An optical field impinging upon, or generated by, a spin-polarized medium is a fundamental light-matter interaction responsible for spin-polarized lasers [1], and the hyperpolarization of ¹²⁹Xe and ³He nuclei through collisional interactions with spin-polarized Cs or Rb atoms [2]. The former produces circularly-polarized radiation owing to the spatial anisotropy of a specific material [1] whereas spin polarization of an alkali atom has, in the past, been realized by depopulating a specific hyperfine level of the ground state with a circularly-polarized optical pump [2,3] and an imposed magnetic field.

We report here the generation of circularly-polarized coherent emission from an isotropic medium, in the vapor phase, by manipulating the hyperfine state populations (and, therefore, the spin polarization) of an atomic excited state. Lasing occurs in alkali-rare gas mixtures on the F′ = 5 → F″ = 4 and F′ = 4 → F″ = 3 transitions of the $6p^2{P}_{\frac{3}{2}}\to 6s^2{S}_{\frac{1}{2}}$(D₂) line of Cs (852.1 nm), and the corresponding process has also been observed in Rb. Spin polarization of the alkali atom excited state is accomplished, in the absence of an external magnetic field, by the photoexcitation and subsequent dissociation of a transient diatomic molecule [4]. For example, the photoassociation of thermal Cs-Xe ground state pairs with a circularly-polarized (σ⁺) optical field populates the dissociative CsXe ($B^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$) state which is correlated with $\text{Cs}\left(6p^2{P}_{\frac{3}{2}}\right)+\text{Xe}\left(5p^6\hspace{0.17em}{}^1{S}_0\right)$ in the separated atom limit. Dissociation of the CsXe(B) excited complex preferentially populates the F = 4, 5 hyperfine levels of the $\text{Cs}\hspace{0.17em}6p^2{P}_{\frac{3}{2}}$ state, thereby enabling the emission of coherent, circularly-polarized radiation on the Cs D₂ transition. Because the nascent populations of the Cs ($6p^2{P}_{\frac{3}{2}}$, 2 ≤ F ≤ 5) photofragment states are dependent upon the local molecular orbital (MO) structure of the $B^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$ interatomic potential, the Cs D₂ line laser exhibits efficiencies 50–110% greater when pumped by a circularly-polarized optical field (as opposed to linear polarization) and the enhancement magnitude is determined by the rare gas, as well as the photoexcitation wavelength λ and the ellipticity of the pump optical field. In these experiments, the effective degeneracy (g₂) of the upper state in an atomic laser is controlled by the ability to vary the electronic spin polarization of the state. For a given value of λ, therefore, the properties of the D₂ line laser (such as its gain) are closely tied to the structure of the transient Cs-rare gas ²Σ⁺ molecule from which excited Cs atoms are derived by photodissociation.

While introducing the quantum theory of radiation in 1917, Einstein [5] invoked the statistical weight of the m^th state of an atom or molecule which is now regarded as its degeneracy, g_m. The statistical weight of a state associated with a laser or maser transition has assumed a pivotal role in the theory of optical oscillators because of its position in the relation for the gain coefficient γ(ν):

Figure 1 is a partial energy level diagram for a few of the lowest energy states of Cs and the CsXe diatomic molecule, illustrating the approach adopted in these experiments for spin-polarizing the $n{p}^2{P}_{\frac{3}{2}}$ state of Rb or Cs (n = 5 or 6, respectively). The photoassociation of alkali-rare gas atomic pairs in the $X^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$ ground state thermal continuum with a circularly-polarized (σ⁺) optical field, having a wavelength lying within the D₂ line blue satellite [4,6], populates the dissociative $B^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$ excited state of the CsXe molecule. In the semiclassical view, photoexcitation of the alkali-rare gas diatomic complex is described by the quasistatic approximation, introduced by Jabloński [7] and developed further by Hedges et al. [8]. Free←free optical transitions of atomic pairs from the vibrational and thermal continuum of the $X^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$ molecular ground state to the dissociative $B^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$ potential define the Cs D₂ line blue satellite, and occur primarily in regions of interatomic separation (R) in which the B − X difference potential varies slowly. Peak B − X absorption is expected in the vicinity of points of stationary phase, values of R (denoted R^†) at which ∊′ = ∊″, where ∊′ and ∊″ are the translational energies of the outgoing Cs(6p)-Xe and incoming Cs(6s)-Xe pairs, respectively. If the difference potential V_B(R) − V_X(R) is a single-valued function of R, then the position of the Franck-Condon region centered at R is uniquely specified by the photoassociation wavelength λ = hc [V_B(R) − V_X(R)]⁻¹ (Refs. 7–9).

 

Fig. 1 Generalized energy level diagram (not to scale) for several of the lowest-lying states of CsXe and Cs, illustrating the optical generation of spin polarization in the $6p^2{P}_{\frac{3}{2}}$ excited state of Cs. Circularly-polarized (σ⁻) laser emission on the F′ = 5 → F″ = 4 and F′ = 4 → F″ = 3 transitions of the D₂ line of $\text{Cs}\hspace{0.17em}\left(6p^2{P}_{\frac{3}{2}}\to 6s^2{S}_{\frac{1}{2}}\right)$ is observed following the photoexcitation of thermalized Cs-Xe pairs in the λ = 838–850 nm wavelength interval.

Download Full Size | PDF

Although not illustrated in Fig. 1, the structure of the transient $B^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$ diatomic state is characterized by a localized barrier at R ≃ 5.3 Å which results from the interaction of the $B^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$ 6pσ anti-bonding molecular orbital (MO) with a 5dσ MO contributed by a higher-lying diatomic potential correlated with Cs(5d)+Xe(5p^{6 1}S₀) in the separated atom limit [4, 10, 11]. First predicted by Pascale and Vandeplanque [10] in 1974 and affirmed by the calculations and unpublished absorption measurements of Refs. 11 and 12, respectively, the 6pσ − 5dσ MO perturbation was only recently observed experimentally [4]. Details of the $B^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}-5d^2\mathrm{\Lambda }$ (Λ = 1, 2) interaction in CsXe in the 5 ≤ R ≤ 6 Å region can be found in Refs. 4,10 and 11.

Because the spin vector S⃗ and magnetic moment μ⃗ for all ²Σ⁺ diatomic states are orthogonal to (e.g., decoupled from) the internuclear axis of the diatomic molecule [13], the dissociation of the transient CsXe(B) species preferentially populates specific hyperfine levels (F = 4, 5) of the $\text{Cs}\hspace{0.17em}6p^2{P}_{\frac{3}{2}}$ excited state when the Cs-rare gas complex is photoexcited by a circularly-polarized optical field. If the statistical populations of the Cs ground state ($6s^2{S}_{\frac{1}{2}}$) hyperfine levels (F = 3, 4) are assumed to be unaltered by the Cs-rare gas photoassociation and dissociation processes illustrated in Fig. 1, one may expect the relative, normalized $\text{Cs}\hspace{0.17em}\left(6p^2{P}_{\frac{3}{2}}\right)$ F = 4 and 5 populations to be 45% and 55%, respectively. Thus, this Cs excited state has been spin-polarized, as demonstrated by the circularly-polarized stimulated emission that ensues. It must be emphasized that the spin polarization process hinges on the R-dependent characteristics of a dissociative ²Σ⁺ state. Consequently, spin polarization of $\text{Cs}\hspace{0.17em}6p^2{P}_{\frac{3}{2}}$ or $\text{Rb}\hspace{0.17em}5p^2{P}_{\frac{3}{2}}$, as reflected by the degree of circular polarization of the alkali D₂ line laser emission, is a sensitive diagnostic of localized deviations of the B²Σ⁺ state molecular orbital (MO) structure from pure ²Σ⁺ character. The aforementioned 6pσ−5dσ interaction in the CsXe diatomic, for example, strongly influences B²Σ⁺ structure near R = 5.3 Å which, in turn, alters the non-statistical $6p^2{P}_{\frac{3}{2}}$ hyperfine state population distribution. Recalling that the Franck-Condon region is specified by the pump wavelength and the B − X difference potential, it is clear that interactions of the B state with its neighbors can be sampled as a function of internuclear separation R. From a laser physics perspective, the ellipticity of the output emission can be controlled solely through the pump wavelength, and the laser efficiency will be enhanced, relative to linearly-polarized pumping, by photoexciting alkali-rare gas pairs with a circularly-polarized optical field. The ability to alter the nascent $6p^2{P}_{\frac{3}{2}}$ hyperfine level population distribution through λ_p and the pump ellipticity is tantamount to specifying the state degeneracy g₂.

A schematic diagram of the experimental arrangement is given in Fig. 2. A dye laser, having a linear (horizontal) polarization and a linewidth of ∼ 0.05 cm⁻¹, served as the pump source and, throughout these experiments, the laser pulse width and repetition frequency were 8 ns FWHM and 10 Hz, respectively. Two quarter wave plates (QWPs) were positioned near both ends of a borosilicate glass cell containing a mixture of an alkali and either Ar, Kr, or Xe at the desired pressure. The oven in which the cell was heated is not shown in Fig. 2. With proper orientation of the QWPs, the pump beam (blue arrow at left, Fig. 2) is transformed from horizontal into left-hand, circular polarization (LHCP, σ⁺) by the first QWP, and then returned to horizontal polarization after traversing the alkali-rare gas cell and the second QWP. A high reflector mirror (> 99.9% reflectivity) and a 50% output coupler form an optical resonator at 852.1 nm, the wavelength of the Cs D₂ line. Because the preponderance of the D₂ laser emission is σ⁻ circularly-polarized (i.e., opposite to that of the pump), the 852 nm laser output is converted into a vertically-polarized field by the QWPs. Both λ/4 plates, as well as the two polarizing beamsplitters (PBS) of Fig. 2, were antireflection coated and most of the experiments reported here were conducted with a Cs number density of [Cs]=1.8 · 10¹⁵ cm⁻³ which corresponds to saturated vapor at a temperature of 473 K. Separate cells were prepared for rare gas densities ranging from 9.6 · 10¹⁸ to 2.6 · 10¹⁹ cm⁻³, which correspond to 300 K pressures of 300–800 Torr.

 

Fig. 2 Experimental arrangement for the circularly-polarized Cs and Rb lasers (852.1 nm and 780.0 nm, respectively). The polarization of the D₂ laser and pump beams are indicated at several points in the optical train by red and blue arrows, respectively. The optical components at upper left serve to measure the degree of circular polarization of the Cs or Rb atomic laser output. The acronyms PBS, HR, and OC represent (respectively) polarizing beamsplitters, a high reflector (R = 99.9%) laser mirror, and an output coupler (R = 50%).

Download Full Size | PDF

A portion of the D₂ laser pulse energy is extracted from the optical cavity by a beamsplitter, and the degree of circular polarization of the output pulse is measured by the optical train at upper left in Fig. 2. Specifically, a PBS resolves the D₂ laser radiation into its horizontally and vertically-polarized components that are received by Detectors 1 and 2, respectively. Both pyroelectric detectors were calibrated so as to be capable of measuring absolute pulse energies with a detection floor of 0.1 μJ. Reliability of the detectors was verified by reversing their positions and confirming that the same results were obtained. Extensive experiments were conducted in which the Cs D₂ line laser pulse energies, produced in photopumped Cs-rare gas mixtures, were recorded as the dye (pump) laser was scanned by computer over the desired wavelength interval. Data were acquired by stepping the pump wavelength (λ_p) in increments of 0.2 nm and, for each value of λ_p, the pump laser pulse energy was varied over the 0–5 mJ range by a computer-controlled, Glan prism-half wave plate attenuator (not shown in Fig. 2). For a specific value of pump wavelength and pulse energy, each measurement was defined as the average of a minimum of 10 pump pulses.

The upper panels of Fig. 3 present a panoramic view of the dependence of the Cs D₂ laser output pulse energy on λ_p and the pump pulse energy (E_p) for a Cs-Xe mixture. Results are shown for both linear (left portion of the figure) and circularly-polarized (right) photoexcitation, and all of the data were recorded for Cs and Xe number densities of [Cs] = 1.8 · 10¹⁵ cm⁻³ and [Xe] = 2.6 · 10¹⁹ cm⁻³. It is clear from Fig. 3 that the optical-to-optical conversion efficiency of the Cs D₂ laser in a Xe background is improved significantly when the pump is σ⁺-polarized, and this conclusion is underscored by the two graphs in the bottom half of Fig. 3 which represent slices through the maps in the upper portion of the figure. At lower left, λ_p was fixed at 842.7 nm (corresponding to the peak of the Cs D₂ blue satellite, and represented by the dashed vertical lines in Figs. 3(a) and 3(b)) and E_p was varied up to 5 mJ. The slope efficiency η for this laser increased by > 70% when the pump polarization was changed from linear to circular (σ⁺). It should also be noted that only 10% of E_p was absorbed owing to the single pass geometry adopted for these experiments. Consequently, the laser slope efficiency is ∼15 and 9% (with respect to absorbed pump energy) for a σ⁺-polarized or linearly-polarized pump field, respectively. We should also mention the indifference of the pump energy absorbed by the gain medium to the pump field polarization. Consequently, the enhancement of the laser efficiency in Fig. 3 cannot be attributed to an increased absorption coefficient. Laser excitation spectra for Cs-Xe and 840 ≤ λ_p ≤ 848 nm are shown at lower right in Fig. 3 for both circularly-polarized and linearly-polarized photoexcitation of the 852.1 nm laser. For these experiments, E_p was fixed at 4.5 mJ (corresponding to the horizontal white lines in Figs. 3(a) and 3(b)). For these experimental conditions, a > 60% increase in the laser pulse energy is observed over the entire Cs-Xe D₂ blue satellite (CsXe B²Σ⁺ ← X²Σ⁺ transition). Furthermore, the profiles for both excitation spectra in Fig. 3(d) are virtually identical.

 

Fig. 3 (a, b) False color intensity maps showing an overview of the dependence of the Cs D₂ line laser pulse energy on the pump wavelength in the 840–848 nm region (D₂ blue satellite), and the pump pulse energy, for a Cs-Xe mixture. The pump energy E_p was varied up to 5 mJ, and the color scale for the output laser pulse energy is at right. Results are illustrated for both linearly and circularly (σ⁺) polarized pump pulses, and all of the data were recorded for [Cs]=1.8 · 10¹⁵ cm⁻³ and [Xe]=2.6 · 10¹⁹ cm⁻³ (pressure of 800 Torr at 300 K). The white lines indicate the pathway along which the data in the lower panels were recorded. (c, d) At left, the variation of D₂ laser output energy with the pump pulse energy is shown. The pump wavelength was fixed at 842.7 nm. Laser excitation spectra for Cs-Xe are given at lower right when E_p is maintained at 4.5 mJ.

Download Full Size | PDF

We interpret the results of Fig. 3 as demonstrating the ability of a circularly-polarized pump optical field to increase the net gain of an atomic laser by modifying the effective degeneracy (g₂) of the upper laser state. Creating a non-statistical hyperfine level population distribution (i.e., preferentially populating F = 4, 5 through dissociation of the CsXe $B^2{\mathrm{\Sigma }}_{\frac{1}{2}}^{+}$ species) has the effect of altering g₂ and, hence, the gain/loss ratio for the laser. This conclusion is borne out by removing the optical resonator of Fig. 2 and recording, in a manner identical to that described in Ref. [4], the amplified spontaneous emission (ASE) generated on the Cs D₂ line. The data of Fig. 4 were acquired with λ_p fixed at 842.8 nm while increasing the energy of σ⁺-polarized pump pulses to a maximum value of 2.5 mJ. The measurements of detectors 1 and 2 represent, respectively, the portion of the ASE energy that is circularly or randomly polarized. Not only is the ASE almost entirely circularly-polarized (σ⁻, opposite to that of the pump), but the threshold energy for the appearance of the circularly-polarized ASE is noticeably lower than that for the randomly-polarized radiation. The inset to Fig. 4 is an expanded view of the data in the vicinity of the threshold, showing that the threshold pump energy for the emergence of the σ⁻-polarized ASE is 0.30 ± 0.03 mJ/pulse for Cs-Xe, whereas the corresponding value for unpolarized ASE (Detector 1, Fig. 4) is 0.45 ± 0.03 mJ/pulse. The measured ratio of ∼ 2/3 for the threshold pump energies is consistent with the reduction in the effective degeneracy g₂ of the $\text{Cs}\hspace{0.17em}6p^2{P}_{\frac{3}{2}}$ state resulting from populating only the F = 4, 5 hyperfine sublevels (with a σ⁺-polarized pump), as opposed to populating all four hyperfine levels (F = 2 – 5) with a linearly-polarized optical field.

 

Fig. 4 Measurements of the D₂ line (852.1 nm) ASE pulse energy by two detectors as the energy of the σ⁺-polarized pump pulse is increased to 2.5 mJ. Obtained by removing the optical resonator of Fig. 2 and employing the optical train of Ref. [4], these data show that most of the ASE generated is σ⁻-polarized. A comparison of the two data sets near threshold (0.2 ≤E_p≤0.6 mJ) is provided by the inset.

Download Full Size | PDF

Before leaving the data of Figs. 3 and 4, it should be emphasized that the ASE measurements of Ref. [4] showed the total output (ASE) pulse energy to remain constant for a given value of E_p, regardless of whether the pump field was circularly or linearly polarized. In contrast, the introduction of an optical cavity in the present experiments yields considerably higher energy extracted from the gain medium when the pump is σ⁺-polarized. The implications of this result for the development of efficient atomic lasers are potentially significant, particularly when high power operation is desired. The opportunity to optically pump an atomic laser through a molecular continuum is attractive because it obviates the need for a narrow-band pump source and to lock its frequency to an atomic resonance.

Data analogous to that of Fig. 3 is presented in Fig. 5 for the Cs-Ar complex. For these experiments, E_p was maintained at 5.7 mJ and [Ar] = 2.6 · 10¹⁹ cm⁻³ (corresponding to a 300 K pressure of 800 Torr). In this case, the enhancement in the 852.1 nm laser energy is > 70% when λ_p is near the peak of the CsAr B ← X spectrum (836.6 nm), and the profiles of the circularly- and linearly-polarized laser excitation spectra (Fig. 5(a)) are identical except in the long wavelength extremity of the spectra. As illustrated by the inset to Fig. 5(a), normalization of the two spectra show that depolarization of the $\text{Cs}\hspace{0.17em}6p^2{P}_{\frac{3}{2}}$ state population becomes noticeable as λ_p is increased beyond ∼ 843 nm. Panel (b) of Fig. 5 compares measurements of absolute 852.1 nm pulse energies for Cs-Ar mixtures when λ_p = 836.6 nm and the pump polarization is changed from linear to circular (σ⁺). The linear, least-squares fits to both data sets, represented by the solid lines in Fig. 5(b), show the threshold values of E_p to be approximately the same for both σ⁺ and linearly-polarized pump fields. However, the slope efficiency of the Cs laser is 8.8% for a circularly-polarized pump field, or a factor of ∼ 1.8 larger than that obtained with linear polarization.

 

Fig. 5 (a) Laser excitation spectra for Cs-Ar in the 833–849 nm range in pump wavelength. The Cs and Ar number densities are [Cs] = 1.8 · 10¹⁵ cm⁻³ and [Ar] = 2.6 · 10¹⁹ cm⁻³ and the pump pulse energy E_p was fixed at 5.7 mJ. A comparison of the normalized spectra is given by the inset; (b) Dependence of the D₂ laser pulse energy on E_p for λ_p = 836.6 nm and all other experimental conditions identical to those in (a). The black lines are least squares fits to the data.

Download Full Size | PDF

Figure 6 provides a comparison of the performance of the optically-pumped Cs-Ar, Cs-Kr, and Cs-Xe lasers. The ordinate of this figure is defined to be the laser slope efficiency for a σ⁺-polarized pump, normalized to the corresponding value measured for a linearly-polarized optical field. Data were obtained for several rare gas number densities, corresponding to 300 K pressures in the 300–1000 Torr interval. The error bars signify one standard deviation in the measurements, each of which represents a minimum of 10 trials. The decline in the output energy enhancement factor with increasing rare gas pressure is the expected result of the collisional depolarization of the $\text{Cs}\hspace{0.17em}6p^2{P}_{\frac{3}{2}}$ state population. Although the beneficial impact of a circularly-polarized pump decreases with rising rare gas pressure, the effect is minimal because of the ∼ 30 ns natural lifetime of the upper laser level.

 

Fig. 6 Dependence on rare gas pressure of the factor by which the Cs D₂ laser slope efficiency increases when the pump optical field polarization is changed from linear to circular (σ⁺). Data are shown for Cs-Ar (blue), Cs-Kr (black), and Cs-Xe (red) alkali-rare gas pairs. The pump wavelength for each data set coincided with the peak of the B²Σ⁺ ← X²Σ⁺ spectrum: 842.7 nm for Cs-Xe, 841.1 nm for Cs-Kr, and 836.6 nm for Cs-Ar. Note the suppression of zero on the ordinate.

Download Full Size | PDF

Of greater interest in Fig. 6 is the observation that the ranking of Ar, Kr, and Xe is not consistent with the relative mass of each atom. That is, Cs-Kr mixtures surprisingly yield Cs D₂ line lasers having efficiencies consistently lower than those for both the Cs-Ar and Cs-Xe complexes. We presume this result to suggest that the CsKr B²Σ⁺ state is more strongly perturbed in the Franck-Condon region corresponding to peak B²Σ⁺ ← X²Σ⁺ absorption than is the case for either Cs-Ar or Cs-Xe. As proposed in Ref. [4], this perturbation is likely the result of a 6pσ−5dσ MO interaction for which the 5dσ MO is supplied by a ²Λ state derived from Cs(5d)+Kr(4p ^{6 1}S₀). Unfortunately, evaluating this suggestion on the basis of calculations is problematic because of the dearth of CsKr potentials available in the literature. The reproducibility of the results of Fig. 6, however, suggest that the local structure of the CsKr B²Σ⁺ state is responsible for the reduced efficiency of the Cs laser in a Kr background.

In summary, circularly-polarized (σ⁻) coherent radiation on the D₂ line of Cs has been observed from Cs-Ar, Cs-Kr, and Cs-Xe mixtures irradiated by a σ⁺-polarized optical field. Circularly-polarized pumping yields improvements in the laser slope efficiency ranging from 50% to beyond 110%, relative to those obtained with a linearly-polarized optical field. Photoexcitation of thermal alkali-rare gas collision pairs with a σ⁺-polarized optical field results in the selective population of the $\text{Cs}\hspace{0.17em}6p^2{P}_{\frac{3}{2}}$ (F = 4, 5) hyperfine levels which, in turn, lowers the effective degeneracy of the upper state of the lasing transition. In effect, an elliptically or circularly-polarized pump is capable of manipulating the population among the $n{p}^2{P}_{\frac{3}{2}}$ hyperfine states. In the present experiments, the degeneracy g₂ was reduced by ∼ 1/3 (relative to a statistical distribution of population among the $6p^2{P}_{\frac{3}{2}}$, F = 2 – 5 states of Cs), thereby increasing the slope efficiency for the Cs D₂ line laser by as much as a factor of two. The enhancement in efficiency, relative to that for a linearly-polarized pump, is greatest for Cs-Ar mixtures because the 6pσ − 5dσ interaction is weakest for Ar which is to be expected, owing to its low polarizability. A surprising result is that Cs-Kr mixtures exhibit the lowest improvement in laser efficiency, suggesting that the interaction of B²Σ⁺ with a ²Λ state derived from Cs(5d)+Ar, Kr, or Xe is, for Kr, the strongest of the three.

The data reported here demonstrate that the small signal gain and slope efficiency for an atomic laser can be controlled by optically altering the spin polarization of an alkali excited state. Consequently, anisotropic coherent radiation is emitted from an isotropic gas/vapor medium. The insertion of a diatomic collision complex into the pumping process for atomic or molecular lasers offers the potential for yielding optical oscillators of improved efficiency. From a fundamental physics perspective, however, these lasers provide a medium having a variable spin polarization in one or more excited states, and a spectroscopic means for probing R-dependent variations in the MO structure of diatomic molecular states.