Fig. 1.

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	Fig. 1. (a) Optical nanofiber with 500-nm diameter and 5-mm length is surrounded by hot Cs atoms. (b) Schematic energy level of ladder-type EIT system. The 852-nm laser is the probe field and the 794-nm laser is the control field. Δp and Δc are the frequency detunings of the probe laser and the control laser, respectively.

In our system, ONF is mounted on a U-shaped bracket and placed in a vacuum system filled with Cs vapor, and release the atomic vapor by applying a current to the Cs dispenser. In order to reduce transmission losses due to the accumulation of atoms on the nanofiber surface, we maintain the fiber temperature with special heater element and keep the temperature of the fiber slightly higher than the vacuum chamber.^[30] Figure 1(b) shows the schematic energy levels. The 852-nm probe field and 794-nm control field couple the 6S_1/2 → 6P_3/2 → 8S_1/2 two-photon transition. When probe light resonates to 6S_1/2 → 6P_3/2 transition, the probe light is strongly absorbed due to the evanescent wave interaction with atoms. However, simultaneously, if the control laser is also resonant to 6P_3/2 → 8S_1/2, the probe absorption is obviously reduced, and thus the EIT effect happens. The two external cavity diode lasers are used to couple these transitions.

The schematic diagram of our experimental scheme is shown in Fig. 2. The 852-nm and 794-nm lasers are counter-propagating through the ONF. The counter-propagating geometry is applied in order to reduce the Doppler effect of the two-photon coupling. Both the 852-nm and 794-nm lasers pass through the neutral density filter (ND) and are split into two beams by 50/50 fiber splitter. By recording one of the 50/50 splitter output with a photodiode, the beam power for the experiment from the other output is continuously monitored. To observe the absorption signal of the probe beam, we use a photomultiplier tube (PMT). To provide a reference signal for the ONF experiments, part of an 852-nm laser is split by a polarization beam splitter (PBS) and enter a saturated absorption spectrum (SAS) setup. The power of two lasers can be controlled by the neutral density filter at the nanowatt level.

Fig. 2.

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	Fig. 2. Schematic diagram of the optical experimental setup: λ/2, half-wave plate; PBS, polarization beam splitter; ND, neutral density filter; PD, photodiode; filter, 852-nm bandpass filter; PMT, photomultiplier tube; SAS, saturated absorption spectrum. The probe and control lasers are counter-propagating through the ONF.

The red line in Fig. 3(a) indicates the {normalized absorption spectroscopy of the probe laser with a power of 1.5 nW in the nanofiber system, and the control laser is turned off. The frequency of the probe laser is scanned around the transition of |6S_1/2, F = 4⟩ → |6P_3/2, F′ = 5⟩ and detect by PMT. The black line in Fig. 3(a) shows the free-space SAS, which acted as a frequency reference. We gain the normalized EIT spectrum with Doppler-broadened background when the control laser with a power of 34.3 μW is locked at the transition of |6P_3/2,F′ = 5 ⟩ → |8S_1/2,F″ = 4⟩, as shown in Fig. 3(b) (the red line).

Fig. 3.

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	Fig. 3. (a) The normalized transmission spectrum of the probe laser in the absence of the control laser. The black line is the free-space SAS spectrum. (b) Experimental observation (red line) and theoretical simulation (black line) of EIT spectrum with Doppler-broadened background. The control laser frequency is fixed on resonance with a power of 34.3 μW.

To get a better understanding of physics behind this observation, we numerically solve the density matrix equation, taking into account the velocity distribution of atoms, and compare the numerically evaluated results with the experimental observations. Start from a three-level model as shown in Fig. 1(b), we apply rotating-wave approximation to the three-level Hamiltonian, leading to the density matrix equation as follows:^[31,32] 1 ρ11.=Γ2ρ22+iΩp(ρ21−ρ12),ρ22.=Γ3ρ33−Γ2ρ22+iΩp(ρ12−ρ21)+iΩc(ρ32−ρ23),ρ33.=−Γ3ρ33+iΩc(ρ23−ρ32),ρ12.=−(γ12−iΔp)ρ12−iΩcρ13+iΩp(ρ22−ρ11),ρ13.=−[ γ13−i(Δp+Δc) ]ρ13+iΩpρ23−iΩcρ12,ρ23.=−(γ23−iΔc)ρ23+iΩpρ13+iΩc(ρ33−ρ22). Here Δ_p = ω_p − ω₂₁ and Δ_c = ω_c − ω₃₂ are the detunings of the probe and control laser frequencies relative to the |1⟩ → |2⟩, |2⟩ → |3⟩ transitions respectively. Ω_p = μ₂₁E_p/ħ (Ω_c = μ₃₂E_c/ħ) is the Rabi frequency of the probe (control) field. Here μ₂₁ and μ₃₂ are the electric-dipole moment for transitions |1⟩ → |2⟩ and |2⟩ → |3⟩, respectively. E_p and E_c are the amplitude of the probe and control fields, respectively. The decay rate is determined by γ_ij = (Γ_i + Γ_j)/2, and the Γ_i represents the natural decay rate of the energy level |i⟩.

In the weak probe limit, the matrix element ρ₂₁ is obtained by solving the above equation with first-order perturbation approximation^[31,32]

In our experiment, the probe laser and control laser are counter-propagating and the Doppler shift needs to be considered due to their large frequency difference. In the Doppler-broadened system, when the atom with velocity ν moves toward the probe laser, the detuning Δ_p of the probe laser should be substituted by Δ_p + ω_pν/c and the detuning Δ_c of the control laser should be substituted by Δ_c − ω_cν/c.^[32] The absorption characteristic of the atomic medium is determined by the imaginary part of total susceptibility^[31,32]

To investigate the effect of control power on the full width at half maximum (FWHM) and transmission intensity of EIT window, the different control powers are used and the probe power is fixed at 1.5 nW. The black dots with error bars in Fig. 4 are the standard deviation of five measurements. The black dots in Fig. 4(a) reveal that the FWHM (the linewidth obtained by fitting the experimental EIT transparent window using the Lorentz function) of EIT} gradually increases when the power of the control field increases. For further clarification about the variation of FWHM with the control power, we use the following formula^[34–36] to compare the theoretical result with the experimental observation

Fig. 4.

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	Fig. 4. The black dots with error bars represent the influence of control intensity in the FWHM (a) and transmission (b) of EIT window. The red lines represent the theoretical curve. Both the FWHM and normalized transmission increase with the control laser power.

Figure 4(b) shows the dependence of normalized transmission (the ratio of the change in the zero-detuning probe transmission in the absence and presence of control laser) as a function of the control power. The increasing tendency of transmission with increasing control power is apparent. According to Eq. (3), we are able to calculate the absorption at the resonance Δ_p = Δ_c = 0, and to predict the change of normalized transmission with the control power. However, theoretical calculation will be very complicated when we take into account the small Doppler-shift of the two-photon transition. Equation (3) can be simplified by ignoring the Doppler broadening of the two-photon transition when the detuning Δ_p = Δ_c = 0, and obtain the following formula:^[32]

In conclusion, we study the three-level ladder-type EIT effect using a nanofiber–Cs vapor interface in the presence of Doppler-broadened and using very low-power probe and control laser beams. We use density matrix equations to numerically reproduce the experimental observations, showing fairly good agreements between the simple theory and experimental observations. The benefit of light confinement in ONF should allow other type of nonlinaer optical experiments, in addition to the ladder-type EIT as in this work. This study may also contribute to realization of EIT-based low-light level optical switch and optical memory.