Table 1 Atomic and quantum laser frequency noise requirements and performance limits and comparison between this work and free-running semiconductor lasers.

From: Sub-Hz fundamental, sub-kHz integral linewidth self-injection locked 780 nm hybrid integrated laser

Application

Offset frequency

Frequency noise at offset

Noise source*

Laser frequency noise

limited performance

This work

DBR**/ ECDL**/ SIL15

This work

Cold atom interferometer gravimeter39

24 kHz, blue diamond in Fig. 4

55 Hz2/Hz

Gravity sensitivity limited by Raman laser frequency noise***

\(\:{\sigma\:}_{\varphi\:}^{2}={\int\:}_{{f}_{x}}^{\infty\:}{H\left(f\right)}^{2}{S}_{{\Delta\:}\nu\:}\left(f\right)df\)

\(\:{\sigma\:}_{g}=\frac{{\sigma\:}_{\varphi\:}}{{g\:k}_{\text{e}\text{f}\text{f}\:}{T}^{2}\sqrt{{\Delta\:}f}}\)

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nm/s2/\(\:\sqrt{\text{H}\text{z}}\)

4

nm/s2/\(\:\sqrt{\text{H}\text{z}}\)

2-photon atomic wavelength reference at \(\:{f}_{0}\) for 778 nm laser 4

160 kHz, red diamond in Fig. 4

15 Hz2/Hz

Short-term (\(\:\tau\:\approx\:1\) s) instability due to intermodulation (IM) effect at \(\:{f}_{m}\)modulation frequency32,35

\(\:{\sigma\:}_{y}^{\left(IM\right)}\left(\tau\:\right)=\:\frac{{\left[{S}_{{\Delta\:}\nu\:}\left(2{f}_{m}\right)/{f}_{0}^{2}\right]}^{1/2}}{2\:\sqrt{\tau\:}}\)

\(\:1\times\:{10}^{-12}\:/\:9\times\:{10}^{-14}\:/\)

\(\:4\times\:{10}^{-14}\)

\(\:5\times\:{10}^{-15}\)

High-fidelity neutral-atom qubit operations36

1 MHz, yellow diamond in Fig. 4

1.5 Hz2/Hz

Single-photon gate operation averaged error for Rabi frequency \(\:{{\Omega\:}}_{0}/2\pi\:=\:\)1 MHz and a \(\:\pi\:\) pulse37.

\(\:\stackrel{-}{\mathcal{E}}=\frac{8\:{\pi\:}^{2}}{3\:}{\int\:}_{{f}_{x}}^{\infty\:}{S}_{{\Delta\:}\nu\:}\left(f\right)\:H\left(f\right)\:df\)

\(\:2\times\:{10}^{-1}\:/\:2\times\:{10}^{-2}\:/\)

\(\:3\times\:{10}^{-2}\)

\(\:2\times\:{10}^{-5}\)

  1. * Noise contribution related to laser frequency noise, assuming all other noise sources are not considered in evaluating the system performance. Calculations with integration assume \(\:{f}_{x}\) = 100 Hz for the gravimeter and \(\:{f}_{x}\) = 1 kHz for qubit operations.
  2. ** Free-running lasers such as a distributed Bragg reflector (DBR) semiconductor laser and an external cavity diode laser (ECDL). Data for the ECDL is taken from32.
  3. *** Using cold atom interferometer parameters from38. \(\:g\:\)is the acceleration due to gravity (9.8 m s-2, \(\:{k}_{\text{e}\text{f}\text{f}\:}\)is the effective wave vector of the two Raman probe lasers, \(\:T\:\)is the time interval between Raman pulses, and \(\:{\Delta\:}f\:\:\)is the atom interferometer cycle rate or bandwidth.
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