Coherent Control Of Light Pulse Information In A Pr:YSO Crystal

The main purpose of my thesis is to investigate coherent control of light pulse information in a Pr³⁺:Y₂SiO₅ (Pr:YSO) crystal, such as light speed reduction, light storage, selective release and controlled erasure of stored information. My thesis is consisted of three parts: I: Optical information transfer between two light channels in a Pr³⁺:Y₂SiO₅ crystal.In this part we report an experimental implementation of light storage and release in a Pr:YSO crystal which exhibits a four-level double lambda atomic system. Under EIT condition, by switching off and switching on the coherent field, we realize the storage and release of the probe pulse. In the release process, by changing the frequency and direction of the switch-on coherent field, the stored information is released into a light pulse with different frequencies and directions. So we realize the optical information transfer between different light channels. Figure 1 shows the energy-level diagram of Pr:YSO. We callω_p,ω_c,ω_c2, andω_r the probe, coherent-1, coherent-2, and repump field, respectively. The probe field is at resonance with the transition of ³H₄(±3/2)→¹D₂(±3/2). The coherent-1 field is at resonance with the transition of ³H₄(±1 /2)→¹D₂(±3/2). The coherent-2 field is at resonance with the transition of ³H₄(±1 /2)→¹D₂(±1/2). The repump field is at resonace with the transition of ³H₄(±5/2)→¹D₂(±5/2). The repump field is used to pump population on levels ³H₄(±1/2) and ³H₄(±3/2). The levels interacting with the probe and coherent-1 field form three-level lambda system.The experimental arrangement is illustrated in Fig. 2. A Coherent-899 ring laser (R6G dye) is used as the light source. The dye laser output is split into four beamsω_p,ω_c,ω_c2, andω_r by four acousto-optic modulators (AOM). To match the setup in Fig. 1, the laser beams are upshifted 178.1, 167.9, 163.1 and 200 MHz from the dye laser frequency, respectively. The applied cw laser powers ofω_p,ω_c,ω_c2, andω_r are 0.5, 3.0, 6.2 and 4.5 mW, respectively. The alignments of laser beams satisfy the phase-matching condition ( K_p2 = K_p+K_c2-K_c) for the generation ofω_p2 at the position indicated on L2. The persistent spectral hole-burning crystal of Pr:YSO is inside a cryostat (Cryomech PT407) and the temperature is kept at 3.5 K. The size of the crystal is 4*4*3mm, and optical B-axis is along 3mm. The slowing of the probe pulse is shown in Fig. 3. The dash line corresponds to the input probe pulse in the absence of the other fields. We can see that both slow and fast light components of the probe pulse pass through the crystal. The fast light emerges first, and is overlapped with the slow light. The presence of the fast light is due to the fact that a portion of the probe pulse does not interact with the ions and the control field, and this portion passes through the crystal freely without absorption. The rise and fall edges of the input pulse are fast, and some of their Fourier frequency components exceed the EIT width. The exceeded components are absorbed by Pr ions, which lead a result that the rise and fall edges of the slow light are attenuated. A time delay of about 40μs is measured from the center of the input pulse to the center of the delayed pulse, which corresponds to the group velocity of Vg≈75 m/s. So the probe pulse is spatially compressed by more than 6 orders of magnitude in 3-mm crystal.Figure 4 shows the storage and release of a probe pulse. When most part of the probe pulse is contained in the crystal, we switch off the coherent-1 field to store the probe pulse. The peak-1 is the portion of the probe pulse which has left the crystal before the coherent-1 field is switched off, which resulted in an observed signal unaffected by the storage operation. The gap of the signal shows the storage time of 10μs. We switch on the coherent fieldω_c in the release process. The stored optical information is released into a light pulse with the original probe frequencyω_p and propagation direction. The observed peak-2 is the portion of the probe pulseω_p that was stored in and subsequently released from the crystal. The released peak-2 maintains the Fig. 4 Light storage and release demonstration for 10μs storage time.(a)and(b)demonstrate that the coherent-1 is switched on in the release process. (c) and (d) demonstrate that the coherent-2 is switched on in the release process same temporal profile as the back portion of the slow light. Note that no output signalω_p2 is observed because the coherent-2 field is not switched on, as shown in Fig. 4(b). Similarly, we switch on the coherent-2 field instead of the coherent-1 field in the release process. As shown in Fig. 4(c) and Fig. 4(d), the stored optical information is released into a light pulse with the frequencyω_p2, but the light pulse with the frequencyω_p is not released. The generated light pulseω_p2 carries the coherent optical information of the probe pulse. We emphasize that the restored pulseω_p2 has a different frequency and propagation direction from the probe pulse, thus this system realizes optical information transfer between two light channels. the restored pulses decrease with increasing storage time. In Fig. 5, we show the restored signal pulses which are stored in the crystal for a time interval of 20μs. The amplitudes of the restored signal pulses are smaller than that in Fig. 4. From Fig. 4 and 5, it is seen that the restored pulseω_p2 has a larger amplitude and a smaller temporal width than that of the restored pulseω_p. This is because that the coherent-2 field has a larger intensity than that of the original coherent-1 field. The actual amplitude of the restored pulseω_p2 should be higher, because it propagates in a new direction, and the crystal is optically dense.II: Erasure of stored optical information in a Pr³⁺:Y₂SiO₅ crystal.We experimentally demonstrate an erasure of stored optical information in a Pr:YSO crystal. Under EIT condition, by switching off the coherent field, the probe pulse is stored in the crystal as atomic spin coherence. Later, by switch on the coherent field, atomic spin coherence is converted back into a released light pulse. During the storage, by employing an erasing pulse to destroy spin coherence, the amplitude of the released light pulse is reduced, then we realize the erasure of stored optical information. The erasing efficiency depends on the energy of the erasing pulse.The levels of Pr:YSO is shown in Fig. 6. We callω_p,ω_c,ω_eandω_r the probe, control, erasing, and repump field, respectively. The probe field is at resonance with the transition of ³H₄(±3 /2)→¹D₂(±3/2). The coherent field is at resonance with the transition of ³H₄(±1 /2)→¹D₂(±3/2). The erasing field is at resonance with the transition of ³H₄(±1 /2)→¹D₂(±1/2). The repump field is at resonance with the transition of ³H₄(±5/2)→¹D₂(±5/2). The four light fields apply to a small subset of Pr ions only. The optical inhomogeneous width in this system is modified by the laser jitter due to the persistent spectral hole burning.The experimental arrangement is illustrated in Fig.7. A Coherent-899 ring laser (R6G dye) is used as the light source. The laser output is split into four beamsω_p,ω_c,ω_e andω_r by four acousto-optic modulators (AOM). The applied cw laser powers ofω_p,ω_c,ω_eandω_r are 3mW, 13mW and 0.5mW, respectively. The laser beams are upshifted 178.1, 167.9, 163.1 and 200 MHz from the dye laser frequency, respectively. All four beams are linearly polarized and focused into the sample by a 30-cm focal-length lens. The persistent spectral hole-burning crystal of Pr:YSO is placed inside a cryostat (Cryomech PT407) and the temperature is kept at 3.5K. The size of the crystal is 4mm*4mm*3mm, and optical B-axis is along 3 mm. The laser propagation direction is almost parallel to the optical axis. When most part of the slowed probe pulse is contained in the crystal, the probe pulse is stored in the crystal by switching off the control field adiabatically. As showed in Fig.8(a), the peak-1 is the portion of the probe pulse that has left the crystal before the control field is switched off, which resulted in an observed signal that was not affected by the storage operation. The gap between peak-1 and peak-2 is the storage time of 10μs. The observed peak-2 is the portion of the probe pulse that was stored in and subsequently released from the crystal by switching on the control field. In light storage process, a weak spin coherence is created when the control field is switched off. It is this coherence that the optical information of the probe pulse could be stored in. During storage time of 10μs, if a square erasing pulse is applied to the crystal, the created spin coherence can be destroyed partially. The breakage of atomic spin coherence leads to the erasure of stored optical information. After 10μs storage time, the energy of the retrieval probe pulse is reduced remarkably due to the erasing operation, as shown in Fig.8(b). So we realize the erasure of stored optical information in a controlled fashion by applying an erasing pulse to destroy atomic spin coherence.We define the erasing efficiency E=1-R, where R is the ratio of the retrieval probe energy with and without the erasing pulse for a fixed storage time. For our experimental system, the attenuation of spin coherence is exp( - AT) in the absence of the erasing pulse, where A is the decay constant, Fig. 9 (a) Erasing efficiency vs the width of the erasing pulse with a constant intensity 25 mW. (b)Erasing efficiency vs the intensity of the erasing pulse with a constant width 0. 9μs.The fitting parameterαis 0.2 for (a) and 0.072 for (b). and T is the storage time. The attenuation of spin coherence is exp[ - AT -Ω²Ï„/(2Γ)] in the presence of the erasing pulse, whereΩandÏ„are the Rabi frequency and the presence time of the light pulse, andΓis the angular linewidth of the light transition.. For a fixed storage time, the ratio of residual spin coherence with and without the erasing pulse is exp( -Ω²Ï„/(2Γ)), which determines the ratio R of the retrieval probe energy with and without the erasing pulse. So R = exp( -Ω²Ï„/Γ), and then E = 1 -exp(-Ω²Ï„/Γ). From the expression of the erasing efficiency, it is seen that the erasing efficiency is determined byΩ²Ï„i. e. the energy of the erasing pulse. For 10μs storage time, we measure the erasing efficiency by varying the width and intensity of the erasing pulse, as shown in Fig.9. The erasing efficiency increases with the width and intensity of the erasing pulse. We can see that, as long as the energy of the erasing pulse is constant, a shorter and stronger erasing pulse results in the same erasing efficiency as a longer and weaker erasing pulse. The experimental data are fitted with the function of y ( x)= 1-exp(-αx), whereαis the fitting parameter. The best fit is shown as solid curve in Fig.9. The experimental results are consistent with the theoretical simulation.III: Storage and selective release of optical information based on F-STIRAP in a Pr³⁺:Y₂SiO₅ crystal.We report an experimental implementation of light storage and release in Pr:YSO crystal, which is fundamentally different from the conventional EIT-based processes because it is critically based on the atomic coherence created by F-STIRAP. The control pulse and signal pulse with the same back edges excite big atomic spin coherence between the hyperfine levels in the crystal. With the help of the control pulse, the information of the signal pulse is stored in the spin coherence created by fractional STIRAP. After a storage time, by turning on a reading pulse with control (signal) frequency, the stored information can be released into a light pulse with signal (control) frequency.Figure 10 shows the levels of Pr:YSO. We callω₂,ω₁ andω_r the probe, control, and repump field, respectively. The probe field is at resonance with the transition of ³H₄(±3 /2)→¹D₂(±3/2). The control field is at resonance with the transition of ³H₄(±1 /2)→¹D₂(±3/2). The repump field is at resonance with the transition of ³H₄(±5/2)→¹D₂(±5/2).The experimental arrangement is illustrated in Fig. 11. We use a frequency stabilized dye laser (Coherent 899 ring laser) as the light source, and its laser jitter is about 0.5MHz. The dye laser output is split into three beamsω₁ ,ω₂ andω_R by three acousto-optic modulators (AOM). The AOMs ensure that laser jitters are correlated, so that the laser frequency Fig. 11 Schematic diagram of the experimental setup.BS: beam splitter, L: lens, AOM: acoustooptic modulator, PD: photodiode, OS: oscilloscope differences are down to a few Hz. The laser beamsω₁ ,ω₂ andω_R are upshifted 167.9MHz, 178.1MHz and 200MHz from the dye laser frequency. The applied cw laser powers ofω₁ ,ω₂ andω_R are 10mW, 14mW and 2mW, respectively. All three beams are linearly polarized and focused into the sample by a 30cm focal-length lens. The angle between the beams is about 10 mrad. The Pr:YSO crystal is inside a cryostat (Cryomech PT407) and the temperature is kept at 3.5K. The size of the crystal is 4mm*4mm*3mm, and optical B-axis is along 3mm.Figure 12 shows the experimental data of the light storage and release processes. Fig. 12(a) gives the time sequences of the three pulses before Pr:YSO crystal. We set the back edge of the control pulse being the same as that of the signal pulse to store the latter one. Due to fraction STIRAP, such two pulses excite big spin coherence between ³H₄(±1/2) and ³H₄(±3/2) levels. With the help of the control pulseω₁ , the information of the signal pulseω₂ is stored in this coherence. After a storage time of 15μs, the reading pulseω₁ is turned on, and then the stored information of the signal pulse is released into a restored pulse with the frequencyω₂, as shown in Fig. 12(b). This restored pulse has the same frequency, polarization and propagation direction as the signal pulse. Similarly, we can turn on the reading pulseω₂ instead ofω₁ , as shown in Fig. 12(c). Then the stored information is released into a restored pulse with the frequencyω₁ , as shown in Fig. 12(d). The peak at the end of the control pulse arises from stimulated emission of the two-photon process.Figure 13 shows the relative amplitude of the restored pulse as a function of time delay between the control pulse and the signal pulse. The positive delay corresponds to the signal pulse being switched off last. Zero time delay corresponds to F-STIRAP, where these two pulses have the same back edges. Under F-STIRAP, the big spin coherence is obtained, thus the restored signal is big. This is pursued in storage fidelity, which meets the requirement of practical information processing. When the time delay increases, the peak power of the restored pulse becomes small. The above results show that when the condition of F-STIRAP is satisfied, the created spin coherence is big, then optical information can be stored effectively...