Quantum-projection-noise-limited interferometry with coherent atoms in a Ramsey-type setup

Every measurement of the population in an uncorrelated ensemble of two-level systems is limited by what is known as the quantum projection noise limit. Here, we present quantum-projection-noise-limited performance of a Ramsey-type interferometer using freely propagating coherent atoms. The experimental setup is based on an electro-optic modulator in an inherently stable Sagnac interferometer, optically coupling the two interfering atomic states via a two-photon Raman transition. Going beyond the quantum projection noise limit requires the use of reduced quantum uncertainty (squeezed) states. The experiment described demonstrates atom interferometry at the fundamental noise level and allows the observation of possible squeezing effects in an atom laser, potentially leading to improved sensitivity in atom interferometers.

Figure 1

(a) Sagnac interferometer setup, based on a nonpolarizing 50:50 beamsplitter. Operation of the interferometer relies on the directivity of the electro-optic phase modulator. (b) Equivalent setup using a Mach-Zehnder-type design. (c) Level scheme for Raman coupling of the states $|1\rangle$ ($F=1,m_F=0$) and $|2\rangle$ ($F=2,m_F=0$).

Figure 2

(a) Measured beat-note amplitude as a function of drive voltage for a microwave frequency of $1$ GHz. $V_0$ is an arbitrary reference voltage. The beat note is measured at $1$ GHz (triangles), $2$ GHz (circles), and $3$ GHz (squares). (b) Calibration curve for the beat-note amplitude as a function of the output power of the Sagnac interferometer. Frequencies of the beat note and phase modulation are $2$ and $1$ GHz, respectively. The power is normalized to the power at maximum beat-note amplitude.

Figure 3

(a) Measured fluctuations of the summed intensity of both beamsplitters (for a drive voltage of 1.5 V at 3.417 GHz) and (b) Allan deviation of the relative intensity measured at the same position. For long integration times, polarization fluctuations in the EOM fiber and the transfer fiber dominate the measured Allan deviation.

Figure 4

Schematic drawing of the interferometer setup. An atom laser pulse originally in state $|1\rangle$ travels through two spatially separated beamsplitters, each containing frequencies with a spacing of ${\omega }_{\mathrm{hf}}/2$. The plot on the right depicts a measurement of the spatial width of each of the light sheets.

Figure 5

Central part of a typical Ramsey fringe measurement. The atom cloud pictures at the top show shot-noise-limited absorption images.

Figure 6

Atom number calibration curve. The graph shows the condensate fraction as a function of normalized temperature of the atomic sample. The solid line is a fit of the form $N_c/N=1-(T/a{T}_0){}^3$, giving an intercept of $a=1.019\pm 0.007$.

Figure 7

Noise measurement on a Ramsey fringe. The graph illustrates a significant improvement in signal-to-noise ratio compared to the data in [25] (see inset).

Figure 8

Measurement of the standard deviation ${\sigma }_p$ as a function of the total atom number $N$ (a) for a single $\frac{\pi }{2}$ beamsplitter and (b) after a Ramsey $\frac{\pi }{2}$-$\frac{\pi }{2}$ sequence. The dashed line depicts the expected quantum projection noise; the dash-dotted line, the photon shot noise; and the solid line, the resulting standard deviation from both contributions. For sufficiently large atom numbers, the measured standard deviation agrees well with what is theoretically expected, showing that our apparatus operates at the quantum projection noise limit.