Absorption spectra of cold cesium atoms confined in a magneto-optical trap are observed around the D2 transition line (6S1/2, F=4→6P3/2, F’=5) with the probe laser frequency detuned near the trapping laser frequency. We observe the dispersion-like profile resulted from the stimulated Raman processes with the sub-natural linewidth, and study the behavior of the group velocity of light in trapped cold atoms. By only changing the blue and red detuning of the probe frequency from the trapping laser frequency, we are able to arbitrarily control the speed of a light pulse from subluminal to superluminal velocity.
©2008 Optical Society of America
The optical response of an atomic medium with a controlling strong coupling laser has been of great interest [1–8]. Dispersive and absorptive properties of an absorbing medium may be modified by the coherence and interference induced by a resonant laser field. Theoretical and experimental studies have shown that quantum interference will result in many possibilities. The optical material with a high index of refraction and low absorption has potential and practical applications and fundamental studies. In a highly dispersive medium, the group velocity can become very different from the speed of light in vacuum, and sometimes may result in “superluminal” propagation [1, 3, 4, 6] or “subluminal” propagation [2–5, 8]. Kim group demonstrated the subluminal and superluminal light by using different coupling laser intensity in a vapor cell . Akulshin has obtained very large anomalous dispersion based on electromagnetically induced absorption (EIA) system . Cold atoms, which are free of Doppler broadening and transit-time broadening, are the most suitable for investigating the strong interaction between light and matter because the coherence lifetime is often limited by the interaction time of the atoms with the lasers. In previous experiments, Zhu group realized the light pulse superluminal and slow propagating in a cold atomic medium by electromagnetically assisted nonlinear optical processes . Hau group can get the group velocity of light down to 17m/s in an ultracold gas of sodium atoms by using the electromagnetically induced transparency (EIT) effect, where the narrow transparency resonance is accompanied by a steep slope of the refractive index dispersion .
In the experiments mentioned above, people usually use EIT or gain medium to get a large normal or positive dispersion (dn/dω>0), or use EIA medium to get anomalous or negative dispersion (dn/dω<0). However, the EIT medium is not a prerequisite for extremely slow propagation. Bennink group  has predicted that slow and fast-light effects can be also obtained in the response of a strongly driven two-level atom, which is much simpler than the multi-level atomic system. An alternative Raman gain scheme is also studied experimentally for the group velocity reduction of light in a hot resonant Rb medium .
In this paper, we observe the dispersion-like spectra resulted from the stimulated Raman processes (SRP) in trapped cold atoms. It will be shown that the probe beam has a group velocity with subluminal or superluminal when it is detuned with respect to the pump beam.
2. Experiment and results
A simplified experimental setup is shown in fig. 1(a). Cold Cs atom sample is produced by a conventional vapor cell MOT . A Littman-Metcalf external-cavity diode laser (NewFocus 6017 model) (ECDL) is used as the repumping source, which is stabilized via the conventional locking technique based on saturated absorption spectroscopy and resonant to the 6S1/2F=3→6P3/2F’=4 transition of Cs D2 line. Relevant hyperfine levels of Cs atoms are shown in fig.1 (b). Three pairs trapping beams with σ+ and σ- polarizations (typically about 8 mW with size of 20 mm per beam), also playing the role of pump beams for SRP, are from a single-frequency Ti: Sapphire laser, whose frequency is shifted by using an acousto-optical modulator (AOM1). We use the first-order diffraction beam from the AOM1 as the trapping beam. We fixed the trapping detuning from the atomic resonant frequency, which is about Δ=2Γ~4Γ (Γ is the Cs transition’s natural linewidth) below the F=4→F’=5 transition. The temperature of cold atoms is about 100µK which corresponds to the atomic velocity in the order of 10 cm/s and the size of cold Cs cloud is about 2 mm. A part of laser from Ti: Sapphire laser is chopped as Gaussian shaped pulse using AOM2 drived by a power amplifier trigged with an arbitrary waveform generator (HP33120A) and works as the probe beam for SRP. The full width at half maximum (FWHM) of the pulse is about 3.4 µs with σ- polarized. The typical peak power is about 16 µW. At the same time, by exactly adjusting the frequency of radio frequency (RF) driver of AOM2, we realize the detuning of the probe beam from the driving frequency ΔP. The probe and reference output signals are recorded simultaneously using a digital oscilloscope (Tektronix TDS1012). The quadrupole magnetic field is on all the time, i.e., the recorded spectra characterize a working MOT rather than an unperturbed cloud of cold atoms. The grating washing effect  is strongly reduced for nearly immobile atoms, which allows us to use a relatively big angle between the pump and the probe beams. In our experiment, the angle between one of the trapping beams and the probe beam is about π/4 radian.
It is well known that manipulation of light speed in an optical medium can be realized by changing the dispersive properties of the medium. The group velocity can be described by Vg=c/(n+ωdn/dω), where c is the speed of light in vacuum, and ω is the angular frequency of the light. In this experiment, we measured the delay time as a function of probe laser detuning ΔP (ΔP=ωT-ωp) by using an AOM2 to scan the probe beam frequency, where ωT is the frequency of the trapping beam and ωp is the frequency of the probe beam. The narrow feature of probe beam has a width of 500 kHz with a complex sub-natural structure, and the ratio of gain and absorption is about 30% based on the stimulated Raman effect (as shown in fig. 2). This resulted in perfect phase correlation between the trapping and probe beams , and the probe beam can obtain larger nonlinear optical susceptibilities. The broad features of absorption spectra are in reasonable agreement with the theory of two-state atoms in a strong field . The dispersion-like lineshape, resulting from the SRP between ground-state Zeeman sublevels, allows us to determine the position of ωT. The positions of the Raman resonances depend on the pump light intensity and the relevant Clebsch-Gordan coefficients . In fig. 2, two dispersion-like absorption profiles are observed. The distance between the two Raman peaks corresponds to differential light shifts between different magnetic substates. We find that the curve (b) is much steeper than curve (a), which means that the trapping beam frequency can effectively affect the dispersive and absorptive properties of the medium. The detuning frequency Δ is -12MHz (curve a) and -17MHz (curve b) below the F=4→F’=5 resonant transition, respectively.
Figure 3 plots the transmitted probe pulses versus the time at ΔP≈145kHz and ΔP ≈-150 kHz with the pump frequency detuning Δ of -17 MHz. The maximum position of the pulse is extracted by a Gaussian fit to the experimental data (the black solid lines). The probe pulse is delayed by 0.25µs and advanced by 0.13µs relative to the reference light pulse, and the corresponding group velocity is Vg=c/37500 and Vg=-c/195000, respectively. Thus, the sign of the group velocity can be strongly changed by tuning the one-photon detuning ΔP, but the distortion of the pulse shape is not strong because the spectral width is within the narrow region of constant dispersion .
We also measure the pulse delay and advancement as a function of one-photon detuning ΔP as shown in fig. 4. The parameters are the same as those in fig. 2. Thanks to the double frequency sweeping technique , the error of one-photon detuning ΔP can be easily controlled within 10 kHz. A wide range group-velocity variation can be achieved by changing one-photon detuning ΔP between normal and anomalous dispersion.
Guo and Berman have given a simple model for calculating the Raman transitions , in which the case of Jg=1→Je=2 transition was driven by two pump beams with σ+ and σ- polarizations and σ- probe beam. We present the theoretical curves as shown in fig.5 based on the result in reference . The solid line shows the probe absorption signal as a function of detuning and dot line is the pulse delay of probe signal. The quantitative description of the spectra should be considered for all the Raman transitions between light-shifted Zeeman sublevels. The parameters are Δ=-17MHz, χ=3MHz, ku=180kHz; where χ is a pump-beam Rabi frequency; ku is Doppler width of cold atom. The experiment results in fig.4 have an agreement with the theory very well.
In conclusion, we have observed the arbitrarily copropagating the group velocity with probe laser detuning based on the SRP. The probe beam has a group velocity with subluminal when it is blue detuned and superluminal when it is red detuned with respect to the pump beam. We have obtained the pulse propagation time up to 0.25µs of delay and 0.13µs of advance by using ΔP≈145kHz and ΔP≈-150kHz, respectively. Coherently prepared medium with optically controlled dispersion can be of interest for the design of new devices for pulse delay or advancement in communication systems and optical computing.
We thank Professor Luis A. Orozco for fruitful discussions. This project was supported by the 973 program (Grant NOs. 2006CB921603 and 2008CB317103), the National Natural Science Foundation of China (Grant NOs. 10574084, 60678003 and 10674086), the Natural Science Foundation of Shanxi province, China (Grant No. 2007011006) and NCET(NCET-06-0259).
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