1. Introduction

Group velocity control of a traveling light pulse by another light has been intensively studied for potential applications of both quantum information processing [1–5] and all-optical information processing [6,7]. Unlike coherent state measurement in classical optics, quantum state measurement results in the quantum state demolition. Therefore, nondemolition measurement of a quantum state has been a key issue in quantum information processing [8]. Using ultraslow light the quantum nondemolition measurement technique has been suggested recently [2]. The principle of quantum nondemolition measurement is found in a giant phase shift of the probe light when the probe light interacts with a quantum state of atoms. Conventionally in nonlinear optics, phase shift of a probe light can be obtained when another light is involved in the context of cross-phase modulation. In the cross-phase modulation method, two parameters contribute to the phase shift: first, light intensity, and second, light interaction time. In the cross-phase modulation, a faster group velocity in two light beams determines the interaction time. In general, interaction time is so short that a longer optical medium is used. On the other hand light intensity can be easily increased and thus becomes a critical factor. Unfortunately, use of intense light is limited in most optical media, and especially must be avoided in quantum information applications because of noise affected on single photon level probe light [2–5,8]. Thus, ultraslow light has drawn much attention not only to nonlinear optics but also to quantum optics owing to extremely lengthened interaction time.

The physics of ultraslow light lies in the Kramers−Kronig relation, where dispersion line shape is correlated with the absorption spectrum. Here, the group velocity of light relates with the derivative of the dispersion line shape [1]. Thus, an abrupt modification of an absorption spectrum can result in the ultraslow light. Ultraslow light techniques include electromagnetically induced transparency (EIT) [1,9], coherent population oscillation (CPO) [10-12], and spectral hole burning [13,14]. For EIT, an optical medium must satisfy certain conditions. One of them is a three-level system whose optical dephasing rate must be less than the coupling Rabi frequency. This constraint severely limits the use of a solid medium, because of a phonon enhanced optical dephasing rate [15]. Although CPO has the advantage of room temperature operation, use of the side band of an optical pump as a probe can be a limitation, where the pump field must be strong and coherent with the probe component in time, space, and frequency. For the spectral hole-burning technique, the hole width is determined by the Rabi frequency or phase relaxation decay rate, whichever is greater. To get a narrow lineshape in a slow relaxation rate medium, the light field must be stable and weak. Therefore long time interaction is necessary, which is not good for faster information processing.

In this paper we investigate transmission enhancement of ultraslow light in an inhomogeneously broadened spectral hole-burning solid medium by using an atom shelved model induced by a precedent dummy optical field whose frequency is identical with the probe light. By the action of the dummy light, atom distribution can be controlled to be balanced between the ground and excited states, so that the medium can be fully transparent to a resonant probe light even with a half excitation. At line center, however, the narrow spectral hole makes the probe light experience ultraslow group velocity. In a persistent spectral hole-burning medium, self-induced ultraslow light and its coherence dynamics already have been demonstrated without dummy light [16,17]. For the self-induced ultraslow light, however, heavy absorption of the probe light is a fundamental limitation. Before observation of the self-induced ultraslow light [16], use of coherent dummy light has been suggested in a persistent spectral hole-burning medium [13]. The hole width, however, broadens as the light intensity increases due to power broadening, or as the light interaction time lengthens due to time-dependent laser jitter. Here, we demonstrate transmission enhancement of ultraslow light in a persistent spectral hole-burning medium using a dummy light-induced atom shelving technique. The atom shelving method alleviates use of intense light or longer pulse duration. The dummy light used in this paper does not have to be coherent with the probe light, because it acts as a pumping light simply to burn a spectral hole in the ground state and coherently excite the atoms onto the excited state. To discuss more about the atom shelved model, several results are presented to support it.

2. Results and discussion

In a three-level Λ-type optical system, any coherent population transfer from one state to another between two ground states via an excited state is normally understood as a persistent spectral hole burning procedure, where the hole-burning time is determined by the population relaxation rate between the two ground states [18]. In rare-earth doped crystals, the spectral hole burning persists for minutes or even hours [15]. Ultraslow light applications using this type of spectral hole burning, however, encounter practical problems such as an unnecessarily long duration of channel occupation or light source dependent spectral hole widening (causing less group delay), and signal loss due to absorption. If the dummy light, whose frequency is the same as the probe, is considered, then such problems can be removed. With the use of ultrashort dummy light and an atom shelving technique, the spectral hole-burning-based ultraslow light can result in full transparency even with half population excitation. To satisfy this outcome, the medium’s optical population decay time must be relatively longer compared with the light pulse to form the optical shelving condition [19], which is a common characteristic of most rare-earth doped solids.

Figure 1(a) shows a partial energy level diagram of a rare-earth Pr³⁺ (0.05% at. %) doped Y₂SiO₅ (Pr:YSO) for the transition of ³H₄ − ¹D₂ at a cryogenic temperature. Doubly degenerate three hyperfine states of the ground (³H₄) and excited (¹D₂) states are due to the low-symmetry crystal field, and their wave functions are mixed, causing the selection rule to break down for electronic transitions between electronic singlets [18]. Thus all nine transitions are allowed. The optical population relaxation time from ¹D₂ to ³H₄ is T₁ ^O = 164 μs [20]. The light pulses R1 and R2 are used for population initialization (reset) on the state |1>. This means that applying R1 and R2 provides the same condition for each probe beam P to interact with the same number of atoms on state |1>. The light pulse A in Fig. 1 acts as dummy light, where it has 3 μs pulse duration and precedes the probe P by t = 16 μs, which are much shorter than the population relaxation time T₁ ^O = 160 μs. Thus, most burnt atoms by the dummy light A must stay in the excited state |3> when the probe beam P enters. This atom shelving condition plays a major role in the present demonstration of transmission enhanced slow light (discussed in Figs. 2 and 3 ). The measured beam size (FWHM) of the R1, R2, and A at the focal point is about 400 μm. All laser beams are frequency locked, so that relative frequency difference is negligible. The beam size of the P is ~200 μm, which is smaller than that of A, R1, or R2 at the focal point. The temperature of the sample is kept at 5 K, and the sample length is 3 mm.

 

Fig. 1 (a) Partial energy level diagram of Pr:YSO. (b) Schematic of light pulse propagation. (c) Light pulse sequence. (d) Schematic of coherently confined atom selection and inhomogeneous spectroscopoy at 5 K. Atom preparation for P is controlled by frequency selection of R1 and R2. Each set of atoms is continuously spanned in an optically inhomogeneous broadening of ~4GHz [21]: Blue and red colored curves indicate two different sets of atoms detuned by δ. If δ is greater than either laser jitter or Rabi frequency of R1 or R2, that atom group becomes inactive to the slow light of P. (e) Schematic of a dummy light-induced spectral hole tunnel, where the probe pulse P experiences reduced absorption. Light power of R1, R2, P, and A, respectively, is 33, 39, 1.4, and 40 mW.

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Fig. 2 Coherent control of ultraslow light with dummy light: Transmission (the peak intensity y of the slow light) increases by a factor of 4.5 when the dummy light exists, while the group velocity v_g increases from v_g = 260 m/s to v_g = 380 m/s.

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Fig. 3 Transmission of the slow light versus pulse separation T between the dummy light A and the probe light P. (a) without A, (b) T = 0, (c) T = 40, (d) T = 140, (e) T = 300, and (f) T = 340 μs. The insets of (b)−(f) are for the dummy light A, where the transmission and self-induced group delay is the same except (b). (g) and (h) Plot of (b)−(f) for transmission of S and group delay τ, respectively. Black squares in (g) and (h), respectively, indicate transmission and group delay of the self-induced slow light in (a). Laser power of R1, R2, P, and A, respectively, is 8, 14, 1.4 and 1.5 mW. Black diamonds in (g) and (h) are not shown in the left column. Black square in (g) and (h) is for (a).

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Figures 1(b) and 1(c) show a pulse propagation scheme and a pulse sequence, respectively. In Fig. 1(b), all laser beams are focused into the sample by a 40 cm focal length lens with an angle of ~20 mrad among them. The angular separation among the beams is not a critical condition but is important for beam overlapping inside the medium. In Fig. 1(b) the calculated overlapping volume is about 80%. The laser beams of R1, R2, P, and A are frequency locked at a linewidth of ~300 kHz, and pulsed by digital delay generators (DDG 535) acting on acousto-optic modulators (AOMs). Even though all laser beams are generated from the same laser output, there is no coherence between P and the others through the atoms, because the pulse separation time is much longer than the optical coherence time t_C. The optical coherence time in the medium is defined by homogeneous spectrum (Δ_A) of pumped atoms: t_C = 1/πΔ_A ~3 μs, where Δ_A = 300 kHz). The laser linewidth is much broader than the optical phase relaxation rate γ (γ ~kHz). All beams’ propagation vectors must be different from one another, but are denoted by k for the sake of simplicity.

Figure 1(d) shows a schematic of spectrally confined atom selection and an observed inhomogeneous broadening (~4GHz) of Pr:YSO at 5 K. The inhomogeneous spectrum is measured by a frequency stabilized Coherent ring-dye laser (899-01) at a 20 GHz free run mode across the absorption center. From the fact that the peak to peak separation corresponds to 20 GHz, the measured inhomogeneous width is calculated to be ~4 GHz. Regarding the spectral modification using three resonant lasers, the spectral broadening of a selected atom group is determined by the laser jitter or Rabi frequency of the R1 or R2, whichever is greater, for a fixed frequency P. Hence, the repump beams R1 and R2 pump spectrally confined atoms at ~300 kHz bandwidth from states |0> and |2> to state |1>, respectively: The blue curve is for an adjacent atom which is not affected by the set of R1, R2, and P if the spectral separation δ is greater than the pump spectral width of 300 kHz. The black line of Fig. 1(e) is for a spectral hole burnt by the dummy light A. The red line is for the probe pulse, where the probe pulse linewidth must be narrower than the dummy light due only to power broadening.

In Fig. 2 the curve (i) shows a self-induced slow light without the dummy light A, where the probe pulse duration is set at 10 μs. The time delay between R1/R2 and P is 200 μs, which is long enough to depopulate the excited state |3>. The light power of R1, R2, A, and P is 33, 39, 40, and 1.4 mW, respectively. The pulse duration of R1 and R2 is 10 ms. The repetition rate of the pulse train in Fig. 1(c) is 20 Hz. As shown, the group delay (τ_x) of the P-pulse-induced slow light (x) in the green curve of (i) is 10.5 μs (v_x = 286 m/s), which is v_g/c ~10⁻⁶. The self-induced slow light already has been observed [16]. As discussed in Ref. 16, the front part of the probe pulse P is used for hole-burning creation, and the remainder of the P pulse experiences a group delay resulting in the ultraslow light. Because the state |1> is heavily populated by the repump fields, probe absorption becomes a critical issue for slow light applications: The transmission of the slow light x compared with the complete hole burning level is ~1/10. Hence any additional hole-burning process preceding the probe may alleviates the absorption problem.

The green curve of (ii) in Fig. 2 shows the probe light intensity transmitted through the medium with the dummy light A. The pulse duration of the dummy light is as short as 3 μs, but much stronger than the probe. The dummy light A also experiences the self-induced ultraslow group velocity as shown in the red curve of (ii). The group delay (τ_z = 6.3 μs; v_z = 476 m/s) of the dummy light (z) is shorter than that of the probe light (x), where τ_x = 10.5 μs (v_x = 286 m/s) for (i). The shorter group delay at the higher intensity of light is due to the power broadening (∝Ω) mechanism resulting in broader spectral hole width: Refer to the Kramers−Kronig relation and Eq. (1) below. The group delay is proportional to the atom density N:

In Fig. 3 we demonstrate how the dummy light A contributes to the atom density N interacting with the probe P in state |1>. The light power of R1, R2, A, and P is 8, 14, 1.5, and 1.4 mW, respectively. The pulse duration of R1 and R2 is 30 ms, and the repetition rate of the pulse train in Fig. 1(c) is 25 Hz. Each pulse duration of P and A is 10 μs. Compared with A used in Fig. 2, A power in Fig. 3 is decreased to compensate for the lengthened pulse duration (10 μs) as well as to minimize the power broadening effect. Thus, the dummy light A deals only with atom density (N) in state |1>. Figure 3(a) is a reference of the self-induced slow light as shown in Fig. 2. In Figs. 3(b) – 3(f), the pulse separation T (T = 0 to T = 350 μs) between the dummy light A and the probe P gradually increases, and transmittance power of the ultraslow light S is measured. Figure 3(g) shows the peak intensity of the slow light S versus pulse separation T. The red curve is a best-fit exponential function of exp(−2t/T₁ ¹), where T₁ ¹ = 350 μs. With the spectral selection Fig. 1(a) can be treated as a closed four-level system composed of |0>, |1>, |2>, and |3>. The population decay rate from the excited state |3> to each ground state varies depending on their transition probabilities. Thus, the (individual) decay time of Fig. 3(g) should be longer than the overall T₁ ^O (T₁ ^O = 164 μs from Ref. 18): Γ₁ ^Ο (1/Τ₁ ^Ο) = Γ₁ ⁰ (1/Τ₁ ⁰) + Γ₁ ¹ (1/Τ₁ ¹) + Γ₁ ² (1/Τ₁ ²), where Γ₁ ^j stands for a population decay rate from the excited state |3> to the ground state |j>. For the calculations, we simply assume that the minimum value of exponential curve is the one (black square) without A as shown in Fig. 3(a). Obviously the minimum transmission with A must be greater than that without A due to persistent spectral hole by A resulting in reduced N in state |1> if the preceding time T of A is less than the spin population decay time of minutes [18]. Investigation of exact T₁ ¹, however, is beyond the scope of this paper.

According to Eq. (1), the gradually increased atom density N in state |1> as a function of the pulse separation T contributes to a slower group velocity as shown in Fig. 3(h). Because the absorption (or transmission) in Fig. 3(g) must relate with the effective atom density N, where the effectiveness is caused by the shelved atoms in the excited state, ρ₁₁ − ρ₃₃, trade-off exists between the transmission intensity and the group delay. The longest group delay (τ_g = 14.0 μs for T = 350 μs in Fig. 3(h)) with A, however, must be smaller than that (τ_g = 15.2 μs; see the black square in Fig. 3(h)) without A of Fig. 3(a). This is due to persistent spectral hole burning. Thus, Fig. 3 proves that the dummy light A contributes on the enhanced transmission of the ultraslow light S. Here, the maximum transmission increase occurs when the dummy light A coincides with the probe light P as shown in Fig. 3(b) due to a zero decay from the atom shelved state |3>. The measured transmission increase of the ultraslow light S in Fig. 3(b) against that of Fig. 3(a) is 7.2, which is equivalent to the amplification factor of ~10⁵ inside the medium when the optical depth (d = 10) is considered: hence 7.2 x exp(10) ~10⁵ as explained in Fig. 2.

In the observations of the ultraslow group velocity [1,9-12], the signal loss due to absorption should pose a serious problem. As shown in Figs. 2 and 3, when a dummy light A is applied, a trade-off occurs between the absorption and the group delay. Thus, nearly perfect slow light transmission should be possible if a weak, long, and ultranarrow dummy light is used. This kind of dummy light scheme in an atom shelving model is much simpler than EIT-based slow light in the context of using (1) a modified absorption spectrum by another light, (2) a weak coupling (dummy) light, and (3) a noncollinear propagation scheme to avoid spectral noise. Thus, the dummy light-enhanced ultraslow light transmission gives a potential for low-loss all-optical information processing such as optical buffer memories, as well as quantum information processing such as quantum nondemolition measurement.

3. Conclusion

In summary we have investigated optical transmission increase of self-induced ultraslow light in an inhomogeneosly broadened rare-earth doped crystal with use of dummy light. The observed transmission increment factor is as high as 7.2, which is equivalent to an amplification factor of 10⁵ considering an optical depth of 10, where the slow light absorption is a critical issue in slow light applications. The present investigation holds potential for use of ultraslow light in a simple scheme of a two-level persistent spectral hole-burning system. With the advantage of the atom shelving model, a single shot of dummy light can make applications of self-induced ultraslow light in a spectral hole-burning optical system effective for use in a packet of probe signals.