Continuous-wave virtual-state lasing from cold ytterbium atoms

While conventional lasers are based on gain media with three or four real levels, unconventional lasers including virtual levels and two-photon processes offer new opportunities. We study lasing that involves a two-photon process through a virtual lower level, which we realize in a cloud of cold ytterbium atoms that are magneto-optically trapped inside a cavity. We pump the atoms on the narrow ${}^{1}S_0\leftrightarrow {}^{3}P_1$ line and generate laser emission on the same transition. Lasing is verified by a threshold behavior of output power vs pump power and atom number, a flat $g^{\left(2\right)}$-correlation function above threshold, and the polarization properties of the output. In the proposed lasing mechanism the trapping beams create the virtual lower level of the lasing transition. The laser process runs continuously, needs no further repumping, and might be adapted to other atoms or transitions such as the ultranarrow ${}^{1}S_0\leftrightarrow {}^{3}P_0$ clock transition in ytterbium.

Figure 1

(a) Schematic setup of the experiment. (b) Relevant transitions in ${}^{174}\mathrm{Yb}$ and their parameters.

Figure 2

Cavity output power and $g^{\left(2\right)}$-correlation function. (a) Output power vs atom number, exhibiting threshold behavior: at about 5000 atoms the fundamental mode starts emitting, and for higher atom numbers the other modes emit as well. (b) Output power vs pump power, exhibiting threshold behavior. Single-mode output is found above 3 mW; above 4.5 mW light is also emitted in higher-order modes (${\mathrm{TEM}}_{37},{\mathrm{TEM}}_{74}$, ...). The cavity mode structure is depicted in the lower right corner. Threshold values and output power depend also on the pump detuning (see Fig. 3 and Sec. 5). (c) The $g^{\left(2\right)}$-correlation function below threshold (blue circles) peaks at $\tau =0$ (2.5 mW pump power, 270 s measurement time, 500 counts/s, and 655-ns bin size). The red continuous line is a fit assuming $g^{\left(2\right)}\left(\tau \right)=1+\exp (-2\left|\tau \right|/{\tau }_{\mathrm{c}})$ for thermal emission [14], yielding ${\tau }_{\mathrm{c}}=4.8\mu \mathrm{s}$, which is on the order of the cavity decay time. (d) The $g^{\left(2\right)}$-correlation function above threshold shows no noticeable peak at $\tau =0$, indicating laser emission (4 mW pump power, 22 s measurement time, 500 000 counts/s after OD1 filter, and 655-ns bin size).

Figure 3

Laser action vs pump and cavity detuning. (a) Overview of output power (color-coded) vs detunings. The color scale ranges from dark (low power) to bright (high power). (b) Level scheme for the virtual-state lasing model (see Sec. 4). (c) More detailed display of the data in panel (a): the steady-state cavity output power is measured for various values of pump detuning (varied in steps of 1 MHz by an AOM) and cavity detuning (scanned via a piezo actuator and calibrated before each scan by an on-axis reference beam with five known frequencies). All detunings were measured relative to the atomic transition. We observe two separated areas of emission, where the pump light is a few MHz red- or blue-detuned, and the cavity output is red-detuned by a few tens of MHz. Lower output powers go along with the single ${\mathrm{TEM}}_0$ mode emission, while at higher power emission is multimode (see Fig. 2). Note that this plot does not represent the emission spectrum: light is only emitted at one frequency at a time.

Figure 4

Effect on lasing of (a) a magnetic offset field and (b) the MOT detuning. For each set of parameters, a map like Fig. 3 is recorded, and the values of optimum pump and cavity detuning are determined from the local maxima. The pump power is chosen such that only the ${\mathrm{TEM}}_0$ mode emits. (a) Adding an offset magnetic field shifts the ${}^{3}P_1$ Zeeman sublevels $m=\pm 1$ (arrows). The measured optimum pump detuning changes by $\pm 1.6$ MHz per Gauss additional magnetic field, respectively. (b) The MOT detuning determines the virtual level (thick red line) of the two-photon process. Two data sets are shown (circles and stars) for MOT detunings between $-40$ and $-20$ MHz; the optimum cavity detuning follows the MOT frequency (diagonal dashed line). The observed offset is attributed to ac Stark shifts and to a locking point offset. The three outliers are caused by a higher-order mode emission that displaces the center of the overall emission peak.

Figure 5

Geometry of trap and polarizations. (a) Cross section of the trapping area along the vertical axis and the cavity axis, showing the magnetic field of the MOT coils. Within the cavity mode volume, the field points predominantly along the cavity axis, thereby favoring ${\sigma }^{+}$ or ${\sigma }^{-}$ emission into the cavity, while $\pi$ emission is suppressed. (b) When the pump laser is linearly polarized along the cavity axis $\left(0^{\circ }\right)$ it excites the $\pi$ transition to the ${}^{3}P_1, m=0$ sublevel. The $m=\pm 1$ sublevels are not populated, and no cavity emission occurs. (c) When the pump laser is linearly polarized perpendicular to the cavity axis $\left({90}^{\circ }\right)$, it excites both $\sigma$ transitions to the ${}^{3}P_1, m=\pm 1$ sublevels, making emission into the cavity mode possible. All other combinations of pump and output polarization are superpositions of these cases.