Carrier-Suppressed Multiple-Single-Sideband Laser Source for Atom Cooling and Interferometry

We present an electro-optic modulation technique that enables a single laser diode to realize a cold-atom source and a quantum inertial sensor based on matter-wave interferometry. Using carrier-suppressed dual-single-sideband modulation, an in-phase and quadrature modulator generates two optical sidebands from separate radio-frequency (rf) signals. These sidebands are controlled independently in frequency, phase, and power using standard rf components. Our laser source exhibits improved rejection of parasitic sidebands compared to those based on phase modulators, which generate large systematic shifts in atom interferometers. We measure the influence of residual laser lines on an atom-interferometric gravimeter and show agreement with a theoretical model. We estimate a reduction of the systematic shift by 2 orders of magnitude compared to previous architectures and reach a long-term sensitivity of $15\mathrm{n}g$ on the gravitational acceleration with an interrogation time of only $T=20\mathrm{ms}$. Finally, we characterize the performance of our integrated laser system and show that it is suitable for mobile sensing applications, including gravity surveys and inertial navigation.

Figure 1

(a) The architecture of the laser source: PI, proportional-integrator lock. (b) A schematic of the electro-optic IQ modulator where, for clarity, only one frequency $\mathrm{\Omega }$ is injected into the hybrid coupler: EDFA, erbium-doped fiber amplifier; AOM, acousto-optic modulator; PPLN, periodically poled lithium niobate waveguide.

Figure 2

(a) The Allan deviation of the optical beat note between the reference laser (blue curve) and the IQ laser source (orange curve) and a third “master” laser at 1560 nm. (b) The Allan deviation of the relative optical power emitted by the laser source. (c) The Allan deviation of the intensity ratio between principal lines ${\mathrm{\Omega }}_{1,1}^{\mathrm{PPLN}}$ and ${\mathrm{\Omega }}_{2,0}^{\mathrm{PPLN}}$ in both static (red curve) and dynamic (green curve) modes. The amplitude of each line is measured on a spectrum analyzer by beating the laser output with a local oscillator. In the static mode, the rf signals remain at fixed frequency and power, while the dynamic mode corresponds to a typical AI sequence with rf signals modulated in amplitude and frequency. The shaded areas in all plots indicates $1\sigma$ uncertainty.

Figure 3

(a) The laser source integrated in a standard 19 in. 9U rack. (b) The three-dimensional design of the laser system, including cooling fans and active temperature controllers for individual components.

Figure 4

The beat note spectrum after CS-DSSB modulation at (a) 1560 nm and (b) 780 nm. The blue lines show the spectra measured during Raman interferometry, obtained by beating with a stable local oscillator at 1560 nm and 780 nm, respectively. The red lines correspond to estimates from a numerical model, which are denoted ${\mathrm{\Omega }}_{n,m}^{\mathrm{IQ}}={\omega }_0+n{\mathrm{\Omega }}_1+m{\mathrm{\Omega }}_2$, where $n$ and $m$ are integers. Here, the principal sidebands are labeled ${\mathrm{\Omega }}_{1,0}^{\mathrm{IQ}}$ and ${\mathrm{\Omega }}_{0,1}^{\mathrm{IQ}}$. Similarly, at 780 nm, the lines are labeled ${\mathrm{\Omega }}_{N,M}^{\mathrm{PPLN}}=2{\omega }_0+N{\mathrm{\Omega }}_1+M{\mathrm{\Omega }}_2$, where the principal sidebands are ${\mathrm{\Omega }}_{2,0}^{\mathrm{PPLN}}$ and ${\mathrm{\Omega }}_{1,1}^{\mathrm{PPLN}}$. The input rf power is 17 dBm and 9 dBm for ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$, respectively, corresponding to modulation depths of 0.55 and 0.23.

Figure 5

Interference fringes for opposite directions of momentum transfer (a) $-k_{\mathrm{eff}}$ and (b) $+k_{\mathrm{eff}}$, obtained by scanning the chirp rate $\alpha$. Data are shown for interrogation times $T=19\mathrm{ms}$ (blue), 25 ms (orange), and 31 ms (green). The solid lines are least-squares fits to the data. The horizontal axis is centered on the local reference of gravity $g=9.805642{\mathrm{m/s}}^2$ [15]. (c) The Allan deviation of raw acceleration measurements for $T=20\mathrm{ms}$ (blue curve) and after subtraction of tides (red curve). The shaded regions correspond to the $1\sigma$ statistical uncertainty in the Allan deviation and the black dotted line is a fit of the form ${\sigma }_a/\sqrt{t}$. Other parameters are as follows: $\pi$-pulse duration $2\tau =6\mu \mathrm{s}$; detuning ${\mathrm{\Delta }}_R/2\pi =-0.88\mathrm{GHz}$.

Figure 6

The effect of an additional laser line on an atom interferometer. (a) Two-photon Raman transitions between ground states $\left|a\right.⟩$ and $\left|b\right.⟩$ coupled by two pairs of laser lines; one with principal Rabi frequency ${\chi }_{0,0}$ and one residual ${\chi }_{p,q}$. The momentum transferred in each case is $\hslash k_{p,q}=\hslash (k_{\mathrm{eff}}+q\mathrm{\Delta }{k}_1+p\mathrm{\Delta }{k}_2)$, where $\mathrm{\Delta }{k}_1=2{\mathrm{\Omega }}_1/c$, $\mathrm{\Delta }{k}_2=2{\mathrm{\Omega }}_2/c$, and ${\mathrm{\Omega }}_2-{\mathrm{\Omega }}_1={\delta }_{\mathrm{HF}}$ is the splitting between ground states. (b) An illustration of the multipath interferometer that results from an additional laser line. For sufficiently cold atoms, these pathways are within the de Broglie wavelength of the diffracted wave packets—causing spatial interference that leads to a phase shift.

Figure 7

A comparison of (a) the normalized Rabi frequency ${\chi }_{\mathrm{eff}}/{\chi }_{0,0}$ and (b),(c) the AI phase shift $\mathrm{\Delta }\mathrm{\Phi }$ produced by a phase modulator (red curves) and an IQ modulator (blue curves). The phase shift is shown as a function of $z_M$ (b) for fixed $T=20\mathrm{ms}$ and (c) as a function $T$ for a fixed atom-mirror distance $z_M=122\mathrm{mm}$. The IQ modulator line intensities are taken from Fig. 4. For the phase modulator, we use relative line intensities $I_{0,m}/I_{0,0}=(-30,-12,-2,0,-2,-12,-30)\mathrm{dB}$ for modulation frequencies $m{\delta }_{\mathrm{HF}}$, with $m=-3,-2,\dots ,3$. These intensities are based on measurements in a similar laser system employing a phase modulator with $\beta =1.254$. Other AI parameters are as follows: $\mathrm{TOF}=15\mathrm{ms}$, $2\tau =6\mu \mathrm{s}$, ${\mathrm{\Delta }}_R=-0.88\mathrm{GHz}$, and the initial velocity $v_0=-15\mathrm{mm/s}$.

Figure 8

(a) Measurements of the normalized Rabi frequency (${\chi }_{\mathrm{eff}}/{\chi }_{0,0}$) as a function of the cloud position. The blue (red) points correspond to mirror position 1 (2). The solid black curve corresponds to our model for the IQ modulator. (b) Measurements of the induced frequency-step bias due to the spatial variation of the Rabi frequency for an interrogation time $T=20\mathrm{ms}$. (c) A schematic of the setup. The atom-mirror distance is varied by letting the cloud (black dot) fall for different heights over a maximum of 35 mm (constrained by our vacuum system). The mirror is then moved from position 1 to position 2 between data sets.

Figure 9

(a) The contribution of each parasitic Raman transition to the phase shift as a function of the atom-mirror distance $z_M$. (b) The predicted AI phase shift due to residual parasitic lines for the current laser parameters (solid black curve), with optimized ${\mathrm{\Omega }}_1$ (dashed curve), and with optimized modulation depths ${\beta }_1$ and ${\beta }_2$ (dotted line). The AI parameters are as follows: $\mathrm{TOF}=15\mathrm{ms}$, $T=20\mathrm{ms}$, and ${\mathrm{\Delta }}_R/2\pi =-0.88\mathrm{GHz}$.

Figure 10

(a) Measurements of the copropagating transition probability between $\left|F,m_F=0\right.⟩$ states as a function of the atom-mirror distance. The red (blue) points correspond to the nominal (shifted) mirror position. The solid curves are sinusoidal fits to the data. (b) A schematic of the experiment and level diagram for copropagating transitions.

Figure 11

The timing diagram for the frequency steps used in the experiments (blue) and the corresponding frequency chirp (red) usually employed in atomic gravimeters.