Saturation Spectroscopic Studies on Yb³⁺ and Er³⁺ Ions in Li₆Y(BO₃)₃ Single Crystals

Abstract

The results of a series of pump–probe spectral hole-burning experiments are presented on Yb³⁺- or Er³⁺-doped Li₆Y(BO₃)₃ (LYB) single crystals in the temperature range of 2–14 K and 9–28 K, respectively. The spectral hole has a complex structure for Yb³⁺ with superposed narrow and broad bands, while a single absorption hole has been observed for Er³⁺. Population relaxation times (T₁) at about 850 ± 60 μs and 1010 ± 50 μs and dipole relaxation times (T₂) with values of 1100 ± 120 ns and 14.2 ± 0.3 ns have been obtained for the two components measured for the Yb³⁺:²F_7/2—²F_5/2 transition. T₁ = 402 ± 8 μs and T₂ = 11.9 ± 0.2 ns values have been found for the Er³⁺:⁴I_15/2—⁴I_11/2 excitation. The spectral diffusion rate at about 1 and 5 MHz/ms has been determined for the narrow and broad spectral line in Yb³⁺-doped crystal, respectively. The temperature dependence of the spectral hole halfwidth has also been investigated.

1. Introduction

Coherent quantum optical processes in rare-earth (RE) ion-doped dielectric crystals are of great interest in the quest for physical systems in order to realize quantum information processing devices. The successful realization of coherent quantum control procedures raises serious demands of atomic systems, such as a sufficiently long population, T₁ and dipole relaxation, T₂ times of the involved quantum states. Among several choices, e.g., magnetic- or laser-trapped ultracold single atoms or atomic clouds or coherent spin dynamics in quantum dots, a potential way to localize atomic systems is doping a single crystal with RE ions. The primary motivation of choosing Er³⁺ dopant ion is that its ⁴I_13/2—⁴I_15/2 transition is resonant with the frequency of the telecommunication laser field with a wavelength of about ~1.5 μm. A number of oxide crystals have been tested as a host of erbium to obtain a long coherence time in this wavelength range [1]. Moreover, the coherence time depends not only on the host material but on the concentration of the dopant, the temperature of the sample and the applied magnetic field as well [2,3,4,5]. Erbium-doped crystals have been used in several coherent quantum optical applications, such as the control of dispersion and group velocity [6], diode laser frequency stabilization [7], interference detection of spontaneous emission of light from two solid state atomic ensembles [8], electromagnetically induced transparency [9], ultraslow light propagation via coherent population oscillation [10], and quantum memories [11,12,13,14,15].

For practical applications, there are other relevant wavelength intervals beside the telecommunication domain. One of them is the near infrared range between 980–1100 nm. The ytterbium-doped crystal and fiber lasers radiate in the wavelength range between 1030–1080 nm, which can be pumped with ~980 nm light. There are several optical devices optimized to this wavelength domain [16,17].

Yb³⁺ and Er³⁺ dopant ions are perspective candidates for coherent quantum optical applications because the transitions ²F_5/2–²F_7/2 and ⁴I_11/2–⁴I_15/2, respectively, lay in the wavelength range 960–980 nm. Our goal is to investigate the use of the LYB crystal as a host for these ions according to the previous properties. Additionally, the solution of the problem about the interaction between the RE ions and the borate lattice could show us new research directions to develop borate crystals with targeted compositions.

Our aim was to study the ytterbium and erbium ions as dopants in a novel host crystal: lithium yttrium borate Li₆Y(BO₃)₃ (LYB). This member of the borate crystal family can be grown by both the Bridgman and the Czochralski methods [18,19,20], which have a monoclinic structure with the P2₁/c space group. The advantage of LYB crystal is that rare-earth dopants can incorporate into Y site with C₁ symmetry in the lattice without any distortion because of the charge neutral substitution and the similar ion radius. LYB:Yb³⁺ and LYB:Er³⁺ have already been investigated by optical spectroscopic methods [21,22,23,24,25] to determine the energy terms of the dopant ions. In addition, LYB:Yb³⁺ has been used for short pulse laser applications [26] and as a diode-pumped laser with Er co-doping [27].

A detailed description of the spectral hole burning procedure carried out by using sequential pump and probe pulses derived from a single laser beam passing through lithium niobate crystals can be found, e.g., in our previous papers [28,29]. The RE ions can be considered as effective two-level systems, where the laser-induced transition between the ground and excited states can be considered as a dipole transition. Thus, we suppose a set of effective two-state atoms interacting with a long and intensive pump and then a short and sufficiently weaker read-out probe pulse with a much longer time delay than the dipole relaxation time. In addition, the probe pulse needs to be much shorter than the population relaxation time but much longer than the dipole relaxation time. If these requirements are met, then by scanning the frequency of the probe field around the pumping frequency the attenuation of the probe field determines a Lorentzian curve, which is called spectral hole. The lifetime of the spectral hole was found to be single exponential with a characteristic time constant T₁. The halfwidth of the spectral hole depends on the intensity of the pumping pulse, thus the value of T₂ comes out only in the low intensity limit, which can be achieved by the Z-scan method described in the next section.

2. Materials and Methods

Lithium yttrium borate single crystals doped with 0.1 mol% Yb³⁺, 0.05 mol% or 1.0 mol% Er³⁺ were grown by the Czochralski method [20]. LYB has a monoclinic structure of the P2₁/c space group. The dielectric x-axis coincides with the crystallographic b-axis <010>, while the dielectric z-axis is perpendicular to the optical plane (-102). Although the crystal is biaxial, it behaves as uniaxial positive at λ = 1064 nm [21]. Yb³⁺-doped sample was prepared with incident plane (010) and a thickness of 0.6 mm, while the Er³⁺-doped sample was prepared with incident plane (-102) and a thickness of 2 mm. The high resolution absorption spectra of Er³⁺- or Yb³⁺-doped LYB crystals have been measured at 9 K by a Bruker IFS 66v/S or a Bruker IFS 120 FTIR spectrometer, respectively. In case of the Er³⁺ dopant, the 1 mol% concentration sample was more suitable for spectroscopy than the one containing fewer Er³⁺ ions, while for saturation spectroscopy, lower dopant concentration is required. The absorption spectra between 10,250 and 10,450 cm⁻¹ wavenumbers are shown in Figure 1. In the case of the Yb³⁺-doped crystal, a single absorption peak was found at 10,283.5 cm⁻¹ with a halfwidth of 0.18 cm⁻¹, corresponding to the transition from the lowest Stark level of ²F_7/2 multiplet to the lowest crystal field level of ²F_5/2 multiplet of the Yb³⁺ ions in LYB at T = 9 K. The other two crystal field components of the ²F_5/2 excited state lie out of this range and are not suitable for our laser spectroscopic measurements. However, all possible six absorption bands of the ⁴I_15/2—⁴I_11/2 transition of Er³⁺ can be identified in this wavenumber range. The positions and halfwidths of the investigated absorption lines are listed in

Table 1. Positions and halfwidths of the absorption lines in the spectrum of LYB:Er³⁺ and LYB:Yb³⁺ crystals at T = 9 K shown in Figure 1, and Stark energies of the crystal field splittings are determined by L. Kovács et al. [25] and J. Sablayrolles et al. [22].

			Wavenumber, Stark Energy (cm−1)	Halfwidth (cm−1)	Reference
Er3+	4I15/2	1	0		[25]
		2	47		[25]
		3	76		[25]
		4	113		[25]
		5	368		[25]
		6	466		[25]
		7	497		[25]
		8	524		[25]
	4I11/2	1	10,275.34	0.14	present work
		2	10,295.97	0.15	present work
		3	10,356.69	0.51	present work
		4	10,394.97	1.17	present work
		5	10,402.08	1.13	present work
		6	10,410.85	0.77	present work
Yb3+	2F7/2	1	0		[22]
		2	367		[22]
		3	507		[22]
		4	676		[22]
	2F5/2	1	10,283.58	0.18	present work
		2	10,475	≈50	present work
		3	10,810	≈80	present work

.

The measurement setup used for the spectral hole-burning experiments can be seen in Figure 2. The light source was a stabilized external cavity diode laser (Sacher Lasertechnik, Manually Tunable Littrow Laser System–Lynx S3, tunable between 930 and 985 nm) with current, temperature, mechanical and piezo wavelength-tuning capability. For the narrow spectral hole measurements, a Toptica Photonics DL Pro grating stabilized tunable single-mode diode laser was used. This laser has a typical linewidth of 25 kHz with 5 μs integration time and less than 100 kHz in a millisecond time scale.

The wavelength of the laser beam was measured real time with a High Finesse WS-6 laser wavelength meter (WLM). The further details of the setup and the measurement method are described in our earlier paper [28]. The measurements presented in the following section were carried out by using an acousto-optic modulator (AOM) for laser frequency modulation, except for the temperature dependence of the broad spectral hole and all experiments on Er³⁺-doped sample, where laser frequency was modulated by the piezo modulation capability of the laser. The samples were mounted in a closed-cycle helium cryostat and cooled down between 9–30 K temperatures for the laser spectroscopic measurements. For the measurement of the narrow spectral hole of the LYB:Yb³⁺ sample, a liquid helium cryostat was used with an additional helium pump in order to cool down the sample to near 2 K.

To determine the low-intensity limit of the spectral hole halfwidth, a Z-scan measurement setup was established. The pumping laser intensity was varied from 1.5 to 190 W/cm² for Yb³⁺- and from 9 to 700 W/cm² for the Er³⁺-doped LYB, while the confocal lens pair in front and behind the cryostat was moved together from the starting position to shift the focal plane passing through the sample. All intensity data given here are the peak value calculated for a two-dimensional Gaussian beam profile. The probing pulse with an intensity of about one tenth of the pumping pulse was delayed at about 10 and 30 μs for Yb³⁺ and Er³⁺ ions, respectively. Assuming a Gaussian laser beam profile, a theoretical function can be fitted to the halfwidth (FWHM) of the spectral hole as the function of the sample position to determine the homogeneous linewidth in the low-intensity limit:

$${\sigma }^2\left(z\right)=\frac{f_2^2}{2}+\frac{k{f}_2}{2\left[1+{\left(\frac{z-z_0}{z_R}\right)}^2\right]}+\sqrt{\frac{f_2^4}{4}+\frac{k{f}_2^3}{2\left[1+{\left(\frac{z-z_0}{z_R}\right)}^2\right]}},$$

(1)

where σ is the spectral hole halfwidth, f₂ = 4/T₂, z_R is the Rayleigh length, and k depends on the material parameters, T₁, optical power, and beam waist:

$$k=\frac{4T_1{\left|d_{eg}\right|}^2{\mu }_{0}cP}{{\hslash }^{2}n\pi w_0^2}.$$

(2)

Here, d_eg is the dipole momentum associated with the transition, μ₀ is the permeability of the vacuum, c is the velocity of the light, P is the power of the focused beam, ℏ is the reduced Planck constant, n is the effective refractive index of the sample, and w₀ is the beam waist.

3. Results

For the LYB:Yb³⁺ sample a special double spectral hole structure consisting of a narrow and a broad spectral hole (see Figure 3) was observed at about 10,283.58 cm⁻¹, similarly to our measurement on LiNbO₃:Yb³⁺ [28]. A potential reason for such a double spectral hole system can be the instantaneous spectral diffusion (ISD) [30]. In the LYB:Er³⁺ crystal, a single absorption hole was generated at the ⁴I_15/2–⁴I_11/2 electronic transition at about 10,275.36 cm⁻¹ (Figure 4). For the higher wavenumber spectral lines in LYB:Er³⁺ (see absorption spectra in Figure 1), we found only weak spectral hole burning effect with a very broad halfwidth (>1400 MHz).

Using the Z-scan technique, homogeneous linewidths of about 0.29 ± 0.03 and 22.5 ± 0.5 MHz, corresponding to the T₂ dipole relaxation times of about 1100 ± 120 and 14.2 ± 0.3 ns, were determined in LYB:Yb³⁺ crystal for the narrow and broad spectral hole components, respectively (for the narrow one see Figure 5). In Figure 5, the Rabi frequency Ω_w of the pump pulse in the middle of the beam, calculated from the fitted parameters, is indicated on the right scale. For Er³⁺-doped LYB crystal a dipole relaxation time of about 11.9 ± 0.2 ns (corresponding to a homogeneous linewidth of about 26.7 ± 0.4 MHz) was determined by weighted averaging of the results of two measurements in different polarization directions. Although there is a strong polarization dependence in the absorption and the spectral hole depth, any significant polarization dependence was obtained neither in spectral hole halfwidth nor in relaxation times.

The determination of population relaxation time (T₁) in LYB:Yb³⁺ and LYB:Er³⁺ crystals is shown in Figure 6, where the points represent the depths of the spectral holes as a function of delay time. In case of Yb³⁺ dopant, the linear behavior of the measured data in logarithmic scale shows a single exponential decay process both for the narrow (T₁ = 850 ± 60 μs) and broad (T₁ = 1010 ± 50 μs) spectral holes. In addition, the line broadening as a function of delay time, i.e., the spectral diffusion rates at about 1 and 5 MHz/ms, have also been determined for the narrow and broad spectral lines during these measurements, respectively, at a temperature of 9 K and an intensity of 40 mW/cm² in the center of the beam at position z = −17 mm (see Figure 7). For this reason, the initial width is larger than its minimal value. The measurement of the population relaxation in the LYB:Er³⁺ crystal exhibits a single exponential decrease with a time constant of 402 ± 8 μs, as a weighted average of results for polarizations parallel to the dielectric axes x and y, since there is no reason to expect polarization-dependence for T₁.

In Figure 8, the temperature dependence of the narrow spectral hole width measured in the LYB:Yb³⁺ crystal is shown, where the solid (red) line is a fitted curve using the direct one-phonon coupling model [31,32,33]:

$$\Gamma \left(T\right)={\Gamma }_0+a\frac{exp(\frac{\hslash {\omega }_{ph}}{k_{B}T})}{{\left[exp(\frac{\hslash {\omega }_{ph}}{k_{B}T})-1\right]}^2}$$

(3)

where Γ(T) is the halfwidth (i.e., full width at half maximum FWHM) of the spectral hole at a temperature T; Γ₀ = Γ(T)_T→0; a = 2(δω)²/γ; δω is the coupling constant; γ is the bandwidth; and ω_ph is the frequency of the phonon band.

Because of the very different halfwidths, the broad and narrow spectral holes were measured by using the piezo and AOM scanning methods, respectively. As a consequence, the measurements of the broad and narrow spectral holes were carried out with a pumping intensity of 2.6 W/cm² and 9 W/cm² and with a delay time of 200 and 20 μs, respectively. Similar temperature dependence was obtained for the LYB:Er³⁺ crystal. One can see that lowering the temperature of the sample below 9 K does not cause further significant decrease of the spectral hole halfwidth. The one-phonon coupling model describes the temperature dependence well for both crystals. The indicated ω₀ parameter, characterizing the phonons playing a role during the relaxation, indicates similar relaxation processes through the lattice vibrations in LYB:Er³⁺ and for the narrow spectral hole in LYB:Yb³⁺ crystals.

For comparison, the T₁ and T₂ parameters measured on Yb³⁺- and Er³⁺-doped LiNbO₃ [28,29] and Yb³⁺-doped Y₂SiO₅ crystals [34] are collected in

Table 2. Results of spectral hole-burning experiments on LYB:Yb³⁺ and LYB:Er³⁺, compared with those of Yb³⁺- and Er³⁺-doped stoichiometric (sLN) and congruent lithium niobate (cLN), and with Y₂SiO₅:Yb³⁺. L is the length of transmitted light path through the sample, i.e., the thickness of the sample; T₁ and T₂ are the population relaxation and dipole relaxation time constants of the transition, respectively; and ω₀ is the characteristic phonon energy for the direct one-phonon coupling process in spatial frequency units.

Material	Yb/Er Conc (mol%)	α (cm−1)	L (mm)	T1 (μs)	T2 (ns)	ω0 (cm−1)
LYB:Yb3+ narrow	0.1 *	9.6	0.60	850 ± 60	1100 ± 120	58 ± 6
broad				1010 ± 50	14.2 ± 0.3	145 ± 8
sLN:Yb3+ [28] narrow	0.09	26	0.57	266 ± 17	134 ± 7	143 ± 20
broad				438 ± 29	18.2 ± 0.5	54 ± 9
cLN:Yb3+ [28] narrow	0.18	11.7	0.48	386 ± 34	240 ± 20	65 ± 8
broad				420 ± 20	16 ± 1	89 ± 7
Y2SiO5:Yb3+ [34]	0.005			4920 ± 10	103,000 ± 10,000
LYB:Er3+	0.05 *	3.1	2.00	402 ± 8	11.9 ± 0.2	58 ± 3
sLN:Er3+ [29]	0.1	3.4	1.85	270 ± 140	6.84 ± 0.13	44 ± 3
cLN:Er3+ [29]	0.1	0.44	1.89	160 ± 80	5.83 ± 0.11	37 ± 4

* in melt.

.

4. Discussion

In the case of the Yb³⁺ ion, the population relaxation time (T₁) of both absorption holes is at least twice larger in LYB than in LiNbO₃. Additionally, though the dipole relaxation time of the broad hole is essentially similar in all cases, that of the narrow hole is much larger in the case of LYB. Similarly, the dipole and population relaxation times of the Er³⁺ electronic transition in LYB crystal are almost double those measured in LiNbO₃. The increase of the population relaxation time can be explained through the higher level of defects in the lattice of LiNbO₃ due to the incorporation of RE³⁺ ions as compared to the LYB crystal, where the incorporation into Y³⁺ sites can be established without charge compensation and lattice distortion. The difference between the dipole relaxation times may originate from the different magnetic environment of the incorporated RE ions. In the LiNbO₃ crystal, the fluctuating magnetic field of the Nb⁵⁺ ions may influence the electronic state of the RE ions in a much stronger manner than any of the ions in the LYB crystal, resulting in significantly shorter relaxation time.

In addition, the temperature dependence of the spectral hole parameters can also give information about the RE ion-lattice coupling, e.g., phonon coupling parameters. Although the phonon band structure of the LiNbO₃ and LYB crystals differs significantly, the similar ω₀ coupling frequencies may show that some of the low frequency vibrational modes, probably localized ones, play an important role in the relaxation process in both crystals. In case of Er³⁺, the transition between the 2nd and 3rd Stark level of the ⁴I_11/2 excited state corresponds to 60.7 cm⁻¹ [26] (see Table 1.), which is very near to the fitted phonon frequency at 58 cm⁻¹ and may confirm that the temperature dependence of the spectral hole width can be explained by the direct one-phonon coupling relaxation process. On the other hand, in case of Yb³⁺, a coupling phonon frequency of 58 ± 6 and 145 ± 8 cm⁻¹ for the narrow and the broad spectral hole components was obtained, respectively, although both are quite far from even the smallest crystal field splitting value of 194 cm⁻¹ of the ²F_5/2 excited state [22]. It has to be mentioned, however, that low energy phonons around 130–160 cm⁻¹ have been detected in the Raman spectra of Ce-doped LYB crystals [35], which is in good agreement with the value of ω₀ obtained for the broad spectral hole component.

Among the other phonon-coupling relaxation processes, a possible one is the Raman relaxation. Its contribution to the spectral hole broadening is the following:

$$\Delta {\Gamma }_R=\alpha {\left(\frac{T}{T_D}\right)}^7{{\displaystyle \int }}_0^{x_0}\frac{x^{6}exp\left(x\right)}{{\left(exp\left(x\right)-1\right)}^2}dx,$$

(4)

where $\alpha$ is the electron–phonon coupling parameter for the Raman process, $T_D=\hslash {\omega }_D$/k_B is the effective Debye temperature, ${\omega }_D$ is the Debye cut-off frequency, k_B is the Boltzmann-constant, and $x_0=T_D/T$[32]. The integral has been calculated numerically, and we found that the single phonon relaxation formula in Equation (3), with appropriate change of the parameter ${\omega }_{ph}\to {\omega }_D$, is almost identical with Equation (4) in the range of T/T_D = 0–0.2. The parameter fitting of this equation describes the temperature dependence of the spectral hole broadening both for the narrow and the broad components quite well, and results in a value for T_D equal to 111 ± 6 K and 131 ± 3 K, respectively. Since the numerical value of the expression in Equation (4) is practically the same as that given by the formula for the direct one-phonon model in Equation (3), the contribution of the direct one-phonon and the Raman relaxation cannot be separated only by fitting the temperature dependence of the spectral hole broadening. The temperature dependence of the spectral hole width may consist of contributions of more than one effect with similar temperature dependence. Orbach and multiphonon processes do not likely give significant contribution in relaxation for trivalent lanthanide ions [33].

5. Conclusions

A pump–probe type saturation spectroscopic experiment has been successfully employed to measure the relaxation parameters of the Yb³⁺: ²F_7/2—²F_5/2 and Er³⁺: ⁴I_15/2—⁴I_11/2 transitions in LYB single crystals in the temperature range of 2–14 and 9–28 K, respectively. The dipole and population relaxation times were found to be at about twice those measured in stoichiometric and congruent lithium niobate single crystals, except for the dipole relaxation time of the narrow component in Yb³⁺, where the increase is much larger. The small number of defects due to the neutral charge substitution of Y for the RE ions in LYB crystals explains the longer population relaxation time as compared to lithium niobate. The difference in the dipole relaxation times can be understood by the fluctuating magnetic field, which seems to be stronger in LiNbO₃ due to the high nuclear magnetic moment of the Nb⁵⁺ ion. Although LYB as a host material seems to be better than LiNbO₃, the coherence time of excitation of the Yb³⁺ dopant is still much shorter than in Y₂SiO₅, and it is likely that there is a similar situation with the Er³⁺ dopant as well as for the ⁴I_11/2–⁴I_15/2 transition.