Resonant transfer of large momenta from finite-duration pulse sequences

We experimentally investigate the atom optics kicked particle at quantum resonance using finite duration kicks. Even though the underlying process is quantum interference, it can be well described by an $\epsilon$-pseudoclassical model. The $\epsilon$-pseudoclassical model agrees well with our experiments for a wide range of parameters. We investigate the parameters yielding maximal momentum transfer to the atoms and find that this occurs in the regime where neither the short pulse approximation nor the Bragg condition is valid. Nonetheless, the momentum transferred to the atoms can be predicted using a simple scaling law, which provides a powerful tool for choosing optimal experimental parameters. We demonstrate this in a measurement of the Talbot time (from which $h/M$ can be deduced), in which we coherently split atomic wave functions into superpositions of momentum states that differ by 200 photon recoils. Our work may provide a convenient way to implement large momentum difference beam splitters in atom interferometers.

Figure 1

Scheme of the experimental sequence. (a) Laser trapping and cooling; SW pulse sequence; expansion of the atomic cloud during time-of-flight; and fluorescence imaging, (b) intensity and detuning $\mathrm{\Delta }$ of light during the same sequence, not to scale, and (c) fluorescence image.

Figure 2

Comparison of $\langle {\mathcal{J}}^2/2\rangle$ (shown in color coding; see color bars) in different models for $\epsilon =0.1,\tilde{V}=1$, as described by Eqs. (1) to (3).

Figure 3

Comparison of experiments and the $\epsilon$-pseudoclassical model. (a) Average of 10 fluorescence images with a logarithmic color map used for calculating momentum distributions. (b) Measured and smoothed momentum distribution without (dash-dotted line) and with a SW pulse sequence (dashed line), and the $\epsilon$-pseudoclassical model for the same parameters (solid line). (c) Difference curves (SW $-$ no SW). The dashed line is measured data, the solid line is from the model, and the dotted line is from the model including a range of potential depths seen by the atoms.

Figure 4

$\mathrm{\Delta }{P}_{\max }$ dependence on $t_{\mathrm{p}}$. Measured data (circles), the quantum $\delta$-kicked particle model (squares with linear fit), the full quantum model (triangles), and the $\epsilon$-pseudoclassical model (thick solid line) for the same parameters.

Figure 5

Scaling law. The lines show calculations from the $\epsilon$-pseudoclassical model with $t_{\mathrm{p}}$ scanned at $N=6,V_{\mathrm{d}}/h=7.24$ MHz (solid line), $N=9,V_{\mathrm{d}}/h=6.64$ MHz (dashed line), $N=10,V_{\mathrm{d}}/h=3.47$ MHz (dotted line), and $N=14,V_{\mathrm{d}}/h=2.57$ MHz (dash-dotted line). Triangles show measured data within the range of $N=5\text{to}12$ and $V_{\mathrm{d}}/h=2.26\text{to}7.24$ MHz. The inset shows the scaling law for $\langle {\mathcal{J}}^2/2\rangle$ with $N=10,50,100$, and $V_{\mathrm{d}}/h=18.5,3.7,0.62$ MHz, respectively, for $\beta =0$.

Figure 6

Measurements of the Talbot time. Optimum performance is at $t_{\mathrm{p}}=430$ ns (circles and dash-dotted line as a guide for the eye). Squares and triangles were measured at $t_{\mathrm{p}}=180$ and 650 ns, respectively.