Ions held in rf traps are a standard system for quantum information processing experiments . One of the key challenges is to realize coherent operations with fidelities high enough to allow the implementation of quantum error correction protocols . The sub-states of the ground level of alkali earth ions are commonly used as the qubit states [3, 4]. In Ca with its nuclear spin () a pair of Zeeman states from the and hyperfine manifolds can be chosen [5, 6]. At specific magnetic field strengths pairs of magnetic-field insensitive clock-states are available that have recently been shown to have extremely long coherence times  making Ca a promising species for quantum information.
Coherent transitions between the qubit states may either be driven by rf/microwave radiation  or by a pair of Raman laser beams near the to transition at nm . Their strong coupling to the motion makes Raman beams particularly attractive for sideband cooling and motional entangling gates.
With Raman lasers the choice of detuning from the to transition is a compromise between higher speed at small detuning (scaling ) and lower off-resonant photon scattering (which introduces qubit errors) at large detuning (scaling ). Typical detunings are in the range of GHz. For a desired gate speed, the fidelity of qubit operations depends on the available Raman beam power. Typically, powers around mW have been used. For common experimental parameters and a desired two-qubit gate error probability of in a gate time of s, beam powers of around mW are required [9, 10].
The two-photon Raman process only depends on the difference frequency between the two beams and its detuning from the qubit resonance which is why there are no stringent requirements for absolute frequency stability. Instead, relative interferometric stability between the beams is needed. The hyperfine ground state splitting in Ca is 3,225,608,286.4(3)Hz . This can be spanned by using an acousto-optic modulator (AOM) in one of two beams derived from a single source but the low diffraction efficiency ( double-pass) and damage threshold (mW) make this approach unattractive. More efficient electro-optic modulators (EOM) are available but here the upper and lower sidebands remain colinear with the carrier and separating them spatially is not straightforward and entails a cost in optical power. Despite recent progress , tapered amplifiers (TAs) are not yet commercially available at nm. Another alternative is injection locking, where only a low intensity seed beam needs to be frequency shifted. This has recently been reported with violet diode lasers . While this approach is currently limited to mW of output power, it shows promise as higher power (mW) diodes have recently become available.
The approach we implement in this Letter makes use of the established techniques of injection locking [14, 15] and the availability of TAs in the infrared  to provide two coherent beams of mW intensity at nm. We use a double-pass MHz AOM
The laser systems are commercial extended-cavity diode lasers (ECDLs) with TA and second-harmonic generation (SHG) stages
The red injection beam is focused through the AOM in double-pass arrangement. We measure first-order diffraction efficiencies of on the first pass and on the second pass giving overall. The zeroth order is blocked by a shutter. Alternatively, the AOM can be switched off and the shutter opened to allow injection without a frequency offset. A neutral density (ND) filter is placed in the beam path to give a similar intensity to the first-order beam and to avoid ASE coming from the slave from being re-injected.
The slave diode is protected by two separate dB isolators. The injection beam is introduced through the side port on the first of these. Since the beam profiles of master and slave match closely, no additional beam shaping is done. The slave power is monitored on a photodiode (PD) in a pick-off. To characterize the injection for different injection beam powers, slave currents and temperatures, a power meter is placed in the main beam after the pick-off mirror. We observe regions of stable injection spaced by mA of slave current. With temperature these shift by mAC with respect to the slave current. In order to seed the TA, powers mW are needed. We typically run the slave diode at mA and C with the available injection power of W giving us mW of beam power.
Just as for the master, the doubling cavity on the slave laser needs to be locked to the diode’s frequency in order to generate the second harmonic. The sidebands generated by current modulation on the master are inherited by the slave via the optical injection. Therefore the master local oscillator signal is also used to generate the slave error signal which is used for feedback on the slave cavity piezo. On short timescales, the slave inherits the frequency stability provided by the master’s fast current lock to its own doubling cavity.
Intensity noise is a disadvantage of using frequency doubling. The intensity of the violet light is monitored on a photo-diode
When switching between the first and zeroth order of the injection AOM, the system takes around ms to relock the doubling cavity. This makes it too slow to be used within a single experimental sequence (due to the typical ms coherence time of a Ca qubit), but convenient to switch between experimental runs.
The relative frequency stability of the frequency-doubled output beams was measured in an optical heterodyne measurement. The violet beams with an offset of GHz were superimposed on a photodiode
The scheme presented here provides a pair of Raman laser beams for quantum information processing which allows the use of high detuning and hence minimizes photon scattering errors. This is a prerequisite for high-fidelity Raman laser gates in trapped ions.
- Brimrose TEF-800-300-.794
- Master: Toptica TA/DL-SHG 110 Pro; Slave: Toptica TA/DL-SHG 110 with AR coated diode
- TAs with output powers of several Watts are available if more power is required
- Hamamatsu S6775, bandwidth MHz
- New Focus 1437
- SRS SR785
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