Laser cooling of trapped beryllium (${\mathrm{Be}}^{+}$) ions has played an instrumental role in the realization of quantum-logic optical clocks [1], quantum information processing [2], coherent optical control of individual quantum systems [3], and precision spectroscopy of light molecular ions [4]. Doppler cooling of ${\mathrm{Be}}^{+}$ typically requires a single laser beam with 0.01–1 mW of power at 313.133 nm, focused to a waist of 0.02–0.2 mm, which is used to drive the ${}^2{\mathrm{S}}_{1/2}(F=2)-{}^2{\mathrm{P}}_{3/2}(F^{\prime }=3)$ cycling transition with a small red detuning from the resonance. In addition, the 313 nm fluorescence photons emitted during laser cooling can be collected to detect ${\mathrm{Be}}^{+}$ ions as well as their internal state [3]. Both the required power level and linewidth ($\sim 1\mathrm{MHz}$) of the cooling laser source are in reach of extended-cavity diode laser (ECDL) systems, which combine a low-complexity setup with good spectral properties and high affordability. However, semiconductor gain materials emitting at 313 nm near room temperature are not generally available, and a similar hiatus exists for laser diodes emitting at the first subharmonic (626 nm) near room temperature. Therefore, 313 nm radiation for laser cooling of ${\mathrm{Be}}^{+}$ has previously been obtained by second-harmonic generation (SHG) of dye lasers operated at 626 nm [3], resonant sum-frequency generation of a laser source at 760 nm (either a Ti:sapphire or a semiconductor laser) and a 532 nm source obtained by SHG of a 1064 nm Nd:YAG laser [5], SHG of 626 nm obtained by sum-frequency generation of amplified fiber laser systems at 1550 nm and 1051 nm [6], and frequency quintupling of an amplified fiber laser system at 1565 nm [7].

In this Letter, we report laser cooling of $6\times {10}^2$ trapped ${\mathrm{Be}}^{+}$ ions using 313 nm radiation obtained through SHG of the output of a single ECDL operated at 626 nm. The ECDL is based on a ridge waveguide diode laser chip with a tensile-strained GaInP single quantum well [8]. The reflectivity of the diode front facet is about 1%, allowing the diode laser chip to operate both with and without external feedback. In the latter case, a maximum optical output power of 100 mW is obtained for a bias current of 150 mA. The diode chip is housed in a hermetically sealed TO-3 package, and the chip substrate is mounted onto a Peltier element for thermoelectric cooling. This allows tuning the center of the gain spectrum from 635 nm at 15°C to 626.266 nm at $-31°\mathrm{C}$, similar to the observation of [9] (obtained with broad area diode lasers), requiring 4.2 W of electrical power from the Peltier driver (Fig. 1).

 

Fig. 1. Unseeded diode laser emission spectra at 100 mA and a temperature of 15°C (red dotted curve), 0°C (orange dashed–dotted curve), $-15°\mathrm{C}$ (green dashed curve), and $-30°\mathrm{C}$ (blue solid curve). 626.266 nm is achieved for a temperature of $-31°\mathrm{C}$.

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The output of the diode laser is directed through an aspheric lens to collimate the beam [Fig. 2(a)]. The polarization state of the laser field is approximately linear and corresponds to the TM mode of the ridge waveguide for which the electric field vector is perpendicular to the epitaxial layers. To reduce the free-running linewidth of the laser, a grating with line density $2400/\mathrm{mm}$ is used in Littrow configuration to provide frequency-selective feedback. The grating lines are oriented vertically so that the TM and TE modes receive 28% and 3% feedback, respectively. The grating holder is based on a three-pivot mirror mount, which allows optical alignment and coarse frequency selection by tuning the grating angle. Fine frequency adjustments and 1 GHz mode-hop-free sweeps are possible through a small piezoceramic actuator (PZT), mounted in series with the horizontal adjustment screw. As (too) high intracavity laser power may damage the diode gain medium, we limit the diode bias current to 100 mA, and we obtain up to 32 mW of 626 nm behind the grating. To avoid feedback by other optical elements, the ECDL output is sent through an optical isolator exhibiting $-33\mathrm{dB}$ return loss and $-2\mathrm{dB}$ insertion loss.

 

Fig. 2. (a) Schematic top view of the ECDL. (b) Three-dimensional computer-aided design drawing of the ECDL. (c) Top and side views of the ECDL including cooling stages and enclosing box. See text for details.

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To effectively remove the heat produced by the diode laser and Peltier cooler, the diode laser package is firmly attached to an aluminum mount, using thermo conductive paste between the mating surfaces to improve the thermal conductance, while the ECDL assembly is kept at a constant temperature of approximately 5°C using a second Peltier cooling stage [Fig. 2(c)]. To enhance the thermal stability and mechanical stiffness of the setup, the aluminum mount is connected to the grating holder assembly through a 10 mm thick aluminum plate [Fig. 2(b)]. The second Peltier element is placed on a water-cooled aluminum breadboard at 16°C–18°C. The breadboard is supported by four rubber (Viton) O-rings for passive vibrational and thermal isolation with the O-rings resting on the bottom of a metal box. The metal box encloses the entire ECDL setup and is purged with dry nitrogen to avoid condensation of water on the parts below 15°C. The inside of the box is furthermore lined with foam rubber to reduce disturbances of the ECDL due to acoustical noise.

A small portion of the 626 nm beam is picked off and coupled into a wavelength meter (0.3 GHz resolution). The main 626 nm beam (20 mW) is further shaped by a series of four cylindrical lenses to match the fundamental transversal mode of a bowtie-shaped enhancement cavity, similar to that described by Koelemeij et al. [10]. The cavity contains a 10 mm long, Brewster-cut beta-barium borate (BBO) nonlinear crystal for type I critically phase matched SHG. The cavity length is stabilized using the Hänsch–Coulliaud scheme [11], applying feedback to a PZT-mounted cavity mirror. The cavity free-spectral range and linewidth are 0.55 GHz and 1.8 MHz, respectively. In principle, the highest circulating (intracavity) power is achieved when the input coupler transmission is matched to the cavity round-trip losses. Having tested input couplers with reflectivities of 98.0%, 98.5%, and 99.3%, we find that the highest circulating power is obtained with the 98.5% reflectivity mirror. By monitoring the power reflected off the input coupler when the cavity is in lock, we estimate that about 70% of the incident light is coupled into the SHG cavity. With 9.7 mW of power coupled into the SHG cavity, we obtain 35 μW of power at 313 nm (as measured behind the output coupler of the cavity). We note that the actual produced power at 313 nm is larger: the exit face of the BBO crystal introduces about 16% Fresnel loss, and the output coupler transmission is 99.4%.

To determine the linewidth of the ECDL, we observe the power of the 626 nm light transmitted by the SHG cavity (while blocking the 313 nm light with a spectral filter) using a sufficiently fast photodiode. Using the SHG cavity as a scanning interferometer, we verify that the ECDL spectrum contains a single longitudinal mode only. When the ECDL wavelength is steered to a half-maximum transmission point, fast frequency fluctuations are converted linearly to voltage fluctuations in the photodiode output, which is recorded using a digital oscilloscope. Intrinsic ECDL power fluctuations ($<1\%$) are negligible compared to the frequency noise-induced power fluctuations. From the known linewidth of the SHG cavity we obtain an intensity-to-frequency conversion factor. This is used together with the recorded photodiode signal (1 ms duration) to obtain the power spectral density of frequency fluctuations from which we obtain an upper limit for the ECDL linewidth of 0.35 MHz.

The apparatus containing the linear Paul trap for storage of ${\mathrm{Be}}^{+}$ ions is described in detail in [12], and is equipped with an electron-multiplied charge-coupled device (EM-CCD) camera for imaging of 313 nm fluorescence photons. A 0.3 mT static magnetic field parallel to the laser beam direction of propagation provides a quantization axis for the $F=2$, $M_F=2-F^{\prime }=3$, $M_F^{\prime }=3$ cycling transition. The 313 nm beam is first passed through a Glan–Taylor polarizer and a zero-order quarter-wave plate to achieve a circular state of polarization, and subsequently focused to a waist of 0.14 mm by a lens and overlapped with the symmetry axis of the ion trap. The 313 nm power at the ion trap is 20 μW, leading to an intensity equal to 0.8 $I_{\text{sat}}$, with $I_{\text{sat}}$ as the saturation intensity of the cycling transition.

${\mathrm{Be}}^{+}$ ions are loaded into the 1 eV deep trap by electron-impact ionization of an effusive beam of Be atoms, produced by a resistively heated oven, and subsequently laser cooled. To optimize the cooling rate by the ECDL, optical pumping out the cycling transition must be minimized, which is achieved by aligning the bias magnetic field along the laser propagation direction (using two pairs of orthogonal shim coils) and adjustment of the quarter-wave plate. During this procedure, the ECDL frequency should not drift. Instead of stabilizing the frequency of the ECDL, we choose to perform the optimization using a few milliwatts from a frequency-doubled and frequency-stabilized dye laser already available in our setup [12]. After this procedure, the dye laser is exchanged with the ECDL within one minute while the ions are either kept (as is the case for the images in Fig. 3) or reloaded after emptying the trap.

 

Fig. 3. EM-CCD fluorescence images of $6\times {10}^2$ trapped and laser-cooled ${\mathrm{Be}}^{+}$ ions, acquired with an exposure time of 3.5 s. Image width corresponds to 1.2 mm, and the trap symmetry axis coincides with the major axis of the ion ensemble. 313 nm intensity is equal to 0.8 $I_{\text{sat}}$. Looking at (a) and (b) from top to bottom, the 313 nm frequency is stepped from about $-0.6\mathrm{GHz}$ from resonance to a few tens of megahertz below resonance. (a) Gaseous state. (b) Coulomb crystals at various laser detunings. Single ions are clearly visible in the region to the right of the image center. Only this part is imaged sharply onto the EM-CCD by the imaging optics, which view the ions at a small angle with respect to the direction normal to the trap axis. (c) Images as obtained from MD simulations (integration time 10 ms) for $590{\mathrm{Be}}^{+}$ and $5{\mathrm{BeH}}^{+}$ impurity ions at 6 mK (top), 10 mK (middle), and 15 mK (bottom) respectively, indicating $\sim 10\mathrm{mK}$ temperatures for the Coulomb crystals shown in (b).

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Laser cooling at 313 nm is achieved by sweeping the frequency at $0.1\mathrm{GHz}/\mathrm{s}$ from about $-0.6\mathrm{GHz}$ to resonance, during which we observe the usual phase transition in the ensemble of ${\mathrm{Be}}^{+}$ ions from a gaseous state to a crystalline state, also known as a Coulomb crystal [13]. This is evidenced by changes in both the fluorescence level and the structure of the ${\mathrm{Be}}^{+}$ ensembles, as visible in the EM-CCD images shown in Fig. 3. From the EM-CCD images of Coulomb crystals, we are able to estimate the number of trapped ions as well as the temperature of the ions, by comparing them to the results of molecular dynamics (MD) simulations [14]. Thus, we find a number of $6\times {10}^2{\mathrm{Be}}^{+}$ ions, and a temperature of about 10 mK. This compares well with previous results obtained for laser cooling of ${\mathrm{Be}}^{+}$ Coulomb crystals of similar size [14]. We note that the power available at 313 nm is also sufficient for optical repumping, as required for ${\mathrm{Be}}^{+}$ cooling and manipulation through two-photon stimulated Raman transitions [3].

In conclusion, we report the demonstration of laser cooling of ${\mathrm{Be}}^{+}$ ions at 313 nm obtained through SHG of the output of an ECDL operated at 626 nm. A key ingredient of this method is the ability to cool down the laser diode chip to $-31°\mathrm{C}$, which is achieved through a two-stage Peltier cooler. A 626 nm ECDL exhibiting a similar wavelength reduction was reported in the parallel work by Ball et al. [15]. We anticipate that the small form factor, low complexity, high affordability, relatively low power consumption, and good spectral properties of this setup will be beneficial for future developments toward compact and practical setups for quantum information processing, quantum sensors, and optical clocks based on trapped ions.