Matterwave interferometric velocimetry of cold Rb atoms

Abstract

We consider the matterwave interferometric measurement of atomic velocities, which forms a building block for all matterwave inertial measurements. A theoretical analysis, addressing both the laboratory and atomic frames and accounting for residual Doppler sensitivity in the beamsplitter and recombiner pulses, is followed by an experimental demonstration, with measurements of the velocity distribution within a 20 µK cloud of rubidium atoms. Our experiments use Raman transitions between the long-lived ground hyperfine states, and allow quadrature measurements that yield the full complex interferometer signal and hence discriminate between positive and negative velocities. The technique is most suitable for measurement of colder samples. ARTICLE HISTORY

Velocimetry of cold atoms by matter-wave interferometry

“…This reduces to a 2-pulse 3π/2-π/2 interferometer, restricting the pulse separation to τ > 0. This can still yield good velocimetry results when the gradient of the detuningdependent phase shift is small, as it is about ∆ ac = 0, unlike in a Ramsey interferometer [27]. This case is considered in Appendix B.…”

“…is then proportional to the velocity distribution P (kv z ), expressed as a function of the frequency kv z [27,28].…”

“…The astute reader will notice that the Fourier transform of the signal defined in Equation (5) can only be measured experimentally for positive pulse separations τ , and that the signal is thus effectively multiplied by a Heaviside step function. With ideal interferometer pulses that perform perfect, instantaneous operations upon all atoms ( Figure 1a) this would introduce an orthogonal component to the Fourier transform that could be separated from the velocity information, but in practice deconvolution becomes intractable because pulses of finite duration ( Figure 1b) themselves exhibit Doppler sensitivity, introducing a velocity-dependent amplitude and phase shift that we have explored in more detail in [27].…”

“…Subharmonic components are no longer present in this output, but quadrature terms are, introducing an effective detuning-dependent phase shift arctan (−B /A ) which, unlike the Ramsey interferometer [27], has a flat gradient through ∆ ac = 0. |A + iB | gives the amplitude of the harmonic components which, for T > 0, exhibits an oscillatory modulation, the envelope of which resembles that of the subharmonics present in case (a).…”

“…The result of this is a multiplication by Θ(τ − δτ ), where δτ is an offset determined by the length of the pulses. This introduces a phase factor into the first term of Equation (B1), irreversibly mixing the real part of the δτ = 0 output with the imaginary part so that the velocity distribution is irretrievable from a single measurement [27].…”