Understanding Basics

According to the theory of Relativity of Einstein the speed of light, c is an absolute constant and its value is 3 5 10⁸ m/s in vacuum. However, it is well known that light can be slowed to a smaller extent in refractive and transparent media. For example, in water or glass the speed of light is 1.5-2.0 times slower than c. This reduction can be understood from the fact that the velocity of light in the medium is given by the group velocity

where n(w ) is the refractive index of the medium and w is the frequency of light. Both n(w ) and are positive for normal material and therefore by increasing n(w ) or the term the velocity of light can be reduced . However, for normal optical material n(w ) ~1 and the region where is large , that is near resonance, the absorption is also very large. Thus although there is a possibility of decreasing the speed of light by making very large, this cannot be realized in practice because at such frequency, the absorption is also very high. Consequently, it is not possible to observe very large reduction in the speed of propagation of light in a normal medium. However, the situation can be changed dramatically, if the medium is made absorption free! Recently, by using the technique of quantum control such a possibility has been brought to fruition. These media show remarkably different dispersive and absorptive characteristic and can cause enormous reduction in the speed of light.

then briefly describe the experiment of Hau et al. To describe EIT we consider a three level system interacting with two laser fields, of frequencies n ₁ and n ₂, as shown in Fig.1. In the system two lower levels |2ñ and |1ñ are coupled

to a single upper level |3ñ and W _c and W _p are the complex Rabi frequency associated with the field coupling |2ñ ® |3ñ and |1ñ ® |3ñ transitions respectively. We assume the initial atomic state to be a superposition of the two lower levels |2ñ and |3ñ , that is

where C₁ and C₂ are the probability amplitude so that | C₁| ² and | C₂| ² are the probabilities of finding the system in states | 2ñ and | 3ñ , respectively. It follows that | C₁| ² + | C₂| ² = 1. Moreover, we also assume that the field W _c to be resonant with |2ñ ® |3ñ transition and W _p with |1ñ ® |3ñ . The time dependent probability amplitude for state |3ñ subject to the above initial condition, i.e. C₃(0)= 0 is

With corresponding eigenvalues , and . The state | y _-ñ has the property that the transition dipole moment between it and | y ₊ñ and | y _-ñ vanishes. As a result of this the state | y _- ñ is immune to any transition due to the presence of any external radiation. We also note that the state | y ₀ ñ is identical to the superposition state of Eq.(2) with C₁ and C₂ given by Eq.(4) and (5) respectively. In EIT, the atom is initially present in the ground state |1ñ and it is pumped into the dark state dynamically by the combined action of the strong coupling laser and weak probe by the mechanism of adiabatic population transfer. For atom initially in | 1ñ and only coupling laser is switched on then the trapped state coincides with | 1ñ Then after some time probe pulse is switched an adiabiaticaly then atomic state of system is time dependent trapping state.

The adiabaticity condition is satisfied if W _c and W _p are much greater than decay rate and inverse of the pulse duration. The refractive index and absorption of the probe as a function probe frequency from line center of |1ñ ® |2ñ transition is shown in Fig.2. It can be seen that absorption is zero at the line center complete transparency and variation refractive index with frequency is very large at resonance. Thus in such a medium the probe pulse will travel at a speed substantially smaller than the speed of light in vacuum without undergoing any appreciable absorption. This kind of quantum controlled system has recently been used by Hau et al. [1] to slow down the speed of light incredibly.

Fig. 2 The refractive index and absorption of the probe as a function probe frequency from line center of |1ñ ® |2ñ transition

In their experiment these authors used sodium atoms cooled by evaporative cooling at transition temperature of T_{c =} 435 nk and a peak density in the cloud is 55 10¹²cm^-3. The relevant levels of sodium atom considered are | 2ñ = | F=2, M_F = - 2 ñ , | 1ñ = | F=2, M_F = - 1ñ and | 3ñ = | F=2, M_F = - 2ñ . By using cooled atoms these authors could reduce the effect of Doppler broadening of the |1ñ ® |2ñ transition thus achieving almost perfect quantum interference and therefore the dispersion curve is much steeper than can be obtained by other methods. Both coupling and probe beams are derived from the same laser and frequency of the coupling laser is set by the acousto-optic modulator to the 12>® 13> resonance. The probe pulse is launched 4 m s after the coupling laser is turned on. The corresponding probe resonance is found by measuring the probe transmission as a function of frequency and it matches well with the theoretical prediction as shown in Fig.1.The velocity of probe pulse is determined by measuring the delay in the probe pulse in comparison to a reference pulse obtained with no atoms present. They found delay of 7.05 m s in passing through atom coloured of 229 m m which corresponds to the light speed of 32.5ms^-1. By further lowering the strength of coupling laser and reducing the temperature of cooled atoms a lowest speed of 17ms^-1 has been achieved.