Ultraviolet Laser Pulses with Multigigahertz Repetition Rate and Multiwatt Average Power for Fast Trapped-Ion Entanglement Operations

The conventional approach to perform two-qubit gate operations in trapped ions relies on exciting the ions on motional sidebands with laser light, which is an inherently slow process. One way to implement a fast entangling-gate protocol requires a suitable pulsed laser to increase the gate speed by orders of magnitude. However, the realization of such a fast entangling-gate operation presents a big technical challenge, as such the required laser source is not available off the shelf. For this, we engineer an ultrafast entangling-gate source based on a frequency comb. The source generates bursts of several hundred mode-locked pulses with pulse energy approximately 800 pJ at 5-GHz repetition rate at 393.3 nm and complies with all requirements for implementing a fast two-qubit gate operation. Using a single, chirped ultraviolet pulse, we demonstrate a rapid adiabatic passage in a ${\mathrm{Ca}}^{+}$ ion. To verify the applicability and projected performance of the laser system for inducing entangling gates we run simulations based on our source parameters. The gate time can be faster than a trap period with an error approaching ${10}^{-4}$.

Figure 1

Schematic of the ultrafast pulsed-laser source. (a) The color panels (purple) represent mostly the in-fiber part of the laser system. In these sections, chirped laser pulses at 5-GHz repetition rate are created with the right optical spectrum to reach the desired wavelength for high-power amplification. Subsequently, amplified pulses travel through free space where nearly transform-limited pulse compression is achieved in CVBG and frequency up-conversion takes place via two nonlinear crystals. The filtered UV pulses coming out of the PPKTP crystal are steered into the pulse shaper before being sent to the ion trap via an optical fiber. (b) The yellow panel depicts our pulse-switching scheme in infrared and visible wavelengths. Black arrows and lines correspond to electronic signals. AWG, arbitrary waveform generator; BD, beam dump; BOA, booster optical amplifier; CFBG, chirped fiber Bragg grating; CVBG, chirped volume Bragg grating; DM, dichroic mirror; EDFA, erbium-doped fiber amplifier; FC, optical frequency comb; HWP, half-wave plate; PBS, polarizing beam splitter; PD, photo detector; PPLN, periodically poled lithium niobate; PPKTP, periodically poled potassium titanyl phosphate; QWP, quarter-wave plate; H maser, passive hydrogen maser.

Figure 2

Fast photodiode trace of residual 786-nm laser pulses exiting the PPKTP crystal. (a) An arbitrary pulse pattern is created with the pulse picker at 1572-nm wavelength. (b) Picking only the payload by using both pulse picker and Pockels cell. Here, the BOA amplifies the pulses after the pulse picker to feed the forthcoming stage in the laser setup. (c) Same as (b), but the BOA is replaced by an EDFA. Now, all transmitted pulses have the same amplitude. Every grid line in the insets of (b) and (c) shows the location of a pulse in the 5-GHz continuous pulse train. Figures (a) and (b) are adapted from Ref. [20, 31].

Figure 3

Fitting fast photodiode data to measure relative phase shifts in the first five consecutive payload pulses at 5 GHz. These five pulses are sent to a Michelson interferometer such that each pulse interferes with its predecessor with a random phase that is the same for all interfering pulse pairs (for details, see main text). We measure the subsequent four output pulses of the interferometer with a fast photodiode and extract the measured pulse area of each with an oscilloscope. In the figure, the area of the first three output pulses (blue crosses, yellow diamonds, green circles, respectively) is plotted against the area of the fourth pulse. (a) Fitting an ellipse to our data allows us to extract the phase shifts between the first and second, second and third, and third and fourth pulses relative to the phase shift between the fourth and fifth pulses. This data is taken when a BOA after the pulse picker is a part of the (old) setup. (b) Same as (a), but the BOA is replaced with an EDFA.

Figure 4

Fast photodiode trace of laser pulses taken before the PPLN crystal, where the idle pulses have a 1.25-GHz repetition rate and the payload pulses have 5 GHz. The change in the repetition rate changes the steady state of the 10-W amplifier, i.e., it changes the pulse energy, but not the average power. Before this change starts to happen, the pulse amplitude remains the same for at least 150 ns (only partially shown), or for 750 consecutive pulses at 5 GHz. During this time and in this case, the average power is increased by a factor of 4 as compared to idle pulses.

Figure 5

Generated time-averaged power $P_{786}$ in the single-pass frequency conversion of the first doubling stage (1572 to 786 nm) as a function of the time-averaged pump power $P_{1572}$. The inset shows the frequency conversion efficiency $P_{786}/P_{1572}$ with respect to the pump power.

Figure 6

Phase-space trajectory of the center-of-mass (dashed) and stretching (solid) modes in the frame of reference that rotates with the frequency of each mode $⟨a{e}^{i{\omega }_{c,s}t}⟩=(⟨x_{c,s}⟩+i⟨p_{c,s}⟩)/\sqrt{2}$ for a gate implemented by a sequence with four pulses. Only the center-of-mass motion contributes to the total phase $\varphi$ in this particular gate.

Figure 7

Demonstration of a rapid adiabatic passage on the $4{\mathrm{S}}_{1/2}\leftrightarrow 4{\mathrm{P}}_{3/2}$ transition in ${\mathrm{Ca}}^{+}$. Each data point is taken by scanning the infrared pump power. Black arrows denote the corresponding UV pulse energy measured after the PPKTP crystal that is high enough to transfer the population to the excited state with near-unit efficiency. The power tunability range is dependent on the minimum to maximum output power of the 10-W EDFA (2 to 10 W). The dashed horizontal line marks the unit probability as a guide to the eye.