Atom Interferometric Measurements of Gravitational Acceleration

We review the development of a gravimeter based on a single state atom interferometer. Two standing wave pulses separated by T are applied to a sample of laser cooled Rb atoms. The traveling wave components of the excitation pulses are far detuned from the excited state. The atoms evolve into a superposition of momentum states separated by 2ħk and produce a density grating in the sample. The grating dephases due to the velocity distribution and is rephased by the second standing wave pulse near t = 2T. The rephased grating has a period of λ/2, where λ is the optical wavelength. It is detected by coherently back scattering a traveling wave readout pulse. The backscattered signal, known as an echo, is detected using a balanced heterodyne detector. The phase of the echo signal is measured relative to an optical local oscillator and is sensitive to the motion of the inertial reference frame. The accumulation of phase as a function of T, which scales as gT², can be used to measure gravitational acceleration g. The main challenges in this experiment include passive and active stabilization of the apparatus to avoid the effect of vibrations. The echo envelope also exhibits temporal oscillations consistent with theoretical predictions that can be detected as a Doppler shift and used to infer g.

Key Papers

Technique for magnetic moment and magnetic state reconstruction of laser-cooled atoms using direct imaging, G. Carlse, A. Pouliot, T. Vacheresse, A. Carew, H. C. Beica, S. Winter, and A. Kumarakrishnan, Journal of the Optical Society of America B 37, 1419-1427 (2020)

Prospects for Precise Measurements with Echo Atom Interferometry, B. Barrett, A. Carew, H. Beica, A. Vorozcovs, A. Pouliot, and A. Kumarakrishnan, Atoms, 4, 19 (2016)

Demonstration of improved sensitivity of echo interferometers to gravitational acceleration, C. Mok, B. Barrett, A. Carew, R. Berthiaume, S. Beattie, and A. Kumarakrishnan, Physical Review A 88, 023614 (2013)

Time Domain Interferometry With Laser Cooled Atoms, B. Barrett, I. Chan, C. Mok, A. Carew, I. Yavin, (McMaster U.), A. Kumarakrishnan (York University), S, B. Cahn (Yale U.) and T. Sleator (NYU), Advances in Atomic, Molecular and Optical Physics Volume 60 Chapter 3, Elsevier (2011) (Edited by E. Arimondo, P.R. Berman and C.C. Lin)

Atom interferometric techniques for measuring uniform magnetic field gradients and gravitational acceleration, B. Barrett, I. Chan, and A. Kumarakrishnan, Physical Review A, 84, 063623 (2011)

Effect of a Magnetic Field Gradient and Gravitational Acceleration on a Time-Domain Grating-Echo Interferometer, M. Weel, I. Chan, S. Beattie, A. Kumarakrishnan (York University), D. Gosset (UBC), and I. Yavin (Harvard U), Physical Review A 73, 063624 (2006).

Experimental setup.

One component of the signal envelope for a fixed value of T, showing the effect of the Doppler shift due to gravity.

Figure showing the theoretical change in momentum states for the experiments

(a) Recoil diagram for two-pulse AI; (b) Predicted modulation of back scattered E field (solid line) and signal amplitude (dashed line) as a function of T (=T₂₁). The interferometer phase ϕ_AI exhibits a chirped modulation due to g and a modulation due to recoil with period 32 ms.

(a) Recoil modulated in-phase (dashed) and in-quadrature (solid) echo signal components for the two-pulse AI as a function of T in stainless cell. To obtain cos (ϕ_AI) and sin (ϕ_AI), each signal component is normalized using the total signal amplitude. A measurement of the chirped frequency of ϕ_AI using four observation windows and a time scale of 20 ms resulted in a measurement of g precise to 5 ppm; (b) Recoil Diagram for the three-pulse AI; (c) AI signal lifetime for two-pulse and various three-pulse configurations in a glass cell with a sample temperature of T ∼ 20 mK. The horizontal axis is the time of the read-out pulse, T_RO, relative to the time of trap turn-off, T₀, which signifies the start of the experiment. The three-pulse AI is less sensitive to B gradients and vibrations than the two-pulse AI. Decoherence due to these effects is limited by adjusting the pulse spacing T₂₁, which controls the separation between wave packets so that the measurement time scale is comparable to the transit time.

(a) Echo signal envelope showing Doppler phase modulation due to the motion of the falling grating (b) cos (ϕ_AI) for the three–pulse AI (blue-data, red-fit) measured by recording echo signal amplitude (stainless cell). The extended time scale, constant modulation frequency and absence of recoil modulation allows g to be measured with a precision of 500 ppb using three observation windows; ;