Light at a Standstill Tim Kuis June 13, 2008

Transcription

1 Light at a Standstill Tim Kuis June 13, Introduction There is something curious about the seed of light. It is the highest obtainable seed. Nothing can travel faster. But how slow can light go? Exeriments have been done to slow down a ulse of light down to only a few meters er second. But that s a few years ago, nowadays ultraslow light is easily available in many lab. But recently a light ulse was even brought to a halt. This ability to tra and hold light ulses is very romising for such fields like quantum informatics or non-linear otics. Also the quantum coherence state where-in the light is contained during standstill might give us information about the foundations of quantum mechanics itself!. Slow light.1 High disersion gives slow grou velocity But what exactly does it mean? Slowing down a light ulse down to a few meters er second? Light always travels with the seed of light. Still, when travelling trough a transarent or translucent medium the light travels slower than it does in vacuum. Classically, this is due to the charges of the electrons in the medium the light-wave it is travelling trough. The charges of each electron interact with the electro-magnetic fields of the light wave, thus slowing its rogress. The amount of which the light is slowed is called the refractive index of the material. This is not a very large effect and can slow (monochromatic) light down to a few times its original seed. Taking into consideration the frequency deendence of the refractive index, we can define the so-called grou velocity of the light. The grou velocity of the wave is the seed of the enveloe of the wave, or in other words the seed of a ulse in the medium. This grou velocity can be much slower than the seed of the light waves itself, and is given by; v g c hcε Ω 0 c dn ω + ω ω µ d ω = n( ) N (1) where n(ω) is the refractive index at frequency ω. The frequency deendence of n is called the disersion of the material. You can see here that strong disersion gives a low grou velocity. The right art of the equation will be exlained in the next section.

2 . EIT (Guiding Beam) To acquire and control a very high disersion electromagnetically induced transarency (EIT) is used. To find a high region of disersion we look at a resonance in the quantum states. Normally, at such a resonance, there is a eak in the absortion of and a stee refractive index deendence of the robe frequency. Now, we do want this high disersion, but the high absortion usually turns the material comletely oaque, making it imossible for a ulse to travel trough the medium. To solve this roblem EIT is used to turn a normally oaque medium into a transarent medium by using a couling laser (also called a control laser). For EIT a three-level FIGURE 1 Schematic view of EIT. The blue line denotes the normal absortion of a ulse frequency, whereas the red line denotes the absortion with the couling laser on, creating a transarent frequency region at resonance. [8] scheme is needed, where the robe beam is at one resonance, the coule beam at another and the third resonance is forbidden. Switching on the couling laser leads to a window at resonance frequency of the robe beam, as can be seen in figure 1, with corresonding high disersion as can be seen in figure. More quantitatively, the right art of equation (1) comes into lay here. Of imortance here are N; the atomic density, µ; the robe resonance diole matrix and Ωc; the Rabi frequency of the couling laser. The square of the Rabi frequency varies linearly with the intensity. N will get higher in dense material. This means to get very low grou velocity a low couling beam ower and a high density material are required, for examle a Bose-Einstein Condensate (BEC). Using this technique, a grou velocity has been reached of 17 m s -1 at 00 nk and a couling beam ower of 1 mw cm -. FIGURE Here the grey line denotes the absortion with the couling laser on and the blue line the refractive index as a function of the robe frequency (both in a.u.). The steeness of the refractive index in this region means a (very) high disersion. [8] The strong disersion leads to strong Kerr nonlinearities. Kerr nonlinearities are broadly used in quantum otics. For EIT on this light a non linear refractive index of 0.18 cm W -1 has been measured. This is about a million times more than normally in cold Cs atoms [4]. Notice here that the light ulse in the disersive medium will have decreased in length by a factor for vg / c and will thus have its energy stored in about one ten thousandth of the normal length, leading to a very high energy density in the

3 material. This energy is stored in the couling wave as well as in the atomic medium. This energy- or information storage is the crucial asect for utting a light ulse to a standstill. 3. Light at a standstill Slow light is one thing, and as been said in the introduction, is widely exerimented with these days in different laboratories, but more recently exeriments have been erformed utting light to a standstill, or rather, saving the information of the light within the material. 3.1 Quantum coherence sin state Using the same method as described in the slow light section, light can be saved within atomic material by switching off the couling beam while the robe ulse is in the medium. The idea is that the information and energy stored within the light are saved in the quantum coherence sin state of the atomic medium (see figure 3c and d), while the total energy and information is reserved as a olariton (figure 3b). To do this a dynamic form of EIT must be used. When smoothly varying the couling field we can slowly turn it off, giving FIGURE 3 Shown here are a; the couling field intensity in time, b; the Total olariton field, which is of constant shae in time, c; the light field and d; the coherence sin state field. [6] the atoms the time to follow the change of the light field, also called writing. And from the right art of equation (1) we can see that with zero couling beam intensity, we have zero Rabi frequency, and thus zero grou velocity. Now, all the information has been transferred to the sin states of the medium. Later switching on the guiding field again makes the medium transarent again and the light will come out of the medium with the same characteristics as before, which means all information about the light was saved within the material in the time between. This is called reading. FIGURE 4 Multile read-outs of one ulse are ossible by ulsing the read-out couling beam. Probe intensities dro over time. [5] By ulsing the couling beam even multile read-outs of the same stored robe ulse are ossible. After some couling beam ulses, all the stored information in the medium is gone and the effect comes to an end. See also figure 4.

4 Exeriments have been erformed with a magnetic field ulse on the medium during the couling beam switch off. This shifts the hase of the sin states, while they contain information about the light. This also changes the hase of the out coming light ulse, thus confirming that the information is indeed stored in the sin states of the medium [5]. 3. Two oosite guiding beams There is another method of saving the light in the medium. Firstly, it has to be saved in the quantum coherence state. Then, in stead of using a single couling beam to get the ulse out again, two oositely directed couling beams are used with equal (or close) Rabi frequencies. The forward and backward couling beams will interfere roducing a satially eriodic intensity, or a standing wave. This standing couling wave leaves the medium oaque in the anti-nodes and transarent in the nodes. The electromagnetic wave is now traed between these absortion regions that act like Bragg mirrors. See also figure 5. All the energy and information of the light must now be saved within about half of the sace, which means the intensity of the traed light will be about twice the intensity of the traed coherence field [1]. FIGURE 5 Light confinement by satial variation of signal field absortion. The blue line is the initial sin state field, the black line is the absortion of the medium and the red lines denote the confined light after couling field switch-on. [1] 4. Lifetime of the stored light Different exeriments have been erformed to kee the light confined in some medium. Peole started out using BECs but later also used hot gas clouds to achieve the same effect. Still, the light cannot be contained forever. For the technique to be useful in different alications we would want to store the light information for as long as ossible. Using a cold cloud of sodium atoms, a decay time of 0.9 ms was found for the atomic coherence of the storage medium, as can be seen in figure 6. For the double couling beam technique as measured on a hot rubidium samle a FIGURE 6 Shown on the left is the decay of the coherence state in a sodium BEC. On the right the intensity decay in the stationary ulses in hot Rubidium. [5] [1] decay time was found of about 7 µs was found, but here

5 it should be noted that only a art of this decay is actually due to coherence decay. Other mechanisms are sreading of the ulse or imerfect EIT. 5. Conclusion The exeriments erformed on the light give rise to many interesting alications, such as quantum informatics and non linear otics. As has been ut forward in the text, very high Kerr nonlinearities can be achieved using the slow light technique, which can be widely used in otical exeriments. But frozen light gives rise to several interesting alications as well, because there is little or no loss, there will also be little or no noise. This is very imortant for quantum informatics where noise needs to at a minimum to avoid decoherence and thus information loss. Lately, it has even been shown that it is ossible to change the light ulse while it is saved in the material [9]. This means that a ulse can be traed and then maniulated with external fields, to later come out in a changed way. This technique oens door for all kinds of alications, besides information technology, the gain of knowledge about the very fundamentals of nature and quantum mechanics. 6. References [1] Bajcsy, M., A. S. Zibrov and M. D. Lukin Stationary ulses of light in an atomic medium [] Cornell, E. A Stoing light in its tracks [3] Griffiths, D. J Introduction to electrodynamics [4] Hau, L. V., S. E. Harris, Z. Dutton and C. H. Behroozi Light seed reduction to 17 meters er second in an ultracold atomic gas [5] Liu, C., Z. Dutton, C. H. Behroozi and L. V. Hau Observation of coherent otical information storage in an atomic medium using halted light ulses [6] Mair, A., J. Hager, D. F. Phillis, R. L. Walsworth, and M. D. Lukin Phase coherence and control of stored hotonic information [7] Scully, M. O., 003. Light at a Standstill [8] htt://en.wikiedia.org/wiki/electromagnetically_induced_transarency [9] Ginsberg, N. S., S. R. Garner and L. V. Hau Coherent control of otical information with matter wave dynamics