Raman scheme to measure the quantum statistics of an atom laser beam

We propose and analyze a scheme for measuring the quadrature statistics of an atom laser beam using extant optical homodyning and Raman atom laser techniques. Reversal of the normal Raman atom laser outcoupling scheme is used to map the quantum statistics of an incoupled atomic beam to an optical probe beam. A multimode model of the spatial propagation dynamics shows that the Raman incoupler gives a clear signal of de Broglie wave quadrature squeezing for both pulsed and continuous inputs. Finally, we show that experimental realizations of the scheme may be tested with existing methods via intensity correlation measurements.

Figure 1

Schematic of a Raman atom laser incoupler. (a) $\Lambda$ configuration of three-level atoms. An untrapped beam of $\mid 2⟩$ atoms is coupled to a trapped state $\mid 1⟩$ via a Raman transition. The two optical fields are a weak probe beam [annihilation operator $\widehat{E}(x,t)$], and a control beam $\left[\Omega \right(x,t\left)\right]$, modeled by a classical field. The transition is detuned from the intermediate state by $\Delta$. Wide lines represent highly occupied states. (b) Spatial configuration of the Raman atom laser system. Beam atoms [field operator ${\widehat{\psi }}_2(x,t)$] reach the condensate $\left[{\widehat{\psi }}_1\right(x,t\left)\right]$ with momentum $2\hslash k_0$, which is transferred during incoupling by absorption and emission of light quanta with momenta $\mp \hslash k_0$ along the propagation axis.

Figure 2

Incoupling an atom laser pulse. (a) Squeezed atomic pulse ($4\mathrm{dB}$ in the $X^{+}$ quadrature, dashed line) of $n_0=5\times {10}^3$ atoms initially centered at $x=-600\mathrm{\mu }\mathrm{m}$, with momentum wave vector $2k_0$, is coupled into the condensate (chain line). The probe field (solid line) has peak intensity occurring at $t=54\mathrm{ms}$ shown here, which is when the maximum of the pulse is centered on the condensate. The atom pulse and optical probe are magnified by factors of $1000$ and $1000mc∕2\hslash k_0$ to plot them on the condensate scale. (b) Time development of the probe quadratures. A value of less than 1 demonstrates quadrature squeezing and the chain lines give the atomic variances.

Figure 3

Incoupling a continuous atom laser beam. (a) Snapshot of the atomic beam (dashed line), condensate (chain line), and probe (solid line) during incoupling. (b) Development of the optical quadratures (solid lines) as the front of the atom laser beam crosses the interaction region. The zero of the time axis is arbitrary. The chain lines show the variances of the $4\mathrm{dB}$ squeezed atomic beam.